Firs a clarification about the title. Most people know who Einstein or Galois are, but maybe not so many will know Margalef. He is an Spanish ecologist who begun his career as a self educated amateur and ended up with a tenure. I choose him because I needed a somewhat Spanish equivalent of the other two personalities.
All those people share a common point. They were brilliant scientifcs (Einstein and Galois simply top notch genius) who did at least part of it´s work outside academia.
The posts, as some can have supposed, is related to the famous "new Einstein" issue initiated by Lee Smollin. For those who don't know this affair simply to say that Lee Smollin published an article entitled "why no new Einstein" where he asked for somewhat who would revolutionize the nowadays physic in a similar way to what Einstein did in its time. Smollin was particularly interested in the philosophical nature of the Einstein contributions.
Well, I think that Einstein had a great intuition and that he presented his ideas in a very elegant way. But I don't think that to consider them Philosophy would make them any justice.
Possibly most interesting was his other consideration about Einstein. He did part of his work (the work in his "anni mirabilis") outside academy, you know, when he was in the patent office. In this respect Einstein was not alone. Before him many well known names had a similar role. Galois never had an academic position (possibly because he was killed before his work was broadly known). Lagrange was a self educated guy. Faraday made significant contributions to physics without a formal academic formation. The list is long and includes a large amount of well known scientifics in the ninety century. Also in the twenty century there are some names beyond Einstein (I am not totally sure but I guess that Banach was one of them).
But the truth is hat nowadays seemingly there are not too many examples (if any) of them. Maybe Perelman is the nearest example. He proved the Poincares conjecture which deserved him the corresponding Claymath prize. Also he was honoured with Fields medal, but he rejected it. He declined his academic position and now works in his home (or his mother home). But it is not the exact situation because as fr as I know he , until them, has followed a conventional way in academy.
Well, Smollin stated that he expected that the revolution of physic would come from out of the academy and was very interested in searching the "new Einstein".
I will say some comments about this particular. There is a difference between Einstein and previous times to nowadays. The scientific knowledge has growth a lot and it is necessary much more time to get the right preparation to be in conditions to publish important and revolutionary things. For example the gap between graduate studies and cutting edge physics is a lot greater now that in Einstein times (I would say that in Einstein times were around two or three years and now is 40 years). that means that an intelligent guy who has ended his undergraduate studies in physics and elaborates creatively with them has very few possibilities to create something valuable.
Another aspect is that in Einstein times there were no computers (nor financial markets). It is very easy that the "should be new Einstein" would end programming in an anonymous software company or doing "econophysic" in the financial markets.
I would add other thing. The goodbeeing state doesn't aim people to make a big effort to make big contributions that would give them fame, and, consequently money if they can live reasonably well without them. Anyone with the intelligent to be a "should be Einstein" surely knows hot to make some money without too much effort so creating something terribly special that would make him famous is not a priority.
Said that, is impossible a "new Einstein"?. I totally agree with Lubos that the most probable place to find him is inside academy. I totally recommend to anyone interested in purchasing a research position to care his expedient and all that. Certainly academy has is dark points (Lubos apparently is out of it because he doesn't like them) but it is not that bad.
Still there is a point about the new Einstein issue that is interesting. To become famous and doing great contributions being inside academy is "easy" (haha). But if you are a real genius it is possible that you would think precisely that, that is too easy and that the good point is to do your great work outside academy. Only the "minor minds" need to depend on good teachers and all the facilities that a first class university offers. Certainly it sound more "fashion", but I wouldn't recommend none to do that way.
And no, I am not at all trying to, subtlety, qualify myself as a "new Einstein" candidate. The main point of this post is to clarify th issue of the gap between undergraduate (or graduate, I always get lost with the correspondence between the Spanish word "licenciatura" and the corresponding English equivalent)and the cutting edge physic. If someone dreams about doing valuable work outside academy after finishing his studies he would be aware that he would need at least five years of intensive study to become near the frontier of knowledge. He would consider seriously if his economic/personal positions would allow him to do that, specially in this incoming years of economic crisis. I think that in that sense the claims of Smollin, and in fact not inly him, are dangerous because in a certain sense they make look glamorous a path that is mainly destined to fail.
Sunday, April 26, 2009
Wednesday, April 22, 2009
Naked singularities
This month, April 2009, the Spanish edition of Scientific American(investigación y ciencia)has an article about naked singularities (the English version was dated on February).
The author, Pankaj S. Joshi, seems to be an total expert in the subject (a common issue in Scientific American)and has a recent book- from 2008- about the particular,
Gravitational Collapse and Spacetime Singularities.
I didn´t read the book, but I found the article interesting so I searched in wikipedia and some of the papers linked there. I´ll try to explain some of the aspects now.
In general relativity there are two well known places where singularities appear, black holes and cosmology. The most naive way of thinking/defining singularities is to characterise them as points where the metric (or curvature) of space-time becomes infinite. According to that the event horizon of a Schwarschild black hole would be a singularity. It was realized that that infinity was due to a bad choice of coordinates. In that solution the centrer of the black hole, the R=0 point, also get an infinity value and this can´t be overcome by any other choice of coordinates so it is a genuine singularity.
As far as we like to have coordinate free definitions there is more technical definition, a singularity is defined to be one which contains geodesics which cannot be extended in a smooth manner. The end of such a geodesic is considered to be the singularity. That definition is useful to probe theorems (as did Penrose and Hawkings in the 70´s) about how singularities can´t be avoided in classical general relativity in cosmological sceneries. It also permit to make a diferentiation about coordinate singularities, the ones I talked before, related to black holes, and what are known as conical singularities, related to things such as cosmic strings. A conical singularity occurs when there is a point where the limit of every diffeomorphism invariant quantity is finite. In which case, spacetime is not smooth at the point of the limit itself. Thus, spacetime looks like a cone around this point, where the singularity is located at the tip of the cone. The metric can be finite everywhere if a suitable coordinate system is used.
The S.A article treats about singularities associated to gravitational collapse. There exists what is known like the cosmic censorship conjecture (or hypothesis) , own to Roger Penrose, which states that there are not naked singularities. That is, every singularity must be hidden behind an event horizon and cant be seen from the outside. It has the status of conjecture because it hasn´t be proved in a rigorous way under physically reasonable assumptions. In fact it hasn´t even stated in a mathemathical rigorous way.
The article, obviously, try to answer the conjecture in the negative. Before describing it's arguments I´ll talk about an aspect closely related to the CCC. If one examines the solutions for rotating black holes (Kerr solution) one sees that if is allowed that J, the angular momentum is greater than the mass M of the black hole, that is J/M>1 a naked singularity (a ringed shaped one) appears. A similar thing goes for charged (electric of whatever associated to U(1) gauge symmetry)black hole solutions (Reissner-Nordstom black holes) where a naked singularity appears if the charge, Q, is greater than the mass of the b-h, i.e., Q/M>1. It is commonly assumed that the CCC holds and the case where the equality would arise are called extremal black holes. The possibility of a reverse, negative, sign in the above expressions is not even contemplated in most theoretical considerations.
That´s a reason why I was somewhat surprised when I read the article and saw that in fact when one makes actual calculations, in classical general relativity, of how gravitational collapse behaves when some oversimplifying assumptions about the state of the star are neglected naked singularities actually are shown to be possible.
If the star is perfectly spherically symmetric and of uniform density everything is o.k and the black hole is formed. But relaxing one of the assumptions separately(or both at once) it can be shown that naked singularities actually appear.
Intuitively the reason is, for the case of non uniform density, that it can happen that the rate of accretion into the centre is never fast enough to actually form an even horizon and a central, unique, singularity appears. In the case of non sphericity it is shown that the collapse is neither spheric so the mass is concentrated in two points that become singularities at the end of the collapse avoiding the formation of the event horizon because of the oblong shape of the infalling matter that forbids the concentration of enough mass inside the Schwarschild radius.
Once that this facts are established one can wonder about how realistic and stable are. After all they mean that a large amount of the mass of a big star is concentrated in a point. The precise nature of what a singularity actually is usually is thought to be a question related to quantum gravity. But for regions relatively close (but not too much) to the singularity classical relativity still holds and it is expected that neighbouring matter would be attracted to the singularity. The inexistence of the event horizon means that there is the possibility of going arbitrarily near the singularity and returning to the original point (well, if tide forces don´t kill you and such that). In particular light can go near the singularity and scape to a distant observer so we can see what happens there. But even thought some matter in certain trajectories could scape I think that it is reasonable that most of the matter would be trapped in the singularity. Intuitively one would think that that increases the mass of the singularity and that it sooner or later it will become a black hole. Possibly that is a too naive way of think and that is one of the particularities of the singularity (but I am not sure about it).
Anyway, if singularities re shown to be possible (at least for a certain time) one could try to consider if they are distinguishable from black holes. The answer is in the positive. Even one could try a little bit further and consider the possibility that an existing black hole could break and leave behind the singularity. The most natural case would be kerr black hole which is led to rotate faster than it´s extremal limit. Because astrophysical black holes are usually believed to be Kerr ones one immediately can answer for particular observable signatures of this breaking. ONe arxiv article where one can read the details is this: Magnification relations for Kerr lensing and testing Cosmic Censorship. There are described some mathematical details of calculations made on the pna (post Newtonian approximation)of some optical effects. The author claim that the differences in behaviour among black holes and naked singularities could be observed with the incoming new generation of available technology.
From the viewpoint of an string theorist 4 dimensions are very restrictive, what about the influence of additional dimensions? You can read a paper about the particular: Spherical gravitational collapse in N-dimensions. It is co-authored by Joshi and the answer is mildly positive. I recommend to read the considerations that he makes in the conclusions.
A later thing I am going to discuss is the role of quantum gravity. If naked singularities actually exist they are a window to do observations of quantum gravitational effects (or at least one so expects). But before going there one could answer if quantum gravity considerations modify the classical predictions of formation of naked singularities. I don´t know the "asscendence" of Joshi, tat is, if he is an string theoretic oriented or an LQG oriented researcher. Being an specialist in general relativity one, maybe, would expect him being an LQG researcher, but reading his papers I guess that a better fir would be to consider him a "naked singularity phenomenologist". Anyway, LQG is easier to learn that string theory and is accepted by a plausible quantum gravity by hundreds of people with a tenures/investigation positions in universities so it is reasonable to expect some paper using LQG to investigate the question. And, effectively, there is such paper: Quantum evaporation of a naked singularity.
This papers point in a different direction that the classical results. Using a toy model with an scalar field (in a way similar to loop quantum cosmology calculations) it is shown that near the should be singularity gravity becomes a repulsive force and the naked singularity isn't formed. I guess that one must understand that this calculations make sense in the case where the classical equations point to the formation of the singularity. That is, classically one expect the formation of the naked singularity, but looking at quantum phenomena one sees that actually the singularity is avoided. I must clarify that this calculations are not claimed to be fully quantum by the authors and they still believe that in full quantum sceneries the naked singularity would easily reappear.
Still this last scenery could have relevant observational consequences in the form of powerful gamma ray bursts that result in the evaporation of the should be singularity. The precise signature of that bursts depend in some free factors of the theory, and, in particular, the claim that can be used to estimate a value of LQG, j, the value of the representation of (complex) SU(2) used.
Well, certainly I don´t believe that string theory people would take too seriously this considerations, but claiming possible near future experimental results I believe it well deserves to say something about the subject.
In fact actually there are some results in string theory about singularities, particularly the enhanchon mechanism, but it is related to "educated" singularities inside a black hole who are prudent enough to not show themselves naked. Abut black holes in string theory I hope to write a post soon.
To end this post to leave a link to a self claimed naked singularity who is kind enough have a blog (in Spanish), that links to this: La Singularidad Desnuda.
The author, Pankaj S. Joshi, seems to be an total expert in the subject (a common issue in Scientific American)and has a recent book- from 2008- about the particular,
Gravitational Collapse and Spacetime Singularities.
I didn´t read the book, but I found the article interesting so I searched in wikipedia and some of the papers linked there. I´ll try to explain some of the aspects now.
In general relativity there are two well known places where singularities appear, black holes and cosmology. The most naive way of thinking/defining singularities is to characterise them as points where the metric (or curvature) of space-time becomes infinite. According to that the event horizon of a Schwarschild black hole would be a singularity. It was realized that that infinity was due to a bad choice of coordinates. In that solution the centrer of the black hole, the R=0 point, also get an infinity value and this can´t be overcome by any other choice of coordinates so it is a genuine singularity.
As far as we like to have coordinate free definitions there is more technical definition, a singularity is defined to be one which contains geodesics which cannot be extended in a smooth manner. The end of such a geodesic is considered to be the singularity. That definition is useful to probe theorems (as did Penrose and Hawkings in the 70´s) about how singularities can´t be avoided in classical general relativity in cosmological sceneries. It also permit to make a diferentiation about coordinate singularities, the ones I talked before, related to black holes, and what are known as conical singularities, related to things such as cosmic strings. A conical singularity occurs when there is a point where the limit of every diffeomorphism invariant quantity is finite. In which case, spacetime is not smooth at the point of the limit itself. Thus, spacetime looks like a cone around this point, where the singularity is located at the tip of the cone. The metric can be finite everywhere if a suitable coordinate system is used.
The S.A article treats about singularities associated to gravitational collapse. There exists what is known like the cosmic censorship conjecture (or hypothesis) , own to Roger Penrose, which states that there are not naked singularities. That is, every singularity must be hidden behind an event horizon and cant be seen from the outside. It has the status of conjecture because it hasn´t be proved in a rigorous way under physically reasonable assumptions. In fact it hasn´t even stated in a mathemathical rigorous way.
The article, obviously, try to answer the conjecture in the negative. Before describing it's arguments I´ll talk about an aspect closely related to the CCC. If one examines the solutions for rotating black holes (Kerr solution) one sees that if is allowed that J, the angular momentum is greater than the mass M of the black hole, that is J/M>1 a naked singularity (a ringed shaped one) appears. A similar thing goes for charged (electric of whatever associated to U(1) gauge symmetry)black hole solutions (Reissner-Nordstom black holes) where a naked singularity appears if the charge, Q, is greater than the mass of the b-h, i.e., Q/M>1. It is commonly assumed that the CCC holds and the case where the equality would arise are called extremal black holes. The possibility of a reverse, negative, sign in the above expressions is not even contemplated in most theoretical considerations.
That´s a reason why I was somewhat surprised when I read the article and saw that in fact when one makes actual calculations, in classical general relativity, of how gravitational collapse behaves when some oversimplifying assumptions about the state of the star are neglected naked singularities actually are shown to be possible.
If the star is perfectly spherically symmetric and of uniform density everything is o.k and the black hole is formed. But relaxing one of the assumptions separately(or both at once) it can be shown that naked singularities actually appear.
Intuitively the reason is, for the case of non uniform density, that it can happen that the rate of accretion into the centre is never fast enough to actually form an even horizon and a central, unique, singularity appears. In the case of non sphericity it is shown that the collapse is neither spheric so the mass is concentrated in two points that become singularities at the end of the collapse avoiding the formation of the event horizon because of the oblong shape of the infalling matter that forbids the concentration of enough mass inside the Schwarschild radius.
Once that this facts are established one can wonder about how realistic and stable are. After all they mean that a large amount of the mass of a big star is concentrated in a point. The precise nature of what a singularity actually is usually is thought to be a question related to quantum gravity. But for regions relatively close (but not too much) to the singularity classical relativity still holds and it is expected that neighbouring matter would be attracted to the singularity. The inexistence of the event horizon means that there is the possibility of going arbitrarily near the singularity and returning to the original point (well, if tide forces don´t kill you and such that). In particular light can go near the singularity and scape to a distant observer so we can see what happens there. But even thought some matter in certain trajectories could scape I think that it is reasonable that most of the matter would be trapped in the singularity. Intuitively one would think that that increases the mass of the singularity and that it sooner or later it will become a black hole. Possibly that is a too naive way of think and that is one of the particularities of the singularity (but I am not sure about it).
Anyway, if singularities re shown to be possible (at least for a certain time) one could try to consider if they are distinguishable from black holes. The answer is in the positive. Even one could try a little bit further and consider the possibility that an existing black hole could break and leave behind the singularity. The most natural case would be kerr black hole which is led to rotate faster than it´s extremal limit. Because astrophysical black holes are usually believed to be Kerr ones one immediately can answer for particular observable signatures of this breaking. ONe arxiv article where one can read the details is this: Magnification relations for Kerr lensing and testing Cosmic Censorship. There are described some mathematical details of calculations made on the pna (post Newtonian approximation)of some optical effects. The author claim that the differences in behaviour among black holes and naked singularities could be observed with the incoming new generation of available technology.
