Bell's Theory of Beables and the Concept of `Universe' by Ian Durham

Dear Ian,

Bell's work takes centre-stage in my research, so your essay (already much annotated) is excellent for me. To keep it simple for now, here's how I parse your Abstract:

"From its earliest days nearly a century ago, quantum mechanics has proven itself to be a tremendously accurate yet intellectually unsatisfying theory to many." This issue is the focus of my research. Please see Fröhner, hyperlinked at Reference [12] in my essay; or via direct link to the PDF (which may be slow) Missing link between probability theory and quantum mechanics: the Riesz-Fejér theorem.

"Not the least of its problems is that it is a theory about the results of measurements." Yes, I prefer to speak of tests (which are secondary to the initial beables).

"As John Bell once said in introducing the concept of 'beables', it should be possible to say what is rather than merely what is observed." Yes, to say also: what is inferable and not observable; what is interactively sensitive and what is not.

"In this essay I consider the question of whether a universe can be a beable and what that implies about the fundamental nature of that universe." Spacetime is a beable in my theorising.

"I conclude that a universe that is a beable within the framework of some theory, cannot be fundamental." I conclude that spacetime is fundamental; it provides the framework for my theory.

Since your comments on my theory will be welcome at any time, here is some background from my essay thread:

Background to Wholistic Mechanics (WM)

Whereas QM emerged from the UV-catastrophe ca1905, WM emerges from the locality-catastrophe typified by John Bell's dilemma ca1965: ie, seriously ambivalent about AAD, Bell adamantly rejected locality. He later surmised that maybe he and his followers were being rather silly -- correctly; as we show -- for WM is the local theory that resolves Bell's dilemma [there is no AAD] and proves the Bellian silliness.

So WM begins by bringing just one change to modern physics: rejecting naive-realism, true realism insists that some beables change interactively, after Bohr's disturbance-dictum. Thus recognising the minimum-action associated with Planck's constant, WM then recognises the maximum speed associated with light: for true locality insists that no influence propagates superluminally, after Einstein.

The union of these two classical principles -- the foundation of WM -- is true local realism (TLR). Under TLR, EPR's naive criterion for "an element of physical reality" is corrected, then the Laws of Malus and Bayes are validated in the quantum world. Then, via the R-F theorem ca1915, Born's Law is seen to derive from elementary Fourier theory. This in turn allows us to understand the physical significance of Dirac's notation; etc. Thus, beginning with these elementary natural principles, WM's universe-of-discourse focuses on beables in spacetime: with mathematics taken to be our best logic.

NB: Formulated in 1989 in response to a challenging article by David Mermin (1988), many leading Bellian physicists and philosophers have committed to review the foundations of WM and its early results. Since no such review has ever been delivered, I am not yet aware of any defect in the theory. Further, WM provides many ways to refute Bell's theorem (BT): one such is provided on p.8 of my essay.

PS: To those who dismiss my essay due to an alleged typo in the heading, I follow C. S. Peirce (absent his severity): "It is entirely contrary to good English usage to spell premiss, 'premise,' and this spelling ... simply betrays ignorance of the history of logic." [End of background story]

Ian, warmly appreciating your essay; assuring you that critical comments on my own ideas are welcome at any time;

and with best regards,

Gordon Watson More realistic fundamentals: quantum theory from one premiss.

Ian,

....Fact is I describe an ontological sequence with a different starting assumption (as now found in OAM, not 'singlet,' 'supposed' or 'no assumed' states), which, like it or not, fully reproduces QM predictions. No silly assumptions are used and no silly outcome found.

If anyone can find a flaw wouldn't it be you? I'd be very grateful for your analysis.

I've just posted the below in my posts as it's impossible to reconstruct the ontological mechanism on a quick scan.

AS MOST STRUGGLE WITH THE CLASSICAL SEQUENCE (TO MUCH TO HOLD IN MIND ALL AT ONCE) A QUICK OUTLINE INTRO IS HERE;

1. Start with Poincare sphere OAM; with 2 orthogonal momenta pairs NOT 'singlets'.

2. Pairs have antiparalell axis (random shared y,z). (photon wavefront sim.)

3. Interact with identical (polariser electron) spheres rotatable by A,B.

4. Momentum exchange as actually proved, by Cos latitude at tan intersection.

5. Result; 'SAME' or 'OPP' vector Re-emit polarised with amplitude phase dependent.

6. Photomultiplier electrons give 2nd Cos distribution & 90o phase values.

7. The non detects are all below a threshold amplitude at either channel angle.

8. Statisticians then analyse using CORRECT assumptions about what's 'measured!

The numbers match CHSH>2 and steering inequality >1 As the matching computer code & plot in Declan Traill's short essay. All is Bell compliant as he didn't falsify the trick with reversible green/red socks (the TWO pairs of states).

After deriving it in last years figs I only discovered the Poincare sphere already existed thanks to Ulla M during this contest. I hope that helps introduce the ontology.

Peter

Dear Ian Durham, In the basis of the New Cartesian Physics is "true local realism". For a long time believed that the Foundation for fundamental theories is matter, an attribute which had mass. Once there was a formula of mass - energy equivalence, and mass lost the status of a value characterizing the amount of matter, about it rarely began to remember and physics has lost the Foundation. Any theory of everything is created in such circumstances would not be fundamental. The principle of identity of space and matter Descartes, according to which physical space is matter and matter is space that moves, gives us the Foundation for fundamental theories.

The principle of identity of physical space and matter allows us to use physics to study living matter. For this we need to pay attention to the fact that matter within the body is the same as outside the body. Our brain creates an image of the outside world not within themselves and the space around them. This way the outside world has an active nature, as it controls the body.

