QM Interpretations: Most Popular & Why?

[MaxwellsDemon]

When I hear all these complex discussions concerning various interpretations, I can't help but think of King Alfonso X who upon studying the Ptolemaic universe stated, "If the Lord Almighty had consulted me before embarking on creation thus, I should have recommended something simpler."

 

[Demystifier]

3 Do you remember your own analogy: MWI is a tree, but without an ant?

Yes I do.

The root of a tree is very simple, the complexity is on the leaves.

You probably mean the complexity is on the branches, not leaves. However, it is important to emphasize that each particular branch must be complex by itself, because otherwise no complexity would be perceived (by "frogs").

Or what do you mean by 'Simple Bohmian condition'?

I said that I will turn YOUR argument on MWI into my argument on BM. So you must first say what do YOU mean by "The root of a tree is very simple". I have some idea what does it mean, but the crucial point of my challenge to you is that I base my arguments on YOUR arguments. In other words, I want to beat you by your own weapon. Otherwise, my arguments will not be sufficiently convincing to you. (This is like the famous case when Bohr beat Einstein by using argument based on General Relativity. Later it turned out that this Bohr's argument was not valid, but at that time it served the purpose to convince Einstein.)

In BM information is conserved (if we include hidden variables), so it was the same at BB.

In MWI information is also conserved (if we include the whole wave function), so it was the same at BB. [That's what I call beating you by your own weapon.]

On the contrary, in MWI the final state is not pre-coded.

Yes it is (if, as I said, we include the whole wave function - the bird view).

 

[Demystifier]

What if these infinitely many values at the BB are defined by very simple equation we don't know yet?

What if Bohmian initial values at the BB are also defined by very simple equation we don't know yet?
[I continue with beating you by your own weapon, including your typos.]

 

[Fredrik]

What was your opinion about Max Tegmark's MUH before and after your trip to the MWI world?

I have always liked that suggestion. What has changed is just that I previously didn't think it was possible to interpret this particular mathematical structure (Hilbert space) as a description of a physical system that we're a part of. Now I think it's possible.

I mean, if there is nothing else except the evolution of omnium, and that evolution is deterministically defined by 1 or more equations, what is Universe but a solution to these equations?

It's too soon to say. I mean, we're still not even able to explicitly construct a Hilbert space and operators on it for the standard model, and it's possible that QM needs to be modified to be fully compatible with gravity.

 

[Hurkyl]

OK, that's a statement I haven't heard before. How does the C*-algebra formulation deal with subsystems, and how is it relevant?

If we start with the algebra of all observables that can be "observed" in the entire universe, then we can (in principle) write down the subalgebra of those observables that relate to the subsystem of interest.

e.g. interested in spin? Then we can look at the algebra generated by the spin observables. Other experiments? Maybe we should restrict to just those observables localized to the laboratory.

Since a state is a function, it automatically restricts to a function on the subalgebra (and the restriction remains a state).

In other words, a state is a function that maps observables to complex numbers... and when looking at a subsystem, the restricted state is just the same map (but with the restricted domain) from observables to complex numbers.

The point I was trying to make (I think) was that dealing with subsystems doesn't require invoking Born's rule or trying to make any sort of statement about (seemingly arbitrary) factorizations of a Hilbert space.

 

[Fredrik]

If we start with the algebra of all observables that can be "observed" in the entire universe, then we can (in principle) write down the subalgebra of those observables that relate to the subsystem of interest.

e.g. interested in spin? Then we can look at the algebra generated by the spin observables.

And for each such subalgebra, the GNS construction gives us a representation of observables as bounded operators on a Hilbert space, right? What's the relationship between these Hilbert spaces and the Hilbert space that corresponds to the huge C*-algebra we started with? Is the latter a tensor product of the former?

 

[Fra]

If we start with the algebra of all observables that can be "observed" in the entire universe, then we can (in principle) write down the subalgebra of those observables that relate to the subsystem of interest.

I do not question the connection between algebras defined by operators, and the corresponding sets/structure space.

The question is, wether there is any physical leap here, but making use on an "in principle" argument, that as far as I see it, can never be physicall realized, and is not a plausible premise to me.

I know many people refer to this GNS reconstruction and seem to somehow feel better there, but I do not find this more plausible, than just accepting other axioms. It mainly suggest a connection between operations and representations. But they both come together IMO.