From the viewpoint of an string theorist 4 dimensions are very restrictive, what about the influence of additional dimensions? You can read a paper about the particular: Spherical gravitational collapse in N-dimensions. It is co-authored by Joshi and the answer is mildly positive. I recommend to read the considerations that he makes in the conclusions.
A later thing I am going to discuss is the role of quantum gravity. If naked singularities actually exist they are a window to do observations of quantum gravitational effects (or at least one so expects). But before going there one could answer if quantum gravity considerations modify the classical predictions of formation of naked singularities. I don´t know the "asscendence" of Joshi, tat is, if he is an string theoretic oriented or an LQG oriented researcher. Being an specialist in general relativity one, maybe, would expect him being an LQG researcher, but reading his papers I guess that a better fir would be to consider him a "naked singularity phenomenologist". Anyway, LQG is easier to learn that string theory and is accepted by a plausible quantum gravity by hundreds of people with a tenures/investigation positions in universities so it is reasonable to expect some paper using LQG to investigate the question. And, effectively, there is such paper: Quantum evaporation of a naked singularity.
This papers point in a different direction that the classical results. Using a toy model with an scalar field (in a way similar to loop quantum cosmology calculations) it is shown that near the should be singularity gravity becomes a repulsive force and the naked singularity isn't formed. I guess that one must understand that this calculations make sense in the case where the classical equations point to the formation of the singularity. That is, classically one expect the formation of the naked singularity, but looking at quantum phenomena one sees that actually the singularity is avoided. I must clarify that this calculations are not claimed to be fully quantum by the authors and they still believe that in full quantum sceneries the naked singularity would easily reappear.
Still this last scenery could have relevant observational consequences in the form of powerful gamma ray bursts that result in the evaporation of the should be singularity. The precise signature of that bursts depend in some free factors of the theory, and, in particular, the claim that can be used to estimate a value of LQG, j, the value of the representation of (complex) SU(2) used.
Well, certainly I don´t believe that string theory people would take too seriously this considerations, but claiming possible near future experimental results I believe it well deserves to say something about the subject.
In fact actually there are some results in string theory about singularities, particularly the enhanchon mechanism, but it is related to "educated" singularities inside a black hole who are prudent enough to not show themselves naked. Abut black holes in string theory I hope to write a post soon.
To end this post to leave a link to a self claimed naked singularity who is kind enough have a blog (in Spanish), that links to this: La Singularidad Desnuda.
Monday, April 13, 2009
Horava´s quantum gravity
I have mentioned many approaches to quantum gravity, other than string theory, in this blog.
Besides LQG none of them has had major success in attracting people to do research in it. Now, at least it seems so, there is a new option, the so called Quantum Gravity at a Lifshitz Point initiated by Peter Horava, a well known string theorist (remember the Horawa-Witten model of heterotic string theory). I had the first new about it in the Lubos blog, but since them a few other papers have appeared. As far as another string theory minirevolution is going on (F-theory GUTs) which is leading to , seemengly, actual predictions testable in the LHC, as well as, maybe, in cosmology, I have had not time to read these articles, beyond an slight overview. I will use this entry mainly to keep track of the actual papers and also to encourage possible readers of this blog to investigate about them.
I will limit, so, to link some of the papers and paste the abstracts. Just to say that the theory will probably be of the liking of the people who likes condensed matter and critical phenomena.
This was the firs paper, Quantum Gravity at a Lifshitz Point. This is the abstract:
We present a candidate quantum field theory of gravity with dynamical critical
exponent equal to z = 3 in the UV. (As in condensed matter systems, z measures the degree
of anisotropy between space and time.) This theory, which at short distances describes
interacting nonrelativistic gravitons, is power-counting renormalizable in 3 + 1 dimensions.
When restricted to satisfy the condition of detailed balance, this theory is intimately related
to topologically massive gravity in three dimensions, and the geometry of the Cotton tensor.
At long distances, this theory flows naturally to the relativistic value z = 1, and could
therefore serve as a possible candidate for a UV completion of Einstein’s general relativity
or an infrared modification thereof. The effective speed of light, the Newton constant and
the cosmological constant all emerge from relevant deformations of the deeply nonrelativistic
z = 3 theory at short distances
This is the second one: Spectral Dimension of the Universe in Quantum Gravity at a Lifshitz Point, and this is the abstract:
We extend the definition of “spectral dimension” (usually defined for fractal and
lattice geometries) to theories on smooth spacetimes with anisotropic scaling. We show that
in quantum gravity dominated by a Lifshitz point with dynamical critical exponent z in D+1
spacetime dimensions, the spectral dimension of spacetime is equal to
ds = 1 + D/z
In the case of gravity in 3 + 1 dimensions presented in arXiv:0901.3775, which is dominated
by z = 3 in the UV and flows to z = 1 in the IR, the spectral dimension of spacetime flows
from ds = 4 at large scales, to ds = 2 at short distances. Remarkably, this is the qualitative
behavior of ds found numerically by Ambjørn, Jurkiewicz and Loll in their causal dynamical
triangulations approach to quantum gravity
The next article is not written by Horova, the authors are Tomohiro Takahashi and Jiro Soda. The paper is this:Chiral Primordial Gravitational Waves from a Lifshitz Point. This is the abstract:
We study primordial gravitational waves produced during inflation in quantum gravity at a Lifshitz
point proposed by Hoˇrava. Assuming power-counting renormalizability, foliation preserving
diffeomorphism invariance, and the condition of detailed balance, we show that primordial gravitational
waves are circularly polarized due to parity violation. The chirality of primordial gravitational
waves is a quite robust prediction of quantum gravity at a Lifshitz point which can be tested through
observations of cosmic microwave background radiation and stochastic gravitational waves.
I find this one particularly important because it claims that it has a measurable prediction that could falsify (or give credit to) the theory.
The last one is neither written by Horava, the authors are H. L¨u †⋆, Jianwei Mei † and C.N. Pope. The paper is: Solutions to Horava Gravity
And the abstract is:
Recently Horava proposed a non-relativistic renormalisable theory of gravitation, which
reduces to Einstein’s general relativity at large distances, and that may provide a candidate
for a UV completion of Einstein’s theory. In this paper, we derive the full set of equations
of motion, and then we obtain spherically symmetric solutions and discuss their properties.
We also obtain the Friedman-Lemaitre-Robertson-Walker cosmological metric.
I would advise the readers of this blog to read the entries in the other blogs that I have linked in this page because the last month there have been many many interesting things that are worth reading. Maybe I will make a post resuming them.
Besides LQG none of them has had major success in attracting people to do research in it. Now, at least it seems so, there is a new option, the so called Quantum Gravity at a Lifshitz Point initiated by Peter Horava, a well known string theorist (remember the Horawa-Witten model of heterotic string theory). I had the first new about it in the Lubos blog, but since them a few other papers have appeared. As far as another string theory minirevolution is going on (F-theory GUTs) which is leading to , seemengly, actual predictions testable in the LHC, as well as, maybe, in cosmology, I have had not time to read these articles, beyond an slight overview. I will use this entry mainly to keep track of the actual papers and also to encourage possible readers of this blog to investigate about them.
I will limit, so, to link some of the papers and paste the abstracts. Just to say that the theory will probably be of the liking of the people who likes condensed matter and critical phenomena.
This was the firs paper, Quantum Gravity at a Lifshitz Point. This is the abstract:
We present a candidate quantum field theory of gravity with dynamical critical
exponent equal to z = 3 in the UV. (As in condensed matter systems, z measures the degree
of anisotropy between space and time.) This theory, which at short distances describes
interacting nonrelativistic gravitons, is power-counting renormalizable in 3 + 1 dimensions.
When restricted to satisfy the condition of detailed balance, this theory is intimately related
to topologically massive gravity in three dimensions, and the geometry of the Cotton tensor.
At long distances, this theory flows naturally to the relativistic value z = 1, and could
therefore serve as a possible candidate for a UV completion of Einstein’s general relativity
or an infrared modification thereof. The effective speed of light, the Newton constant and
the cosmological constant all emerge from relevant deformations of the deeply nonrelativistic
z = 3 theory at short distances
This is the second one: Spectral Dimension of the Universe in Quantum Gravity at a Lifshitz Point, and this is the abstract:
We extend the definition of “spectral dimension” (usually defined for fractal and
lattice geometries) to theories on smooth spacetimes with anisotropic scaling. We show that
in quantum gravity dominated by a Lifshitz point with dynamical critical exponent z in D+1
spacetime dimensions, the spectral dimension of spacetime is equal to
ds = 1 + D/z
In the case of gravity in 3 + 1 dimensions presented in arXiv:0901.3775, which is dominated
by z = 3 in the UV and flows to z = 1 in the IR, the spectral dimension of spacetime flows
from ds = 4 at large scales, to ds = 2 at short distances. Remarkably, this is the qualitative
behavior of ds found numerically by Ambjørn, Jurkiewicz and Loll in their causal dynamical
triangulations approach to quantum gravity
The next article is not written by Horova, the authors are Tomohiro Takahashi and Jiro Soda. The paper is this:Chiral Primordial Gravitational Waves from a Lifshitz Point. This is the abstract:
We study primordial gravitational waves produced during inflation in quantum gravity at a Lifshitz
point proposed by Hoˇrava. Assuming power-counting renormalizability, foliation preserving
diffeomorphism invariance, and the condition of detailed balance, we show that primordial gravitational
waves are circularly polarized due to parity violation. The chirality of primordial gravitational
waves is a quite robust prediction of quantum gravity at a Lifshitz point which can be tested through
observations of cosmic microwave background radiation and stochastic gravitational waves.
I find this one particularly important because it claims that it has a measurable prediction that could falsify (or give credit to) the theory.
The last one is neither written by Horava, the authors are H. L¨u †⋆, Jianwei Mei † and C.N. Pope. The paper is: Solutions to Horava Gravity
And the abstract is:
Recently Horava proposed a non-relativistic renormalisable theory of gravitation, which
reduces to Einstein’s general relativity at large distances, and that may provide a candidate
for a UV completion of Einstein’s theory. In this paper, we derive the full set of equations
of motion, and then we obtain spherically symmetric solutions and discuss their properties.
We also obtain the Friedman-Lemaitre-Robertson-Walker cosmological metric.
I would advise the readers of this blog to read the entries in the other blogs that I have linked in this page because the last month there have been many many interesting things that are worth reading. Maybe I will make a post resuming them.
Tuesday, February 24, 2009
Fermi-Glast satelite and the status of LQG predictions
2003 probably was the bes yer for LQG. It was published a relatively short paper (authored by Rovelli) that presented the basics of the canonical LQG. It stated the result of quantization of the area operator, related it to the idea of a minimal lenthg and, and this is the important point, stated that it implied an experimental prediction: "Vacuum light speed depends on it´s frequency". The paper also contained an introduction to LQC (loop quantum cosmology) and the results on big bounce evitancy and a few other topics. But the mimportant one, at least for a lot of people, was the first.
Also, Nic Mavromatos, an Jonh Ellis, from CERn, published around the same time a paper stating that noncrititical Liouville strings predictes similar results (with the dependence of speed on the frequency going in the opossite direction that in LQG.
Those people expressed the hope taht the launch , around 2005, of the GLAST satelite, could experimentally test tht ideas. GLAST satelite laucnhing got somewhat delayed. In the meantime, in august 2007, an experimental recipe, known as MAGIC, obtained some results that indicated a possible confirmation of those ideas. I told
something about it in this entry. But GLAST satelite was finally launched and at last there are some results. You can read a press release by NASA here.
The NASA paper speaks about gamma ray bursts, not about quantum gravity. Where is the relation?
Well, in the end of the release you can read this:
One curious aspect of the burst is a five-second delay separating the highest-energy emissions from the lowest. Such a time lag has been seen clearly in only one earlier burst.
That´s the point. The idea expresed but that proposals of quantum gravity is that the more energetic fotons travelat different speed than the slower ones. That implies that the fastests one arrive sooner than the slower ones. In ordinary distances that can´t be observed, but for very distant objects the path is long enought to give meausereable results.
So, has LQG been confirmed? Not quite. I´ll soon tell why. But first I´ll make a few clarifications. The way LQG was supposed to predict those effects was by means of it´s prediction of a minimal length. That leads to DSR (double special relativities) that take tha minimal length as a premise and from that they obtain the dispersion relations of vacuum light speed. I have also heard of another argument, supposedly stated by Fotini Markopuolu Kalamara. The idea is that the more energetic fotons , of shorter wave-lengt collide more ofthem with the "atoms of space-time". I did a search in arxiv of the actual paper of fotini but I wasn´t able to find it (if some reader know the link I would knoowledege if he would leave it in the comments).
Let´s return to the question of why the GLAST satelite results don´t favour this LQG (or noncritical string theory) prediction. The trick is that there are models on how the GRB are formed. The GRB are supossed to be originated in matter beeing acreted into a black hole. The models of disk acrretion predict that less energetic photons are produced sonner that more energetic ones. I have´t readed the actual papers about those models (semeengly that calculations are available here ). I simply readed the conclusion, that the variations on light speed are excluded.
You can read more about it in the Lubos motl blog. Also there is a discusion about the topic in physic forums, concretely in this post.
In physics forums it is stated that , in fact, that presumably firm prediction of LQG in facthaas been progresively desestimated. To beguin with it has not been possible to rigurously deduce that behaviiour directly from canonical LQG. In fact the whole subject of canonical LQG is nowadays almost forgoten. Accordin to Marcus actually lQG is focussing in:
There is really only one form of LQG that is getting the bulk of attention. It is designated EPRL (gamma<1) and also FK(gamma < 1). These two turned out to be equivalent as long as the Immirzi gamma is < 1. Two different vertex amplitude formulas which coincide in the important case.
Essentially every new paper I see about the full theory (not the LQ cosmo offspring, but LQG)
as well as every new video-stream seminar talk at PIRSA is about this one version of LQG.
From my perspective it is getting all the attention since sometime in 2007.
Rovelli and his group call it Covariant LQG.
EPRL is Engle Pereia Rovelli Livine, FK is Freidel Krasnov.
There was a revolution and convergence starting in 2006.
It is misleading to say there are a whole lot of LQGs. There HAVE been in the past. But in 2007 the old vertex amplitude formula of BarrettCrane was thrown out and several new ones tried and the two I mentioned turned out to coincide and to give results on hypersurfaces consistent with those of the old pre-2000 canonical LQG. So it amounts to a rederivation of the whole theory.
Rovelli gives a good summary of this in his talk to the string theorists at Strings 2008. Ask if you don't have the link and want to watch the talk.
I am almost not following LQG development nowadays. ALl I can say is that I listened the Rovelli talk at strings 2008 (I folllowed almost all talks) and most of it´s talk looked very similar to the introductory 2003 paper I talked at the beguining. If he actually told about the new developments it was a very brief mention that resulted almos ot perceibed by most participants (at least i I must judge by other blog entries about strings 2008).
Well, if LQG doesnt predict that light speed dispersion, does it predict something. Well, a new thread in PF was created in the subject, this. Seemengly most of that predictions are related to LQC and not to LQG. And the conexion among LQC and LQG is not totallly clear.
Well, LQG comunity clearly has the right to change it´s opinion about what it is or what it is not a prediction of their theories. But certainly, it makes sound the previous claim somehow as a publicitary strategy. It is not as if that publicity trick are not something totally new in physics, but, certainly, are not the bes way to give credibility. Anyway, LQG people will probably keep doing researche in their theories, but probably they have lost a great oportunity to win a clear triumph.
Also, Nic Mavromatos, an Jonh Ellis, from CERn, published around the same time a paper stating that noncrititical Liouville strings predictes similar results (with the dependence of speed on the frequency going in the opossite direction that in LQG.
Those people expressed the hope taht the launch , around 2005, of the GLAST satelite, could experimentally test tht ideas. GLAST satelite laucnhing got somewhat delayed. In the meantime, in august 2007, an experimental recipe, known as MAGIC, obtained some results that indicated a possible confirmation of those ideas. I told
something about it in this entry. But GLAST satelite was finally launched and at last there are some results. You can read a press release by NASA here.
The NASA paper speaks about gamma ray bursts, not about quantum gravity. Where is the relation?
Well, in the end of the release you can read this:
One curious aspect of the burst is a five-second delay separating the highest-energy emissions from the lowest. Such a time lag has been seen clearly in only one earlier burst.
That´s the point. The idea expresed but that proposals of quantum gravity is that the more energetic fotons travelat different speed than the slower ones. That implies that the fastests one arrive sooner than the slower ones. In ordinary distances that can´t be observed, but for very distant objects the path is long enought to give meausereable results.
