Quantcast
  • Register
PhysicsOverflow is a next-generation academic platform for physicists and astronomers, including a community peer review system and a postgraduate-level discussion forum analogous to MathOverflow.

Welcome to PhysicsOverflow! PhysicsOverflow is an open platform for community peer review and graduate-level Physics discussion.

Please help promote PhysicsOverflow ads elsewhere if you like it.

News

New printer friendly PO pages!

Migration to Bielefeld University was successful!

Please vote for this year's PhysicsOverflow ads!

Please do help out in categorising submissions. Submit a paper to PhysicsOverflow!

... see more

Tools for paper authors

Submit paper
Claim Paper Authorship

Tools for SE users

Search User
Reclaim SE Account
Request Account Merger
Nativise imported posts
Claim post (deleted users)
Import SE post

Users whose questions have been imported from Physics Stack Exchange, Theoretical Physics Stack Exchange, or any other Stack Exchange site are kindly requested to reclaim their account and not to register as a new user.

Public \(\beta\) tools

Report a bug with a feature
Request a new functionality
404 page design
Send feedback

Attributions

(propose a free ad)

Site Statistics

160 submissions , 130 unreviewed
4,191 questions , 1,562 unanswered
5,027 answers , 21,345 comments
1,470 users with positive rep
593 active unimported users
More ...

  Infinite-dimensional Hilbert spaces in QM vs. finite-dimensional Hilbert spaces in quantum gravity?

+ 3 like - 0 dislike
92 views

It seems to me that there are fairly good reasons to assume that quantum theories need to rely in their formulation on infinite-dimensional spaces, cf. https://physics.stackexchange.com/q/149786 or https://physics.stackexchange.com/q/29740/ . @Arnold Neumaier wrote in a stackexchange thread:

With a finite-dimensional Hilbert space, the whole apparatus of practical QM is lost. Very little is left - no continuous spectra, no scattering theory, no S-matrix, no cross sections. No Dirac equation, no relativity theory, no relation between symmetry and conservation laws, no quantum fields.

It appears, however, that in some contexts, e.g. quantum gravity, people have been making claims to the effect that it is enough to consider finite-dimensional Hilbert spaces. Here's Ed Witten:

We discuss some general properties of quantum gravity in de Sitter space. It has been argued that the Hilbert space is of finite dimension. (http://cds.cern.ch/record/504347/files/0106109.pdf)

How is it possible to reconcile those two statements? Are the respective contexts vastly different in some sense? 

asked Jul 25 in Theoretical Physics by skids (15 points) [ revision history ]
edited Jul 26 by skids

Your answer

Please use answers only to (at least partly) answer questions. To comment, discuss, or ask for clarification, leave a comment instead.
To mask links under text, please type your text, highlight it, and click the "link" button. You can then enter your link URL.
Please consult the FAQ for as to how to format your post.
This is the answer box; if you want to write a comment instead, please use the 'add comment' button.
Live preview (may slow down editor)   Preview
Your name to display (optional):
Privacy: Your email address will only be used for sending these notifications.
Anti-spam verification:
If you are a human please identify the position of the character covered by the symbol $\varnothing$ in the following word:
$\varnothing\hbar$ysicsOverflow
Then drag the red bullet below over the corresponding character of our banner. When you drop it there, the bullet changes to green (on slow internet connections after a few seconds).
To avoid this verification in future, please log in or register.




user contributions licensed under cc by-sa 3.0 with attribution required

Your rights
...