Bohm trajectories and protective measurements?

[bohm2]

Bohm trajectories and "protective" measurements?

I'm having trouble understanding the arguments presented in these papers. They seem to be both arguing against the de Broglie-Bohm theory bassed on the concept of "protective measurements". Is this just a rehash of the problems with the meaning of "weak measurements" described in previous threads and summarized in Demystifier's blog on that topic?

Accordingly, one has to concede either that the particle’s Bohm trajectory and its position are unrelated, or that the particle’s position is irrelevant for its participation in local interactions...Therefore we can hardly avoid the conclusion that the formally introduced Bohm trajectories are just mathematical constructs with no relation to the actual motion of the particle.

Protective measurements and Bohm trajectories
http://www.tau.ac.il/~yakir/yahp/yh26

One may also want to deprive the Ψ-field of mass and charge density to eliminate the electrostatic self-interaction. But, on the one hand, the theory will break its physical connection with quantum mechanics, as the wave function in quantum mechanics has mass and charge density according to our analysis, and on the other hand, since protective measurement can measure the mass and charge density for a single quantum system, the theory will be unable to explain the measurement results either. Although de Broglie-Bohm theory can still exist in this way as a mathematical tool for experimental predictions (somewhat like the orthodox interpretation it tries to replace), it obviously departs from the initial expectations of de Broglie and Bohm, and as we think, it already fails as a physical theory because of losing its explanation ability.

Meaning of the wave function
http://arxiv.org/ftp/arxiv/papers/1001/1001.5085.pdf

 

[Demystifier]

The conclusion of the first paper is a variant of the so-called surrealistic Bohmian trajectories. They conclude that "Either the particle’s Bohm trajectory and its position are unrelated, or the particle’s position is irrelevant for its participation in local interactions." But this is almost the same as saying that either Bohm's trajectories are not real or they interact with other particles non-locally. Indeed, it is well known and accepted that Bohm's particles have non-local influences on each other, and the present paper just rediscovers it.

However, this type of nonlocality is slightly softer than nonlocality needed for violation of Bell inequalities. Unlike violation of Bell inequalities, thys type of nonlocality CAN be explained in classical terms without superluminal velocities.

Essentially, this is like arguing in the following way: "Bohmians claim that president Obama is a local object moving only within America. However, there is experimental evidence that Obama's decisions leave trace in Iraq and Afganistan. Therefore, the experiments show that Obama is present in Iraq and Afganistan and hence Bohmians are wrong." I think I don't need to explain why this argument is incorrect. But I have to say that the argument in the first paper is incorrect for exactly the same reason.

Indeed, it is well known that Obama's decisions have a global impact and that, to understand THAT, it does not help much to think of Obama as a local object moving only within America. And yet, it is perfectly consistent, and even helpful to explain some OTHER phenomena, to think of Obama as a local object moving within America. The Bohmian particle trajectories are just like Obama - they are local and move under certain trajectories, but have some impacts far from their trajectories.

 

[Demystifier]

Another good and relatively neutral paper (by Lev Vaidman who is NOT a strong supporter of the Bohm interpretation) on this subject is this:
http://xxx.lanl.gov/abs/1207.0793

 

[bohm2]

This was a recent paper trying to combine aspects of Everett and Bohmian:

...here proposed theory describes the flow of a continuum of worlds through configuration space, with each world following a Bohmian trajectory

But I think this part discussing the empty branches in Bohm's and what it implies is inaccurate:

As the wavefunction is taken to describe a really existing field, all their branches really exist and will evolve forever by the Schrödinger dynamics, no matter how many of them will become empty in the course of the evolution. Every branch of the global wavefunction potentially describes a complete world which is, according to Bohm’s ontology, only a possible world that would be the actual world if only it were filled with particles, and which is in every feature identical to a corresponding world in Everett’s theory. Only one branch at a time is occupied by particles, thereby representing the actual world, while all other branches, though really existing as part of a really existing wavefunction, are empty and thus contain some sort of “zombie worlds” with planets, oceans, trees, cities, cars and people who talk like us and behave like us, but who do not actually exist. Now, if the Everettian theory may be accused of ontological extravagance, then Bohmian mechanics could be accused of ontological wastefulness. On top of the ontology of empty branches comes the additional ontology of particle positions that are, on account of the quantum equilibrium hypothesis, forever unknown to the observer.

Combining Bohm and Everett: Axiomatics for a Standalone Quantum Mechanics
http://lanl.arxiv.org/pdf/1208.5632.pdf

As T. Maudlin points out:

Since it is not supposed that cats are made of wavefunction, but rather that cats are made of particles, the obscurity of the physical nature of the wavefunction does not threaten the transparency of the lived world.