So, has LQG been confirmed? Not quite. I´ll soon tell why. But first I´ll make a few clarifications. The way LQG was supposed to predict those effects was by means of it´s prediction of a minimal length. That leads to DSR (double special relativities) that take tha minimal length as a premise and from that they obtain the dispersion relations of vacuum light speed. I have also heard of another argument, supposedly stated by Fotini Markopuolu Kalamara. The idea is that the more energetic fotons , of shorter wave-lengt collide more ofthem with the "atoms of space-time". I did a search in arxiv of the actual paper of fotini but I wasn´t able to find it (if some reader know the link I would knoowledege if he would leave it in the comments).
Let´s return to the question of why the GLAST satelite results don´t favour this LQG (or noncritical string theory) prediction. The trick is that there are models on how the GRB are formed. The GRB are supossed to be originated in matter beeing acreted into a black hole. The models of disk acrretion predict that less energetic photons are produced sonner that more energetic ones. I have´t readed the actual papers about those models (semeengly that calculations are available here ). I simply readed the conclusion, that the variations on light speed are excluded.
You can read more about it in the Lubos motl blog. Also there is a discusion about the topic in physic forums, concretely in this post.
In physics forums it is stated that , in fact, that presumably firm prediction of LQG in facthaas been progresively desestimated. To beguin with it has not been possible to rigurously deduce that behaviiour directly from canonical LQG. In fact the whole subject of canonical LQG is nowadays almost forgoten. Accordin to Marcus actually lQG is focussing in:
There is really only one form of LQG that is getting the bulk of attention. It is designated EPRL (gamma<1) and also FK(gamma < 1). These two turned out to be equivalent as long as the Immirzi gamma is < 1. Two different vertex amplitude formulas which coincide in the important case.
Essentially every new paper I see about the full theory (not the LQ cosmo offspring, but LQG)
as well as every new video-stream seminar talk at PIRSA is about this one version of LQG.
From my perspective it is getting all the attention since sometime in 2007.
Rovelli and his group call it Covariant LQG.
EPRL is Engle Pereia Rovelli Livine, FK is Freidel Krasnov.
There was a revolution and convergence starting in 2006.
It is misleading to say there are a whole lot of LQGs. There HAVE been in the past. But in 2007 the old vertex amplitude formula of BarrettCrane was thrown out and several new ones tried and the two I mentioned turned out to coincide and to give results on hypersurfaces consistent with those of the old pre-2000 canonical LQG. So it amounts to a rederivation of the whole theory.
Rovelli gives a good summary of this in his talk to the string theorists at Strings 2008. Ask if you don't have the link and want to watch the talk.
I am almost not following LQG development nowadays. ALl I can say is that I listened the Rovelli talk at strings 2008 (I folllowed almost all talks) and most of it´s talk looked very similar to the introductory 2003 paper I talked at the beguining. If he actually told about the new developments it was a very brief mention that resulted almos ot perceibed by most participants (at least i I must judge by other blog entries about strings 2008).
Well, if LQG doesnt predict that light speed dispersion, does it predict something. Well, a new thread in PF was created in the subject, this. Seemengly most of that predictions are related to LQC and not to LQG. And the conexion among LQC and LQG is not totallly clear.
Well, LQG comunity clearly has the right to change it´s opinion about what it is or what it is not a prediction of their theories. But certainly, it makes sound the previous claim somehow as a publicitary strategy. It is not as if that publicity trick are not something totally new in physics, but, certainly, are not the bes way to give credibility. Anyway, LQG people will probably keep doing researche in their theories, but probably they have lost a great oportunity to win a clear triumph.
Monday, February 16, 2009
An invitation to algebraic geometry
I have mentioned previously in this blog that I was studying algebraic geometry. O.K. I have concluded my first phase of study and it is time to tell something about it.
Algebraic geometry is a very broad topic with different possible approaches and epochs of development. Most traditional courses/books of initiation on the subject go through the algebraic approach. As the name suggests there is a lot of algebra involved. It is expected that the reader would be familiar with basic abstract algebra (groups, rings and the basics of ideals of rings), possibly field (in the mathematical sense nothing to do with a physic field, of course) theory and the very related subject of Galois theory. This is the standard content of undergraduate courses in alge3bra. In addition it is needed what is known under the name of "commutative algebra" which may, or maybe not, be covered in undergraduate courses. Commutative algebra consists mainly of a deeper analysis of rings and ideals. In particular noetherian rings, Hilbert nullentensantz theorem and things like that.
A bibliography of all this could be DORRONSORO, J. : NUMEROS GRUPOS Y ANILLOS (in Spanish, for sure there are lot of books covering the same topic in the English literature)for basic abstract algebra. For field/Galois theory a very canonical reference could be Ian Stewart: Galois Theory.
About commutative algebra a classical reference is the book of atiyah with precisely that name. Actually a friend of me, disr3ecomended me that book and considered a much better choice Miles Reid: Undergraduate Commutative Algebra.
Well, that are the expected prerequisites. Quite a lot if you are a physicist and not a mathematician. Later I´ll suggest other paths, but by now I´ll follow the traditional way.
With That algebraic basic you could try to bit one of the hard books, but it would be a better option to begin with an introductory book. One of the traditional introductory books is Fulton´s one algebraic curves available on line for free (info posted by Peter Woit in his blog, not even wrong). The books begins with a introductory chapter which serves a remaindering of the necessary algebra, but if you don´t previously know it it will not be too helpful. I must say that this summer I followed a course on that subject. The teacher was a physicist reconverted in mathematician. He has a paper, in collaboration, about string theory. It was that background of the teacher which aimed me to follow the course. I must say that it was a great course. To begin not all the audience were mathematicians so the teacher took a lot of time to reminder, and exemplify, the algebraic machinery. It also explained very clearly the geometric aspects. Later in this post ll say actually something about algebraist geometry and not only about the bibliography, by now I´ll just say that a (regular) algebraic curve can be identified with a Riemann surface. Every string theorists is well aware of the fact that the theory of Riemann surfaces is the basic of the Polyakov path integral. But, in fact, a traditional course in algebraic curves doesn't include the material specifically necessary for that purpose. Fortunately it includes some concepts, mainly the theory of divisor, which has become important for the subject of compactifications. Later more about it. It also tells about Blowing ups, which are actually of interest for compactifications.
After such a book, or similar ones (for example, "undergraduate algebraic geometry", also by Miles Reid one could try more serous books. For example Shafarevich: basic algebraic geometry, which covers most general algebraic spaces, aspects of the analytic approach as well as abstract geometry (schemes and all that, more on it later), or the book of Robin Hartsone which is still harder (and cover more topics), or, much better, both books.
Certainly that is a lot for a physicist. And he will not go into the most necessary goals until the last books. It is time to offer alternatives.
Recently it has appeared totally recommendable book, that gives name to this post, An Invitation to Algebraic Geometry by various authors, mainly Karen Smith.
The algebraic prerequisites of the book are only linear algebra. It gives a concise, and worked, intro to the necessary extra algebra. It does a very good job in explaining the flavour of the traditional algebraic geometry (which is not present in analytic geometry). The geometric aspects, and it´s relations to geometry are very well explained. It covers most of the topics necessary for string theory, the previously mentioned, (divisor,blowing ups), it gives some hints on abstract algebraic geometry (schemes, which is related to sheaves and the analytic side of algebraic geometry) and also, and this is important, families of algebraic surfaces. Under that name probably is not familiar for an sting theorist. The important fact is that is the concept which is behind the idea of moduli space. Loosely speaking a moduli space is an algebraic space which has the property that any of its point can be identified with other algebraic space. The most basic example is the projective plane. Any point of the projective plane can be identified with the rect that pass through it.
The concept of moduli space is a very recent one. The book of Joe Harris: Algebraic Geometry, a first course, cover more details about it than the book I was talking previously. The precise definition of the concept is very hard. The problem is that a moduli space usually is going to have singular points. To work in a proper way with that point you must go to abstract algebraic varieties (schemes), and, further, orbifolded schemes and things like that. The first introduction of the idea of moduli space dates back to the work of grothendieck which goes beyond the previous works of Teichmuller. There the re talking about families of algebraic curves (Riemann surfaces) and their complex structures. The teichmuller space of Riemann surface S of a given genus (intuitively, the genus is the number of holds) is the quotient of Conf(S)/Diff(S). Here Conf(S) is Met(S)/Cinf(S) where Met(s) is the set of possible metrics on S and Cinf is the group al infinite differentiable functions on S, which acts in the group o f metrics generating conformal transformations. -this is well known material for string theorists. It is covered in the chapters about the Polyakov integral. There one is explained how to get the moduli space form the teichmuller space and that the beltrami differentials form a basic of the tangent space to the moduli space and many other things. Is one is familiarized with differential geometry on manifolds, some basic group theory and complex analysis(and who ins´t nowadays) he can follow the ideas and accept that space3s as "abstract" spaces whose dimension can be determined (with the help of the Riemann Roch theorem) and can work with them to get the desired result, expressions for the cross sections. But if one reads books on algebraic geometry one becomes aware of the fact that those topic have a more geometric, and not so abstract, nature. Of course, as I said, the precise formulation of the idea requires heavier machinery that the one covered in string theory books. The pre3cise concept of moduli space of a Riemann surfaces is due to David Mumford and he got a Fields medal for it. And it is a very recent work, it is dated in the last sixtie3s and former seventies. It is somewhat incredible how soon such an abstract and difficult concept, combined with the also very recent, for the date, theory of conformal field theory, were combined in a baby string theory in a time where the math basic of more physicists was essentially the book of Arfken (or Mathews Walker) plus some tensor analysis and pedestrian Lie groups theory. I guess that there3 is a history in that achievement that deserves to e told, pity I have idea of that.
Well, we have a recommended book in the algebraic part. Lets go for a book in the analytic part. My choice 8freely available online) is U. Bruzzo. INTRODUCTION TO. ALGEBRAIC TOPOLOGY AND. ALGEBRAIC GEOMETRY.
It is a short book. the first part covers algebraic topology,almost form the beginning. It, later, introduce the very important concept of presheaves and sheaves. Them he introduces Cech co-homology. He treats fibered spaces, de rham theory, characteristic classes, the very hard topic of spectral sequences and, in general it covers a good part the material covered in canonical books of algebraic topology such as the one by Spanier, or the famous "differential forms in algebraic topology" of Bott and Tue (see this entry int he U-duality blog for more info in that book and in the general subject of math for string theory).
The second part of the book covers, from the analytic viewpoint, the same material on divisors (and the related concept of line bundles,ample and very ample bundles) that is mentioned in the book y Karen Smith and others. It also covers algebraic curves and the Riemann Roch theorem. The last chapter has a somewhat misleading title "nodal curves". The "nodal" makes reference to a type of singularity in an algebraic curve. An algebraic curve (it is time to say at last something about them xD) is, roughly speaking the set of zeros of a polynomials (enough polynomials to get a one dimensional space in the field of definition of the polynomials-note, a complex one dimensional space is a two dimensional real space-). A singularity is a point where the tangent space is not defined. That can e due to a self-intersection of the curve (so we have "two tangent spaces) or a point where the tangent space is not defined (the curve has not a derivative). The former is a nodal point, and can be resolved by the technique of blowing-up. This consist of cutting the singular point and to replace it by the projective space over it (see the books for the details). Well, the question is under the name of "nodal curves" is hidden the most well known concept of blowing-up. I would mention that I have followed this semester a course in the UCM which covered this analytic viewpoint of algebraic geometry. The official teacher was a mathematician who also has a publication on string theory, actually, a good amount of the course was finally imparted by a different teacher. I previously knew sheave theory, but certainly my knowledge on the subject has greatly growth ;-).
Well, with that two books one has a decent basic in algebraic geometry. He could go from there directly to specific reviews relating this to string theory. Soon ill comment something about it. Firs another suggestions. In the blog entry of U-duality it is recommended the Nakaharas book. I would add another book which I have already mentioned here. Topology and quantum field theory, by Charles Nash. It covers Riemann surfaces, and it relation to string theory. It also cover many other subjects. For example the theory of elliptic operators and its relation to topology, which is central to many results in the analytic part of algebraic geometry. In fact the Nash book covers that aspects (I suspect that it follows closely the book of Weill on analytic manifolds). Certainly a great book.
ON the pure math side one could go with the previously mentioned books of shafarevich and Hartsone (I have read some chapters of the former and I have been teach ed the first chapter of the second). An additional recommendation is the encyclopedic Principles of Algebraic Geometry by Griffith & Harris. Of those books the only one that covers moduli spaces is the one of Hartsone.
OK, what about not pure math books? Where is the string theory?. Lets go to it.
The canonical reference would be the book Mirror symmetries freely available on-line form the claymath institute (yes,the same claymath institute of the millenium prizes). Really one could begin with that book and to forget about all the above ones. It is a very extensive one, and covers almost all the mentioned subjects, together with the new, ones that I´ll speak now, toric varieties. The first part is reasonably accessible to a physicist with a decent basic on modern math (without need of abstract algebra). I guess that the book somewhat fails in providing the geometric-geometric viewpoint of the subject, something that , I insist, is very well covered in the Karen Smith book in a very acce3sible way.
OK, last references, arxiv reviews of the application of all this to string theory.
I would begin by TASI LECTURES ON COMPACTIFICATION AND DUALITY by DAVID R. MORRISON. It dates in nov 2004 and the arxiv signature is: hep-th/0411120v1
The third and fourth part are specifically related to the subject of algebraic geometry in string theory. It explains how Calaby -Yau manifolds are good compactifications of string theory and it explains how the theory of divisors and ample line bundles are good tools to get kahler classes of Calabi-Yau manifolds and why that is a good thing.
A different use of algebraic geometry,and specially the blowing up techniques, is for resolution of singularities in orbifolds and also, of conifolds. Resolving singularities of conifolds one can describe process where by varying the moduli space of a calabi-yau one gos trought transitions where some topological aspects of the calabi yau change.You can describe that changing aspects in terms of intersection theory. And you can describe intersection theory in terms of divisors. The first papers on topological change are due to Brian Green and Aspinwell (who, B.T.W. also has a book named Mirror Symmetry which covers those topics) on one side and Witten on the other side. Perhaps the most closed paper to the algebraic geometric techniques is this. the paper is form 1993. Later the topic got a different, more complete, treatment by placing D-branes in the conifold singular point (sorry, I have not time now to search the arxiv reference for the paper).
For papers explaining toric geometry , kind of generalization of projective spaces, very useful in F-theory construction you can read the3 recommended papers of the string wiki:
Toric geometry and calabbi yau compactifications y Maximilian Kreuzer (arXiv:hep-th/0612307v2)
Lectures on complex geometry, Calabi–Yau manifolds and toric geometry by Vincent Bouchard (arXiv:hep-th/0702063v1) or, also:
The Geometer’s Toolkit to String Compactifications (arXiv:0706.1310v1)
Certainly I don´t find them the more funny papers in math and I have not, still, readed them completely.
Once you have all this math background you could go without fear to study string compactifications, specifically F-theory ones. If you want a complete and detailed physical guide on the field of aplication you could use this paper:
LES HOUCHES LECTURES ON CONSTRUCTING STRING VACUA by Frederik Denef (arXiv:0803.1194v1)
I apologyce by not saying nothingn about the subject of elliptic curves (a very special kind of algebraic curves) and the related topics of eliptic integrals and aliptics function and of its generalizations (modular forms), maybe in other post. In fact from now to that point I´ll probaly have a better knowledge of that subjects and it will be a better post anyway ;-).
Sunday, February 08, 2009
Spanish physicists offers a possible explanation of the pioneer anomaly
The pioneer anomaly is a rather well established phenomena wichs is still lacking a satisfactory explanation.
The Spanish physicist Antonio F. Rañada, well known in his country by his textbook about classic dynamics, and also by a semi divulgative book of introduction to physics (I would add that his theory of topological treatment of electromagnetism, elaborated in collaboration with Jose Luis Trueba is very estimable) in collaboration with Alfredo Tiemblo (sorry Alfredo, I don´t know anything about your work to cite it)have just written this paper that offers a possible explanation.
The idea goes as follows. The pioneer anomaly consist of an apparent excess of slowing down of the spacecraft, in his way out of the solar system, respect to the one predicted by general relativity. The most obvious interpretation of this anomaly would be a modification to the behaviour of gravity, in MOND (modified newton dynamics) like theories. A second possible interpretation, proposed by Anderson, is that the anomaly is apparent and not real. It comes from the way in the measurement of the effect. It involves the measurement of time by two methods, one depending in an atomic clock and the other depending on astrophysical inputs. Anderson introduces and ad-hoc difference in this two times as a possible explanation of the effect, but he gives no glimpse on how this desynchronization could arise.
Precisely that is the point of the Rañeda paper, they argue that the well know indeterminacy of energy and time, E.t=hbar, (which is referred by them as the fourth heisenberg indeterminacy) is affected by the averaged dimensionless
gravitational potential, i. e. the potential of all the mass-energy in the entire universe assuming that it is uniformly distributed. That leads to an increase of the lifetime of virtual pairs of electrons-positrons and , consequently, to a modification of the behaviour of atomic clocks (the details are actually a little more involved and go through the use of the optical density of vacuum, see the paper to re3ad about them.The order of magnitude of the effect agrees with the one needed to explain the Pioneer anomaly.
