Solving the Mystery of Guided Particles in a Black Hole

[Dmitry67]

Some matter (non-empty waves) formed a Black Hole.
Black Hole emits Hawking Radiation.
After a while, Black Hole dissapears, and there is nothing but radiation going in all directions.

My question,
How 'guided particled' managed to escape from the Black hole?
Or, if they did not escape, how they dissapeared?

 

[tom.stoer]

This is not a question for dBB but for quantum gravity, is it?

 

[Demystifier]

Or, if they did not escape, how they dissapeared?

The Bohmian interpretation of QFT involves a Bohmian description of particle creation and destruction. The destruction of particles by black-hole evaporation is included. Now, if you ask HOW that description works, then you must specify what kind of answer would satisfy you. For example, a detailed answer, both technical and intuitive, is presented in
http://xxx.lanl.gov/abs/0904.2287 [Int. J. Mod. Phys. A25:1477-1505, 2010]
but I know you will not read it. But then, it is difficult to explain anything to someone who does not want to read anything that includes more than a couple of sentences without equations. It is possible to explain something even to such people, but only if they specify what exactly they want to hear.

Let me also note that the formalism developed in the Bohmian paper above led also to a resolution of the black-hole information paradox that does not depend on the Bohmian interpretation at all:
http://xxx.lanl.gov/abs/0905.0538 [Phys.Lett.B678:218-221,2009]
http://xxx.lanl.gov/abs/0912.1938

Anyway, perhaps the simplest answer that could satisfy Dmitry is the following one:
The destroyed particles are not really destroyed; they have just never arrived to the presence from the past.

 

[Dmitry67]

The evaporation process is described by the semiclassical approach.
So I guess dBB should be ready to explain this even before TOE is created.

 

[Dmitry67]

UPD: will check the article provided by Demystifier first.

 

[tom.stoer]

The evaporation process is described by the semiclassical approach.

The Hawking radiation is derived in a limit where the BH mass M remains constant, so there's no backreaction from the Hawking radiation to the BH. This corresponds to quantum field theory on curved but classical spacetime. This limit cannot be used for the evaporation due to several reasons:
1) it violates unitarity, so there must be some quantum effect on the Hawking radiation to save unitarity (the BH information paradox)
2) for small BHs and evaporation the above described limit w/o backreaction is not applicable
3) for zero-mass BH one would have to describe how the singularity goes vanishes - but this cannot be described by GR as GR breaks down at the singularity.

 

[Demystifier]

The Hawking radiation is derived in a limit where the BH mass M remains constant, so there's no backreaction from the Hawking radiation to the BH. ... T
1) it violates unitarity ...

Actually, as long as you neglect backreaction and M remains constant, there is NO violation of unitarity.

 

[tom.stoer]

If you consider the radiation only, you are right; but then you have to neglect formation and final evaporation.

 

[Dmitry67]

The Bohmian interpretation of QFT involves a Bohmian description of particle creation and destruction. The destruction of particles by black-hole evaporation is included. Now, if you ask HOW that description works, then you must specify what kind of answer would satisfy you. For example, a detailed answer, both technical and intuitive, is presented in
http://xxx.lanl.gov/abs/0904.2287 [Int. J. Mod. Phys. A25:1477-1505, 2010]
but I know you will not read it. But then, it is difficult to explain anything to someone who does not want to read anything that includes more than a couple of sentences without equations. It is possible to explain something even to such people, but only if they specify what exactly they want to hear.

Let me also note that the formalism developed in the Bohmian paper above led also to a resolution of the black-hole information paradox that does not depend on the Bohmian interpretation at all:
http://xxx.lanl.gov/abs/0905.0538 [Phys.Lett.B678:218-221,2009]
http://xxx.lanl.gov/abs/0912.1938

Anyway, perhaps the simplest answer that could satisfy Dmitry is the following one:
The destroyed particles are not really destroyed; they have just never arrived to the presence from the past.

I understand, in the first article you describe the Bohmian view on creation/destroying the particles, and then hawking radiaction becomes non-issue (2nd article)

P.S. As I understand, (commonly accepted) dBB is still non-relativistic, as in 1st article you had mentioned several alternative approaches to the relativitic QFT, so there is no single commonely accepted QFT in dBB, which gives several additional "flavours" to dBB interpretation?

 

[Demystifier]

... several alternative approaches to the relativitic QFT, so there is no single commonely accepted QFT in dBB, which gives several additional "flavours" to dBB interpretation?

True.

 

[JustinLevy]

dBB is treated inconsistently by its proponents:

1) If the "hidden" variables are truly inaccessible, then the experimental results can only depend on the wavefunction, and the hidden variables serve no purpose.