Remarks on flat-footed ontolgy
www.math.rutgers.edu/~tumulka/shellyfest/maudlin.ppt

Similar remarks were made in this paper by Peter J. Lewis:

Empty Waves in Bohmian Quantum Mechanics
http://philsci-archive.pitt.edu/2899/

 

[Demystifier]

Many-world people argue that decoherence provides dynamical branching of the wave function which is sufficient to explain the illusion of collapse, and that Bohmian trajectories (as entities the only role of which is to fill up one particular branch) are superfluous.

In a recent paper
http://arxiv.org/abs/1209.5196
I argue that Bohmian trajectories are more than that. I argue that they are needed even to explain the decoherence and branching itself. Namely, in a closed system (e.g., the whole Universe) in a state with definite total energy, the wave function governed by the Schrodinger equation does not depend on time at all. Without time dependence, there is no no change in the system, so there is no decoherence and no branching. One needs some additional time dependence not described by the Schrodinger equation. Bohmian formulation provides such a needed time dependence in a natural way in terms of conditional wave functions.

For a closed system in a state with definite total energy it is not impossible to explain the time dependence with the many-world interpretation, but this requires a redefinition of the concept of time itself. (See Appendix A of the paper above.) Bohmian formulation explains it more naturally than the many-world interpretation, without any redefinition of the concept of time.

 

[bohm2]

http://arxiv.org/abs/1209.5196
I argue that Bohmian trajectories are more than that. I argue that they are needed even to explain the decoherence and branching itself.

Thanks, Demystifier. I had already seen your paper and I'm looking forward to reading it. There was another previous paper taking a different, more critical argument of Bohmian trajectories. I'm still trying to understand it and haven't read it fully but I'm thinking you have already read it but just in case you haven't:
Are Bohmian trajectories real? On the dynamical mismatch between de Broglie-Bohm and classical dynamics in semiclassical systems
http://arxiv.org/pdf/quant-ph/0609172.pdf

 

[Demystifier]

There was another previous paper taking a different, more critical argument of Bohmian trajectories. I'm still trying to understand it and haven't read it fully but I'm thinking you have already read it but just in case you haven't:
Are Bohmian trajectories real? On the dynamical mismatch between de Broglie-Bohm and classical dynamics in semiclassical systems
http://arxiv.org/pdf/quant-ph/0609172.pdf

Semiclassical is not classical, so a mismatch is expected. I don't see a problem with it.

 

[Quantumental]

Demystifier:

Could you explain in a bit more layman terms what this parsimony with time dependence and why it's not as natural in MWI?
I've never heard anyone else mention any "time" problems for MWI, so this was intriguing.

 

[Demystifier]

Demystifier:

Could you explain in a bit more layman terms what this parsimony with time dependence and why it's not as natural in MWI?
I've never heard anyone else mention any "time" problems for MWI, so this was intriguing.

MWI says that there is nothing else except the wave function and that its evolution is always given by the Schrodinger equation. In this respect MWI is unique, because all other interpretations say that either there is something else except the wave function, or that the wave function does not always evolve according to the Schrodinger equation. I guess you already know that.

Now consider the total wave function for the whole Universe. It is reasonable to expect that the total energy of the whole Universe has some definite value E. But then it is a simple consequence of the Schrodinger equation that the wave function does not depend on time. On the other hand, we see that the Universe does depend on time. This is not a problem for other interpretations, because either there is something else which depends on time, or the wave function itself depends on time because it does not really evolve according to the Schrodinger equation. But it is a problem for MWI, because MWI rejects both possibilities.

I hope it is layman enough.

 

[Quantumental]

Ok, makes sense, but isn't this then a well-known "problem" ?
What would be a MWI'ers response?

 

[kith]

On the other hand, we see that the Universe does depend on time.

How do we see this? The state of the universe can't be observed by an observer who is part of the universe.

 

[Demystifier]

Ok, makes sense, but isn't this then a well-known "problem" ?
What would be a MWI'ers response?

This problem is known, but perhaps not sufficiently well. I suspect that most MWI'ers would not know how to respond. Nevertheless, those who do know will say the following: The time independent wave function psi(x1,...,xn) depends, among other things, on positions which represent readings of clocks. So even if wave function does not depend on the evolution time t, it does depend on the clock time. In other words, there is no time without a clock. Of course, not everybody is satisfied with it, but this seems to be the best what can be done within MWI.

 

[Demystifier]

How do we see this? The state of the universe can't be observed by an observer who is part of the universe.

We certainly see that a part of the Universe depends on time, which is sufficient to conclude that Universe as a whole depends on time as well. I don't see how a part of the Universe could depend on time if the whole Universe did not depend on time.