The latter part of the article explains how this effect is good because it explains the anomaly without conflicting general relativity. Also they explain that the nature of the effect makes that it is very hard to detect for other natural bodies in the solar system (mainly planets) so that it avoids conflicts with other observations.
Well, I am not at all expert in the pioneer anomaly so I cant judge how good this theory fits incorporation with other proposals. About the somewhat "quantum gravity" related effect that is behind his explanation the authors refers to other papers where they go into further details that I haven't read. With this limitations my judgement can´t be considered authoritative but my impression is that the paper looks very elegant and I hope that it will go in the right direction.
I will end this entry with an apology. I had begun(and almost has finished) to write a post about the recent claim by Craig Hogan about a possible observation of a quantum gravity related effect in the measurements of the geo 600 interferometer related to a theory developed by Hogan named "holographic noise". That theory is, basically, an implementation of the holographic principle of -hooft and susskind by a different mechanism to the already proposed (mainly the AdS/CFT correspondence). I had read two of the relevant arxiv papers and had outlooked the other and I explained briefly the ideas. Unfortunately my computer hanged before submitting the post and because of some unknown reason blogspot didn't conserve any draft copy. I hate to write things twice so I refer to the interested reader to press releases, like this one or to an blog entry on the subject in the bog "dynamics of cats".
The Spanish physicist Antonio F. Rañada, well known in his country by his textbook about classic dynamics, and also by a semi divulgative book of introduction to physics (I would add that his theory of topological treatment of electromagnetism, elaborated in collaboration with Jose Luis Trueba is very estimable) in collaboration with Alfredo Tiemblo (sorry Alfredo, I don´t know anything about your work to cite it)have just written this paper that offers a possible explanation.
The idea goes as follows. The pioneer anomaly consist of an apparent excess of slowing down of the spacecraft, in his way out of the solar system, respect to the one predicted by general relativity. The most obvious interpretation of this anomaly would be a modification to the behaviour of gravity, in MOND (modified newton dynamics) like theories. A second possible interpretation, proposed by Anderson, is that the anomaly is apparent and not real. It comes from the way in the measurement of the effect. It involves the measurement of time by two methods, one depending in an atomic clock and the other depending on astrophysical inputs. Anderson introduces and ad-hoc difference in this two times as a possible explanation of the effect, but he gives no glimpse on how this desynchronization could arise.
Precisely that is the point of the Rañeda paper, they argue that the well know indeterminacy of energy and time, E.t=hbar, (which is referred by them as the fourth heisenberg indeterminacy) is affected by the averaged dimensionless
gravitational potential, i. e. the potential of all the mass-energy in the entire universe assuming that it is uniformly distributed. That leads to an increase of the lifetime of virtual pairs of electrons-positrons and , consequently, to a modification of the behaviour of atomic clocks (the details are actually a little more involved and go through the use of the optical density of vacuum, see the paper to re3ad about them.The order of magnitude of the effect agrees with the one needed to explain the Pioneer anomaly.
The latter part of the article explains how this effect is good because it explains the anomaly without conflicting general relativity. Also they explain that the nature of the effect makes that it is very hard to detect for other natural bodies in the solar system (mainly planets) so that it avoids conflicts with other observations.
Well, I am not at all expert in the pioneer anomaly so I cant judge how good this theory fits incorporation with other proposals. About the somewhat "quantum gravity" related effect that is behind his explanation the authors refers to other papers where they go into further details that I haven't read. With this limitations my judgement can´t be considered authoritative but my impression is that the paper looks very elegant and I hope that it will go in the right direction.
I will end this entry with an apology. I had begun(and almost has finished) to write a post about the recent claim by Craig Hogan about a possible observation of a quantum gravity related effect in the measurements of the geo 600 interferometer related to a theory developed by Hogan named "holographic noise". That theory is, basically, an implementation of the holographic principle of -hooft and susskind by a different mechanism to the already proposed (mainly the AdS/CFT correspondence). I had read two of the relevant arxiv papers and had outlooked the other and I explained briefly the ideas. Unfortunately my computer hanged before submitting the post and because of some unknown reason blogspot didn't conserve any draft copy. I hate to write things twice so I refer to the interested reader to press releases, like this one or to an blog entry on the subject in the bog "dynamics of cats".
Friday, January 09, 2009
Some review papers in string theory
There are a bunch of things that I would like to post about, but I prefer to take a bit of time to present them in the best possible way.
In the meantime I am going to leave links to some review articles. Of course one always go to the string wiki, or search for them in arxiv, but anyway Ill link them.
The first one is this. It is a "pedestrian" introduction to the use of the ADS/CFT correspondence to QCD, that is, AdS/QCD. In fact you cant actually get exact QCD from the duality but only an approximate theory. Still this approach offers some advantages over other methods in QCD such as, for example, lattice computations which lacks of time evolution because of the need to go to euclidean signature.
I would recomend also to read the blog of Dimitry (NeQ) for aditional information. Concretely these two entries
http://www.nonequilibrium.net/163-adsqcd/ and http://www.nonequilibrium.net/170-back-ads-qcd/
The second one is a brief (12 pages) review of dark energy and the alternatives. I cite here the abstract which is very self explanatory:
We present a brief review of various approaches to late time acceleration of universe. The cosmological
relevance of scaling solutions is emphasized in case of scalar field models of dark energy. The
underlying features of a variety of scalar field models is highlighted. Various alternatives to dark
energy are discussed including the string curvature corrections to Einstein-Hilbert action, higher
dimensional effects, non-locally corrected gravity and f(R) theories of gravity. The recent developments
related to f(R) models with disappearing cosmological constant are reviewed.
Another paper about cosmology is this. Concretely it verses about inflation in string cosmology.
The last one is about heterotic string theory. It is more extense tahtthe others and it is based in a PhD. it covers mainly orbifold compactifications. It is most specialized, and more detailed, than the others. That meansalsothat it is longest (158 pages, 102 if the appendix are discounted).
In the meantime I am going to leave links to some review articles. Of course one always go to the string wiki, or search for them in arxiv, but anyway Ill link them.
The first one is this. It is a "pedestrian" introduction to the use of the ADS/CFT correspondence to QCD, that is, AdS/QCD. In fact you cant actually get exact QCD from the duality but only an approximate theory. Still this approach offers some advantages over other methods in QCD such as, for example, lattice computations which lacks of time evolution because of the need to go to euclidean signature.
I would recomend also to read the blog of Dimitry (NeQ) for aditional information. Concretely these two entries
http://www.nonequilibrium.net/163-adsqcd/ and http://www.nonequilibrium.net/170-back-ads-qcd/
The second one is a brief (12 pages) review of dark energy and the alternatives. I cite here the abstract which is very self explanatory:
We present a brief review of various approaches to late time acceleration of universe. The cosmological
relevance of scaling solutions is emphasized in case of scalar field models of dark energy. The
underlying features of a variety of scalar field models is highlighted. Various alternatives to dark
energy are discussed including the string curvature corrections to Einstein-Hilbert action, higher
dimensional effects, non-locally corrected gravity and f(R) theories of gravity. The recent developments
related to f(R) models with disappearing cosmological constant are reviewed.
Another paper about cosmology is this. Concretely it verses about inflation in string cosmology.
The last one is about heterotic string theory. It is more extense tahtthe others and it is based in a PhD. it covers mainly orbifold compactifications. It is most specialized, and more detailed, than the others. That meansalsothat it is longest (158 pages, 102 if the appendix are discounted).
Wednesday, December 24, 2008
A christmas present for string theorists from Matthew Headrick
Today in Arxiv it hs appeared the following paper: A solution manual for Polchinski's "String Theory"
The name says it all. The abstrac dissipates any possible dude:
We present detailed solutions to 81 of the 202 problems in J. Polchinski's two-volume textbook "String Theory".
Also I find interesting the announcement of Tommaso Dorigo in his blog about an upper limit on the mass of the graviton (or at least the mass of the graviton in the context of certain Randall-Sundrum models). The bblog entry is this. Of course it will be better to wait untill the corresponding arxiv paper, but it looks certainly very interesting.
Also I have noticed that Amelio Camelia is publishing recently a few papers about nonconmutative geometry in string theory. Camelia is famouse because of the paper whre he presented the idea of double special relativity. Ultimately the idea of DSR has been flawed with many problems, but still I think that it was a brilliant proposal so I am interested in reding that new papers. But before that I am reading other things that I had pending about more well stablised topics in string theory. Anway, if the papers of Camelia are interesting Ill try to bblog about then when I would read them.
The name says it all. The abstrac dissipates any possible dude:
We present detailed solutions to 81 of the 202 problems in J. Polchinski's two-volume textbook "String Theory".
Also I find interesting the announcement of Tommaso Dorigo in his blog about an upper limit on the mass of the graviton (or at least the mass of the graviton in the context of certain Randall-Sundrum models). The bblog entry is this. Of course it will be better to wait untill the corresponding arxiv paper, but it looks certainly very interesting.
Also I have noticed that Amelio Camelia is publishing recently a few papers about nonconmutative geometry in string theory. Camelia is famouse because of the paper whre he presented the idea of double special relativity. Ultimately the idea of DSR has been flawed with many problems, but still I think that it was a brilliant proposal so I am interested in reding that new papers. But before that I am reading other things that I had pending about more well stablised topics in string theory. Anway, if the papers of Camelia are interesting Ill try to bblog about then when I would read them.
Monday, December 15, 2008
Some recomended papers in string theory and cosmology
Status of Superstring and M-theory
If someone is interested in getting an idea of the status of string theory today, in a readable form for non specialists, I seriously recommend this paper by John Schwarz Status of Superstring and M-theory.
It begins with an introduction to the very subject of string theory, explaining the basic of string theory. It explains in more detail than usual the connection between the former "hadronic" string and the actual unified field theory string (and gives the link to another paper by the author devoted to the beginnings of string theory which is worth reading also). Later, in the paper, it explains the second string revolution and the dualities among the five string theories. It talks about the D-branes revolution, the flux compactifications, the warped compactifications sceneries and the possible role of string theory in cosmology. Obviously such a lot of material compressed in 13 pages means that it doesn’t go nearly deep in any of the subjects. It can be readed as an almost divulgative article (a divulgative article suited for theoretical physicists not specialist in string theory, if such thing still exists at all xD).
The second part of the article is devoted to the actual subject, the review of the status of sting theory. Or, to be more concrete, the status of string theory phenomenology. It discuss the most studied sceneries of "compactification" (understood in a general sense). It briefly mentions the early attempts of compactifitcation in perturbative string theory, specially in the heterotic string.
Later he talks about heterotic M-theory, the Horawa-Witten model (you can read additional info about it in this entry of my blog). Later he briefly discuses compactifications of (non heterotic, i.e. type-IIA strong limit coupling) M-theory in G2 Manifolds. Up to here most of the material of the article is written in form that closely resembles the introductions of the corresponding chapters in his recent book (Becker-Becker-Schwartz) about string theory. The remaining part is devoted to subjects not covered in the book.
For example, it follows with an intro to intersecting D-branes in type II string theory. He explains very clearly the relevant points and later he gives bibliography with appropriate reviews (as, in fact, makes for all the subjects). The next subject is type II in calaby-yaus with fluxes. In this kind of sceneries string theory admits a lot of vacuums. This enormous amount of vacuums have been used to implement an old idea of Weinberg to explain the existence of a positive and small cosmological constant and have given rise to the string landscape and, even worst, the resurgence anthropic principle. Schwarz, as many others, doesn’t support too much the idea of the landscape.
Perhaps the most interesting chapter is the last one. It is devoted to a review of the recent papers by Vafa et all about F-theory based phenomenology. This is a very recent subject and excepting for the corresponding entries in the blogs of Motl and Distler (well, Woit did his try, but he lacks of enough knowledge in string theory to be able to extract usfull info from the papers, as he admits in the post)there has not been, as far as I know, too much discussion on this papers (why the hell is the string coffee clossed?). I have not still readed the original papers of Vafa (I am waiting to conclude a doctorate courses I am assisting about algebraic geometry before doing that) so this chapter is the first non blog info I have about it. I must say that Schwarz exposition of the subject is very, very clear. He introduces very well what F-theory is. He explains that these models are based in a novel idea, the decoupling between the GUT scale and the Planck scale. Models with this feature are named local models to distinguish them from the usual models, named global models. I´ll not try to describe here the details of how local models of F-theory are constructed and I remit the readers to the actual paper.
Quintessence from string theory
Another interesting paper, at least for me, is arXiv:0810.5346v1 entitled "Where in the String Landscape is Quintessence". When the expanded acceleration was firs observed there were many proposals. Nowadays the most commonly accepted one is that the universe is de-Sitter, that is, there is a cosmological constant. Apparently one of the reasons for this broad acceptance stems from string theory and the works of Bousso, Polchinsky and others who explain this cosmological constant in the scenario of the string theory landscape. I guess that the logical chain is something like: String theory must be true->string theory can explain an small positive constant->we have an small positive constant. Well, this paper uses similar ideas to that of Bousso and Polchinsky to support quintessence.
Some readers of the blog may be don’t know what quintessence is. Let’s remember first that a cosmological constant may be seen as due to the vacuum expectation value of a quantum field. That field, usually a scalar one, must have constant value in space and time. Quintessece also should be due to a scalar field. But this would vary in space and time. It must also fit some additional features related to its equation of state (the equation of state that represent the field in the cosmological models based on general relativity. In particular it must have pq = wρq. Here p is the pressure, rho the density and w is the quotient of bothe (w=p/rho). The actual value of w must equal to 1/3 during radiation domination and 0 during matter domination) until w undergoes a transition to less than -1/3 which initiates the accelerated expansion of the universe. For more details I suggest to read the relevant wikipedia entries: http://en.wikipedia.org/wiki/Physical_cosmology , http://en.wikipedia.org/wiki/Dark_energy, http://en.wikipedia.org/wiki/Quintessence_(physics) and http://en.wikipedia.org/wiki/Equation_of_state_(cosmology). Or, if they have time and are very interested in cosmology they could try to read the recent book of Steven Weinberg on the subject: http://www.amazon.com/Cosmology-Steven-Weinberg/dp/0198526822
The reason I find this paper particularly interesting is because many solutions which allow the existence of wormhole solutions, a topic that I find particularly interesting. Maybe people not so wormholmy wouldn’t find so interesting this paper.
Astrophysical Probes of Unification
The last paper that I want to mention is this. It is very recent, it has appeared just today in arxiv, and I guess that soon Sean Carrol and/or Lubos Motl (or Distler if he decides to reapear from it's retire) and possibly others will make extenses comments on it so I will only copy here the abstract:
Traditional ideas for testing unication involve searching for the decay of the proton and its branching
modes. We point out that several astrophysical experiments are now reaching sensitivities that allow
them to explore supersymmetric unied theories. In these theories the electroweak-mass DM particle can
decay, just like the proton, through dimension six operators with lifetime 1026 sec. Interestingly, this
timescale is now being investigated in several experiments including ATIC, PAMELA, HESS, and Fermi.
Positive evidence for such decays may be opening our rst direct window to physics at the supersymmetric
unication scale of MGUT 1016 GeV, as well as the TeV scale. Moreover, in the same supersymmetric
unied theories, dimension ve operators can lead a weak-scale superparticle to decay with a lifetime of
100 sec. Such decays are recorded by a change in the primordial light element abundances and may well
explain the present discord between the measured Li abundances and standard big bang nucleosynthesis,
opening another window to unication. These theories make concrete predictions for the spectrum and
signatures at the LHC as well as Fermi.
If someone is interested in getting an idea of the status of string theory today, in a readable form for non specialists, I seriously recommend this paper by John Schwarz Status of Superstring and M-theory.
It begins with an introduction to the very subject of string theory, explaining the basic of string theory. It explains in more detail than usual the connection between the former "hadronic" string and the actual unified field theory string (and gives the link to another paper by the author devoted to the beginnings of string theory which is worth reading also). Later, in the paper, it explains the second string revolution and the dualities among the five string theories. It talks about the D-branes revolution, the flux compactifications, the warped compactifications sceneries and the possible role of string theory in cosmology. Obviously such a lot of material compressed in 13 pages means that it doesn’t go nearly deep in any of the subjects. It can be readed as an almost divulgative article (a divulgative article suited for theoretical physicists not specialist in string theory, if such thing still exists at all xD).
The second part of the article is devoted to the actual subject, the review of the status of sting theory. Or, to be more concrete, the status of string theory phenomenology. It discuss the most studied sceneries of "compactification" (understood in a general sense). It briefly mentions the early attempts of compactifitcation in perturbative string theory, specially in the heterotic string.