2) If the "hidden" variables are always accessible, then the 'distribution' requirement is trivially falsified and dBB doesn't reproduce standard quantum predictions.

3) If the "hidden" variables are only accessible in some limit (classical limit), then they are proposing a dichotomy / their own "measurement problem".

Most proponents fall into category 3, in which they state it is "obvious" the classical measurement is what the "hidden variable" is in. They have not then solved anything. Instead they have added non-local interactions to a local theory, just to try to restore some classical reasoning. In thus destroying the elegance, they don't even gain anything useful.

Some wave their hands "decoherence" as if that explains how the hidden variables become non-hidden. It doesn't actually explain anything. I've read some dBB papers, and even took time to talk to some quantum foundations people at an APS meeting, and the consensus seems to be that dBB just transfers the problems to worse problems.

Symmetries are a beautiful and usefully constraining tool. To throw it away because of wishes for a-priori demands on physics, is to me like the continual chatter of aether proponents divorced from mainstream.

One thing I think all sides can agree to: dBB gets WAY more attention on this forum, than it does in classrooms and useful calculations and papers in academia. (I believe this is due to certain posters here promoting dBB -- I don't feel that is appropriate for physicsforums, but it doesn't seem to be against the rules.)

 

[zenith8]

dBB is treated inconsistently by its proponents:

1) If the "hidden" variables are truly inaccessible, then the experimental results can only depend on the wavefunction, and the hidden variables serve no purpose.

2) If the "hidden" variables are always accessible, then the 'distribution' requirement is trivially falsified and dBB doesn't reproduce standard quantum predictions.

3) If the "hidden" variables are only accessible in some limit (classical limit), then they are proposing a dichotomy / their own "measurement problem".

Most proponents fall into category 3, in which they state it is "obvious" the classical measurement is what the "hidden variable" is in. They have not then solved anything. Instead they have added non-local interactions to a local theory, just to try to restore some classical reasoning. In thus destroying the elegance, they don't even gain anything useful.

Some wave their hands "decoherence" as if that explains how the hidden variables become non-hidden. It doesn't actually explain anything. I've read some dBB papers, and even took time to talk to some quantum foundations people at an APS meeting, and the consensus seems to be that dBB just transfers the problems to worse problems.

Symmetries are a beautiful and usefully constraining tool. To throw it away because of wishes for a-priori demands on physics, is to me like the continual chatter of aether proponents divorced from mainstream.

One thing I think all sides can agree to: dBB gets WAY more attention on this forum, than it does in classrooms and useful calculations and papers in academia. (I believe this is due to certain posters here promoting dBB -- I don't feel that is appropriate for physicsforums, but it doesn't seem to be against the rules.)

You've been making similar lazy and ill-informed rants against deBB theory - complete with sinister hints that the Forum moderators should ban it - for quite a few years now. It's still quite clear that you have only a very modest understanding of the subject, and I don't know why you think this qualifies you to make such sweeping negative generalizations. I suspect dark, underlying motives..

In 2011 deBB is a thriving subject with a huge peer-reviewed literature and its own international conferences. At most quantum foundations events that I've had anything to do with in recent years, it's arguably the most popular subject.

 

[Demystifier]

dBB is treated inconsistently by its proponents:

1) If the "hidden" variables are truly inaccessible, then the experimental results can only depend on the wavefunction, and the hidden variables serve no purpose.

2) If the "hidden" variables are always accessible, then the 'distribution' requirement is trivially falsified and dBB doesn't reproduce standard quantum predictions.

3) If the "hidden" variables are only accessible in some limit (classical limit), then they are proposing a dichotomy / their own "measurement problem".

Most proponents fall into category 3, in which they state it is "obvious" the classical measurement is what the "hidden variable" is in. They have not then solved anything. Instead they have added non-local interactions to a local theory, just to try to restore some classical reasoning. In thus destroying the elegance, they don't even gain anything useful.

I partially agree with you here, but not completely. I agree that hidden variables are only partially accessible (a kind of your 3, but not exactly), and that this makes the measurement problem only partially resolved, and that this makes the whole idea less useful than one could hope for. Yet, if a theory still has unresolved problems, it does not imply that it is completely useless. If nothing else, the Bohmian interpretation helps to have an intuitive view of otherwise counterintuitive quantum phenomena. Even a shut-up-and-calculate approach is more comfortable when it is augmented with an intuitive picture (see e.g. Feynman diagrams). Even if particle trajectories do not really exist, in many cases it is simpler to arrive at the right final results when one imagines that they do.