New Cartesian Physics needs your support to develop further. Visit my page and give your assessment there.

I hope on highly appreciate her ideas.

FQXi Fundamental in New Cartesian Physics by Dizhechko Boris Semyonovich

I wish you success! Sincerely, Boris Dizhechko

Ian,

I won't comment or question as you seem to have disengaged and left many good ones above unanswered so it seems pointless.

Shame.

Richard.

Hi Ian,

I'd hoped you'd answer mine, and the only other one seems to be Gordon Watson's. Richard was one of the few who made the effort to follow and check out the classical QM derivation and agreed it. Declan Traill's plot shows the correlations are correct with loophole closed, so the mechanism explains the low intensity geometry inadequate to trigger 'clicks' in terms of the minor axis of highly elliptical 'polarity'.

But Richard's not a full time professional in the field like yourself so your own unencumbered analysis would be greatly appreciated.

How familiar are you with the spin stats theorem SST? You'll probably know what I learned; that in the SST the SO(1,3) group can be decomposed into the direct product of two different SU(2) subgroups. The Lie algebras of the two different groups can be exchanged by hermitean conjugation. This implies that one SU(2) group is left handed and the other is right-handed. Also the Dirac spinor we're so fond of is actually a left-handed spinor stacked on top of a right-handed spinor (a 4-component spinor). The stacked spinors can be exchanged by hermitian conjugation.

One of the spinor representations (let's say the left-handed one) corresponds to a matter particle. The other (conjugate) representation corresponds to an antimatter particle. The Dirac equation is nothing more than a projection operator which projects out either the upper spinor or the lower one.

None of that is needed for the derivation ontology & mechanism and it's incomplete anyway, but can you see how it all corresponds?

All shocking I know, but now you've had a couple of weeks to get used to the new way of looking. Heisenberg 'position' was only a guess as 'momentum' seemed to have been 'taken', but that really means more 'orbital' position, which is the the 2nd orthogonal momentum. I can't recall; Did you see the non integer spin derivation & video?

Very Best

Peter

Finally it was an ox, and the mathematician, the economist, and

the logician were all wrong.... ;-)

Quantum mechanics is a theory about quantum motion. Measurements would be explained by the theory.

Bells' beables aren't really needed or useful, and several of his definitions only add confusion to a topic which already has a good amount of it.

Indeed the universe is colloquially "the totality of everything that

exists". There is no problem with the idea of multiple 'universes'; they would be simply regions of the real universe. The problem here is on Everettians that want to change the meaning of universe to pretend that there are many.

The operational definition confounds the universe with the observable universe.

Defining the universe based in a based on a wavefunction is wrong. First because wavefunction is a definition of a state of an object not the object. Second, because wavefunctions only can describe some quantum states. And using wavefunctions associated to the WdW equation even adds more problems, because the equation is wrong, as even one of his authors admitted.

"IS THE UNIVERSE FUNDAMENTAL?" No. The universe is a collection of particles.

Dear Ian; further to my earlier comments, please: Since we cannot both be right, would you mind commenting on my half-page refutation of Bell's theorem?

See ¶13 in More realistic fundamentals: quantum theory from one premiss.

NB: I clarify Bell's 1964-(1) functions by allowing that, pairwise, the HV (λ) heading toward Alice need no be the same as that (μ) heading toward Bob; ie, it is sufficient that they are highly correlated via the pairwise conservation of total angular momentum. Thus, consistent with Bell's 1964-(12) normalization condition:

[math]\int\!d\boldsymbol{\lambda}\:\rho(\boldsymbol{\lambda})=\int\!d\boldsymbol{\mu}\:\rho(\boldsymbol{\mu})=1.\;\;\;(1)[/math]

Further, in my analysis: after leaving the source, each pristine particle remains pristine until its interaction with a polarizer. Then, in that I allow for perturbative interactions, my use of delta-functions represents the perturbative impact of each such interaction.

My equation (26) then represents the distribution of perturbed particles proceeding to Alice's analyzer. Thus (with b and μ similarly for Bob):

[math]\int\!d\lambda\;\rho(\lambda)_{Alice}=\tfrac{1}{2}\int\!d\,\lambda[\delta\;(\lambda\sim a^{+})+\delta\,(\lambda\sim a^{-})]=1.\;\;\;(2)[/math]

PS: Bridging the continuous and the discrete -- and thus Bell's related indifference -- integrals are used here by me for generality. Then, since the arguments of Bell's 1964-(1) functions include a continuous variable λ, ρ(λ) in Bell 1964-(2) must include delta-functions. Thus, under Bell's terms, my refutation is both mathematically and physically significant.

PLEASE: When you reply -- or if you will not -- please drop a note on my essay-thread so that I receive an alert. Many thanks; Gordon

Current FQXi essay

Dear Ian,

Congratulations of your success in the essay contest!

Is it too much for me to now hope that this success has bought you some time to defend your view re Bell against my own: so that my essay-writing might improve?

For, in the context of EPRB, Bell believed: "In a theory in which parameters are added to quantum mechanics to determine the results of individual measurements, without changing the statistical predictions, there must be a mechanism whereby the setting of one measuring device can influence the reading of another instrument, however remote. Moreover, the signal involved must propagate instantaneously, so that such a theory could not be Lorentz invariant." Subsequently, by his own admission, he lived with the unresolved dilemma of AAD: yes or no.

In my Lorentz-invariant theory -- and in the context of EPRB -- I bring local (non-contextual) hidden-variables to quantum mechanics to determine the results of individual measurements without changing the statistical predictions. So it seems to me that AAD and well-known Bellian inequalities and claims are thereby refuted.

With my best regards, please let me know if you'll not be critiquing my view; Gordon