Later he talks about heterotic M-theory, the Horawa-Witten model (you can read additional info about it in this entry of my blog). Later he briefly discuses compactifications of (non heterotic, i.e. type-IIA strong limit coupling) M-theory in G2 Manifolds. Up to here most of the material of the article is written in form that closely resembles the introductions of the corresponding chapters in his recent book (Becker-Becker-Schwartz) about string theory. The remaining part is devoted to subjects not covered in the book.
For example, it follows with an intro to intersecting D-branes in type II string theory. He explains very clearly the relevant points and later he gives bibliography with appropriate reviews (as, in fact, makes for all the subjects). The next subject is type II in calaby-yaus with fluxes. In this kind of sceneries string theory admits a lot of vacuums. This enormous amount of vacuums have been used to implement an old idea of Weinberg to explain the existence of a positive and small cosmological constant and have given rise to the string landscape and, even worst, the resurgence anthropic principle. Schwarz, as many others, doesn’t support too much the idea of the landscape.
Perhaps the most interesting chapter is the last one. It is devoted to a review of the recent papers by Vafa et all about F-theory based phenomenology. This is a very recent subject and excepting for the corresponding entries in the blogs of Motl and Distler (well, Woit did his try, but he lacks of enough knowledge in string theory to be able to extract usfull info from the papers, as he admits in the post)there has not been, as far as I know, too much discussion on this papers (why the hell is the string coffee clossed?). I have not still readed the original papers of Vafa (I am waiting to conclude a doctorate courses I am assisting about algebraic geometry before doing that) so this chapter is the first non blog info I have about it. I must say that Schwarz exposition of the subject is very, very clear. He introduces very well what F-theory is. He explains that these models are based in a novel idea, the decoupling between the GUT scale and the Planck scale. Models with this feature are named local models to distinguish them from the usual models, named global models. I´ll not try to describe here the details of how local models of F-theory are constructed and I remit the readers to the actual paper.
Quintessence from string theory
Another interesting paper, at least for me, is arXiv:0810.5346v1 entitled "Where in the String Landscape is Quintessence". When the expanded acceleration was firs observed there were many proposals. Nowadays the most commonly accepted one is that the universe is de-Sitter, that is, there is a cosmological constant. Apparently one of the reasons for this broad acceptance stems from string theory and the works of Bousso, Polchinsky and others who explain this cosmological constant in the scenario of the string theory landscape. I guess that the logical chain is something like: String theory must be true->string theory can explain an small positive constant->we have an small positive constant. Well, this paper uses similar ideas to that of Bousso and Polchinsky to support quintessence.
Some readers of the blog may be don’t know what quintessence is. Let’s remember first that a cosmological constant may be seen as due to the vacuum expectation value of a quantum field. That field, usually a scalar one, must have constant value in space and time. Quintessece also should be due to a scalar field. But this would vary in space and time. It must also fit some additional features related to its equation of state (the equation of state that represent the field in the cosmological models based on general relativity. In particular it must have pq = wρq. Here p is the pressure, rho the density and w is the quotient of bothe (w=p/rho). The actual value of w must equal to 1/3 during radiation domination and 0 during matter domination) until w undergoes a transition to less than -1/3 which initiates the accelerated expansion of the universe. For more details I suggest to read the relevant wikipedia entries: http://en.wikipedia.org/wiki/Physical_cosmology , http://en.wikipedia.org/wiki/Dark_energy, http://en.wikipedia.org/wiki/Quintessence_(physics) and http://en.wikipedia.org/wiki/Equation_of_state_(cosmology). Or, if they have time and are very interested in cosmology they could try to read the recent book of Steven Weinberg on the subject: http://www.amazon.com/Cosmology-Steven-Weinberg/dp/0198526822
The reason I find this paper particularly interesting is because many solutions which allow the existence of wormhole solutions, a topic that I find particularly interesting. Maybe people not so wormholmy wouldn’t find so interesting this paper.
Astrophysical Probes of Unification
The last paper that I want to mention is this. It is very recent, it has appeared just today in arxiv, and I guess that soon Sean Carrol and/or Lubos Motl (or Distler if he decides to reapear from it's retire) and possibly others will make extenses comments on it so I will only copy here the abstract:
Traditional ideas for testing unication involve searching for the decay of the proton and its branching
modes. We point out that several astrophysical experiments are now reaching sensitivities that allow
them to explore supersymmetric unied theories. In these theories the electroweak-mass DM particle can
decay, just like the proton, through dimension six operators with lifetime 1026 sec. Interestingly, this
timescale is now being investigated in several experiments including ATIC, PAMELA, HESS, and Fermi.
Positive evidence for such decays may be opening our rst direct window to physics at the supersymmetric
unication scale of MGUT 1016 GeV, as well as the TeV scale. Moreover, in the same supersymmetric
unied theories, dimension ve operators can lead a weak-scale superparticle to decay with a lifetime of
100 sec. Such decays are recorded by a change in the primordial light element abundances and may well
explain the present discord between the measured Li abundances and standard big bang nucleosynthesis,
opening another window to unication. These theories make concrete predictions for the spectrum and
signatures at the LHC as well as Fermi.
Tuesday, November 18, 2008
The fqxi time essay contest
At least some readers of this blog will read some of the links, and also other blogs (and phorums) not linked here.
If so it is very probable that they will already know about the fqxi foundation and it´s content about time nature. The actual webpage of the essay is this .
The content, or at least many of the papers appeared when he id the post, has been judged by Jonh Baez, in a post in the n-cathegory coffeé as "crackpot". I find that crackpot obession somewhat,well, crackpot. For example Jonh Baez itsefl, author of the crackpot indicator belongs (whether if he wants or not) to the LQG comunity which is considered crackpot. I think that this crackpotery issue is becoming totally nonsensic and very boring.
Said this, the truth is that some of the published articles are very philosofical (to classify them in some way) and very non phyisical. And, certainly, up to now no heavy weigth of string theory has sended an essay (and he is not expected). Of course there are good reasons for that which can be guessed easilly by anyone who thinks about that a bit.
That is not necesarilly a bad thing and invites to physicians not belonging to the top notch spheres to participate, simply because they have some reasonable possibilities to win (or at least to get some of the secondary primzs). In fact I am aware that some bloggers such as Mitta pitkannen, Cristinhe Dantas (I must add therem egregium to the links sections some day of these), Carle Brannen and, may be, Kea has sended their essays. Among the best known phyisicians are Carlo Rovelly, Rodolfo Gambini and Clauss Kiefer.
In a diferent category i would point to Hrvoje Nikoli, who has some papers in arxiv about string theory (certainly a bit outside of the mainstream of string theory) and, one of the last essays, by his biographycal note I think that he could be considered as an cosmologist in the orbit of the Randall-Sumdrum brane worlds, that is, in a position related to the mainstream of stringy cosmologists.
Also I will make a separate mention of an Spanish competitor, Venerando Solis Barrado. I must say that for good o bad I am somehat responsible of his participation because it was bye mans of me that he knew of the conent. Al i can say is (almost) good luck ;-).
I have readed some of the papers, and I have intention to read most of them, at least the ones written by known people and that have recibed votes and/or responses.
And now the delicate question. Will I participate?
Well, I wasaware for some years on the problem of canonical gravity (wheler-de Witt or LQG) with the problem of no evolution in time. I had readed their guessed solution by means of the relational time. I had readed (as is reflected by some posts on the topic) about wormholes. Womrmholes can work as time machines and peoplee working in wormhles usually make discusion about the topic, including non womrholmy time machines. I had readed about tachyons outside string theory (I guess I have readed most of the relevants papers) and something about tachyon condensation. I had readed various books by Illya Prigogyne aout the arrow of time. And, still worst, I was demanded by a friend to invent a guessed explanation about the amercian film "the butterfly effects" which covers the topic of time travel. That resulted in a toy theory which I like to call "cronoquantum mechanics".
I think that that means that I have a reasonable background in the topic. Reading some of the already published articles I see that I was not aware of some things, but not of too many. Well, physic of time and specially of time travel is a funny topic for fans of science fiction, and I am one of them. That is mainly the reason I have learned about that topics. For a while I tried to develope a litle bit more the "quantum cronomechanics" but I ended up bored of the topic (and I must add that it is a good source to get a headcache to try to think too much about it).
Even thought now there is this content and they pay a good money to the winner, and also there are some secondary prizes which result interesting. Certainly I can live withouth them, but, hey, this blog is freelance quantum gravity, and my other blog is freelance science. The name of the blogs is inspired in the freelance workers in the infomaic market. The idea is easy to understand. In the informatic buisenes there are people who don´t like to work in fixed position in an enterprise (or governement position) and prefer to work as freelances from their homes. I must say that there is a wide market for that sector and that many people in that sector are formers top notch programmers working on well known enterprises who decided to be iindependents.
The physic market, quite on the countrary, is based on an academic/funtionary paradigm. People want to get positions at universities and research institutes and devote to that purpose a lot of effort, from the very begining of their universiary studies. Of course there are good reasons for that, to begin with, tradition.
But if one analyzes the situation the fact is that the model has some serious drawbacks. The academic positions are got by people who has a reasonable expectation of beeing in the charge for around 40 years. That means that he will be blocking that postion for around 8 promotions of students (assuming a promotions takes a romedia of 5 years). It is important to note that universitary positions are permanent and that new universities (specially ones wich need theoretical physics working in that topic) are not created too ofthem.
That means that there is very few possibilities to get a permanent possition. Once this is realized there are two possibilties. To begin a fierce competition from the very begining triying to get the best possible academic quailifications and triying to convence to your teacher that you are the smartes guy since Newton. It is important to note that getting the best qualifitaions relay a lot in learning `rmarly what your teacher decides that is important about a topic. If you decide that you are interested in other aspects of the topic and study them it results ofthem in a worst qualification.
Other possible way is to organize life in a way that you could have reasonable amounts of time working, when possible, in topics related to physics. You can use that time to learn what you prefer. I certainly have opted always by this way. Of course that doesn´t mean that I reject the possibilty to do a PhD and all that. But it would be in maths, I belive that I know too much physics to do a PhD in physics (yeah, it is contradictory).
Well, all this las diegressions it to congratulate the fqxi foundation for their iniciative. To publish a paper requires to do some very specific work,no always fun. And I like to be payed for my work (at least if it is a good work). I mean, I am sure that now I could publish papers on string theory or LQG. Certainlly they would, very probably, would be not too goood papers (ate least not now). But even that papers would requiere good amounts of time. And I wouldn´t get any rewar for them. So i see not point in triying to publish anything if I am not almost sure that it is not crystal clear that would be a top notch paper (a definitve prrof of the AdS/CFT conjecture, the millenium prize in the yang-mills masss gap or things like that). Certainly I think it is not a good idea to depend on that possibiilities.
On the other sie this more modests fqxi prizes are very interesting because they are a more realistic objective which can serve to animte people to do good papers that he woind´t do otherwise.
Ok, a lot of sociology. Am I going to publish a paper in that content?. Well, today I have had an ocurrence for a very nice title for the paper, It would be a mesh to not use it. Most important, I am really tired of the topic of time physics and I think that the best way to never to have to woory about the topic is to publish the paper. But I still dind´t answer (I know that people who know me personally have realized that point perfectlly), shal I try to send a paper to the content? Well, may be, if I have time... ;-).
Update: The deadline for the submition of the paper is over and I still haven´t it ready. Un unfortunate minor illnes has had me down (for purposes of doing serious work) for around a week and that is bad for someone like me that belongs to the "wait last minute" category. If there is some flexibility byt the fqxi comite maybe still it could be some chance. If not I´ll try to put the paper somewhere (once it is finished) in order people could read it (if any is interested).
If so it is very probable that they will already know about the fqxi foundation and it´s content about time nature. The actual webpage of the essay is this .
The content, or at least many of the papers appeared when he id the post, has been judged by Jonh Baez, in a post in the n-cathegory coffeé as "crackpot". I find that crackpot obession somewhat,well, crackpot. For example Jonh Baez itsefl, author of the crackpot indicator belongs (whether if he wants or not) to the LQG comunity which is considered crackpot. I think that this crackpotery issue is becoming totally nonsensic and very boring.
Said this, the truth is that some of the published articles are very philosofical (to classify them in some way) and very non phyisical. And, certainly, up to now no heavy weigth of string theory has sended an essay (and he is not expected). Of course there are good reasons for that which can be guessed easilly by anyone who thinks about that a bit.
That is not necesarilly a bad thing and invites to physicians not belonging to the top notch spheres to participate, simply because they have some reasonable possibilities to win (or at least to get some of the secondary primzs). In fact I am aware that some bloggers such as Mitta pitkannen, Cristinhe Dantas (I must add therem egregium to the links sections some day of these), Carle Brannen and, may be, Kea has sended their essays. Among the best known phyisicians are Carlo Rovelly, Rodolfo Gambini and Clauss Kiefer.
In a diferent category i would point to Hrvoje Nikoli, who has some papers in arxiv about string theory (certainly a bit outside of the mainstream of string theory) and, one of the last essays, by his biographycal note I think that he could be considered as an cosmologist in the orbit of the Randall-Sumdrum brane worlds, that is, in a position related to the mainstream of stringy cosmologists.
Also I will make a separate mention of an Spanish competitor, Venerando Solis Barrado. I must say that for good o bad I am somehat responsible of his participation because it was bye mans of me that he knew of the conent. Al i can say is (almost) good luck ;-).
I have readed some of the papers, and I have intention to read most of them, at least the ones written by known people and that have recibed votes and/or responses.
And now the delicate question. Will I participate?
Well, I wasaware for some years on the problem of canonical gravity (wheler-de Witt or LQG) with the problem of no evolution in time. I had readed their guessed solution by means of the relational time. I had readed (as is reflected by some posts on the topic) about wormholes. Womrmholes can work as time machines and peoplee working in wormhles usually make discusion about the topic, including non womrholmy time machines. I had readed about tachyons outside string theory (I guess I have readed most of the relevants papers) and something about tachyon condensation. I had readed various books by Illya Prigogyne aout the arrow of time. And, still worst, I was demanded by a friend to invent a guessed explanation about the amercian film "the butterfly effects" which covers the topic of time travel. That resulted in a toy theory which I like to call "cronoquantum mechanics".
I think that that means that I have a reasonable background in the topic. Reading some of the already published articles I see that I was not aware of some things, but not of too many. Well, physic of time and specially of time travel is a funny topic for fans of science fiction, and I am one of them. That is mainly the reason I have learned about that topics. For a while I tried to develope a litle bit more the "quantum cronomechanics" but I ended up bored of the topic (and I must add that it is a good source to get a headcache to try to think too much about it).
Even thought now there is this content and they pay a good money to the winner, and also there are some secondary prizes which result interesting. Certainly I can live withouth them, but, hey, this blog is freelance quantum gravity, and my other blog is freelance science. The name of the blogs is inspired in the freelance workers in the infomaic market. The idea is easy to understand. In the informatic buisenes there are people who don´t like to work in fixed position in an enterprise (or governement position) and prefer to work as freelances from their homes. I must say that there is a wide market for that sector and that many people in that sector are formers top notch programmers working on well known enterprises who decided to be iindependents.
The physic market, quite on the countrary, is based on an academic/funtionary paradigm. People want to get positions at universities and research institutes and devote to that purpose a lot of effort, from the very begining of their universiary studies. Of course there are good reasons for that, to begin with, tradition.
But if one analyzes the situation the fact is that the model has some serious drawbacks. The academic positions are got by people who has a reasonable expectation of beeing in the charge for around 40 years. That means that he will be blocking that postion for around 8 promotions of students (assuming a promotions takes a romedia of 5 years). It is important to note that universitary positions are permanent and that new universities (specially ones wich need theoretical physics working in that topic) are not created too ofthem.
That means that there is very few possibilities to get a permanent possition. Once this is realized there are two possibilties. To begin a fierce competition from the very begining triying to get the best possible academic quailifications and triying to convence to your teacher that you are the smartes guy since Newton. It is important to note that getting the best qualifitaions relay a lot in learning `rmarly what your teacher decides that is important about a topic. If you decide that you are interested in other aspects of the topic and study them it results ofthem in a worst qualification.
Other possible way is to organize life in a way that you could have reasonable amounts of time working, when possible, in topics related to physics. You can use that time to learn what you prefer. I certainly have opted always by this way. Of course that doesn´t mean that I reject the possibilty to do a PhD and all that. But it would be in maths, I belive that I know too much physics to do a PhD in physics (yeah, it is contradictory).