Let me use an analogy. In a sense, Bohmian mechanics in its present form is analogous to Newtonian mechanics for the motion of planets without a theory of light. The Newton theory predicts the motion of planets in agreement with observations, but without a theory of light one cannot really understand why planets are observed in the first place. The similar is the case with Bohmian particle trajectories.

Even better analogy is a dark-matter analogy. All the observed phenomena in astronomy and cosmology is easy to explain by assuming the existence of dark matter, and yet we cannot directly observe this dark matter. Instead, we merely INTERPRET the observed phenomena in terms of dark matter. And still, almost nobody doubts that this dark matter (i.e., "hidden variables") exists.

 

[Demystifier]

dBB just transfers the problems to worse problems.

I would agree that dBB transfers problems to new problems (which can be said for ANY new theory in science!), but I wouldn't agree that these new problems are worse.

 

[Dmitry67]

But in general, how many flavors of dBB exist?
In your article you had referenced two, if I remember it correctly.
(Of course I am talking about relativistic dBB, there is no reason to talk about non-relativistic dBB).

 

[JustinLevy]

While I would classify Demystifier's hopes as overly optimistic about deBB, that is an opinion. He is at least self-aware of the issues, and proceeds forward hoping the theory will be useful anyway or issues will be resolved at a later time. While we differ in opinion, I can respect that.


Zenith8's post however is worrisome. Your response instead seems self-deluding of the mathematical issues and therefore crosses over opinion into un-scientific.

It's still quite clear that you have only a very modest understanding of the subject, and I don't know why you think this qualifies you to make such sweeping negative generalizations. I suspect dark, underlying motives..

Dark, underlying motives? There is no conspiracy here.

If you'd like to explain for my benefit, or other reader's benefit, precisely how the "hidden variables" become accessible in deBB please do so. I left out the "consciousness knows its state variables" idea I have seen, because it is even more vague than the classical measurement dichotomy with at minimal the same problem. I assume (maybe wrongly) that this was only an idea kicked around, and not taken seriously by any deBB proponents.

There is no dark plot. Scientific ideas should be able to stand on their own.

In 2011 deBB is a thriving subject with a huge peer-reviewed literature and its own international conferences. At most quantum foundations events that I've had anything to do with in recent years, it's arguably the most popular subject.

This is misrepresenting the situation. When a theorist works out a tough quantum problem in (loosely) the two regimes: 'condensed matter' / many body problem or 'fundemental interactions' / collider physics ... they use standard QFT, string theory (yes it has applications), etc. None of the advances in theory were developed in DeBroglie-Bohm's pilot wave ideas.

If you want to say: people interested in DeBB have become more organized. Fine. But again I repeat that I think there should be absolutely no debate to this: dBB gets way more attention on this forum, than it does in classrooms and useful calculations and papers in academia.

 

[Dmitry67]

Another thought. dBB and gravity.

Say, based on QM event I accelerate massive body (or don't do it). Hence I emit (or don't do it) Gwaves, detected (or not detected) by a distant detector. That detector is isolated from the source, so no particles (including thermal photons) hit it.

So we see that information has been transferred by spacetime metrics. Obviously, detector was able to actually measure the position of the guided particles, because they affect the spacetime.

 

[JesseM]

3) If the "hidden" variables are only accessible in some limit (classical limit), then they are proposing a dichotomy / their own "measurement problem".

Most proponents fall into category 3, in which they state it is "obvious" the classical measurement is what the "hidden variable" is in. They have not then solved anything.

I haven't studied this subject but I was under the interpretation that dBB could treat macroscopic measuring devices as just large assemblages of particles evolving according to the same deterministic rules that govern the systems being measured, and that in this way you could use the theory to predict the position of macroscopic "pointers" and show that they would match those predicted by the usual QM approach. For example, this section of the "Bohmian Mechanics" article at the Stanford Encyclopedia of Philosophy says:

By contrast, if, like Einstein, we regard the description provided by the wave function as incomplete, the measurement problem vanishes: With a theory or interpretation like Bohmian mechanics, in which the description of the after-measurement situation includes, in addition to the wave function, at least the values of the variables that register the result, there is no measurement problem. In Bohmian mechanics pointers always point.

Am I misunderstanding the dBB approach to measurement here?

 

[JustinLevy]

JesseM,

Let me summarize for you.

In Bohmian mechanics, the state is specified by both the wavefunction (pilot wave) and the "hidden variables" which are called particle positions (or 'pointers'). The wavefunction evolves according to ordinary quantum mechanics. The particle positions move based, non-locally, on the wavefunction. (There are other details such as requirements for the interpretation of the wavefunction as a distribution of particle positions, but that is not necessary for this discussion.)

