Copenhagen interpretation of Big Bang

[atrchi]

How old was the universe when the first wave function collapsed?

Just wondering. I've checked all the FAQs on this, and the one hit in Google doesn't really cover it from a cosmological angle. I see there is a "Participatory Anthropic Principle" but my question is really more about, well, how long after the Big Bang we think this happened -- anthropic implications aside.

Thanks!

 

[marcus]

Copenhagen isn't good for Cosmology because no outside classical observer. So a longstanding problem has been how to generalize QM so you can deal with cosmos as a whole (not just a limited region).

The bestknown people to work on this problem (in recent years) have been James Hartle and Murray Gel-Mann. You can look up their papers on arxiv. The ones they have written together, and the ones Hartle has written by himself.

There was a Solvay Conference in around 2006 where Hartle was invited to give a talk about this. The Conference was on the topic of "the quantum structure of space and time". I will see if I can find the paper.

http://arxiv.org/abs/gr-qc/0602013
Generalizing Quantum Mechanics for Quantum Spacetime
James B. Hartle (University of California, Santa Barbara)
(Submitted on 2 Feb 2006)
Familiar textbook quantum mechanics assumes a fixed background spacetime to define states on spacelike surfaces and their unitary evolution between them. Quantum theory has changed as our conceptions of space and time have evolved. But quantum mechanics needs to be generalized further for quantum gravity where spacetime geometry is fluctuating and without definite value. This paper reviews a fully four-dimensional, sum-over-histories, generalized quantum mechanics of cosmological spacetime geometry. This generalization is constructed within the framework of generalized quantum theory. This is a minimal set of principles for quantum theory abstracted from the modern quantum mechanics of closed systems, most generally the universe. In this generalization, states of fields on spacelike surfaces and their unitary evolution are emergent properties appropriate when spacetime geometry behaves approximately classically. The principles of generalized quantum theory allow for the further generalization that would be necessary were spacetime not fundamental. Emergent spacetime phenomena are discussed in general and illustrated with the example of the classical spacetime geometries with large spacelike surfaces that emerge from the `no-boundary' wave function of the universe. These must be Lorentzian with one, and only one, time direction. The essay concludes by raising the question of whether quantum mechanics itself is emergent.
31 pages, 4 figures, contribution to the 23rd Solvay Conference, The Quantum Structure of Space and Time

You cannot solve this problem by working within a fixed space with a fixed geometry. The geometry must be quantum and it must interact dynamically with the quantum matter that lives in it. And there is no OUTSIDE, where an observer can see a wave function collapse. Everything in the model is quantum and contained in the universe which could, for example, be contracting, condensing, rebounding and reexpanding.

This is a hard problem and I think it is not yet satisfactorily solved. If someone tells you it is solved and gives you some quick answers, I would be skeptical. Hartle knows his business and at times has sounded confident, but I don't think as of today he would claim to have a satisfactory final solution to a version of QM appropriate for Cosmology.

 

[RUTA]

What does it mean to say "spacetime geometry is fluctuating?" You need an additional temporal dimension to make sense of this statement in any conventional sense. Is Hartle proposing the addition of meta-time? And what possible scientific consequence obtains from the computation of probabilities associated with a phenomenon that is only observed once (as is the case with the universe)?

 

[marcus]

What does it mean to say "spacetime geometry is fluctuating?"

The words have no meaning out of context. Perhaps he should have said "indefinite". Let's not grab a phrase out of the brief summary of his talk, but rather try to figure out what he meant by looking at the context and, if possible, reading the article!

http://arxiv.org/abs/gr-qc/0602013
Generalizing Quantum Mechanics for Quantum Spacetime
James B. Hartle (University of California, Santa Barbara)
(Submitted on 2 Feb 2006)
Familiar textbook quantum mechanics assumes a fixed background spacetime to define states on spacelike surfaces and their unitary evolution between them. Quantum theory has changed as our conceptions of space and time have evolved. But quantum mechanics needs to be generalized further for quantum gravity where spacetime geometry is fluctuating and without definite value.

He certainly does not introduce a "meta-time" in which the geometry oscillates, as you might be imagining!
He is basically just talking about the usual quantum uncertainty, applied to spacetime geometry.

A spacetime geometry history is intuitively like the trajectory of a particle. One cannot say with certainty which "slit" of shape it went thru. I guess that's what he means. That's the sense I get from his abstract.