 

[kith]

I don't see how a part of the Universe could depend on time if the whole Universe did not depend on time.

It just isn't immediately clear to my, why it can't depend on time.

Lets say the universe is in an eigenstate of the full Hamiltonian H = H_observer + H_{everything else} + H_interaction. Now we know for the full state that ∂_tρ = 0. Why does this imply that already ∂_t(tr_observer{ρ}) = 0? Maybe I'm overlooking something really obvious here. ;-)

 

[kith]

I got it. Tracing and differentiating commute. D'oh ;-)

 

[Quantumental]

This problem is known, but perhaps not sufficiently well. I suspect that most MWI'ers would not know how to respond. Nevertheless, those who do know will say the following: The time independent wave function psi(x1,...,xn) depends, among other things, on positions which represent readings of clocks. So even if wave function does not depend on the evolution time t, it does depend on the clock time. In other words, there is no time without a clock. Of course, not everybody is satisfied with it, but this seems to be the best what can be done within MWI.

Could you expand a little? I feel like I have missed a very important point in the fundamentals debate.
Is this tied to the preferred basis ( position basis ) ? Is this how they "get away" with the issue?

Is there any litterature on this? I can not recall ever hearing this objection raised or adressed by either proponents or opponents of MWI

 

[Demystifier]

Is there any litterature on this? I can not recall ever hearing this objection raised or adressed by either proponents or opponents of MWI

See the references in the paper, especially 13, 16, and 17. The most explicit referring to MWI is in Ref. 17, Sec. 6.2.3.

 

[Quantumental]

Ok that became quite complicated quick. But I noticed all the papers were from the early 90s.
Are you sure this issue hasn't been dealt with in tmore modern times? E.G. Wallace's FAPP etc?

 

[Demystifier]

Ok that became quite complicated quick. But I noticed all the papers were from the early 90s.
Are you sure this issue hasn't been dealt with in tmore modern times? E.G. Wallace's FAPP etc?

As far as I know, there was no much progress since then.

Note also that most people who use MWI don't say it explicitly. They just use Schrodinger equation to describe everything they talk about, but they rarely mention the existence of "many worlds".

Similarly, people who use textbook QM, rarely mention the fact that they use "Copenhagen" interpretation. Instead, they simply and carelessly talk about collapse, observers, and classical macro world, as if the meaning of these terms is self-evident.

 

[Quantumental]

As far as I know, there was no much progress since then.

Note also that most people who use MWI don't say it explicitly. They just use Schrodinger equation to describe everything they talk about, but they rarely mention the existence of "many worlds".

Yes, I am aware of this, but what about those that really do?
The people who has done the most work on MWI claim it's almost inevitably true; Deutsch, Wallace, Zeh, Joos, Tegmark etc.
I can't find anything about this in any of their papers.

 

[unusualname]

Of course the problem only exists if we are sure the Hamiltonian of the Universe is zero. The zeroness relies on General Relativity being completely correct in its application to Cosmological models. But General relativity will almost certainly be replaced by a more correct theory when Quantum Gravity is solved. So, in fact, we can't really be sure that the Hamiltonian is zero. Thus we can still believe that nontrivial Schrodinger Evolution of the Universe State Vector is possible.

 

[kith]

The fact that eigenstates of the Hamiltonian are stationary is true for all time-independent Hamiltonians. But I don't know much about GR.

I think it is an interesting fact if we apply it to the whole universe. But I'm not sure if there's more to it than the "why are the initial conditions of the universe the way they are?"-question. If we get no time evolution in an eigenstate universum, well, then we don't live in one. Assuming a superposition state makes the problem vanish.

 

[Lord Crc]

Now consider the total wave function for the whole Universe. It is reasonable to expect that the total energy of the whole Universe has some definite value E.

I'm another layman so this may be silly, but is it really reasonable to expect the total energy to have a definite value? Or even the total energy in a region? I thought energy in GR was a tricky subject.

 

[Demystifier]

Yes, I am aware of this, but what about those that really do?
The people who has done the most work on MWI claim it's almost inevitably true; Deutsch, Wallace, Zeh, Joos, Tegmark etc.
I can't find anything about this in any of their papers.

Among those guys, I think Zeh is the only one who was writing about time for systems with a definite total energy. More precisely, he was writing about time in quantum gravity, e.g., in his book "The Physical Basis of the Direction of Time".

 

[Demystifier]

Of course the problem only exists if we are sure the Hamiltonian of the Universe is zero.

Not only then. The problem also exists if the energy of the Universe is not zero, but has some definite value E. It is briefly explained in the Introduction of the paper.

 

[Demystifier]

I'm another layman so this may be silly, but is it really reasonable to expect the total energy to have a definite value? Or even the total energy in a region? I thought energy in GR was a tricky subject.