If we could always access the particle positions directly, quantum mechanics (QM) and bohmian mechanics (BM) would trivially predict different experimental outcomes.

If we can never access the particle positions, then the outcome of (for example) a Stern-Gerlach experiment will have the measurement device wavefunction in a superposition of both cases -- fully equivalent to QM, and leaves us in the same situation.

Instead, most BM proponents take a third option. They decide that by the time we get to the classical regime, somehow these two outcomes are distinguishable. Since the only way to distinguish the two cases are by the hidden variables, they can only be distinguished if at some level we can access the "hidden variable" particle positions directly. ie. that the pointer "points" somehow. They don't explain this dichotomy any more than normal quantum mechanics does. And the point is, unless they make the hidden variables accessible, they can't solve the problem unless it is also solvable in QM. For example, if decoherence can solve this without permitting access to the hidden variables, then decoherence can solve this for QM as well.Once one admits dBB is in the same boat as QM, then there is nothing preventing it from being completely (experimentally) equivalent with QM. This leaves us with the situations similar to Lorentz's ether theory which became equivalent to maxwell's equations + special relativity's predictions for electrodynamics. Lorentz felt strongly that the philosophical difference was still important, and could someday in the future prove useful in physics. Einstein felt otherwise. I feel Einstein was correct, as his idea proved far more useful for physics. This analogy is quite apt as BM proponents require a preferred foliation of spacetime, despite it not being measureable, just like aether theories.

 

[Demystifier]

This analogy is quite apt as BM proponents require a preferred foliation of spacetime, despite it not being measureable, just like aether theories.

That is not completely true, as there is a variant of BM without a preferred foliation:
http://arxiv.org/abs/1002.3226

 

[Demystifier]

If we can never access the particle positions, then the outcome of (for example) a Stern-Gerlach experiment will have the measurement device wavefunction in a superposition of both cases -- fully equivalent to QM, and leaves us in the same situation.

That is not correct. If we can never access particle positions, then, according to BM, experiments have no outcomes at all. This is certainly not equivalent to QM. In fact, the whole point of BM (and other hidden-variable theories) is to explain why experiments have outcomes. Standard QM calculates probabilities of different outcomes, but does not explain why and how outcomes themselves occur.

 

[JustinLevy]

That is not completely true, as there is a variant of BM without a preferred foliation:
http://arxiv.org/abs/1002.3226

Two comments.

1] First the obvious: Special relativity doesn't require local interactions, but it is not possible to have non-local interactions and causality. If you succeed in doing this, you are essentially trading requiring foliations for removing causality.

2] You still have a preferred foliation. All you did is move the foliation to a scalar s on spacetime. This allows you to put the equations in coordinate invariant form, but only in the same way that introducing an external lorentz violating term (as in modern "aether" theories) makes those theories coordinate independent. Similarly Newton's gravity can be cast in coordinate independent notation, but this alone doesn't mean it is relativistically invariant. Essentially, your equations are still not invariant to changes in foliation (direction of gradient of scalar s in spacetime). So you have supplied a "vacuum state" that breaks Lorentz invariance.

That is not correct. If we can never access particle positions, then, according to BM, experiments have no outcomes at all. This is certainly not equivalent to QM. In fact, the whole point of BM (and other hidden-variable theories) is to explain why experiments have outcomes. Standard QM calculates probabilities of different outcomes, but does not explain why and how outcomes themselves occur.

I was comparing trying to get classical measurements from the underlying (unitary) quantum evolution in BM and QM. I don't understand where you are disagreeing with me, as you start by repeating my points.

"If we can never access particle positions, then, according to BM, experiments have no outcomes at all."
Yes, exactly -- without access to the hidden variables, we only have the wavefunction which will be in a superposition of measurement eigenstates. So you agree with me here, BM needs the experimenter to get access to the hidden variables in order to distinguish the possibilities.

But if we had access to the hidden variables, we can know the particles do not meet the distribution requirements of a wavefunction. This would break one of the requirements for making the unitary parts of BM and QM evolution appear equivalent.

You can't have it both ways. As you said previously, you fall in 'category three'. You are simultaneously requiring the variables to be hidden when doing quantum interactions, and requiring the variables somehow become unhidden when doing classical interactions. This is presenting a similar quantum/classical dichotomy as the Copenhagen QM classical measurement issue.

 

[Demystifier]

1] First the obvious: Special relativity doesn't require local interactions, but it is not possible to have non-local interactions and causality. If you succeed in doing this, you are essentially trading requiring foliations for removing causality.

