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Could such a statement be tested? What are the parts of string theory that are unique to it and not just invariants that apply to a large basket of theories?

by rytill 5y ago

PaulHoule 5y ago
One thing I'd point to is unitarity, which is essential to any kind of quantum mechanics. https://en.wikipedia.org/wiki/Unitarity_(physics) 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
- ianai 5y ago
  "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.
  - PaulHoule 5y ago
    ... 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. https://www.researchgate.net/publication/263170709_Wavepacket_dynamics_and_quantum_mechanical_energy_densities_in_the_quartet_N_2_O_2_system 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.
    - ianai 5y ago
      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.
- civilized 5y ago
  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.
- tsimionescu 5y ago
  > 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).

Could such a statement be tested? What are the parts of string theory that are unique to it and not just invariants that apply to a large basket of theories?

by rytill 5y ago

Could such a statement be tested? What are the parts of string theory that are unique to it and not just invariants that apply to a large basket of theories?

PaulHoule 5y ago

One thing I'd point to is unitarity, which is essential to any kind of quantum mechanics. https://en.wikipedia.org/wiki/Unitarity_(physics) 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

ianai 5y ago
"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.
- PaulHoule 5y ago
  ... 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. https://www.researchgate.net/publication/263170709_Wavepacket_dynamics_and_quantum_mechanical_energy_densities_in_the_quartet_N_2_O_2_system 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.
  - ianai 5y ago
    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.
civilized 5y ago
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.
tsimionescu 5y ago
> 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).