Energy of MATTER ALONE is tricky in GR. But total energy-density in GR of matter and gravity together is not tricky at all. It is exactly zero.

 

[Quantumental]

Among those guys, I think Zeh is the only one who was writing about time for systems with a definite total energy. More precisely, he was writing about time in quantum gravity, e.g., in his book "The Physical Basis of the Direction of Time".

Yes, Zeh has written a whole bunch of papers on time:
http://www.rzuser.uni-heidelberg.de/~as3/page2/page2.html

But he is also as certain as they come that decoherence = many worlds inevitable.

 

[unusualname]

Not only then. The problem also exists if the energy of the Universe is not zero, but has some definite value E. It is briefly explained in the Introduction of the paper.

Sorry I deleted an incorrect comment, what I meant to say was that it does not matter that the probability distribution GLOBALLY is invariant in time, in fact this would be expected otherwise the entire universe might flip into some unnatural state every 10^-43 secs.

You only see this as a problem because you don't believe in fundamental probability, so you see a stationary (global) probability distribution as not allowing the natural local type of evolution we observe. And I agree with you that MWI has to make a ridiculous argument to allow this. But if you have fundamental probability, then it is no problem, local observations are "evolving" exactly as QM and the Schroedinger Equation predicts.

 

[unusualname]

edit, to be more precise, it does not matter that |Psi|^2 is invariant in time (globally)

 

[bohm2]

Ok that became quite complicated quick. But I noticed all the papers were from the early 90s.
Are you sure this issue hasn't been dealt with in tmore modern times? E.G. Wallace's FAPP etc?

Doesn't Julian Barbour treat time in the manner discussed in those papers:

The Nature of time
http://www.fqxi.org/data/essay-contest-files/Barbour_The_Nature_of_Time.pdf

I'm basing this on the following quote in Wallace's et al. book:

Another problem is the nature of time. In 1983 Don Page and Bill Wootters discovered that times are Everett universes. They were addressing, again, an apparently unrelated theoretical problem, namely: since the total energy is conserved, how can we tell that the world isn’t in an eigenstate of it? They discovered that we can’t tell; we can assume without loss of generality that the world is in an eigenstate of its Hamiltonian: a stationary state. But then, what’s all this motion that we see? By analysing closed physical systems that included clocks, they showed that motion is an entanglement effect: clock states are correlated with states of other systems. This important result should be the basis of everyone’s conception of time. Yet it has barely, and rarely, been taken on board. (Julian Barbour [1999] is an honourable exception, as is Andreas Albrecht’s talk at this conference.)

Many Worlds? Everett, Quantum Theory, and Reality
http://bacon.umcs.lublin.pl/~lukasik/wp-content/uploads/2010/12/Many.Worlds.EverettQuantum.Theory.and.Reality.pdf

 

[lugita15]

Now consider the total wave function for the whole Universe. It is reasonable to expect that the total energy of the whole Universe has some definite value E. But then it is a simple consequence of the Schrodinger equation that the wave function does not depend on time. On the other hand, we see that the Universe does depend on time. This is not a problem for other interpretations, because either there is something else which depends on time, or the wave function itself depends on time because it does not really evolve according to the Schrodinger equation. But it is a problem for MWI, because MWI rejects both possibilities.

Why isn't the conclusion simply that the "reasonable" expectation is wrong?

 

[lugita15]

Nevertheless, those who do know will say the following: The time independent wave function psi(x1,...,xn) depends, among other things, on positions which represent readings of clocks. So even if wave function does not depend on the evolution time t, it does depend on the clock time. In other words, there is no time without a clock. Of course, not everybody is satisfied with it, but this seems to be the best what can be done within MWI.

Could you elaborate on this? You can have the wave function depend on the position of a clock pointer, but then you're just pushing the question one step back: why does the pointer state of a clock ever change?

 

[Lord Crc]

Energy of MATTER ALONE is tricky in GR. But total energy-density in GR of matter and gravity together is not tricky at all. It is exactly zero.

Ah ok, thanks for clearing that up :)

 

[Demystifier]

Why isn't the conclusion simply that the "reasonable" expectation is wrong?

It is explained in the Introduction of the paper. See also post #30.

 

[Demystifier]

Could you elaborate on this? You can have the wave function depend on the position of a clock pointer, but then you're just pushing the question one step back: why does the pointer state of a clock ever change?

It is a different type of question. If some quantity depends on t, it does not help to understand why t "changes", or even what does it mean that t "changes". Similarly, if another quantity depends on x, where x is the position of needle of a clock, it does not help to understand why x "changes".

MWI, but also physics in general, usually does not attempt to explain why things change. It only explains why values of some quantities depend on values of some other quantities.