My guess is that that quantum gravity is constrained by not just the holographic principle but similar invariants. Many things you calculate from string theory might well turn out to be also true in other theories not so much because string theory is right but because string theory is bound by the same constraints.
Its worth mentioning that string theory went through quite few 'recalibrations', it feels like it string theorists are throwing stuff to see what sticks sometimes.
(For my PhD thesis I found out that you didn't need an orthogonal basis set to do quantum mechanical calculations but rather you could do it just fine with an overdetermined basis set such as coherent states over p and q so long as you had resolution of unity over the basis set.)
If there is unitarity than there is no information loss in a black hole. If that's the case, the controversy that Stephen Hawking promoted about information loss shouldn't have been controversial -- in fact it held back progress in quantum gravity for 20-30 years which is a serious tragedy.
There is no idea at all how to do quantum mechanics without unitarity so if you believe in information loss you are rejecting the possibility of quantum gravity. My take is that the classical picture of black hole interiors is entirely wrong, even though it is a difficult concept to formulate exactly, I'm pretty sure that what's on the other side of the event horizon is something completely different though there is no way we can know
"For my PhD thesis I found out that you didn't need an orthogonal basis set to do quantum mechanical calculations but rather you could do it just fine with an overdetermined basis set such as coherent states over p and q so long as you had resolution of unity over the basis set"
Isn't this just a fact from the definition of R^n topologies? i.e. There are only n-basis vectors possible and any transformation of them which is still R^n will be linearly related to those original n-basis vectors. (It's been over a decade since LA, though, so I'm not 100% on my verbiage.) Put another way, any non-zero determinate/linearly independent set of vectors within R^n can have at most n-elements.
... but also the vector space can be infinite (like position q or momentum p) which are very familiar but you can take the trace integrating over both q and p to get the density of states. There is a community in chemical physics that does this all the time and here is a run-of-the-mill paper that uses the method.
Roughly a wavepacket which is localized in both q and p propagates on a path similar to a classical particle located at q, p and you can use trick to do quantum mechanical calculations based on the classical mechanics. It is not a method of investigating the "classical quantum correspondence" but rather a method of calculating QM quantities.
Which is what makes simulating things within QM compute-able in finite time, too, as I recall.
I wonder if unitarity could be tested with analogs to black holes like the sonic analog. Otherwise this seems testable in a weak sense.
[edit] I just want to point out that, to my intuitive idea of how a black hole would work in string theory - it seems all the information would not be lost. It would be compressed to the event horizon along with everything else.
The article mentions unitarity and Lorentz invariance as the key constraints used in the "bootstrapping" method they used to calculate alpha "from accepted truths" and without relying on any new theory.
> There is no idea at all how to do quantum mechanics without unitarity so if you believe in information loss you are rejecting the possibility of quantum gravity.
I always understood that one of the hopes for quantum gravity is exactly to find a new theory that replaces quantum mechanics, hopefully a fully deterministic (and single-world) theory. So, if some possible property of quantum gravity somehow forced us to abandon unitarity, that actually seems like it might have been an enticing aspect to explore, not some obvious dead end. (Note: I'm using the term "quantum gravity" here to refer to any theory of gravity that matches the observed results of quantum mechanics, which might be a replacement for standard QM, not necessarily a theory consistent with QM).
> They simply add a series of possible “corrections” to general relativity that might become important at short distances. Say you want to predict the chance that two gravitons will interact in a certain way. You start with the standard mathematical term from relativity, then add new terms (using any and all relevant variables as building blocks) that matter more as distances get smaller.
How do you know what the correct values/labels are.
You can throw all sorts of interaction terms with unknown coefficients in there and the renormalization will pare down any inconsistent with large distance symmetries. The remaining unknown coefficients are equated to combinations of known and unknown physical constants, to find the unknown ones requires a new measurement (AKA massive international experiments or cosmological observation).
My understanding was that has always been the basis for string theory the math works out very nicely and it is so beautifully self consistent, it is elegant, mathematically sound and ornate, it has everything anyone could ever want from a theory of everything, except for having any actual testable thesis, making any real predictions, and actually providing any real direction to anything besides funding committees.
Without understanding any of the details whatsoever: if it does provide a simpler explanation of known phenomena only, shouldn't it then be adopted by Occam's Razor?
Any theory has to have predictability, meaning your theory is more relyable in explaining every future phenomenon than the current working theory. without that your theory is as good as claiming 'god' or divine intervention at every corner.
Prior to reading Brian Greene’s The Elegant Universe, I was unfamiliar with the details, but under the assumption that the string theory is sound. Greene is one of its chief popularizers (as well as a minor researcher), and writes with great clarity on the topic. I enjoyed the book.
