Implications of Verlinde entropy on string theory

[ensabah6]

String theory posits spacetime that is infinitely continuous.

Earlier at PF there was a discussion of lorentz invariance and Fermi Gamma-ray Space Telescope showing that very high energy photons travel at c, which makes discrete theories of QG less favored and string theory more favored, as continuous spacetime is a natural home for exact lorentz invariance.

Smolin and Kowalski offered accounts of how Verlinde's proposal can fit within LQG and BF theory respectively.

I'm wondering what are the ramifications of Verlinde entropy on string theory --

1- if spacetime itself has entropy of a specific quantity, does this imply discrete spacetime? if spacetime is continuous can an infinite amount of entropy be packaged in an arbitrarily small volume of space?

2- Verlinde's account of gravity as entropy as equation of state, v.s string theory account of gravity as mediated by closed string (spin-2)

3- Verlinde's derivation effect on higher dimensions, would it work in spaces above 3? Would higher spaces carry additional entropy and hence not give Newton's gravity?

4- Does Verlinde's account of gravity have any effect on supersymmetry? cosmological constant?

5- if Verlinde's account of gravity and entropy is valid, what would be the degrees of freedom that would account for it within string theory? Do string worldsheets carry the needed degrees of freedom to give entropy?

6- how does the idea that spacetime is emergent and carries degrees of freedom from which entropy counts as microstates merge with the idea of exact lorentz invariance at arbitrarily high energy gamma rays?

7- any other ramifications ?

 

[marcus]

...

I'm wondering what are the ramifications of Verlinde entropy on string theory --
...
...
7- any other ramifications ?

'Sabah, wouldn't the person best equipped to spell out the implications for string be Verlinde himself?

Have you read what he says?

If you have, how about reporting for us what Verlinde indicates the ramifications are?

 

[Demystifier]

Verlinde proposal works in any number of dimensions. However, if the actual number of dimensions is 3+1, then string theory cannot be used even as an effective theory.

 

[ensabah6]

Verlinde proposal works in any number of dimensions. However, if the actual number of dimensions is 3+1, then string theory cannot be used even as an effective theory.

Wouldn't gravity in higher dimensions fall off in distance r to the power of the number of spatial dimensions, minus 1?

So in 3d it's r^2 but 10d r^9?

 

[tom.stoer]

Wouldn't gravity in higher dimensions fall off in distance r to the power of the number of spatial dimensions, minus 1?

So in 3d it's r^2 but 10d r^9?

If no dimensions are compactified - yes.

 

[Naty1]

String theory posits spacetime that is infinitely continuous.

No it does not; string theory is background dependent.

 

[Demystifier]

Wouldn't gravity in higher dimensions fall off in distance r to the power of the number of spatial dimensions, minus 1?

So in 3d it's r^2 but 10d r^9?

Yes, if all dimensions are flat. But we certainly don't live in such a universe. If other dimensions exist, then they are probably compactified or warped.

Note also that the holographic principle in D spatial dimensions says that information is localized on a D-1 dimensional surface.

 

[tom.stoer]

No it does not; string theory is background dependent.

Maybe yes, but what has this to do with continuous spacetime?

 

[Naty1]

Hi tom, I like your posts in other threads...

No it does not; string theory is background dependent.

Maybe yes, but what has this to do with continuous spacetime?

In a number of other discussions here I believe we concluded, or at least I sure did, that spacetime is an independent input to string theory, not a conclusion drawn from it. In other words, you pick a fixed spacetime background you want to use, anyone you want, then impose string formulations afterwards. It is a major drawback, a severe limitation, to string theory.

Here is how Brian Greene expresses it in THE FABRIC OF THE COSMOS, page 487:

...all approaches envision strings...in a spacetime inserted into the theory "by hand"...spacetime does not emerge from the theory...but is supplied to the theory by the theorist...Many reasearchers consider the development of a background independent formulation to be the single greatest unsolved problem facing string theory.

Perhaps what the poster is thinking, but did not express, is that because of the extended nature of strings where point infinites can be avoided, there are no discontinuities as are experienced in both GR and QM...but that avoidance is due to the formulation of the string theories, not the selectively chosen background space and time in which they reside. An example might be the R to 1/R "duality" within string theories where a small string size in one theory translates to a larger string dimension in another...hence there is never a "point size" string...
so maybe the poster takes this to be continuous space...what "infinitely continous" means in the context of his questions I have no idea

 

[Fra]

I'm wondering what are the ramifications of Verlinde entropy on string theory --

1- if spacetime itself has entropy of a specific quantity, does this imply discrete spacetime? if spacetime is continuous can an infinite amount of entropy be packaged in an arbitrarily small volume of space?

2- Verlinde's account of gravity as entropy as equation of state, v.s string theory account of gravity as mediated by closed string (spin-2)

3- Verlinde's derivation effect on higher dimensions, would it work in spaces above 3? Would higher spaces carry additional entropy and hence not give Newton's gravity?

4- Does Verlinde's account of gravity have any effect on supersymmetry? cosmological constant?

