2
$\begingroup$

There is a loose set of ideas going under various names ("It from Qubit"; "Space from Hilbert Space"; "Geometry from Entanglement") which propose that spacetime is not fundamental, but instead emerges from the entanglement structure of an underlying Hilbert space (e.g. https://arxiv.org/abs/1606.08444). Instead of formulating a QFT on a background spacetime, we do away with spacetime altogether and hope that Lorentz-covariant QFT emerges in some appropriate limit.

These ideas are not new but seem to be gaining traction recently, with Sean Carroll being a vocal supporter.

However, if this approach were correct, it would seem to render Lorentz covariance a "coincidence": given a Hilbert space with some factorization into spatial sites, we shouldn't expect a randomly chosen Hamiltonian to generate anything like Lorentz invariant dynamics. Even if we constrain the Hamiltonian to be local (with respect to the factorization) we'll almost always end up with a non-Lorentzian evolution.

As a concrete example, consider the quantization of a real scalar field φ. We know that the Hamiltonian density $$ H = \Pi^2+|∇φ|^2+m^2φ^2 $$ gives us Lorentz-covariant dynamics, but unless we had the explicit goal of Lorentz-covariance, how would we know to choose this Hamiltonian over any other? This problem only gets worse when multiple fields are present, which we want to all be Lorentz-covariant with the same speed of light c. On the other hand, the Lagrangian/path integral approach is manifestly Lorentz-covariant from the start and doesn't face the same problem.

I'd be grateful if anyone can explain how "emergent spacetime" approaches deal with this issue - is there some "natural" constraint on the Hamiltonian (i.e. something stronger than just locality) which ensures Lorentz covariance? Or do these approaches just treat SR as a happy coincidence?

TL;DR - "Space from Hilbert Space" doesn't mesh naturally with SR. How should we expect to get Lorentz covariance to emerge?

$\endgroup$
4
  • $\begingroup$ Hi Jacob! Welcome to Physics SE and thanks for asking a question I've been hoping to be explained to me for a while :) A general suggestion: always include links to the arXiv homepage of a preprint rather than to its PDF. People often don't want to straightaway download the paper (this is an issue especially for phone where a link to the PDF downloads the paper straightaway) ;) $\endgroup$
    – user87745
    Commented May 3, 2020 at 14:29
  • $\begingroup$ Ah, my bad. Thanks for pointing that out. $\endgroup$ Commented May 3, 2020 at 14:45
  • $\begingroup$ You may be interested in this answer of mine: physics.stackexchange.com/a/521712/30833 $\endgroup$ Commented May 3, 2020 at 17:19
  • $\begingroup$ Related?: Emergence of space from quantum mechanics $\endgroup$ Commented May 11, 2020 at 1:31

1 Answer 1

0
$\begingroup$

IMO it just can't. Not without lots of hoop jumping.

The correct program should be "Hilbert/Fock space from Spacetime" Not saying that I'm working on it, but get in contact if that's an idea you like.

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Not the answer you're looking for? Browse other questions tagged or ask your own question.