As explained in the paper, it depends on what exactly do you mean by causality. If you mean "causes precede consequences", then the theory is causal. However, in this theory "precede" does not necessarily mean "happens at an earlier time".

2] You still have a preferred foliation.

No I don't.

All you did is move the foliation to a scalar s on spacetime.

The parameter s does not define a foliation. In fact, this parameter can be eliminated from the equations and particle trajectories can be calculated even without this parameter.

Take for example two particles with their spacetime positions for the same s. You may say that these two positions lie at the same hypersurface. However, there is an infinite number of different hypersurfaces connecting these two points (positions) and none of them is preferred. Moreover, such a hypersurface plays no role in the theory. You don't need to know or choose this hypersurface in order to calculate the trajectories.

This allows you to put the equations in coordinate invariant form, but only in the same way that introducing an external lorentz violating term (as in modern "aether" theories) makes those theories coordinate independent.

There is no Lorentz-violating term in the theory. (If you claim that there is, then write it down or point to it in the paper.)

Essentially, your equations are still not invariant to changes in foliation

Yes they are.

(direction of gradient of scalar s in spacetime).

No equation of the theory involves a gradient of s.

As you said previously, you fall in 'category three'. You are simultaneously requiring the variables to be hidden when doing quantum interactions, and requiring the variables somehow become unhidden when doing classical interactions. This is presenting a similar quantum/classical dichotomy as the Copenhagen QM classical measurement issue.

I said that I fall to something SIMILAR to 'category three', but not exactly. In particular, I never said (nor thought) that the variables become unhidden only when we do classical interactions.

 

[JustinLevy]

I'm surprised we can't agree on math, so let me start there.

Essentially, your equations are still not invariant to changes in foliation

Yes they are.

Let's consider two particles, and look at the evolution of one of them
\frac{dX^\mu_1(s)}{ds} = - \partial^\mu_1 \mbox{Arg}\left[ \psi(X_1(s),X_2(s)) \right]

Unless it is always the case that
\partial^\mu_1 \partial^\nu_2 \mbox{Arg}\left[ \psi(X_1,X_2) \right] = 0
then clearly changing the foliation will change the evolution. Consider the case where at s=0 the particles are space-like separated. Now change the foliation to s'=s=0 at particle one and s'=0,s=1 at particle 2.

So if the equations were invariant to choice of foliation then we could write
\frac{dX^\mu_1(s=0)}{ds} = - \partial^\mu_1 \mbox{Arg}\left[ \psi(X_1(s=0),X_2(s=0)) \right]
or we could write it in the new foliation
\frac{dX^\mu_1(s'=0)}{ds} = - \partial^\mu_1 \mbox{Arg}\left[ \psi(X_1(s'=0),X_2(s'=0)) \right]
which is just
\frac{dX^\mu_1(s=0)}{ds} = - \partial^\mu_1 \mbox{Arg}\left[ \psi(X_1(s=0),X_2(s=1)) \right]

Only in contrived cases will these evolutions at s=0 be the same. Note that if the interactions were local, this wouldn't even be an issue.

The Lorentz violating factor is the fixed background telling what pairs of spacetime points in the worlds lines X_1 and X_2 correspond to a "simultaneous time". This is provided by the foliation given by s.

The evolution equation is only invariant to foliations that don't change this pairing (ie. don't change the "parametric time" where the particles are located).

 

[JesseM]

JesseM,

Let me summarize for you.

In Bohmian mechanics, the state is specified by both the wavefunction (pilot wave) and the "hidden variables" which are called particle positions (or 'pointers').

I understood from the Stanford Encyclopedia entry (and other nontechnical descriptions I've read) that Bohmian mechanics includes both exact particle positions and a pilot wave to coordinate them in a deterministic way, but I think you misunderstand something when you treat "pointer" as a synonym for the hidden variable giving the position of some individual particle. Usually when the word "pointer" is discussed in the context of the QM measurement problem (whether in a Bohmian interpretation or a different one), it refers to pointers on some macroscopic measuring-instrument used by human experimenters, like the needle on a dial which "points" to some numerical value of the quantity being measured. For example, on p. 1 of this paper about a non-Bohmian analysis of the measurement problem, they write:

Furthermore, due to the absence of a collapse of the wavefunction, our unitary description implies that quantum measurement is inherently reversible, overturning the common view. However, in an experiment where quantum entanglement is transferred to a macroscopic “pointer” variable (as is essential for classical observers) the reversibility is obscured by the practical impossibility of keeping track of all the atoms involved in the unitary transformation, rendering the measurement as irreversible as the thermodynamics of gases.