Yet I ended up becoming agnostic on the string theory after reading it. There seem to be some genuine contributions to mathematics, but those are side products. The theory has yet to make any correct predictions regarding physics and our understanding of the universe, and it is likely completely unfalsifiable.
To this layman, a lot of it seem like a bunch of extraordinarily smart people twisting their minds (and our conception of the universe) into a pretzel attempting to make post hoc explanations of existing phenomena.
> if it does provide a simpler explanation of known phenomena only, shouldn't it then be adopted by Occam's Razor
Yes, but it doesn't describe known phenomena only, it describes things we haven't seen, things we can't ever see, and can be tweaked so much that it can accommodate phenomena that we know can't be true.
The maths isn't rigorous and well-defined AFAICT. There aren't any definitive equations either, as far as I know. However, there are some cool geometric observations like AdS/CFT.
There are some very polemical critics of string theory like Peter Woit and Sabine Hossenfelder, who suggest that it's a complicated philosophy that started off simple and neat, encountered some problems, and then grew in complexity and vagueness.
There aren't any definitive equations of string theory AFAICT. For the Standard Model, there are. This is on top of the lack of rigour that's already in QFT.
The result is a theory that isn't really mathematics as mathematicians understand it, and nor is it physics as many physicists understand it.
The entire point of string theory not being testable is not specific to string theory but rather to quantum gravity. Any theory of quantum gravity will only deviate from our current understanding (general relativity) at the Planck Scale. So, if one has an issue with string theory not being testable, one actually has an issue with pursuing any version of quantum gravity.
The interesting thing about string theory that sets it apart from all other theories of quantum gravity is that it's actually not just a theory of gravity. Because of this, there is actually hope that string theory could produce nontrivial testable predictions at energy scales much lower than the Planck Scale. However, it turns out that teasing out these predictions is very nontrivial, primarily because of a structure called the string landscape. Basically it turns out that the equations of string theory, while being tidy at high energy, produce a multitude of solutions at low energy and, unless you know which solution to look at, making definitive predictions is hard.
Normally the way around a situation like that is to make some observations and try to constrain which solution we should look at. Unfortunately our current best understanding of the landscape is only one-way; we can't currently constrain which solution to look at based on observational evidence. It's sort of like a one-way hash. If we can invert this 'hash function', we could in principle make measurements to constrain which solution we're in and at that point string theory would be falsifiable.
The bigger problem is that some of String Theory's few predictions have in fact been falsified. Supersymmetry has been predicted twice already, once at LHC energy levels and once before. Those predictions turned out wrong, but instead of abandoning the theory, it was easily tweaked to make a new prediction at a slightly higher energy level that LHC can predict.
The very fact that such tweaks can be made is a known problem with string theory as a component of physics.
I know people attempted to correct the definition of 'theory' to discredit the 'It's only a theory' argument, but claiming it's only called a theory when it's "proven" is an overcorrection. In fact no theories are "proven" per se, the better theories just have known limitations.
“A hypothesis is a tentative explanation that can be tested by further investigation. A theory is a well-supported explanation of observations. A scientific law is a statement that summarizes the relationship between variables.” - The Internet
It’s not about string theory or about conventional quantum gravity in four space-time dimensions. The topic is graviton scattering in maximally supersymmetric theories in ten flat space-time dimensions, and the argument is that the basic principles of supersymmetry, Lorentz invariance, analyticity and unitarity imply a bound on the coefficient of the lowest order correction term. The only relation to string theory is that a string theory calculation of this correction coefficient satisfies the bound (as expected, since string theory is supposed to satisfy the assumed basic principles). Much is made of the fact that in string theory one can get any value of the coefficient consistent with the bound. This is taken as evidence for the “inevitability” of string theory, but I don’t see this at all. It’s more accurately evidence for the usual problem with string theory: it’s consistent with anything.
(I am a person who knows some physics but not a lot).
If any of this stuff turned out to be true, what would the lab experiments and positive outcomes look like?
I'm accustomed to particle accelerators and all sorts of other physical experiments, but I really struggle to relate these sorts of theories to anything that could be done in the lab, and if the theories were predictive, what sort of applied science could be done? No wide-eyed "we could make space elevators and travel FTL", just realistic extrapolation.
One clear requirement for at least some versions of String Theory is Supersymmetry - the existence of supersymmetric partners to some of the particles in the SM at some energy level. This energy level is not really pinned down, except that it must be higher than anything we've tried so far (since we've been unable to find these particles). The sky is the limit on what is a maximal bound - probably all the way down to the Planck scale, or close to it.
The same is true of the extra dimensions - those are detectable, but again only at energy levels that far exceed what is plausible not just for the near future, but probably for the entire future of life in the universe.
