Are there still other models/interpretations?

Neo-Newtonian Mechanics for example:

If the gravitational waves measurement seems to indicate that Einstein was still right, the theory of the Relativity remains inconsistent with Quantum Mechanics. And while Newtonian mechanics would be out of date, paradoxically it remains used in 99% of cases, even in astrophysics. To propose to treat this remaining 1% by removing the 'principle' of equivalence is the interest of the Neo-Newtonian Mechanics.

Presentation Let's free Newtonian Mechanics from the equivalence 'principle'!

Dear Sydney Ernest Grimm

Thank you for your observations.

In Carlo Rovelli's RQM when you do a measurement a relation is established which modifies at the same time the observer and the observable, which become related. I had in mind this phenomenon. It is a typical effect of quantum physics.

Classical or newtonian mechanics is not out of date, like in mathematics euclidian geometry kept its importance even after discovery of spherical and hyperbolical geometry.

The basic problem with quantum mechanics is that the standard interpretation of quantum mechanics requires an act of measurement to reduce a (pure) state (which is in general a superposition of basis states) to one of the basis states. We end up with macroscopic objects (if tied to a quantum process) in a superposition of states, which could be a cat or a human being. Einstein believed that this interpretation of quantum mechanics is fundamentally incomplete, as elements of reality seem to come into existence only when a measurement takes place. K. Popper's view of quantum mechanics was that it must be objective (i.e. not depend on a subject to do the measurement) and that probabilities (of reduction to a basis state) should be interpreted as objective propensities. Other ways to make quantum mechanics objective include representing measurement as a physical process that is subject-independent and introducing new hidden variables (which have to be non-local) that make sense of the quantum mechanics as a theory of particles with objective, definite properties (such as position and momentum). Given that it is the quantisation of quantity that leads to the need for re-interpretation of quantities below a quantum, there is no reason to suppose that such quantities cannot be interpreted objectively.

Dear Andrew Powell ,

I think Alain Aspects experiments refuted statistically (using Bell inequalities) the hidden variables interpretation at least concerning the paradox of Einstein-Rosen-Podolski?!

I don't know if I interprete well Popper, but I think QP always needs an observer.

(To connect this question to my pet theory: In terms of categories I would suggest the following parallel: cartesian closed categories relate to classical physics as symmetric monoidal closed categories to quantum theory.)

Dear @Thomas Krantz,

Aspect’s experiments refuted local hidden variable theories that extend quantum mechanics, but David Bohm’s formulation using a pilot wave has not been refuted.

Dear Thomas Krantz

I should have added that non-local hidden variable theories have a problem with Ockham's Razor, since they are more complicated than quantum mechanics. That said, quantum mechanics itself is a non-local theory, and if you want completeness (in the sense of a correspondence with elements of reality) then there have to be some additional variables which are hidden due to the fact that otherwise quantum mechanics would use them.

The alternative is to go to an observer-dependent model (as your question suggests). This would be fine (a bit like special relativity) if the measurements of the observer were independent of the observer's internal state (a bit like "frames of reference"). Then the frames of reference are a set of locally defined global variables for an observer, where there is a mapping between frames of reference such that the law of physics are invariant under the mapping. I think it is possible to interpret quantum mechanics in this way, but the nature of the measurement would still be a mysterious process. What is special about about an "observer" that enables a measurement to collapse the wave packet? If weak measurement that does not collapse the wave packet is possible, then we can study the conditions of collapse, which may be fruitful.

Thank you Andrew Powell , and readers, for the explanations.

In Roger Penrose's book "The Road to Reality: A Complete Guide to the Laws of the Universe" I found a chapter on the different interpretations of QP. Most of the interpretations ar though not presented very explicitely. But it made things clearer to me though. Do you know other good sources?

I would recommend Michael Redhead’s book Incompleteness, Nonlocality and Realism. It is an old book, but it rigorous and covers the key issues.

The book "Deep Beauty: Understanding the Quantum World through Mathematical Innovation" by Hans Halvorson, makes a good impression to me.