Similarly http://omnis.if.ufrj.br/~ldavid/arquivos/mesoscopic.pdf says in the introduction:

von Neumann’s collapse postulate introduces two distinct types of evolution in quantum mechanics: the deterministic and unitary evolution associated to the Schrödinger equation, which describes the establishment of a correlation between states of the microscopic system being measured and distinguishable classical states of the macroscopic measurement apparatus (for instance, distinct positions of a pointer); and the probabilistic and irreversible process associated with measurement, which transforms the correlated state into a statistical mixture.

If you search for "quantum measurement pointer" on google scholar it appears that this is standard terminology in discussions of the measurement problem. And I'm pretty sure the section I quoted from the Stanford Encyclopedia article on Bohmian mechanics was using "pointer" to refer to macroscopic pointers like needles on dials as well:

The problem is as follows. Suppose that the wave function of any individual system provides a complete description of that system. When we analyze the process of measurement in quantum mechanical terms, we find that the after-measurement wave function for system and apparatus arising from Schrödinger's equation for the composite system typically involves a superposition over terms corresponding to what we would like to regard as the various possible results of the measurement — e.g., different pointer orientations. It is difficult to discern in this description of the after-measurement situation the actual result of the measurement — e.g., some specific pointer orientation. But the whole point of quantum theory, and the reason we are to believe in it, is that it is supposed to provide a compelling, or at least an efficient, account of our observations, that is, of outcomes of measurements. In short, the measurement problem is this: Quantum theory implies that measurements typically fail to have outcomes of the sort the theory was created to explain.

And again, my understanding of the basic Bohmian approach to the measurement problem was just that a macroscopic pointer such as a needle on a dial could be assumed to be made up of a large collection of particles, so the deterministic pilot wave would guide their position just as it guides other particles, and of course the macroscopic position of the needle follows from the micro-positions of all the particles that make it up. So as long as the Bohmian approach always says the particles are in definite positions, the needle or other macroscopic pointer must always be in a definite position as well, and then you can check that the probability of finding the pointer in different macro-positions in an ensemble of measurements matches the predictions of ordinary QM. If it does, it seems to me there is no real "measurement problem" in Bohmian mechanics, since there is no need for any special rule about measurement analogous to the "collapse of the wavefunction", the particles that make up the measuring apparatus follow the same deterministic rules as the particles being measured and this suffices to get correct predictions about all measurement results (since all measurements that humans can perform must ultimately boil down to orientations of macroscopic pointers visible to the human eye).

 

[Dmitry67]

The biggest problem with dBB is well known, dBB is MWI “in chronic denial”. Why non-tagged observers are not conscious?

There is, of course, a response to that critics (“dBB is MWI in chronic denial”). The response, in brief, explains how dBB is self-consistent from it’s own point of view: tagged observers would see only tagged objects. This argument is circular: assuming that I am tagged, I would see only tagged world. But why observer is tagged in a first place? The circular nature of the argument does not make the theory inconsistent, but it has almost no real value.

The second argument is more interesting: tagged observer would see that the world obeys the Born rule. This is much more interesting, but it does not address the issue: between huge number of empty branches, there are many where Born rule is obeyed. Still, there observers are not conscious. So the fact that conscious observers observe Born rule looks as a coincidence, but not a consequence.

 

[JustinLevy]

I think you misunderstand something when you treat "pointer" as a synonym for the hidden variable giving the position of some individual particle

No, that was intentional. The issue is that if these variables aren't "hidden" for macroscopic objects, they shouldn't in principle be for microscopic objects either. We've gotten objects as large as a virus to demonstrate quantum intereference -- where do you draw the line? What makes something "macroscopic enough"? If the hidden variables are accessible, then we can see all the perverse things Bohmian mechanics predicts for these variables: such as non-local interactions and faster than light motion.

And again, my understanding of the basic Bohmian approach to the measurement problem was just that a macroscopic pointer such as a needle on a dial could be assumed to be made up of a large collection of particles, so the deterministic pilot wave would guide their position just as it guides other particles, and of course the macroscopic position of the needle follows from the micro-positions of all the particles that make it up. So as long as the Bohmian approach always says the particles are in definite positions, the needle or other macroscopic pointer must always be in a definite position as well

But to resolve measurement this way, we need to be able to access the positions of these particles directly. Your explanation mirrors mine exactly. I'm not sure where we are mis-communicating.

You are saying: BM solves the measurement problem because we can just observe the particles positions of macroscopic objects.