There's a good reason why most people who specialize in quantum gravity work in string theory: violating any axioms of string theory leads to theories which are self-evidently inconsistent with themselves and/or experiment. It's worth spending time trying to understand why, but unfortunately a lot of air is sucked out of the room by Woit's petulant negativity. It makes for fun podcasts but I'm glad researchers are willing to actually sit and think about the consequences of physics that doesn't match our intution, even when it's hard.
And indeed this quote misses the point. The point is that there aren't "additional" effective theories of gravity that are self-consistent but couldn't be explained by string theory. This isn't a smoking gun that string theory is correct, but if the opposite were true, it would have suggested that string theory was missing something.
So it's incorrect to conclude from this evidence that string theory is "consistent with everything"; it's merely consistent with the range of things that are consistent, and no more and no less. (Suspicious! But not conclusive.) One can complain that this isn't predictive, and indeed if you want to look for predictive power you look at other physical quantities. String theory makes very precise and unique predictions for the way that e.g. gravitons scatter off each other. The fact that humans don't (yet) have the ability to do such experiments is regrettable from a fundamental physics perspective, but it's a problem with humans, not string theory. So string theory continues to be a demonstrably self-consistent, (in principle) falsifiable, and stunningly beautiful theory--and dismissing it out of hand is a tragically common mistake.
> The trio specifically considered the range of values of α permitted by those two principles in supersymmetric 10D universes.
The two main problems with string theory are supersymmetry and the fact that it requires 10 dimensions. This is a problem because we have no evidence for either of those things, and have to make up new physics to explain them away.
So this paper says nothing more than string theory isn't inconsistent... with itself. Which it shouldn't be since the whole point of string theory was to come up with a consistent mathematical model that combines relativity and quantum mechanics.
The more I read about string theory, including Brian Greene's books, the more it seems akin to arguing over how many angels can dance on the head of an n-dimensional pin.
If anything good comes out of string theory research it will probably be the development of the mathematical machinery and the computational power that is needed to perform and analyze more experiments and the observational data we are gathering in the study of high energy events out in the cosmos.
48 comments
[ 3.4 ms ] story [ 143 ms ] threadThank you for being generous :)
What are the parts of string theory that are unique to it and not just invariants that apply to a large basket of theories?
https://en.wikipedia.org/wiki/Unitarity_(physics)
(For my PhD thesis I found out that you didn't need an orthogonal basis set to do quantum mechanical calculations but rather you could do it just fine with an overdetermined basis set such as coherent states over p and q so long as you had resolution of unity over the basis set.)
If there is unitarity than there is no information loss in a black hole. If that's the case, the controversy that Stephen Hawking promoted about information loss shouldn't have been controversial -- in fact it held back progress in quantum gravity for 20-30 years which is a serious tragedy.
There is no idea at all how to do quantum mechanics without unitarity so if you believe in information loss you are rejecting the possibility of quantum gravity. My take is that the classical picture of black hole interiors is entirely wrong, even though it is a difficult concept to formulate exactly, I'm pretty sure that what's on the other side of the event horizon is something completely different though there is no way we can know
Isn't this just a fact from the definition of R^n topologies? i.e. There are only n-basis vectors possible and any transformation of them which is still R^n will be linearly related to those original n-basis vectors. (It's been over a decade since LA, though, so I'm not 100% on my verbiage.) Put another way, any non-zero determinate/linearly independent set of vectors within R^n can have at most n-elements.
https://www.researchgate.net/publication/263170709_Wavepacke...
Roughly a wavepacket which is localized in both q and p propagates on a path similar to a classical particle located at q, p and you can use trick to do quantum mechanical calculations based on the classical mechanics. It is not a method of investigating the "classical quantum correspondence" but rather a method of calculating QM quantities.
I wonder if unitarity could be tested with analogs to black holes like the sonic analog. Otherwise this seems testable in a weak sense.
[edit] I just want to point out that, to my intuitive idea of how a black hole would work in string theory - it seems all the information would not be lost. It would be compressed to the event horizon along with everything else.
I always understood that one of the hopes for quantum gravity is exactly to find a new theory that replaces quantum mechanics, hopefully a fully deterministic (and single-world) theory. So, if some possible property of quantum gravity somehow forced us to abandon unitarity, that actually seems like it might have been an enticing aspect to explore, not some obvious dead end. (Note: I'm using the term "quantum gravity" here to refer to any theory of gravity that matches the observed results of quantum mechanics, which might be a replacement for standard QM, not necessarily a theory consistent with QM).
How do you know what the correct values/labels are.
edit: Weinberg explains: https://www.int.washington.edu/PROGRAMS/talent13/refs/weinbe...
Yet I ended up becoming agnostic on the string theory after reading it. There seem to be some genuine contributions to mathematics, but those are side products. The theory has yet to make any correct predictions regarding physics and our understanding of the universe, and it is likely completely unfalsifiable.