Dear Thomas Krantz,

I will have a look out for Halvorson's book. I assume that physicists have tried the approach which I mentioned in a previous post, i.e. use Einstein's principle of invariance of physical laws under change of co-ordinate system to treat a quantum mechanical system as a manifold where the tangent space is a complex Hilbert space and there is mapping (a homeomorphism?) that makes measurements in any Hilbert space consistent with those in neighbouring Hilbert spaces.

Dear Andrew Powell & readers,

To give a personal overview:

You have a generalized notion of complex manifold, it has been studied in Bourbaki's monumental work (in the corresponding volume) and also in Serge Lang's 'Foundations of differential geometry' where the local model is even more generally a Banach space. Chart changes are smooth mappings in general.

What physicists call gauge theory has been studied by mathematicians under the name G-structures. If you have a connection on a manifold it is invariant with respect to some representation of a Lie-group G. In Yang-Mills theory the Lie group would be e.g. U(1)xSU(2) in case one would like to consider electromagnetism and weak forces.

Instead of considering space you could use a dual approach and look at the algebras of functions on the space, which for classical spaces are commutative. But as soon as you work in QP you will be interested also in non-commutative algebras. In quantum physics observables do very often not commute. Functional Analysis complements then also geometry, in the domain of non-commutative geometry.

Another generalization would be sheaf and topos theory (and synthetic differential geometry). I think for quantum physics this level of generality is useful, though some others prefer to work in a particular setting as Manifolds modeled on Hilbert spaces. This is related to a question I asked in another forum on the importance of the underlying field.

Dear Arno Gorgels

I am not always sure about the meaning of some words you use like "creational" related to "observer's principle". These sound a bit mysterious to me, who am used to more classical physics and geometry. I would appreciate that you give more references on which you rely. (I think you use also sources like Kabbala or am I completely mistaken?) Your observations show interesting perspectives, but I sometimes need detailed and complete presentation in order to understand.

Best,

Tom Krantz

Dear Thomas Krantz,

Many thanks for setting out the mathematics of the general notion of manifold with Hilbert (or Banach) spaces as tangent spaces and for the observation that what the physics corresponding to the general notion of manifold amounts to is treating physical theories as gauge theories. I suppose the problem is that the notion of a gauge theory is somewhat obscure, covering local symmetries of a manifold under a Lie group and having choice of the equations governing a physical situation because the observations do not fix the values of all parameters. I suppose they are connected by Noether's theorem: all local symmetries of the action of a Lie group on a manifold correspond to conversation laws. If a parameter value is not fixed by observation, presumably every mapping between values is a symmetry. So is the conclusion that all of physics should be expressible as a gauge theory? The standard model is a a gauge theory I believe.

Dear Arno Gorgels

Sorry, I wrongly interpreted your sources. I think you should make more explicit references to commonly accepted works or start explanations from scratch.

Holistic science, why not, but please make it traceable!

Best regards,

Tom

Dear Andrew Powell,

Thank you for recalling the 'theorem' about conservation laws.

I do not know enough about the standard model, I think gauge in-variance is only one aspect oft it.

I give preference to versatile and 'light weight' theories, like category theory, to approach stable physical truth rather than to something which claims to be a nearly definite model of matter.

Dear Arno,

Thank you for your message. In fact I don't know your work. You have interesting intuitions but you should work out the foundations and pedagogy in order to convince the poor skeptic that I am.

Best,

Tom

Dear Arno,

Taceo et laboro - Qui laborant, tacent.

It may be true or not, how to answer if you state things in such a generality?

Other question : I would need suggestions about how von Neumann came to the idea to identify an observable with a hermitian operator on a Hilbert space. What are the main papers who lead to this theory that every physics student learns in first year?

Best,

Tom

Dear Arno,

Are you recruiting or trying to be recruited?

I spend once a lecture at your nice university in Potsdam....

Dear Arno,

I mean Schloss Sanssouci. But I remember there is an Institute for highperformance physical calculus as well.

Dear Arno,

Thank you for your observations.

I am rather busy these days and hope that some other readers would like to comment on it.

Best,

TK

Dear Arno

Natura abhorret a vacuo...

said Blaise Pascal (among others).

https://en.wikipedia.org/wiki/Horror_vacui_(physics)

Best,

t.