Well, all this las diegressions it to congratulate the fqxi foundation for their iniciative. To publish a paper requires to do some very specific work,no always fun. And I like to be payed for my work (at least if it is a good work). I mean, I am sure that now I could publish papers on string theory or LQG. Certainlly they would, very probably, would be not too goood papers (ate least not now). But even that papers would requiere good amounts of time. And I wouldn´t get any rewar for them. So i see not point in triying to publish anything if I am not almost sure that it is not crystal clear that would be a top notch paper (a definitve prrof of the AdS/CFT conjecture, the millenium prize in the yang-mills masss gap or things like that). Certainly I think it is not a good idea to depend on that possibiilities.
On the other sie this more modests fqxi prizes are very interesting because they are a more realistic objective which can serve to animte people to do good papers that he woind´t do otherwise.
Ok, a lot of sociology. Am I going to publish a paper in that content?. Well, today I have had an ocurrence for a very nice title for the paper, It would be a mesh to not use it. Most important, I am really tired of the topic of time physics and I think that the best way to never to have to woory about the topic is to publish the paper. But I still dind´t answer (I know that people who know me personally have realized that point perfectlly), shal I try to send a paper to the content? Well, may be, if I have time... ;-).
Update: The deadline for the submition of the paper is over and I still haven´t it ready. Un unfortunate minor illnes has had me down (for purposes of doing serious work) for around a week and that is bad for someone like me that belongs to the "wait last minute" category. If there is some flexibility byt the fqxi comite maybe still it could be some chance. If not I´ll try to put the paper somewhere (once it is finished) in order people could read it (if any is interested).
Friday, October 31, 2008
New physics for Hallowen
Dos papers salieron ayer dando señales claras de nueva física. De un lado anlizando los datos del satélite PAMELA se ha confirmado un exceso de positrones en los rayos cósmicos respecto a lo esperado según los modelos convencionales.
Para explicarlo se sugieren modelos basados en producción de positrones basados en ciertos tipos de materia oscura como puede leerse en este paper: http://arxiv.org/PS_cache/arxiv/pdf/0810/0810.5344v1.pdf
Podeis leer una entrada de blog dónde lo explican con mas detalle aquí: http://resonaances.blogspot.com/2008/10/pamelas-coming-out.html
El otro gran evento es el que describen en este paper: http://arxiv.org/PS_cache/arxiv/pdf/0810/0810.5357v1.pdf
El CDF es uno de los dos detectores del acelerador de partículas americano Tevatron (el otro detector es el D0). El grupo encagado de analizar los datos de ese detector se ha encontrado con que encuentran muchos evento que producen un muón producido a mas de 1.5 cms del centro de colisiones dónde se produce un evento dimuón. Para que esto sea posible se arguye que debe haberse formado una partícula en la colisión que se aleja esos 1.5 cms antes de desintegrarse en el muón.
Lo interesante es que ningún componente cnocido del modelo standard parece ser un posible candidato a ser esa partícula y por tanto todo apunta a qu ese trata de una nueva partícula.
¿que tipo de partícula? Un paper de hace unas 3 semanas por Nima-Arkani-Hamed y Neal Weiner presentaban un modelo que pretendía , basado en ideas similares a lo que ha revelado PAMELA sobre la dark matter un a predicción sobre que el lHC podria encontrar cierto tipo de nueva física que encaja muy bien con lo que, anticipándose, parece haber encontrado el tevatrón. El modelo de nima-Weiner es un modelo en que se hace una aplicación de la supersimetría al sector escondidio de la materia oscura. Podeis leer detalles al respecto en varios blogs:
Lubos: http://motls.blogspot.com/2008/10/cdf-sees-dark-unified-susy-in-lepton.html
Woit (que no se entera muy bien de lo que dice el paper de nima y Weiner): http://www.math.columbia.edu/~woit/wordpress/?p=1045
Dorigo (que de hecho estan en el grupo de trabajo del CDF): http://dorigo.wordpress.com/2008/10/31/cdf-publishes-multi-muons/
Pitkannen: http://matpitka.blogspot.com/2008/10/two-birthday-gifts.html
Para explicarlo se sugieren modelos basados en producción de positrones basados en ciertos tipos de materia oscura como puede leerse en este paper: http://arxiv.org/PS_cache/arxiv/pdf/0810/0810.5344v1.pdf
Podeis leer una entrada de blog dónde lo explican con mas detalle aquí: http://resonaances.blogspot.com/2008/10/pamelas-coming-out.html
El otro gran evento es el que describen en este paper: http://arxiv.org/PS_cache/arxiv/pdf/0810/0810.5357v1.pdf
El CDF es uno de los dos detectores del acelerador de partículas americano Tevatron (el otro detector es el D0). El grupo encagado de analizar los datos de ese detector se ha encontrado con que encuentran muchos evento que producen un muón producido a mas de 1.5 cms del centro de colisiones dónde se produce un evento dimuón. Para que esto sea posible se arguye que debe haberse formado una partícula en la colisión que se aleja esos 1.5 cms antes de desintegrarse en el muón.
Lo interesante es que ningún componente cnocido del modelo standard parece ser un posible candidato a ser esa partícula y por tanto todo apunta a qu ese trata de una nueva partícula.
¿que tipo de partícula? Un paper de hace unas 3 semanas por Nima-Arkani-Hamed y Neal Weiner presentaban un modelo que pretendía , basado en ideas similares a lo que ha revelado PAMELA sobre la dark matter un a predicción sobre que el lHC podria encontrar cierto tipo de nueva física que encaja muy bien con lo que, anticipándose, parece haber encontrado el tevatrón. El modelo de nima-Weiner es un modelo en que se hace una aplicación de la supersimetría al sector escondidio de la materia oscura. Podeis leer detalles al respecto en varios blogs:
Lubos: http://motls.blogspot.com/2008/10/cdf-sees-dark-unified-susy-in-lepton.html
Woit (que no se entera muy bien de lo que dice el paper de nima y Weiner): http://www.math.columbia.edu/~woit/wordpress/?p=1045
Dorigo (que de hecho estan en el grupo de trabajo del CDF): http://dorigo.wordpress.com/2008/10/31/cdf-publishes-multi-muons/
Pitkannen: http://matpitka.blogspot.com/2008/10/two-birthday-gifts.html
Wednesday, October 29, 2008
Non quantum gravity and dark matter
I keep reading Physicsforums, specially the beyond the standard model forum. Recently there was a discussion about a new proposal appeared in arxiv arguing that maybe gravity wouldn’t need to be quantized after all.
The paper in question, authored by Stephen Boughn is this.
It is a very clear paper where the usual assumptions are reviewed. As is commonly known we actually have a quantum theory, the standard model, which describes all known interactions but gravity. The best available description, experimentally supported, of gravity is Einstein theory of gravity, which is a non quantum theory.
In order to approach both theories one can begin by quantizing the standard model in the curved backgrounds of general relativity, instead of doing it in plain Minkowsky space (see my previous post for an easy introduction- in Spanish, sorry for non Spanish people-).
The next step one could try is simply to consider the gravitational field created by the averaged value of the energy momentum tensor and forget the idea of quantizing gravity at all. That is to replace:
1.
by:
2.
This proposal has many well known problems, both theoretical and practical. The author discuss them in the chapter 6 of his paper. Consider a state of matter, with probability !/2 of being in O1 region of space time and a probability ½ of being in a disjoint region O2. If you use equation 2 you get a gravitational field appropriate for matter being distributed in both regions. If later a measurement is made and the state is resolved to one of the Oi then the gravitational field would change in a discontinuous and acausal manner.
The key point of the paper is to keep eqt. 1 as valid and forget about 2. Of course one can’t do it without further assumptions. The author establish that the energy momentum tensor must satisfy the following prerequisite. In the language of decoherence theory, that the system is in a decoherent, mixed quantum state for it is only then that the probability predictions of quantum theory agree with those of classical physics. (You can read about decoherence in, for example, this paper by Lubos Motl.).
This assumption immediately implies another one, that non-localized, coherent quantum systems are not sources of gravity. That sounds as a very hard assumption, but the author argues that It will turn out that for microsopic systems, in which quantum coherence is most commonly observed, the effects of gravity are, in principle, unobservable. For larger macroscopic systems, decoherence is the norm and classical stress-energy is well defined. This leaves open the question of gravitational interactions of mesoscopic, coherent sytsems.
After that he goes through some chapters reviewing the detectability of possible quantum gravity phenomena. He begins, in chapter two, considering the detectability of gravitons. Remember that a graviton should be the quanta that would mediate gravity interactions if one insist in doing quantum gravity in a particle physicist like way. This chapter is very well written, and it relates the gravitons to gravity waves. Note that one of the authors research activities is precisely in the field of experimental detection of gravity waves so he can be considered an authority in that particular.
In chapter 3 he dwells with gravity and quantum interference, that is, double slit like thought experiments. He concludes the existence of a conditions that must be satisfied for a gravitational measurement to be made that will sufficiently localize the incident particle so as to destroy the quantum interference which are stated in terms of the separation of the two slits, r, the acceleration of the test mass at, the velocity of the incoming particle vi. The actual conditions are:
r >¯h r^2/Gm^3 (here ¯h is h bar, i.e. h/2π)
t >¯h^3 / G2m^5
at < G^3m7 /¯h^4
vi < Gm^2 / ¯h
If the conditions are not satisfied, the gravitational interaction is insufficient to detect the incident particle and quantum interference remains intact..He concludes that for quantum coherent systems with masses less than ∼ 10^7mp (mp=Planck mass), there is not a measurable gravitational effect that would compromise their coherence. He does further analysis and get further restrictions. The conclusion of the arguments is that the question of whether or not coherent quantum systems are sources of gravity is unanswerable for systems with masses < 10^10 mp. That leaves unanswered the question of mesoscopic systems, which he analyzes later.
The chapter 4 is a continuation, in a certain sense, of the previous. The most interesting is the chapter 5 where he fully analyzes the central issue of the paper. The key point, if I rightly understand is the following statement:
“Because macroscopic systems
invariably undergo decoherence on very short time scales, they behave as they would
in a classical world, i.e., no quantum interference effects.”
Or stated, together with another claims of the chapter, in a more generic way it could be said: “the experimental data available to date only takes account of interactions between matter systems in a decoherent state.”
That raise the question of what would be the behaviour of macroscopic, or at least, mesoscopic, systems which are in coherent states. He talks about the copper pairs in superconductivity, Bose-Einstein condensates and systems like that. Here I would add a few things. A few years ago an condensate-matter physicist, Podkeltnov, made a claim, in a press conference, about some kind of gravity shielding that appeared unexpectectly in experiments which implied some kind of high temperature superconducting devices. He didn’t provide all the details of the experimental device and ulterior attempts to reply the experiment, based on the available data, are until now unsuccessful. Later Podkelnov he improved the experiment and even tried to conjecture an explanation. His argument was related to the suppression of Fourier modes of gravity because of coupling of the Landau-Ginzburg lagrangian which could be used to describe the superconductor to the energy of the cosmological constant. Certainly the “non quantum gravity” proposal could be considered as an alternative explanation if one would try to insist in explaining an effect non firmly established experimentally, of course.
To conclude my review of this proposal I’ll mention a few problems that the own Stephen Boughn recognizes. The main one, in my opinion, is that if a coherent system exchange momentum with a coherent one, and later becomes non coherent his proposal could lead to a violation of momentum conservation. Another one is a legitimate criticism of the conjecture put forward in this paper is its lack of predictive power. Except possibly in the case of the coherent to decoherent transitions in mesoscopic systems, and even in these cases the conjecture makes no specific prediction, the nonquantum conjecture makes no additional predictions that can not already be made by quantum theory and general relativity. There are some more concerns, that the author acknowledge in the final chapter and I´ll not talk here about them.
Let’s go now with the next topic of this post, dark matter. A few weeks after this paper appeared Sean Carrol in his blog, cosmic variance, made this post. Soon there was a reply by Lubos Motl here.
They are very interesting posts in their own. But I bring them here because it is stated there that dark matter, if it interact only by means of gravity with itself, and the rest of the universe, would decohere very solowly. In fact, if the non quantum gravity proposal would be taken to it’s full consequences it could be expected that it wouldn’t decohere at all. But if so, it wouldn’t interact gravitatorilly at all. That is a very bad thing because dark matter is postulated to explain unobserved mass in the universe which accounts the observed rate of cosmological expansion.
In fact, in a very recent paper it is discussed the possibility that dark matter could not exist, or, at least, not be the main responsible of some experimental data. The paper is this. It is discussed in a blog entry by Lubos Motl here. Quickly, the idea is that a field associated to string theory, could take a nonvacuum expected value and that if particles are actually strings, would couple to it resulting in a Lorentz type force which would explain the problem with the way galaxies rotate in an alternative way to the usual explanations of dark matter of MOND (modified newtoninan dynamics). If this non quantum gravity proposal would be taken seriously the stringy paper would gain additional value because dark matter, even if it exists, could not interact gravitationally, or at least not too much.. Of course if we accept the nonquantum gravity proposal string theory would loose one of it’s more important reason to exist, it’s status as a quantum theory of gravity and it would have to be questioned if it’s explanation of galaxies rotations could be still accepted.
In fact I admit that I actually didn’t do the actual calculations of exactly how much dark matter would interactuate gravitationally if the non quantum gravity proposal would be truth. I find surprising that the author, Stephen Boughn, wouldn’t consider it in his paper when he claims that he is actually working on cosmology, but, of course, he could easily not have realized this lack of coherence in dark matter, which is only obvious once one is told about it, but not before.
Anyway, the paper is interesting in it’s own, even if it’s wrong, because of the review of many aspects related to gravity and it has served me to take quote of some issues that have happened in the quantum gravity world in the recent times. Hope the reader would find them interesting.
The paper in question, authored by Stephen Boughn is this.
It is a very clear paper where the usual assumptions are reviewed. As is commonly known we actually have a quantum theory, the standard model, which describes all known interactions but gravity. The best available description, experimentally supported, of gravity is Einstein theory of gravity, which is a non quantum theory.
In order to approach both theories one can begin by quantizing the standard model in the curved backgrounds of general relativity, instead of doing it in plain Minkowsky space (see my previous post for an easy introduction- in Spanish, sorry for non Spanish people-).
The next step one could try is simply to consider the gravitational field created by the averaged value of the energy momentum tensor and forget the idea of quantizing gravity at all. That is to replace:
1.
by:
2.
This proposal has many well known problems, both theoretical and practical. The author discuss them in the chapter 6 of his paper. Consider a state of matter, with probability !/2 of being in O1 region of space time and a probability ½ of being in a disjoint region O2. If you use equation 2 you get a gravitational field appropriate for matter being distributed in both regions. If later a measurement is made and the state is resolved to one of the Oi then the gravitational field would change in a discontinuous and acausal manner.
The key point of the paper is to keep eqt. 1 as valid and forget about 2. Of course one can’t do it without further assumptions. The author establish that the energy momentum tensor must satisfy the following prerequisite. In the language of decoherence theory, that the system is in a decoherent, mixed quantum state for it is only then that the probability predictions of quantum theory agree with those of classical physics. (You can read about decoherence in, for example, this paper by Lubos Motl.).
This assumption immediately implies another one, that non-localized, coherent quantum systems are not sources of gravity. That sounds as a very hard assumption, but the author argues that It will turn out that for microsopic systems, in which quantum coherence is most commonly observed, the effects of gravity are, in principle, unobservable. For larger macroscopic systems, decoherence is the norm and classical stress-energy is well defined. This leaves open the question of gravitational interactions of mesoscopic, coherent sytsems.
After that he goes through some chapters reviewing the detectability of possible quantum gravity phenomena. He begins, in chapter two, considering the detectability of gravitons. Remember that a graviton should be the quanta that would mediate gravity interactions if one insist in doing quantum gravity in a particle physicist like way. This chapter is very well written, and it relates the gravitons to gravity waves. Note that one of the authors research activities is precisely in the field of experimental detection of gravity waves so he can be considered an authority in that particular.
In chapter 3 he dwells with gravity and quantum interference, that is, double slit like thought experiments. He concludes the existence of a conditions that must be satisfied for a gravitational measurement to be made that will sufficiently localize the incident particle so as to destroy the quantum interference which are stated in terms of the separation of the two slits, r, the acceleration of the test mass at, the velocity of the incoming particle vi. The actual conditions are:
r >¯h r^2/Gm^3 (here ¯h is h bar, i.e. h/2π)
t >¯h^3 / G2m^5
at < G^3m7 /¯h^4
vi < Gm^2 / ¯h
If the conditions are not satisfied, the gravitational interaction is insufficient to detect the incident particle and quantum interference remains intact..He concludes that for quantum coherent systems with masses less than ∼ 10^7mp (mp=Planck mass), there is not a measurable gravitational effect that would compromise their coherence. He does further analysis and get further restrictions. The conclusion of the arguments is that the question of whether or not coherent quantum systems are sources of gravity is unanswerable for systems with masses < 10^10 mp. That leaves unanswered the question of mesoscopic systems, which he analyzes later.
