Exploring Lee Smolin's Quantum Mechanics Theory - max.variety principle

[Jimster41]

I'd be very interested in any of the expert's thoughts on this paper, assuming it's okay to discuss it. I couldn't see what journal it was published in or submitted to.

It's even zany by my standards but I really like it because it seems to take the seemingly dual notions of

• non-local, holographic screen
• AdS MERA entangled boundary dimension
• CFT global wave state

(sorry about the imprecise lumps, I can hardly tell them apart)

directly as it's subject, proposing how some space-like separated process thus connected, operates in the bulk. It even seems to allude to the SLOT as extension of the fundamental principle (just my liberal and rough alt+interpretation of the "Maximal Variety" principle).http://arxiv.org/abs/1506.02938
Quantum mechanics and the principle of maximal variety
Lee Smolin
(Submitted on 9 Jun 2015)
Quantum mechanics is derived from the principle that the universe contain as much variety as possible, in the sense of maximizing the distinctiveness of each subsystem.
The quantum state of a microscopic system is defined to correspond to an ensemble of subsystems of the universe with identical constituents and similar preparations and environments. A new kind of interaction is posited amongst such similar subsystems which acts to increase their distinctiveness, by extremizing the variety. In the limit of large numbers of similar subsystems this interaction is shown to give rise to Bohm's quantum potential. As a result the probability distribution for the ensemble is governed by the Schroedinger equation.
The measurement problem is naturally and simply solved. Microscopic systems appear statistical because they are members of large ensembles of similar systems which interact non-locally. Macroscopic systems are unique, and are not members of any ensembles of similar systems. Consequently their collective coordinates may evolve deterministically.
This proposal could be tested by constructing quantum devices from entangled states of a modest number of quits which, by its combinatorial complexity, can be expected to have no natural copies.

 

[marcus]

Thanks for starting a separate discussion thread on this one. There is also another Smolin paper that came out about the same time, and could be related (though I don't immediately see how.)

http://arxiv.org/abs/1506.03733
A naturalist account of the limited, and hence reasonable, effectiveness of mathematics in physics
Lee Smolin
(Submitted on 11 Jun 2015)
The aim of this essay is to propose a conception of mathematics that is fully consonant with naturalism. By that I mean the hypothesis that everything that exists is part of the natural world, which makes up a unitary whole.
10 pages. Awarded third place in the 2015 FQXi essay contest

BTW here is the Inspire link to the "Maximal Variety" paper:
http://inspirehep.net/record/1375483?ln=en

The Inspire entry for a paper often gives additional info such as publication and citations to the paper.
So if and when this is published, and or cited in other research, this Inspire link may register that.

 

[Jimster41]

Thanks for starting a separate discussion thread on this one. There is also another Smolin paper that came out about the same time, and could be related (though I don't immediately see how.)

http://arxiv.org/abs/1506.03733
A naturalist account of the limited, and hence reasonable, effectiveness of mathematics in physics
Lee Smolin
(Submitted on 11 Jun 2015)
The aim of this essay is to propose a conception of mathematics that is fully consonant with naturalism. By that I mean the hypothesis that everything that exists is part of the natural world, which makes up a unitary whole.
10 pages. Awarded third place in the 2015 FQXi essay contest

Re that one, I look forward to reading it. I clearly relates to the "Singular Universe..." Book he did with Unger. I finally got through Unger's section at 2/3's of the book. I enjoyed it but I had to pause before getting too far in Smolin's bit. For some reason I thought his section would be easier, but it started out not...

 

[strangerep]

I started reading the paper as I usually do -- since his papers usually have an interesting-sounding abstract. I also liked the emphasis (p3) on relational observables. I.e., taking seriously the idea that only relative variables have physical meaning -- which harks back to Mermin's Ithaca interpretation of QM, and Rovelli's relational QM, and also banishes concepts like "the state of the universe" outside the realm of physics -- because there is nothing that the entire universe can relative to.

But as I read a little further, I became uneasy about concepts being put in by hand. In particular: causality, an arbitrary relative displacement cutoff "R", and the constants $\hbar$ and $m$. OTOH, since systems with different mass are known to be belong to distinct superselection sectors, maybe that's a good thing.