5- if Verlinde's account of gravity and entropy is valid, what would be the degrees of freedom that would account for it within string theory? Do string worldsheets carry the needed degrees of freedom to give entropy?

6- how does the idea that spacetime is emergent and carries degrees of freedom from which entropy counts as microstates merge with the idea of exact lorentz invariance at arbitrarily high energy gamma rays?

7- any other ramifications ?

Just to add an opinon, a possible convergence of the general entropic ideas (of which verlindes paper is considered to be a step in the right direction, but still awaiting more), holography and strings that I imagine is that:

- continuum strings are just an "effective continuum description" of emergent as self-organising sets, as cardinality increases. Actually, I think even most people that work on continuum models does not consider the mathematical continuum to be "physical". The continuum models, calculus etc are just a very nice language for things. But I think we might now face domains where the effectiveness of this language fails, it just comes with too much non-physical padding that isn't helping.

- the holographic idea might suggest that a constrained worldsheet is in effect coded as a piece of worldsheet "string" on the observer side of the "screen". Nothing prevents further histories of these strings to be coded internally as long as the complexity is respected. In this sense higher "dimensions" might exists behind the screen, that are "internal" to the code. When entropic arguments are applied to these, perhaps all other forces also fit into the same framework. So isntead of tihnking that the communication channel (surface) is always and only of one less dimensionality, why not consider more general cases? Think morse code. What would be interesting is an explanation in terms of coding, why the emergent communication channels does not exceed 3 large space dimensions.

- a lot of the string dualities could probably be understood as two different ways to encode the same information, but the problem is that the choice of code does matter if they are not equally effective in terms of datacompression, which is hardly true in general. Evolution should select the most efficient code. as I see it the problem of producing a prediction of the expected population of codes (incl. symmetries of interactions) in such an darwinic steady steay is pretty much another view of seeing the landscape problem and the lack of an BI formulation.

I think the BI formulation should take thte form of an "expectations" of coding algorithms that are likely to be table in such an equilibrium. The choice of code is also conceptually analogous to the choice of strategy in a nash equilibirum in an economic system.

/Fredrik

 

[tom.stoer]

Hi tom, I like your posts in other threads...

So do I (I mean your posts, not mine :-)

Anyway, we absolutely agree on background dependence of ST.

1) We are discussing fundamental degrees of freedom, atoms of space, ... carrying entropy. In ST these degrees of freedom can only be strings (as classical spacetime cannot carry entropy); so either the strings carry the entropy, or there is no entropy at all. I think you agree.

2) The question now is, "what is spacetime in ST?". We agree that it is some background - but there is a deep relation to strings in terms of consistency conditions for ST; only certain (classes of) geometries are allowed. Once you fix such a background there is some hope to derive entropy in terms of strings; it works in some limited sense for extremal black holes!

Now let's look at the statements in question - with some minor changes:

Does string theory posit spacetime that is infinitely continuous? No it does not; string theory is background dependent.

As far as I can see your answer applies to a different question:

Does spacetime emerge from string theory? No it does not; string theory is background dependent.

The interesting question in our context would be

Does entropy of spacetime emerge from string theory? No it does not; spacetime is a backround for ST only.

or

Does entropy of spacetime emerge from strings? No it does not; spacetime is a infinitely continuous.

...only words ...

 

[Naty1]

The question now is, "what is spacetime in ST?".

Interesting, I just posted a new thread "String theory and twistor theory combined" asking about that.

 

[Naty1]

1) We are discussing fundamental degrees of freedom, atoms of space, ... carrying entropy. In ST these degrees of freedom can only be strings (as classical spacetime cannot carry entropy); so either the strings carry the entropy, or there is no entropy at all. I think you agree.

I would not agree on the spot, but I trust your judgement...for all I know the following is nutty...

The entropic spacetime (EST) defines space; in this theory there is no vacuum - EST is space. Made up of energy and dipole charges, its values can be converted into length and time

from wikipedia: http://en.wikipedia.org/wiki/Entropic_Spacetime_Theory .

However, Verlinde's new theory, discussed here recently, on entropy would cause me to have to think real hard about #1.


2) The question now is, "what is spacetime in ST?". We agree that it is some background - but there is a deep relation to strings in terms of consistency conditions for ST; only certain (classes of) geometries are allowed. Once you fix such a background there is some hope to derive entropy in terms of strings; it works in some limited sense for extremal black holes!

If you are referring to Calabi Yau spaces, I get your drift but not the specific relationship with entropy...then again there is a lot about entropy that makes my eyes glaze over... If you are referring to the fact that major string theories rely on Calabi Yau spaces to provide the appropriate energy vibration constraints and characteristics then that link clearly suggests to be a relation to entropy/energy considerations...maybe geometry determines entropy.

I don't understand the remainder of your points but that's ok by me...I can only relate to sources I have used...like the quote from Brian Greene's above...which apparently you don't accept...since that one does not ring a bell, there seems little point referencing other sources along those lines...there is certainly more in all this than I understand...I am trusting explanations from prominent physiscts and if history shows anything, it repeatedly shows they are ALL wrong much of the time...