/Fredrik

 

[Hurkyl]

The question is, wether there is any physical leap here, but making use on an "in principle" argument, that as far as I see it, can never be physicall realized, and is not a plausible premise to me.

I confess that I'm not aware of any way in which this differs from dealing with subsystems in any other physical theory. Would you elaborate?

 

[Hurkyl]

And for each such subalgebra, the GNS construction gives us a representation of observables as bounded operators on a Hilbert space, right? What's the relationship between these Hilbert spaces and the Hilbert space that corresponds to the huge C*-algebra we started with? Is the latter a tensor product of the former?

Don't forget GNS takes a state as input too! Your question seems a little off -- but since I only have a shallow understanding of the subject, I don't have a good guess what the right question to ask is.

So two notes:
. Every representation of the big algebra is automatically a representation of the subalgebra.
. (Once I'm sure what we're asking) I imagine the tensor product factorization is somewhat unlikely... but I expect there is no essential difference whether or not a factorization exists, so it's useful to look at the algebraically simpler case.

 

[Fra]

The question is, wether there is any physical leap here, but making use on an "in principle" argument, that as far as I see it, can never be physicall realized, and is not a plausible premise to me.

I confess that I'm not aware of any way in which this differs from dealing with subsystems in any other physical theory. Would you elaborate?

If we are talking about existing mature "theories", then I think you have a point.

But since my opinon as expressed earlier in this thread, is that to me these interpretational questions are justified only to the extent that they make a difference to extending the theory. Also your argument isn't a theory IMO, it's more a supposed possible plausible argument for motivating parts of it, and I just think it isn't that plausible after all.

So my opinion, implies that I think that QM needs revision. Not because it doesn't make sense for most of particle and atomic physics, but becaues we still have several issues, including gravity, that is not on par with this framework, and because there are IMHO clearly identifiable highly questionable assumptions in it's construction or axiomatisation.

What I mean specifically in the comment above is that I think a real observer, can not in a way that makes sense to me at least never simultaneously relate to all possible observables in the universe. This means that a justified argument, instead should acknowledge this and see how this changes the inference.

I think the result would be that the notion of a large state space of the universe, or a large set of possible measurements, from which one can shave out the observables and measurements state space seen by any subsystem is making the mistake byt not acknowledging where THIS very inference lives. As I see it, this inference must be executed by a third real observer. And in general an observer is bounded.

The implications of this, would then suggest a new direction to be explore. Namely one where the QM framework with hilber spaces and operators, rather is a result of evolution, but not in the decoherence sense, but in a more intrinsic sense where there is no outside description of it. It would be an evolving law.

What I HOPE to eventually understand, but which isn't yet developed, is why the specific representations and structures of operators incl commutators in QM is the way is is, from a fitness perspective. I've always had as a for me plasible working hypothesis that QM logic is a result of a kind of data compression. Where the information state space (hilbert state space) can be understood as the state space of an encoded observations, that is preferred since it provides a more memory/cost effective basis for actions.

/Fredrik

 

[Fredrik]

Your question seems a little off

You're right. It's a little off, because your example earlier shows that subalgebras in the algebraic formulation do not in general correspond to subsystems in the Hilbert space formulation. I don't know what I should be asking instead, so I'll just say that nothing that I know of gives me any reason to think that the problems I've been talking about can be avoided by using the algebraic approach to QM. We're going to need the Born rule or something equivalent to it, no matter what approach we're using, and its main purpose (in the MWI) is to define ways to decompose the "omnium" into subsystems.

Each decomposition defines a specific way to describe the unitary time evolution of the state vector of the universe in terms of correlations between subsystems. (This is a lot like how each inertial frame in SR gives us a specific way to describe what's going on in the universe).

 

[helenk]

You guys might be interested in some info on the many minds approach (essentially MWI) here:

http://thestargarden.co.uk/The%20Everett%20Approach.html"
http://thestargarden.co.uk/What%20happens%20when%20the%20world%20splits.html"
http://thestargarden.co.uk/What%20are%20probabilities.html"
http://thestargarden.co.uk/Lockwood%20and%20utilitarianism.html"
http://thestargarden.co.uk/Proving%20parallel%20worlds%20exist.html"
http://thestargarden.co.uk/Quantum%20mechanics%20and%20biology.html"
http://thestargarden.co.uk/The%20anthropic%20principle.html"
http://thestargarden.co.uk/Freewill.html"