Then he introduces a momenum beable via a complex phase factor beable $\omega_i$ (one for each subsystem) [p7], and then postulates a form for kinetic energy in terms of these. At this point it seems like things are just being postulated so that one gets the right answer in the end. Nevertheless, it's commendable that he mentions [sect. 4] how his framework is "highly vulnerable to experimental test".

Maybe I should read his section 6 ("Motivations") more carefully...

 

[Jimster41]

I definitely got the feeling the R, r and r' are of interest in exploring the implications of theory (or hypothesis). I'm still trying to understand his experiment proposal, but it seems to be about looking for just where the low energy cut-off is inside of which the "non-linear corrections to the Schroedinger" fit. I guess he's proposing measuring a bunch of the largest possible arguably QM things (electrons?) to see if what?? There are violations of locality.

I'm a crazy idiot about it for sure, blinded by my lust for a picture I already have, but this had been my point w/respect to ensembles like Saturn's rings - are there any Macroscopic violations of locality assumptions. He's quite fuzzy it seems to me on just where and why the low energy "it's all classical from here" line could/should be. Since the normalization and cutoff interact. And, I notice how he defines one R for all "beables" rather than having potetially different R's for each. Also what other beables are possible, spin? What else? Since it an invented or "evoked" metric space, it doesn't seem obvious what DOF might be enumerated. And if the cutoff is not global in that space?

He seems to be assuming the minimal "distinctiveness" cutoff, as a High Energy cutoff. I thought that was a very interesting way of framing that concept. New to me but it illuminates my fuzzy cartoon.

I was struck but the way the first part, the whole setup of "distinctiveness" and "Variety" seems reminiscent of a neural-net or radial-basis-function, which also sort of smacks of MERA. I've been thinking about multi-variate "anomaly detection" and I found the "distinctiveness", "Variety" and terms really clear ways of interfacing to such.

A discussion of just how the negative potential energy of low variety might point off toward cosmological expansion a(t) and the SLOT, would be interesting (to me anyway).

This paper is out there, no doubt, but for me it connects a number of big dots.

 

[strangerep]

This paper is out there, no doubt, but for me it connects a number of big dots.

With this style of paper, one must keep track of the extra assumptions that are quietly slipped in by hand during the development, instead of being explicitly mentioned up front. The number of (directional) connections between your dots is not necessarily what's important, rather how many dots are "primary" (i.e., have arrows going out, not in).

 

[Jimster41]

Fair enough.

That's the second time I've seen "superselection" in two days, and it's new to me? (I have no idea what it means)?? I'm all over it but the wiki is pretty deep, any summary of it's intuitive meaning as you use it?

[edit] the more I read about it the more interesting it is... I see it is related to critical points and phase transitions, and spontaneous ordering.

 

[ftr]

Well, I am no expert but you can check this thread

https://www.physicsforums.com/threads/what-is-meant-actually-by-superposition.819055/

This paper is an outgrowth of an earlier paper with J.Barbour and the paper that I have linked to in the thread post #10.

 

[Jimster41]

Well, I am no expert but you can check this thread

https://www.physicsforums.com/threads/what-is-meant-actually-by-superposition.819055/

This paper is an outgrowth of an earlier paper with J.Barbour and the paper that I have linked to in the thread post #10.

Thanks. "Superposition" I have an inkling of. It's "Superselection" that I'm trying to pseudo-wrangle.

 

[ftr]

Thanks. "Superposition" I have an inkling of. It's "Superselection" that I'm trying to pseudo-wrangle.

They are both linked. Things like mass, charge... lose the superposition and they become classical values through superselection(that is as much as I understand it).

http://physics.stackexchange.com/questions/19424/is-mass-an-observable-in-quantum-mechanics

 

[strangerep]

That's the second time I've seen "superselection" in two days, and it's new to me? (I have no idea what it means)??

How much QM have you studied? E.g., can you read and understand Ballentine's textbook without difficulty? If not, then,... see my signature lines below.

I'm all over it but the wiki is pretty deep, any summary of it's intuitive meaning as you use it?

It basically means that not all quantum states can form superpositions -- usually due to some underlying symmetry structure. Have look at this thread about superselection rules in which I offered an answer for why such rules occur.

If you need to discuss superselection further, then it's probably better to open a new thread in the quantum forum.