Quantum Determinism: Exploring the Black Hole Information Paradox

[secur]

My question is about so-called "Quantum Determinism". Consider two quotes from the Wikipedia article on "Black Hole Information Paradox":

"A fundamental postulate of quantum mechanics is that complete information about a system is encoded in its wave function up to when the wave function collapses." (my italics)

"Quantum determinism means that given a present wave function, its future changes are uniquely determined by the evolution operator."

Obviously the second quote should finish with "... until the wave function collapses due to measurement or some other process."

It almost appears that Stephen Hawking - and others who work on this "paradox" - is assuming something like MWI, where the "collapse doesn't happen"; simply forgetting that of course it does happen in the real world. And when it does, information (about the eigenstates not instantiated) is lost forever.

Please clear up my apparent misunderstanding.

 

[AlexCaledin]

Getting my nose into some Stapp's and Hartle's writings, I got some idea about these two fundamentally different processes:

1 - "automatic" deterministic calculation of potentiality (of what may be observed/measured) - that's what the wavefunction evolution performs; it does generate (Gell-Mann and Hartle explained how it works) those "many worlds", but they are only potentialities, not reality;

2 - actual observation / measurement; every observation discards some part of that pre-calculated potentiality, thus providing what appears to us as "collapse".

So the seeming contradictions come from confusing those two processes.

Dr. Henry P. Stapp says it's actually Heisenberg who came to that worldview if I got it right.

 

[A. Neumaier]

Obviously the second quote should finish with "... until the wave function collapses due to measurement or some other process."

Quantum gravity is always about spacetime as a whole, i.e., the whole universe.
The state of the whole universe never collapses, since there is no outside observer. Collapse only happens in open systems, when there is some measurement apparatus outside the system to which it is coupled.

 

[secur]

The state of the whole universe never collapses, since there is no outside observer.

It hasn't been established that an observer is required to collapse the wave. If so we have to assume the universe's state was indeterminate until conscious observers came along - and so on; you've heard all this before. It's likely that it happens without observers - look how very hard it is to prevent spontaneous collapse in a qubit. At the least, we can't simply assume that the chaotic conditions around a black hole (for instance) don't cause wavefunctions to constantly collapse.

Also, you're considering only the Black Hole Information Paradox and similar (admittedly, I did stress that in OP). But "Quantum Determinism" applies not only to the universe as a whole but locally also. Consider this recent paper from Lev Vaidman "Quantum Theory and Determinism" http://arxiv.org/abs/1405.4222:

"Historically, appearance of the quantum theory led to a prevailing view that Nature is indeterministic. The arguments for the indeterminism and proposals for indeterministic and deterministic approaches are reviewed. These include collapse theories, Bohmian Mechanics and the many-worlds interpretation. It is argued that ontic interpretations of the quantum wave function provide simpler and clearer physical explanation and that the many-worlds interpretation is the most attractive since it provides a deterministic and local theory for our physical Universe explaining the illusion of randomness and nonlocality in the world we experience." (my italics)

He's calling the collapse an "illusion" in all quantum experiments - in the lab as well as the universe. I could quote from Deutsch and Carroll as well.

1 - "automatic" deterministic calculation of potentiality (of what may be observed/measured) - that's what the wavefunction evolution performs; it does generate those "many worlds", but they are only potentialities, not reality;

2 - actual observation / measurement; every observation discards some part of that pre-calculated potentiality, thus providing what appears to us as "collapse".

Apart from one thing, you've summarized the situation well. There's Schroedinger's eqn (and Dirac's, etc - not to mention matrix mechanics) which describes the unitary evolution prior to collapse, with all its potentialities. Then the collapse "discards some part of that pre-calculated potentiality" - i.e. information is irretrievably lost, indeterministically. Fine.

But the only thing a bit off is your words "what appears to us as" ... collapse. Who else would it appear to? All experimental results, systems, scholarly papers - everything to do with science - appears to us to be, well, as it appears. And of course we go with those appearances, we have no choice. So yes, the collapse appears to be a collapse. And, therefore - it IS a collapse - if results are results, apparati are apparati, and papers can be taken to be papers.

So the seeming contradictions come from confusing those two processes.

You're asserting that all these famous scientists - including Hawking himself - are confusing these two processes? Well I agree it seems to be the case; but surely they couldn't make such an elementary mistake in logic. I do admire your courage, but can't accept that explanation; these are people with very high IQ's.

