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

PO is now at the Physics Department of Bielefeld University!

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

205 submissions , 163 unreviewed
5,082 questions , 2,232 unanswered
5,353 answers , 22,789 comments
1,470 users with positive rep
820 active unimported users
More ...

  What is the motivation for introducing "ontological state" in 't Hooft's deterministic quantum mechanics

+ 4 like - 0 dislike
5410 views

I tried to read Prof. 't Hooft's new paper The Cellular Automaton Interpretation of Quantum Mechanics A View on the Quantum Nature of our Universe, Compulsory or Impossible? and encountered difficulty about the motivation for introducing ontological states and cogwheel models.

Suppose quantum mechanics is deterministic, the probabilistic nature in the Born's rule must be an artifact. Namely the Born's rule somehow likes throwing a classical dice. The probability comes from our incomplete knowledge and limited computational power.

In another paper, How a wave function can collapse without violating Schroedinger's equation, and how to understand Born's rule, it is stated that

According to our ontological theory of quantum mechanics, the probabilities generated by Born’s rule, are to be interpreted exactly in the same terms. If we do not know the initial state with infinite accuracy then we won’t be able to predict the final state any better than that.

I am fine with all that. However, in the "The Cellular Automaton Interpretation of Quantum Mechanics", if I understood correctly, Prof. 't Hooft constructed a series cogwheel models to show these deterministic models exhibit Schrodinger equation.

My question is, what is the motivation for introducing ontological states and cogwheel model? Would the Schrodinger equation itself to be sufficient, since it is already deterministic anyway? If one wants to get rid of Bell's inequality, Schrodinger equation seems to be sufficient (Related post, Why was quantum mechanics regarded as a non-deterministic theory? ). And even tried to derive Born's rule?

If one feels the Schrodinger equation is insufficient, i.e. there is something behind it, why the object behind Schrodinger equation is so essential? I think I missed some important aspect in his paper... (Presumably I did not read it carefully enough)

This post imported from StackExchange Physics at 2014-06-13 15:23 (UCT), posted by SE-user user26143
asked Jun 12, 2014 in Theoretical Physics by user26143 (405 points) [ no revision ]
I gave an answer to a similar question a while ago (since migrated to Philosophy.SE) which you might find helpful. philosophy.stackexchange.com/q/6670

This post imported from StackExchange Physics at 2014-06-13 15:23 (UCT), posted by SE-user Nathaniel
Thank you very much, though I am not sure whether it is helpful for understanding 't Hooft's approach...

This post imported from StackExchange Physics at 2014-06-13 15:23 (UCT), posted by SE-user user26143
From reading a few of 't Hooft's papers a while ago, I got the impression his motivation was very similar to what I wrote. I guess the part I didn't answer was "would the Schrodinger equation itself to be sufficient, since it is already deterministic anyway?". If I get time I will try to formulate a good answer to that and post it.

This post imported from StackExchange Physics at 2014-06-13 15:23 (UCT), posted by SE-user Nathaniel

1 Answer

+ 1 like - 0 dislike

Thanks for the links, I will read through,

Ontological states are somehow "real" states of the underlying deterministic system, to be distinguished by quantum states which are a superset. Still a bit of unclarity for me here an ontological state can be a quantum state but the way round is not always true. I would start from the perspective that the underlying theory may have states in a totally different domain than the quantum theory, but you can argue that experimental results should match, and is easier if some states match. Therefore the most simple case is this one.

The standard approach was to do this starting from some microscopic hyphotesis (e.g. Bohm) and build it up from there. This was rejected as politically incorrect because it introduce hidden variables and ad hoc hyphothesis. Ideally this approach should be able to derive schrodinger, Bell and all the rest.

In this approach presented he is saying more or less, whatever theory/system is there below this system and theory will have states and transitions between states, that is why the cogweel models.

If the theory below is deterministic, fine, then there will be less states available for choice.

Therefore approaching it top down from the quantum perspective going down, the quantum world is somehow a continuos set of states plus a discrete set of them. Therefore is politically correct to state that may be we need to throw away some of them, such as two atoms at the opposite end of the solar system cannot really do strange swapping or tunnel effects between the two.

Therefore a reasonably generic theory of the below is in any case a shape of cogwheel theory, and as far as we can reasonably derive something for all these theories we can investigate further what is the mapping between the above and the below, and we can somehow derive what is a correct hyphotesis about the below.

There is a legitimate separate discussion for the entanglement part/Bell, that needs to be justified and expanded.

One example of the below is the hyphothesis of the discretization of time, we don't really experimentally know if time is discrete or not beyond a certain scale, and that he glance across.

As far as you have a brand new fundamental hyphothesis of the below (the time one is just one of many and has a couple of big names on it, but there is one per each armchair physicist on this planet), then you can try to achieve the next goal which is a non-lagrangian/non-perturbative theory of the below, from which ideally you want to derive the rest.

What is the rest for thoff is substantially what has not been achieved with strings and is a kind of back to basics for everybody.

There are a few people that can take these directions of research because of the "heretics" issue, susskind on last but one number of nature is another example.

This post imported from StackExchange Physics at 2014-06-13 15:23 (UCT), posted by SE-user flyredeagle
answered Jun 12, 2014 by flyredeagle (10 points) [ no revision ]

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:
p$\hbar$ysics$\varnothing$verflow
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).
Please complete the anti-spam verification




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

Your rights
...