I am saying: yes, that is what proponents claim, but to be consistent they require we can't observe positions of microscopic objects, only macroscopic objects. This introduces a dichotomy just like Copenhagen's vague cutoff for macroscopic interactions being measurements.

Even if you disagree with me, do you at least understand my point now? For I am very confused how you essentially repeated back what I said, but seem to be disagreeing.

---

Dmitry67,
Yes, I've heard dBB related to MWI as such.
That's quite related to my point here: dBB with true hidden variables can't solve the measurement problem, unless unitary evolution of QM can as well. Entangled states decohering via interactions with the environment such as to become separate, and non-inertacting -- is that what you mean in your discussion above? I've heard people use several different ideas for MWI, and am unsure on what the accepted meaning of the phrase is in modern discussion (or maybe there are variants?).

 

[JesseM]

No, that was intentional. The issue is that if these variables aren't "hidden" for macroscopic objects, they shouldn't in principle be for microscopic objects either.

Well, as I understand it the only hidden variable in Bohmian mechanics is position, and that isn't "hidden" in the sense that you can measure it to arbitrary precision at any moment. But if you're performing an alternate type of measurement that corresponds to what we call measuring "momentum" (which I think in Bohmian mechanics won't relate in any straightforward way to change in position/change in time), you can't at the same time measure the position accurately. If you think that "in principle" you should be able to, it should be possible to prove that by dreaming up an appropriate experimental setup that would have pointers for both position and momentum, and showing that the Bohmian prediction about position of the the "momentum" pointer matches up with what it would be even if that was the only thing being measured, while the Bohmian prediction about the "position" pointer matches up with the actual value of the position variable of the particle. But I see no justification for the view that "in principle" such an experimental setup should be possible in Bohmian mechanics, and in fact I was under the impression that the Bohmian statistical predictions about macroscopic pointers had been shown to be identical to the standard QM ones.

We've gotten objects as large as a virus to demonstrate quantum intereference -- where do you draw the line? What makes something "macroscopic enough"?

But all our measurements of viruses involve looking at the values of pointers which are much larger than a virus.

And again, my understanding of the basic Bohmian approach to the measurement problem was just that a macroscopic pointer such as a needle on a dial could be assumed to be made up of a large collection of particles, so the deterministic pilot wave would guide their position just as it guides other particles, and of course the macroscopic position of the needle follows from the micro-positions of all the particles that make it up. So as long as the Bohmian approach always says the particles are in definite positions, the needle or other macroscopic pointer must always be in a definite position as well

If the hidden variables are accessible, then we can see all the perverse things Bohmian mechanics predicts for these variables: such as non-local interactions and faster than light motion.

I'm not sure I understand what you mean by "accessible"--do you agree the only way we can know about the values of any microscopic variable is by looking at some pointer big enough that its value can be determined by unaided human senses? If you think the "perverse things Bohmian mechanics predicts" should be "accessible" in this sense, then you should be point to a specific experimental setup where some human-viewable macroscopic pointer shows them; if not either your claim is unjustified, or you are using some fundamentally different notion of "accessible" which doesn't involve human-scale pointers.

Of course you could point out that what is the "human scale" is just an accident of biology, probably the laws of physics would allow for intelligent beings much smaller than ourselves, like AIs running on carbon nanotube computers. But surely if such small intelligent beings existed, they would be able to communicate anything they observed up to the human scale, say by arranging molecules into a message that we could view with a scanning tunneling microscope (and the pixels on the screen which we use to view pictures taken with an scanning tunneling microscope can be seen as a type of macroscopic pointer). So there's no real loss of generality by talking about the human scale, because any physically possible smaller agents could be part of the "experimental setup" whose end result is supposed to be a pointer state visible to unaided human senses. And again I was under the impression that there was some sort of proof that all conceivable experiments give the same observable results in Bohmian mechanics as in standard QM; even if I'm wrong about that, your idea that Bohm-specific behavior should "in principle" be observable seems completely hand-wavey, unless you have a specific experimental setup that demonstrates this I see no reason why this must be the case.

 

[JustinLevy]

JesseM,
We clearly are "talking past" each other. I'm not sure how to fix this. I am going to read your post, think about it, reread, see if I missed anything, and reread a third time to try to confirm if it matches my best effort from the previous reads at understanding your points. I would appreciate it if you also implement the "read three times" strategy, as you keep stating things that I agree with while disagreeing with me. I feel like I have to read between the lines, as I really don't understand what you are missing. Ok? Between the two of us, we can figure this communication gap out.
------

And again I was under the impression that there was some sort of proof that all conceivable experiments give the same results in Bohmian mechanics as in standard QM

The specific proof is that if you assume an ensemble starts out with the particle positions distribution matching the usual probability distribution of the wavefunction according to QM, the evolution equations of BM will maintain the ensemble probability distribution property.