The chapter 4 is a continuation, in a certain sense, of the previous. The most interesting is the chapter 5 where he fully analyzes the central issue of the paper. The key point, if I rightly understand is the following statement:
“Because macroscopic systems
invariably undergo decoherence on very short time scales, they behave as they would
in a classical world, i.e., no quantum interference effects.”
Or stated, together with another claims of the chapter, in a more generic way it could be said: “the experimental data available to date only takes account of interactions between matter systems in a decoherent state.”
That raise the question of what would be the behaviour of macroscopic, or at least, mesoscopic, systems which are in coherent states. He talks about the copper pairs in superconductivity, Bose-Einstein condensates and systems like that. Here I would add a few things. A few years ago an condensate-matter physicist, Podkeltnov, made a claim, in a press conference, about some kind of gravity shielding that appeared unexpectectly in experiments which implied some kind of high temperature superconducting devices. He didn’t provide all the details of the experimental device and ulterior attempts to reply the experiment, based on the available data, are until now unsuccessful. Later Podkelnov he improved the experiment and even tried to conjecture an explanation. His argument was related to the suppression of Fourier modes of gravity because of coupling of the Landau-Ginzburg lagrangian which could be used to describe the superconductor to the energy of the cosmological constant. Certainly the “non quantum gravity” proposal could be considered as an alternative explanation if one would try to insist in explaining an effect non firmly established experimentally, of course.
To conclude my review of this proposal I’ll mention a few problems that the own Stephen Boughn recognizes. The main one, in my opinion, is that if a coherent system exchange momentum with a coherent one, and later becomes non coherent his proposal could lead to a violation of momentum conservation. Another one is a legitimate criticism of the conjecture put forward in this paper is its lack of predictive power. Except possibly in the case of the coherent to decoherent transitions in mesoscopic systems, and even in these cases the conjecture makes no specific prediction, the nonquantum conjecture makes no additional predictions that can not already be made by quantum theory and general relativity. There are some more concerns, that the author acknowledge in the final chapter and I´ll not talk here about them.
Let’s go now with the next topic of this post, dark matter. A few weeks after this paper appeared Sean Carrol in his blog, cosmic variance, made this post. Soon there was a reply by Lubos Motl here.
They are very interesting posts in their own. But I bring them here because it is stated there that dark matter, if it interact only by means of gravity with itself, and the rest of the universe, would decohere very solowly. In fact, if the non quantum gravity proposal would be taken to it’s full consequences it could be expected that it wouldn’t decohere at all. But if so, it wouldn’t interact gravitatorilly at all. That is a very bad thing because dark matter is postulated to explain unobserved mass in the universe which accounts the observed rate of cosmological expansion.
In fact, in a very recent paper it is discussed the possibility that dark matter could not exist, or, at least, not be the main responsible of some experimental data. The paper is this. It is discussed in a blog entry by Lubos Motl here. Quickly, the idea is that a field associated to string theory, could take a nonvacuum expected value and that if particles are actually strings, would couple to it resulting in a Lorentz type force which would explain the problem with the way galaxies rotate in an alternative way to the usual explanations of dark matter of MOND (modified newtoninan dynamics). If this non quantum gravity proposal would be taken seriously the stringy paper would gain additional value because dark matter, even if it exists, could not interact gravitationally, or at least not too much.. Of course if we accept the nonquantum gravity proposal string theory would loose one of it’s more important reason to exist, it’s status as a quantum theory of gravity and it would have to be questioned if it’s explanation of galaxies rotations could be still accepted.
In fact I admit that I actually didn’t do the actual calculations of exactly how much dark matter would interactuate gravitationally if the non quantum gravity proposal would be truth. I find surprising that the author, Stephen Boughn, wouldn’t consider it in his paper when he claims that he is actually working on cosmology, but, of course, he could easily not have realized this lack of coherence in dark matter, which is only obvious once one is told about it, but not before.
Anyway, the paper is interesting in it’s own, even if it’s wrong, because of the review of many aspects related to gravity and it has served me to take quote of some issues that have happened in the quantum gravity world in the recent times. Hope the reader would find them interesting.
Saturday, September 20, 2008
The LHC is your friend, trust the LHC
Afther listenign almost all the confrences of strings 2008 that I mentioned in the earlier post I had to make a break into blogging because of a few diferent reasons (computer virus, preparing people for september exams and so on). In the while I have ahd time to read a few papers and a few books, the books not mainly about quantum gravity related things.
In all this time the most interesting source of news has, umdoubtly, been the LHC. Oo one side because of all those people worring about the end of the world black hole. On the other the bets about what will be discovered when the machine at last would collide protons.
About the first subject I have readed a few arxiv articles about evaluationof the possible danger of black holes. The subject depends (once Hawking radiation is discarded as a way to destroy the black hole, a very unprobable thing) on classical general relativity and rates of acrretion and things like that. I must say that I had no previous knowwledge on the subject and I have found it interesting althought certainly a bit far from the usual target of cutting edge theoretical physics. As a side effect I have had to reconsider the precise meaing of the grouth of a black hole. It could seen obvious, but in fact it isn´t. The classical scenary is to calculate the rate of accretion (using Bondi theory or whatever) and later relay on the classical laws of black holes stated by Hawkings, specially the one relating the icrement of area to the increment of mass. But the reality is more complex and to get a precise mathematical tratement one must go to the theory of dynamical and isolated horizonts. I´ll write a post about the details in the other blog as soon as possible.
But the LHC is important not because of the black hole and similar catastrofic secenaries (all of them very unlikely, to say the less, people worried about real problems have a lot of better places to wath for). The real interst is if it will find the higgs bososn, supersymmetry or whatever. In fact it seems that it has benn an increasing amount of papers diving into the data of the tevatron with the aim of profiling the best chances for the LHC finding new physyc. In one of hat scenaries there was a good chance tht in the first five days, or so, of activity (that is, colliding activity) of the LCH the supersymmetry could be found. That was supposed to be as soon as the next week (althought probably the actual annalisis of data would require most time). I was, partially, waiting that notice. It would be certainly a relly good notice for a post (afther all it would be the best new in particle physics in around 30 years). But unfortunatelly it seems that ther has been a somewhat serious problem in the LHC, rupture in a part of the collider has resulted in the lost of liquid hellium. It is still ot known how seriously the problem is but some people say it could mean that the LHC propgram would be dealyed untill the winter shutdown so we would need to wait a litle bit more to get relevant experimental data. If this is confirmed stil there are possibilties of getting new physic from astrophysic/cosmology. In fact this week has been seen what looks like a bridge of dark matter aaround which galaxied penetrate into regios that, untill now, where considered as giant vacua in the universe. And the GLAST satelite is working propoerly for more than a mounth so it is possible that it could find signals of WIMPS (weakly interacting massive particles) a favourite candidate of same people for dark matter constituent, or, maybe a final answer (possitive or negative) for the LQG prediction about dispersion of light speed in vacuum. In fact I had readed in a newspaper that a great gamma ray burst had been detected a week ago and I have been waitng since them to read that the GLAST had looked at it so the question could be really, reaaly, next to be answered, but, unfourtunately, It seems that the GLAST losed it, aand we must wait a litle bit more.
Anyway, as unfourtunately it seens that great news are delaying I decided to blog agin about more conventional things.
In all this time the most interesting source of news has, umdoubtly, been the LHC. Oo one side because of all those people worring about the end of the world black hole. On the other the bets about what will be discovered when the machine at last would collide protons.
About the first subject I have readed a few arxiv articles about evaluationof the possible danger of black holes. The subject depends (once Hawking radiation is discarded as a way to destroy the black hole, a very unprobable thing) on classical general relativity and rates of acrretion and things like that. I must say that I had no previous knowwledge on the subject and I have found it interesting althought certainly a bit far from the usual target of cutting edge theoretical physics. As a side effect I have had to reconsider the precise meaing of the grouth of a black hole. It could seen obvious, but in fact it isn´t. The classical scenary is to calculate the rate of accretion (using Bondi theory or whatever) and later relay on the classical laws of black holes stated by Hawkings, specially the one relating the icrement of area to the increment of mass. But the reality is more complex and to get a precise mathematical tratement one must go to the theory of dynamical and isolated horizonts. I´ll write a post about the details in the other blog as soon as possible.
But the LHC is important not because of the black hole and similar catastrofic secenaries (all of them very unlikely, to say the less, people worried about real problems have a lot of better places to wath for). The real interst is if it will find the higgs bososn, supersymmetry or whatever. In fact it seems that it has benn an increasing amount of papers diving into the data of the tevatron with the aim of profiling the best chances for the LHC finding new physyc. In one of hat scenaries there was a good chance tht in the first five days, or so, of activity (that is, colliding activity) of the LCH the supersymmetry could be found. That was supposed to be as soon as the next week (althought probably the actual annalisis of data would require most time). I was, partially, waiting that notice. It would be certainly a relly good notice for a post (afther all it would be the best new in particle physics in around 30 years). But unfortunatelly it seems that ther has been a somewhat serious problem in the LHC, rupture in a part of the collider has resulted in the lost of liquid hellium. It is still ot known how seriously the problem is but some people say it could mean that the LHC propgram would be dealyed untill the winter shutdown so we would need to wait a litle bit more to get relevant experimental data. If this is confirmed stil there are possibilties of getting new physic from astrophysic/cosmology. In fact this week has been seen what looks like a bridge of dark matter aaround which galaxied penetrate into regios that, untill now, where considered as giant vacua in the universe. And the GLAST satelite is working propoerly for more than a mounth so it is possible that it could find signals of WIMPS (weakly interacting massive particles) a favourite candidate of same people for dark matter constituent, or, maybe a final answer (possitive or negative) for the LQG prediction about dispersion of light speed in vacuum. In fact I had readed in a newspaper that a great gamma ray burst had been detected a week ago and I have been waitng since them to read that the GLAST had looked at it so the question could be really, reaaly, next to be answered, but, unfourtunately, It seems that the GLAST losed it, aand we must wait a litle bit more.
Anyway, as unfourtunately it seens that great news are delaying I decided to blog agin about more conventional things.
Monday, August 18, 2008
Strings 2008: TV en directo
¿Alguna vez te has planteado asistir en directo a un congreso sobre física de cuerdas?
Ahora puedes, al menos virtualmente:
P.S. Podeis ver los horarios, con las diversas conferencias aquí
Lubos esta actualizando su blog con comentarios sobre las diversas conferencias (a la fecha de escribir este post script van 3). Podeis seguirlo en esta entrada Yo por mi parte intentaré comentar alguna cosa, pero sería absurdo plantearse competir con Lubos xD.
Ahora puedes, al menos virtualmente:
P.S. Podeis ver los horarios, con las diversas conferencias aquí
Lubos esta actualizando su blog con comentarios sobre las diversas conferencias (a la fecha de escribir este post script van 3). Podeis seguirlo en esta entrada Yo por mi parte intentaré comentar alguna cosa, pero sería absurdo plantearse competir con Lubos xD.
Saturday, August 09, 2008
Ideas básicas sobre cuantización en espacios curvos
Un entrada "ligerita", para que no se quede esto abandonado demasiado tiempo.
La teoria cuántica de campos ordinaria se formula en espacios planos, en partícular en el espacio de Minkowsky. Se empieza explicando la teoria de campos libres, interesante para explicar el concepto de vacio y de espacio de Fock. En cuántica ordinaria (no relativista) se suele hacer teoria cuántica de una partícula. Y lo más importante, podemos tener fijo el número de partículas. Esto no es posible en relatividad especial por aquello del E=mc2 que permite fabricar partículas "desde el vacio" durante un tiempo muy pequeño debido a la relacion de incertidumbre entre tiempo y energía. Así pués debemos describir la física, no en un espacio de Hilbert (hablando libremente, que en realidad la partícula libre no va en un espacio de Hilbert según lo definen los matemáticos ya que la funcion de onda de una particula libre no pertece a L2, conjunto de funciones de cuadrado integrable) sino en un espacio de Fock. ¿Y esto que es? Pués una serie infinita de productos tensoriales del espacio de hilbert de una particula adecuadamente simetrizado o antisimetrizado, según tengamos bosones o fermiones. Osease, algo así cómo (uso una notacion simbolica para aclarar ideas):
1. F=0 +H + H1xH2 + H1xH2xH3+ ...
Aquí H es el espacio de hilbert de una partícula. Cuando hay dos partículas tenemos H1 Y H2, el espacio de hilbert de cada una de las dos partículas. X denotaría el producto tensorial simetrizado o antisimetrizado de las dos partículas. El signo + indicaría suma directa. Vamos, que debemos considerar la posibilidad de tener una sóla partícula, dos partículas, tres partículas o un número infinito de partículas, y nuestro formalismo debe contemplar esa posibilidad. Eso es el espacio de Fock, y parte de la idea de la mecánica cuántica relativista. El desarrollo de la teoria relativista requiere considerar particulas en interacción, lo que nos llevaría a la matriz S y etc, etc.
Pero para el tema de cuantización en espacios curvos sólo necesito campos libres. Fijaros que en la ecuación 1 he puesto, un tanto libremente un 0. Esto es el vacio, donde no hay partículas. Por otro lado la mecánica relativista es una teoria cuántica de campos. Esta sutil diferencia semántica puede interpretarse como que los campos crean partículas. Sin entrar en detalles simplemente comentar que tenemos un lagrangiano clásico en términos de los campos (por ejemplo el campo electromagnético, expresado en términos de sus potenciales) o el de una partícula de klein-gordon. La ecuacion de Euler-Lagrange para esos campos es una ecuación en derivadas parciales que puede resolverse por separación de variables y resultado de ella sale una expansión del campo clásico en términos de modos de fourier. Bien, cuantizar es imponer relaciones de conmutación a los campos, sustituyendo los campos clásicos por operadores, que actuan en el espacio de Fock. Imponerlas "a saco" es un tanto dificil. Pero cuando tenemos el desarrollo en serie de Fourier cada modo de Fourier se convierte en un operador. Y puede interpretarse como un operador de creación, o de aniquilación. Un operador de creación crea una partícula y uno de aniquilacion la destruye.
Esto es para campos libres en el espacio plano de Minkowsky. En espacios curvos la cosa se complica. Resulta que lo que un observador ve como vacio otro observador puede verlo como no vacio. El caso más sencillo es el conocido como espacio de Rindler. Este es simplemente el espacio de Minkowsky visto por un observador enmovimiento unifromemente acelerado. El observador acelerado ve el vacio de Minkowsky lleno de partículas con una distribucion térmica. La temperatura de esa distribución depende de la aceleracion. A más aceleración más temperatura. La forma técnica de expresar esto es mediante lo que se conoce como transformaciones de Bogolubov que transforman el vacio de un observador en otro. Otro ejemplo, mucho mas famoso, de cuantización en un espacio curvo es cuando se cuantiza un campo libre en una geometría de Schwarschild, la que describe un agujero negro. Ahi se tienen que un observador en caida libre que este muy cerca del horizonte de sucesos vería vacio la zona cercana al miso. Sin embargo otro observador que estuviera inmovil a una distancia fija del horizonte de sucesos vería lo que el otro observador encuentra vacio lleno de partículas. Esto puede interpretarse como que el agujero negro esta emitendo partículas y es lo que se conoce como radiacion de Hawkings (por cierto, no confundir esto con un concepto muy similar aprentemente, el de entropia de un agujero negro). La intensidad de la radiacion depende de una magnitud, la gravedad superficial del agujero negro, que puede demostrarse que esta ligada a una potencia inversa del área del agujero negro. Así pués a menor área mayor emision de Hawkings.
Las fórmulas concretas del resultado son:
$$ T_H=\alpha_H/2\pi $$ dónde $$\alpha$$ es la gravedad superficial del agujero negro, de valor: $$ \alpha= 1/4M$$
Si no trabajamos en unidades naturales la fórmula se convierte en:
$$T_H=hc^3/16\pi^2GMk $$ dónde todos los factores tiene un significado obvio, excepto quizás la k, que es la constante de Boltzman.
Si el agujero negro esta cargado y/o gira se pueden obtener las fórmulas concretas usando las métricas de Reissner-Nordstrom o la de Kerr-Newman. No pondré los resultados pues serían mas adecuados para una entrada específica.
