Robert Wilson on Hidden Assumptions

[Doug Mounce]

Dear David (Bibby),

I am interested if you have any time to comment on Robert Wilson's latest preprint.  I don't know group theory, but I like the way he is pursuing an insight that would have explanatory power. 

"As you know, there is a symmetry group in the theory of relativity, called the Lorentz group. There is also a symmetry group in quantum mechanics, called the Lorentz group. In physics, it is assumed that these are the same group, acting as the same symmetries of different things. This assumption leads to a contradiction, which physicists have struggled unsuccessfully to deal with for 96 years."

https://robwilson1.wordpress.com/

[David Bibby]

Dear Doug,

Thank you for your interesting question.

Unfortunately, I can't pass judgement on Wilson's work, as I would need to understand it first, and I'm not up to date with all the theories and developments of which he writes.  However, I can add some comments and observations.

This is from the conclusion of his paper on the problem of unifying particle physics and gravity:

"The problem of unification of particle physics and gravity goes back almost a century, and occupied Einstein for at least a quarter of that century. Yet the problem seems no nearer to a solution today than it did fifty years ago, and even further away than it seemed forty or thirty years ago. This indicates that there must be something subtly wrong in the basic assumptions somewhere. My analysis locates this problem in the concept of spacetime itself. The way that spacetime is treated in relativity, using the Lorentz group in the form SO(3, 1), is mathematically (never mind physically) inconsistent with the way that spacetime is treated in quantum mechanics, using the Lorentz group in the form SL2(C). It isn’t a question of one of them being ‘right’ and the other one ‘wrong’, it is a question of there being no consistent definition of spacetime at all, and no possible way to measure spacetime in the absence of objects embedded in spacetime." (https://arxiv.org/pdf/2404.18938)

He diagnoses the problem as the lack of a consistent definition of spacetime.  This is an inverse insight, a defect of intelligibility.  On this Lonergan says,

"But a mere defect in intelligibility is not the basis of a scientific method.  There is needed a complementary direct insight that turns the tables on the defect." (Insight, chapter 2, section 4.2, page 80)

Wilson continues,

"Therefore I have considered the possibility of describing physics without using spacetime, but instead using only phase space, as Hamilton taught us to do. This involves re-interpreting the Dirac algebra, the Einstein field equations and the Riemann curvature tensor in terms of a complex phase space, in order to include both momentum and current."

This is a direct insight, the use of phase space instead of descriptive space-time.  This does seem a promising, albeit speculative, approach, but if I were to be critical, I should say that the evidence lies in the correlation of theory with experiment, and a purely physical model will not account for the emergence of intelligence.  We can know this despite our ignorance of the physics, because intelligence is the fashioner and creator of rules, and cannot be subsumed under the rules themselves.

Where does this leave unified physics?  I am speculating now, but I would like to see unification on the methodological level, whereby we understand the principles underlying physical laws, and can adapt laws to the concrete as new evidence arises.  The work of physicists and mathematicians such as Wilson is needed to help us understand the laws and how they combine, but we should also see these theories in their proper perspective, as explanatory conjugates of an abstract system which may apply to an increasing range of physical situations, but will never exhaust the mysteries of the universe.

Kind regards,

David

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[Doug Mounce]

Thanks David,

One of the things Wilson wants is reflective insight on an implementation of Mach's Principle.  I recall Polanyi's comment about how Einstein was inspired by Mach when Mach said that Newton's idea of absolute space was meaningless because it couldn't be tested; Einstein was inspired to show that, not only could the concept be tested, it could be proven false.

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https://staff.washington.edu/mounce/

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