To this layman, a lot of it seem like a bunch of extraordinarily smart people twisting their minds (and our conception of the universe) into a pretzel attempting to make post hoc explanations of existing phenomena.
Yes, but it doesn't describe known phenomena only, it describes things we haven't seen, things we can't ever see, and can be tweaked so much that it can accommodate phenomena that we know can't be true.
There are some very polemical critics of string theory like Peter Woit and Sabine Hossenfelder, who suggest that it's a complicated philosophy that started off simple and neat, encountered some problems, and then grew in complexity and vagueness.
(No one has proven that there is a 3D QFT for anything more than U(1), iirc? Or maybe even for U(1) ? Idr. There’s a prize for showing one iirc.)
I don’t think that contradicts the claim of the mathematical beauty motivating things.
The result is a theory that isn't really mathematics as mathematicians understand it, and nor is it physics as many physicists understand it.
AFAIK, nobody knows if it's self consistent yet.
Beauty is on the eye of the beholder. But I count "unsolvable" as a very ugly trait.
The interesting thing about string theory that sets it apart from all other theories of quantum gravity is that it's actually not just a theory of gravity. Because of this, there is actually hope that string theory could produce nontrivial testable predictions at energy scales much lower than the Planck Scale. However, it turns out that teasing out these predictions is very nontrivial, primarily because of a structure called the string landscape. Basically it turns out that the equations of string theory, while being tidy at high energy, produce a multitude of solutions at low energy and, unless you know which solution to look at, making definitive predictions is hard.
Normally the way around a situation like that is to make some observations and try to constrain which solution we should look at. Unfortunately our current best understanding of the landscape is only one-way; we can't currently constrain which solution to look at based on observational evidence. It's sort of like a one-way hash. If we can invert this 'hash function', we could in principle make measurements to constrain which solution we're in and at that point string theory would be falsifiable.
The very fact that such tweaks can be made is a known problem with string theory as a component of physics.
...unless you're in the "string theory == baloney" camp.
It’s not about string theory or about conventional quantum gravity in four space-time dimensions. The topic is graviton scattering in maximally supersymmetric theories in ten flat space-time dimensions, and the argument is that the basic principles of supersymmetry, Lorentz invariance, analyticity and unitarity imply a bound on the coefficient of the lowest order correction term. The only relation to string theory is that a string theory calculation of this correction coefficient satisfies the bound (as expected, since string theory is supposed to satisfy the assumed basic principles). Much is made of the fact that in string theory one can get any value of the coefficient consistent with the bound. This is taken as evidence for the “inevitability” of string theory, but I don’t see this at all. It’s more accurately evidence for the usual problem with string theory: it’s consistent with anything.
Also, see John Baez's comment: https://www.math.columbia.edu/~woit/wordpress/?p=12641#comme...
If any of this stuff turned out to be true, what would the lab experiments and positive outcomes look like?
I'm accustomed to particle accelerators and all sorts of other physical experiments, but I really struggle to relate these sorts of theories to anything that could be done in the lab, and if the theories were predictive, what sort of applied science could be done? No wide-eyed "we could make space elevators and travel FTL", just realistic extrapolation.
The same is true of the extra dimensions - those are detectable, but again only at energy levels that far exceed what is plausible not just for the near future, but probably for the entire future of life in the universe.
And indeed this quote misses the point. The point is that there aren't "additional" effective theories of gravity that are self-consistent but couldn't be explained by string theory. This isn't a smoking gun that string theory is correct, but if the opposite were true, it would have suggested that string theory was missing something.
So it's incorrect to conclude from this evidence that string theory is "consistent with everything"; it's merely consistent with the range of things that are consistent, and no more and no less. (Suspicious! But not conclusive.) One can complain that this isn't predictive, and indeed if you want to look for predictive power you look at other physical quantities. String theory makes very precise and unique predictions for the way that e.g. gravitons scatter off each other. The fact that humans don't (yet) have the ability to do such experiments is regrettable from a fundamental physics perspective, but it's a problem with humans, not string theory. So string theory continues to be a demonstrably self-consistent, (in principle) falsifiable, and stunningly beautiful theory--and dismissing it out of hand is a tragically common mistake.
The two main problems with string theory are supersymmetry and the fact that it requires 10 dimensions. This is a problem because we have no evidence for either of those things, and have to make up new physics to explain them away.
So this paper says nothing more than string theory isn't inconsistent... with itself. Which it shouldn't be since the whole point of string theory was to come up with a consistent mathematical model that combines relativity and quantum mechanics.
If anything good comes out of string theory research it will probably be the development of the mathematical machinery and the computational power that is needed to perform and analyze more experiments and the observational data we are gathering in the study of high energy events out in the cosmos.