 

[RUTA]

He certainly does not introduce a "meta-time" in which the geometry oscillates, as you might be imagining!
He is basically just talking about the usual quantum uncertainty, applied to spacetime geometry.

A spacetime geometry history is intuitively like the trajectory of a particle. One cannot say with certainty which "slit" of shape it went thru. I guess that's what he means. That's the sense I get from his abstract.

Thanks, marcus, I'm on the road and have a migraine, so I was hoping for clarification without having to wait until I could read the article myself. Your notion that spacetime can have a "history" introduces the notion of "meta-time." Every experiment ever done and that will ever be done resides in one spacetime. Talk of the "history" of that single spacetime is therefore empirically meaningless. Where am I mistaken?

 

[marcus]

Hi RUTA, on the road with a migraine is not the time to get into the realm of discourse of Hartle (and Murray Gell-Mann) "consistent histories" or "decoherent histories" approach to 4d geometry of universe.

I hope you do read the paper when you get home and have time. I'd like to hear your thoughts about it.

they have a generalized QM that does not require a classical outside observer making measurements. I don't think my trying to explain will save you any time and could cause you confusion or make you LESS interested in going to the original papers.

You know way more about this subject than I do so it may be absurd for me to start trying to explain, but the basic idea is you have a set of micro-histories (which could be represented in various ways) and you have PARTITIONS of that set. And you specify some way (a "decoherence functional") to determine that some partition is sufficiently independent that ordinary additive probabilities can be assigned to the sets in the partition (the "macro-histories").

And what defines a partition are things you care about, or want to make bets on, like whether your plane will crash, or the bridge fall down,whichyou want to be reasonably sure t won't. Or a certain cat dies. Or doesn't.

they manage to set up a generalized QM which can be EQUIVALENT to ordinary QM in certain circumstances but which really is more general and does not require an observer and a division between the quantum system in the box and the observer outside the box.
It's a different mathematical machinery. I don't think it even requires a Hilbert space.

It may also not require a differential manifold. But it can be specialized so as to recover Copenhagen QM, as needed. It requires EVENTS that we can make bets about, whether or not they occurred or will occur. These events are what help to make the partition, and define the (macro?) histories.

It's been a while since I was reading the Hartle and Gell-Mann papers and I may have already said several inaccurate things that could get you on the wrong track. So I advise reading Hartle's 23rd Solvay Conference paper about it when you are rested---it is very "wide audience" written for non-specialists, in style because all kinds of people come to these Solvay Conferences. And that was 2006, so there are various other followup papers primarily by Hartle that one can look at.

Folks should not get this confused with "no boundary" papers by Hartle and Hawking. Those are about something different from his "generalized quantum mechanics" and his consistent/decoherent "histories" approach to quantum cosmology.

 

[twofish-quant]

Quantum gravity is terribly, terribly interesting and important as far as interpretations of quantum mechanics. The situation seems to be that for any "table top" experiment, they all lead to the same result so that you can just pick one at random. This doesn't work for the big bang.

 

[RUTA]

I read the 06 arXiv paper above. You were right, it's simply a poor choice of wording on their part, they don't have "meta-time," i.e., there is no time-evolved state vector in their configuration space, and they marry up their approach cleanly with the 3+1 view of QM. However, they do have a configuration space of cosmological spacetimes, which strikes me as empirically meaningless, since we only have one trial for that experiment. We use a similar (but discrete) path integral approach with spacetime blocks that are subsets of our single (cosmological) spacetime to render the approach empirically meaningful. In accord with twofish's statement, our approach was motivated by our interpretation of QM. Ok, enough with the digression. So, marcus, do I understand correctly that they use a configuration space of cosmological spacetimes?

 

[bcrowell]

IMO this is a non-issue. The Copenhagen interpretation isn't a theory, isn't the only interpretation of QM, and doesn't make predictions that would allow it to be distinguished from other interpretations of QM such as the many-worlds interpretation. You don't have to get into quantum gravity to find situations in which it's impossible to take the CI seriously. For example, there is a continuum of levels of consciousness from, say, Niels Bohr as a zygote to Niels Bohr as an adult. It obviously doesn't make sense to imagine that at some point along that continuum, he started collapsing wavefunctions. The CI is a description of the psychological experience of making measurements; it is not anything fundamental about physics.