P.S. Un buen artículo de review es el siguiente: arXiv:gr-qc/0010055
La teoria cuántica de campos ordinaria se formula en espacios planos, en partícular en el espacio de Minkowsky. Se empieza explicando la teoria de campos libres, interesante para explicar el concepto de vacio y de espacio de Fock. En cuántica ordinaria (no relativista) se suele hacer teoria cuántica de una partícula. Y lo más importante, podemos tener fijo el número de partículas. Esto no es posible en relatividad especial por aquello del E=mc2 que permite fabricar partículas "desde el vacio" durante un tiempo muy pequeño debido a la relacion de incertidumbre entre tiempo y energía. Así pués debemos describir la física, no en un espacio de Hilbert (hablando libremente, que en realidad la partícula libre no va en un espacio de Hilbert según lo definen los matemáticos ya que la funcion de onda de una particula libre no pertece a L2, conjunto de funciones de cuadrado integrable) sino en un espacio de Fock. ¿Y esto que es? Pués una serie infinita de productos tensoriales del espacio de hilbert de una particula adecuadamente simetrizado o antisimetrizado, según tengamos bosones o fermiones. Osease, algo así cómo (uso una notacion simbolica para aclarar ideas):
1. F=0 +H + H1xH2 + H1xH2xH3+ ...
Aquí H es el espacio de hilbert de una partícula. Cuando hay dos partículas tenemos H1 Y H2, el espacio de hilbert de cada una de las dos partículas. X denotaría el producto tensorial simetrizado o antisimetrizado de las dos partículas. El signo + indicaría suma directa. Vamos, que debemos considerar la posibilidad de tener una sóla partícula, dos partículas, tres partículas o un número infinito de partículas, y nuestro formalismo debe contemplar esa posibilidad. Eso es el espacio de Fock, y parte de la idea de la mecánica cuántica relativista. El desarrollo de la teoria relativista requiere considerar particulas en interacción, lo que nos llevaría a la matriz S y etc, etc.
Pero para el tema de cuantización en espacios curvos sólo necesito campos libres. Fijaros que en la ecuación 1 he puesto, un tanto libremente un 0. Esto es el vacio, donde no hay partículas. Por otro lado la mecánica relativista es una teoria cuántica de campos. Esta sutil diferencia semántica puede interpretarse como que los campos crean partículas. Sin entrar en detalles simplemente comentar que tenemos un lagrangiano clásico en términos de los campos (por ejemplo el campo electromagnético, expresado en términos de sus potenciales) o el de una partícula de klein-gordon. La ecuacion de Euler-Lagrange para esos campos es una ecuación en derivadas parciales que puede resolverse por separación de variables y resultado de ella sale una expansión del campo clásico en términos de modos de fourier. Bien, cuantizar es imponer relaciones de conmutación a los campos, sustituyendo los campos clásicos por operadores, que actuan en el espacio de Fock. Imponerlas "a saco" es un tanto dificil. Pero cuando tenemos el desarrollo en serie de Fourier cada modo de Fourier se convierte en un operador. Y puede interpretarse como un operador de creación, o de aniquilación. Un operador de creación crea una partícula y uno de aniquilacion la destruye.
Esto es para campos libres en el espacio plano de Minkowsky. En espacios curvos la cosa se complica. Resulta que lo que un observador ve como vacio otro observador puede verlo como no vacio. El caso más sencillo es el conocido como espacio de Rindler. Este es simplemente el espacio de Minkowsky visto por un observador enmovimiento unifromemente acelerado. El observador acelerado ve el vacio de Minkowsky lleno de partículas con una distribucion térmica. La temperatura de esa distribución depende de la aceleracion. A más aceleración más temperatura. La forma técnica de expresar esto es mediante lo que se conoce como transformaciones de Bogolubov que transforman el vacio de un observador en otro. Otro ejemplo, mucho mas famoso, de cuantización en un espacio curvo es cuando se cuantiza un campo libre en una geometría de Schwarschild, la que describe un agujero negro. Ahi se tienen que un observador en caida libre que este muy cerca del horizonte de sucesos vería vacio la zona cercana al miso. Sin embargo otro observador que estuviera inmovil a una distancia fija del horizonte de sucesos vería lo que el otro observador encuentra vacio lleno de partículas. Esto puede interpretarse como que el agujero negro esta emitendo partículas y es lo que se conoce como radiacion de Hawkings (por cierto, no confundir esto con un concepto muy similar aprentemente, el de entropia de un agujero negro). La intensidad de la radiacion depende de una magnitud, la gravedad superficial del agujero negro, que puede demostrarse que esta ligada a una potencia inversa del área del agujero negro. Así pués a menor área mayor emision de Hawkings.
Las fórmulas concretas del resultado son:
$$ T_H=\alpha_H/2\pi $$ dónde $$\alpha$$ es la gravedad superficial del agujero negro, de valor: $$ \alpha= 1/4M$$
Si no trabajamos en unidades naturales la fórmula se convierte en:
$$T_H=hc^3/16\pi^2GMk $$ dónde todos los factores tiene un significado obvio, excepto quizás la k, que es la constante de Boltzman.
Si el agujero negro esta cargado y/o gira se pueden obtener las fórmulas concretas usando las métricas de Reissner-Nordstrom o la de Kerr-Newman. No pondré los resultados pues serían mas adecuados para una entrada específica.
P.S. Un buen artículo de review es el siguiente: arXiv:gr-qc/0010055
Monday, July 14, 2008
A watch at the string landscape
Like many physicist I am a reader of science fiction. String theory is not a topic which is too broadly covered in SF, and, anyway, it is not covered too properly. For example, it could be that the author limits to cite the words "calaby-yau" as some kind of manra. Even thought there is one particular novel, writen in the eiguthies, where there was a fine usage of string theory. There an alien spae-craft arrived to earth and they tripulants beguined a discusion with relevant human figures in art, politics an scince. In paarticular, in the sicence area, they tolked with string theorists and discused with them many mathematical aspects and conceptula developments that they found terribly exciting. Despite that no concrete experimental evidence was provided. While doing that the aliens had throught a black hole inside the earth which growed slowly, but fast enought to eat the whole earth a few mounths later, toward the end of the novel. Fortunately anonther space-craft had appeared, tripulated by a diferent alien specie, and saved some selected humans. I guess that any informed reader will be able to see the possible funny possible analogies with the actual situation :-).
The purpose of this introduction was to sign the fact that string theory has grown a lot in many directions since the eighties, and it is somewhat discouragint to try to get a prcise idea of the many lines (some of them alsmost death) of development followed in the while. But if I wuld be one of the "bad aliens" that would try to give some guidance to an eighties string theoretic maybe I could use this post as a begining, or at least that is my intention.
The great chalenge in string theory is to get a proer way to get a decent way to go from 10 to 4 dimensions. In the eighties the most pomising way was to look for compactifications of heterrotic string theory in calaby-yau mamifolds, or maybe in orbifolds. Soon it as realized that it was interesting to study not one, but families of calaby-yaus. One went from one to other by variiying some moduli. Another easy way to compatify were orbifolds, tori acted by some discrete group. The fixeed points of that action were singular, and the studie of that singularities revealed to be very interesting. It was necesary to go troguht a revolution, the discovering of the importance of branes, to give more fuel to the compactifications. One could use branes to solve the singularities of the orbifold fixed points. And it was found that that pints could do transitions among calaaby-ayus with diferent topologies. Also the Calabi-Yau moduli space revealed to hae singular points, called conifold points. Coriosly the own moduli space of a C-Y could be, in some sense, characterized a calaby yau of an special type, one with conifold points (i.e., a point similar to the edge of a cone, that is, a continuous but not diferentiable point). If one suits a D-Brane at that point one can "blow-up" the singularitie. But, anyway, the thing is that conifolds can also give transitions betwen vacua of diferent topology. In fact the scenarie is worst. Ther ecan be transitions to phases where the vacua doesnt´admit an obvious gemoetric description and one must use CFT/non linear sigma models, to describe the theory. In fact Witten argued that in M-theory, an aditional development of string theoyr corresponding to strongly coupled type II A strings, only geometric phases were allowed.
In adition to compactification "braane worlds" were considrd. The idea was that the observable world would be some kind of brane. Precise realizations of that idea were purchased form many viepoints (I guess that the most recent try use the idea of intersecting D6-Branes).
In the mean time it was discovred that the universe is accelerating. And there are som kind of consensun that at a constant rate. That means that "phantm energy" scenaries seen to be ruled out and we must look for a de sitter universe emerging from string theory. The firs realization of this was the KKLT theory. In that scenarie there were required vacuums where supersymmetry was broken in a way that it gived some cosmological constant. It was argued that the univrse could be populated by manu diferne vacua. Each vacuawith a diferent value of the cosmological constant would expand at diferents speeds so we would live in some buble of a particular vacua. That lead to the counting of vacua that shrd some properties, and to do an analisys of the statistical distribution of other properties. For example, in some kind of vacua compatible with aa certain value of the cosmological constant there were more solutions with large extra dimensions. But another kinds of such vacua ere in the opposite direction. By the way, vaua with cosmological constants are not tru vacuums, they are metastable states whose decay rate is graater that the actual ge of the universe, oh yeah ;-).
Some interesting remarks about this models are that they give a potential for the scalar fields that describe the moduli of the vacuas. Taht is, they re, in a certain sense, properly defined theories with all the measurable values fixed. This had proved to be a very difcould task. The Dine-Seiberg conjecture stated that a proper determination of the value of the modulis required to go to non-perturbative range of string theory. But the hope was that once one had a theory with aall that values fixed one would have a unique, of almost unique, theory. In fact one has, in some scenaries, around 10^500 theory (i.e. vacua). whose average cosmologicla constant is the observed one (the counting was made by first time by Bousso and Polchinsky for some particular kind of models). Another point is that there is not a natural way to make statistic mechanic for that diferent vacua. I.E, Ine can´t make a proper statistichal ensmble out of them because that vacua should be separated into diferent sectors with superselection rules not allowing going from one to another. I recmend to llok at the blog of Dimityr (non equibrium net) to get a mch better discusion of this topic.
By the way. Most of this studies were made for type II theories. What was of the hetrotic string?. Well, infact there is an heterotic landscape also. It is courious. Another development of string theory was to prove a counting of the benckenstein entropy of a black holes (or at least a paarticular kind of them). for that puropose Type II theories, and their D-Branes, were used. But later it was seen that one also could use heterotici strings to describe black holes. It seems like if heterotic string theory always has aa delay in the achievement of the resoults. But, in the positive point, heterotic strings still seem to be promising. FOr example teh heterotic landscape contians many fewer vacua.
In the eighties ther was a hope that string field theory could provide some kind of dynamics which could indicate how these compactifications could be achieed. Unfortunately string field theory had not succes and has proved to be very dificoult anyway. I fact one would have an string field theory fo rany of the diferen string theories.
With all that I have exposed it looks like if there are too many things going on. In fact it is so. I think taht what I would like to see is a way to see how topologicla transitions could be used to connect diferent vacua. In fact the vacua of the landscape aare, as I said, not aall of them supersymmetric vacua. That would mena to consider a more generic king of compactifications, and studie the possible topologicla transitions betewem them. One way to consider taht could be the use of instanton/euclidean wommholes. And also to see how to describe this in some kind of SFT. Also it one consider that the diferent string theories are related by dualities, meaning that in some sense they re a single one, one could study wormholes, ot whatever, connecting them. A way to beguin this program could be to try to describe some kind of wormhle like solution connecting diferent compactifications (or a noncapctifed space to a compactified one).
I muist advertize that like this post contain many, many, topics, I have not pretended to be very exact in the descriptions. My idea was just to give a broad perspective. I hope to wite in a near future more detailed posts on more concrete topics, but I guess it was too much tiem since the last posts and that It was a good idea not to bee too lazy and write smething ;-).
The purpose of this introduction was to sign the fact that string theory has grown a lot in many directions since the eighties, and it is somewhat discouragint to try to get a prcise idea of the many lines (some of them alsmost death) of development followed in the while. But if I wuld be one of the "bad aliens" that would try to give some guidance to an eighties string theoretic maybe I could use this post as a begining, or at least that is my intention.
The great chalenge in string theory is to get a proer way to get a decent way to go from 10 to 4 dimensions. In the eighties the most pomising way was to look for compactifications of heterrotic string theory in calaby-yau mamifolds, or maybe in orbifolds. Soon it as realized that it was interesting to study not one, but families of calaby-yaus. One went from one to other by variiying some moduli. Another easy way to compatify were orbifolds, tori acted by some discrete group. The fixeed points of that action were singular, and the studie of that singularities revealed to be very interesting. It was necesary to go troguht a revolution, the discovering of the importance of branes, to give more fuel to the compactifications. One could use branes to solve the singularities of the orbifold fixed points. And it was found that that pints could do transitions among calaaby-ayus with diferent topologies. Also the Calabi-Yau moduli space revealed to hae singular points, called conifold points. Coriosly the own moduli space of a C-Y could be, in some sense, characterized a calaby yau of an special type, one with conifold points (i.e., a point similar to the edge of a cone, that is, a continuous but not diferentiable point). If one suits a D-Brane at that point one can "blow-up" the singularitie. But, anyway, the thing is that conifolds can also give transitions betwen vacua of diferent topology. In fact the scenarie is worst. Ther ecan be transitions to phases where the vacua doesnt´admit an obvious gemoetric description and one must use CFT/non linear sigma models, to describe the theory. In fact Witten argued that in M-theory, an aditional development of string theoyr corresponding to strongly coupled type II A strings, only geometric phases were allowed.
In adition to compactification "braane worlds" were considrd. The idea was that the observable world would be some kind of brane. Precise realizations of that idea were purchased form many viepoints (I guess that the most recent try use the idea of intersecting D6-Branes).
In the mean time it was discovred that the universe is accelerating. And there are som kind of consensun that at a constant rate. That means that "phantm energy" scenaries seen to be ruled out and we must look for a de sitter universe emerging from string theory. The firs realization of this was the KKLT theory. In that scenarie there were required vacuums where supersymmetry was broken in a way that it gived some cosmological constant. It was argued that the univrse could be populated by manu diferne vacua. Each vacuawith a diferent value of the cosmological constant would expand at diferents speeds so we would live in some buble of a particular vacua. That lead to the counting of vacua that shrd some properties, and to do an analisys of the statistical distribution of other properties. For example, in some kind of vacua compatible with aa certain value of the cosmological constant there were more solutions with large extra dimensions. But another kinds of such vacua ere in the opposite direction. By the way, vaua with cosmological constants are not tru vacuums, they are metastable states whose decay rate is graater that the actual ge of the universe, oh yeah ;-).
Some interesting remarks about this models are that they give a potential for the scalar fields that describe the moduli of the vacuas. Taht is, they re, in a certain sense, properly defined theories with all the measurable values fixed. This had proved to be a very difcould task. The Dine-Seiberg conjecture stated that a proper determination of the value of the modulis required to go to non-perturbative range of string theory. But the hope was that once one had a theory with aall that values fixed one would have a unique, of almost unique, theory. In fact one has, in some scenaries, around 10^500 theory (i.e. vacua). whose average cosmologicla constant is the observed one (the counting was made by first time by Bousso and Polchinsky for some particular kind of models). Another point is that there is not a natural way to make statistic mechanic for that diferent vacua. I.E, Ine can´t make a proper statistichal ensmble out of them because that vacua should be separated into diferent sectors with superselection rules not allowing going from one to another. I recmend to llok at the blog of Dimityr (non equibrium net) to get a mch better discusion of this topic.
By the way. Most of this studies were made for type II theories. What was of the hetrotic string?. Well, infact there is an heterotic landscape also. It is courious. Another development of string theory was to prove a counting of the benckenstein entropy of a black holes (or at least a paarticular kind of them). for that puropose Type II theories, and their D-Branes, were used. But later it was seen that one also could use heterotici strings to describe black holes. It seems like if heterotic string theory always has aa delay in the achievement of the resoults. But, in the positive point, heterotic strings still seem to be promising. FOr example teh heterotic landscape contians many fewer vacua.
In the eighties ther was a hope that string field theory could provide some kind of dynamics which could indicate how these compactifications could be achieed. Unfortunately string field theory had not succes and has proved to be very dificoult anyway. I fact one would have an string field theory fo rany of the diferen string theories.
With all that I have exposed it looks like if there are too many things going on. In fact it is so. I think taht what I would like to see is a way to see how topologicla transitions could be used to connect diferent vacua. In fact the vacua of the landscape aare, as I said, not aall of them supersymmetric vacua. That would mena to consider a more generic king of compactifications, and studie the possible topologicla transitions betewem them. One way to consider taht could be the use of instanton/euclidean wommholes. And also to see how to describe this in some kind of SFT. Also it one consider that the diferent string theories are related by dualities, meaning that in some sense they re a single one, one could study wormholes, ot whatever, connecting them. A way to beguin this program could be to try to describe some kind of wormhle like solution connecting diferent compactifications (or a noncapctifed space to a compactified one).
I muist advertize that like this post contain many, many, topics, I have not pretended to be very exact in the descriptions. My idea was just to give a broad perspective. I hope to wite in a near future more detailed posts on more concrete topics, but I guess it was too much tiem since the last posts and that It was a good idea not to bee too lazy and write smething ;-).
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