So the question remains, why do "quantum determinists" seem to pretend the collapse is an illusion of some sort? Obviously they can't really believe it, so I'm missing something here.

 

[A. Neumaier]

It hasn't been established that an observer is required to collapse the wave.

An external measuring apparatus is necessary and sufficient for the collapse
- this constitutes the observer. Consciousness is not involved at all.

He's calling the collapse an "illusion" in all quantum experiments - in the lab as well as the universe.

In this case he is mistaken, no matter what you quote. Open quantum systems must behave non-unitarily because of their interaction with the lab. Quantum jumps are observable. See, e.g., https://www.physicsforums.com/posts/5393675

 

[secur]

An external measuring apparatus is necessary and sufficient for the collapse - this constitutes the observer. Consciousness is not involved at all.

Clearly the equivalent of an "external measuring apparatus" without conscious observer could be present around BHs, and throughout the universe, implemented by some natural process.

He [Vaidman]'s calling the collapse an "illusion" in all quantum experiments - in the lab as well as the universe.

In this case he is mistaken, no matter what you quote

That's what I was afraid of - they're all bonkers.

 

[A. Neumaier]

could be present around BHs, and throughout the universe, implemented by some natural process.

Yes, but they must be part of the environment of the measured system, hence the system is open and there is collapse.

 

[secur]

Probably, they just wisely avoid mentioning them, because such things belong to controversial implications.

Perhaps they wisely avoid mentioning them, because they don't want to wind up in Bedlam? If that institution is still in business?

It's hard to accept they're simply wrong, but we all seem to agree ... still, let's wait and see if someone else can help avoid this unsavory conclusion.

Yes, but they [measuring apparati] must be part of the environment of the measured system, hence the system is open and there is collapse.

- Ok.

 

[A. Neumaier]

why do "quantum indeterminists" seem to pretend the collapse is an illusion of some sort?

Because they only think of closed systems. Closed systems are unobservable from the outside, hence have no collapse. If you treat the black hole as being alone in the world, it is a closed system.

 

[secur]

... they only think of closed systems. Closed systems are unobservable from the outside, hence have no collapse. If you treat the black hole as being alone in the world, it is a closed system.

To the extent they confine themselves to indubitably closed systems, I have no problem with their methods and conclusions (as far as I understand them). I've mentioned elsewhere that MWI is a good way to approach certain problems, and here I'd say you've put your finger on that class of problems.

Still I strongly suspect Quantum Determinists also apply their approach to open systems, as shown by Vaidman's quote above (and many others I could give). But in those cases the correct analytic approach leads to an objective, reduced dynamics in terms of a piecewise deterministic process (with unitary dynamics interspersed by quantum jumps at random times) when a discrete variable is observed, or in terms of a quantum diffusion process if instead a continuous quantity (such as a quadrature) is monitored. Averaged over many subsystems, these stochastic processes lead to a deterministic dynamics for the density operator, given by a Lindblad equation ---- to quote a physicist who makes a lot of sense.

I understand you're not interested in the question whether they (Vaidman et al) treat such open systems correctly, or not, so I thank you for your time.

My hope is that someone who does support the full panoply of Quantum Determinism, applied to open systems in particular, will show up, and explain how that's justified. It's hard to believe people would hassle with Lindblad-type equations and stochastic processes when the much easier route - assuming unitary evolution throughout - is available.

 

[eloheim]

So the question remains, why do "quantum indeterminists" seem to pretend the collapse is an illusion of some sort?

I think you have this part backwards. It would be the determinists who see collapse as an illusion.

Also I've been thinking about this exact question with the B.H. information paradox lately too. I think the answer is that they're inquiring in a theoretical sense about a theory-related question which could still shed light on real-world situations.

I'm going to look back at some papers I read about the b.h. info paradox and see if anything jumps out at me though.

 

[eloheim]

Here's how Matt Strassler describes the situation in the beginning of his blog post on the paradox in question:

"Quantum Theory (sometimes called “Quantum Mechanics”) is the mathematics that is currently believed to underlie all physical processes in nature. It can’t be used to predict precisely what will happen, but only the probability for any particular thing to happen. But probabilities only make sense if, when you add up all the probabilities for all of the different things that can possibly happen, you find the sum is equal to one. A quantum theory where this isn’t true makes no sense. One consequence of this is that in a quantum theory, information is never truly lost, nor is it truly copied; at least in principle, you can always determine how a system started (its “initial state”) from complete information about how it ends (its “final state”)."

Found here: http://profmattstrassler.com/articl...ack-hole-information-paradox-an-introduction/

 

[secur]

I think you have this part backwards. It would be the determinists who see collapse as an illusion.

- Right, thanks, I corrected my mistake above.

Matt Strassler: Quantum Theory is the mathematics that is currently believed to underlie all physical processes in nature. It can’t be used to predict precisely what will happen, but only the probability for any particular thing to happen. But probabilities only make sense if, when you add up all the probabilities for all of the different things that can possibly happen, you find the sum is equal to one.

Right. Before the collapse we have a number of possible eigenstates whose probabilities add up to 1. After, we have one eigenstate, with probability 1. (Ignoring some details - the new state could still be a subspace with multiple eigenstates).

Matt Strassler: One consequence of this is that in a quantum theory, information is never truly lost, ...

Wrong. When the "collapse operator" projects onto the Hilbert subspace, of course all the eigenstates which weren't instantiated are lost, together with their information. Nevertheless the probability afterwards is still 1. He seems to be supposing that if the selected eigenstate's probability before was (let's say) 1/6, it still is after! But no, the collapse made its probability 1.

Consider rolling a die. Prior to the roll, chance of "2" is 1/6. After the roll, it's either 0 or 1. Same thing with eigenstates.

Matt Strassler: ... at least in principle, you can always determine how a system started (its “initial state”) from complete information about how it ends (its “final state”).

- Assertion is not proof.

Matt Strassler: See Figure 1, which shows two particles colliding, and several particles exiting from the collision, carrying off, in scrambled form, the information about the nature and properties of the two initial particles. ... (Fig. 1) In any type of quantum theory, information that goes in must come back out, scrambled but complete.

He's now asserted that "information is not lost" three times. According to the Bellman ("Hunting of the Snark") that makes it true - but Lewis Carroll, for all his intelligence, was no scientist.

Fig 1 shows a single scattering event, which is governed by an S-Matrix. S-matrices are always time-reversible (unitary, invertible) - at least, all the ones I've dealt with. They connect the initial state, coming from -infinity, to the final states at +infinity. So if you stop there, information is not lost. Similar to Heisenberg matrix mechanics, an S-matrix represents the unitary evolution of the system - without the collapse.

Usually we're dealing with many scattering events. More-or-less all final states are populated, so again you can invert the results. But that's not so for one scattering event, like that shown in Fig. 1.

With one scattering event you get one specific result in your detectors. For instance if you fire one alpha particle at a piece of gold foil, you will get one hit; usually it passes through, sometimes comes back at you, often deflects to the side. Suppose it deflects at 35 degrees (horizontal, let's say). Does Strassler suppose that's enough info to reconstruct the initial state? IF the alpha particle, and the gold nucleus, were perfectly-elastic billiard balls of exact known radius; all error bars were non-existent; you could calculate the positive electrostatic forces exactly; and knew exactly whence it was launched - in short, everything was perfect - then I suppose you could reverse the path. But none of that is the case. That one piece of info, 35 degrees, is NOT enough to time-reverse to the initial state - you can only, at best, make a poor guess. Your detector system caused the outgoing wave to collapse to just one result; all the other info, necessary to invert the S-matrix, was lost.

Strassler goes on, after his "Bellman" proof, to apply this unsubstantiated "Quantum Determinism" theorem to Black Hole Information Paradox.

At this point I'll leave him. As A. Neumaier said, we can suppose BH is a closed system; if so information isn't lost and the rest of Strassler's work may be valid. Even though he didn't even begin to prove no-info-lost, perhaps it happens to be true here.

I regret mentioning BH information paradox because really I'm concerned with open systems. To be frank I rather suspect a BH is an open system also but am not competent to defend that.

Bottom line: Strassler's "proof" of Quantum Determinism is totally inadequate. Admittedly this is just a popular discussion. I've looked for, and never found, any substantial proof, just this sort of hand-waving. By the way, although I'm not that good at QM, I'm an expert hand-waver. My thesis adviser was the world champion hand-waver 3 years in a row, so I've studied with the best. Matt Strassler is not in that class.

Thanks eloheim, if you have any better proof - rather, any proof - of Quantum Determinism please let's see it!