That is not at debate here.

that isn't "hidden" in the sense that you can measure it to arbitrary precision at any moment.

This falls into 'category 2' here, the option where the variables are not hidden at all.

If they are not hidden, then there is no unknown ensemble for the observed particles. More importantly though, unless you introduce a macro-micro dichotomy, this allows one to entangle the wavefunctions of two macroscopic objects and observe non-local interactions by watching the macroscopic particle positions. Even super-luminal motion, as the position evolution equation does not limit the rate of change of the "hidden" particle positions.

Only by producing a dichotomy (which you appear to be strongly promoting in your last post, seemingly using "consciousness" as the line for the cutoff), can we relegate the "unknowns" of microscopic to ensembles to allow evolution to match the wavefunction, and yet have macroscopic pointer be directly seen and not match the wavefunction ensemble.

I'm not sure I understand what you mean by "accessible"--do you agree the only way we can know about the values of any microscopic variable is by looking at some pointer big enough that its value can be determined by unaided human senses?

If we could directly observe electrons, do you feel this would somehow change the discussion? Why? Either all objects evolve according to the same quantum rules, or there is a dichotomy between microscopic and macroscopic.

You saying the equivalent of "but you can only indirectly observe microscopic objects" is completely missing the point. The point is that you can directly observe ANY particle positions. You are promoting a dichotomy.

Of course you could point out that what is the "human scale" is just an accident of biology, probably the laws of physics would allow for intelligent beings much smaller than ourselves, like AIs running on carbon nanotube computers.

Please please don't be one of those people that uses the dichotomy "the distinction is interactions with a sentient being". If you are, please say so now, for this will lead down a road that is not worth either of our times discussing.

 

[JesseM]

So you fall into 'category 2' here. You don't feel the variables are hidden at all.

I don't know what you mean by "hidden" in this context, it seems kind of like your argument is a purely verbal one based on poorly-defined terminology, and that it might fall apart if you tried to give everything a precise mathematical definition. We can know the exact positions in some experimental setups (like ones where we are measuring position) but not others (like ones where we are doing momentum measurements). So is position a "hidden variable" when we are doing a momentum measurement, or not?

If we could directly observe electrons, do you feel this would somehow change the discussion?

How would we directly observe electrons, would large numbers of photons scatter off them? Whatever the physical details of how we would "directly observe" them, presumably you could model this form of observation using either orthodox QM or Bohmian mechanics, and both would make the same predictions about what our actual observations would be, so no Bohm-specific behaviors would be seen. If you disagree, then again verbal handwaving won't do, you'd need to provide a model of a "visible electron" world which worked according to general Bohmian principles (but with the electron having a much larger mass or charge, perhaps), and show that Bohmian predictions about how the visible electron would register on an eyeball or camera would exhibit Bohm-specific behaviors.

Please please don't be one of those people that uses the dichotomy "the distinction is interactions with a sentient being". If you are, please say so now, for this will lead down a road that is not worth either of our times discussing.

I'm not saying there is any change in the way the laws of physics work when conscious beings are involved (unlike those who think "consciousness collapses the wavefunction" which is at other times evolving according to the deterministic Schroedinger equation, for example) if that's what you're suggesting. I'm just making the pragmatic point that the only way of judging how well a theory agrees with observation is by checking its theoretical predictions about things that intelligent beings like ourselves (or any conceivable physical intelligent beings that could communicate their observations to us) can actually observe. If Bohmian mechanics makes predictions about all such observations that are identical to those of orthodox QM, and it does so using a mathematical model which says that the same dynamical laws are operative at all times (both between measurements and during measurements) and apply to all systems (the systems being measured, the measuring apparatus, the beings looking at the measuring apparatus), then it seems to be a model that accounts for all possible quantum-mechanical observations without any "measurement problem" (though it may suffer from other problems like inelegance or Lorentz violation or the fact that the dynamics of the pilot wave might be implicitly "computing" many other possible configurations so that it might be said to be a MWI in disguise, which perhaps is what Dmitry67 was arguing though I'm not sure).

 

[Dmitry67]

dBB does not use any new ideas to solve the first part of the measurement problem - it uses the quantum decoherence approach.

dBB solves the second part of the measurement problem, which is not solved by decoherence. Decoherence just shows how interaction effectively splits system into pairs like happy observer-alive cat and sad observer-dead cat. Based on dBB only one pair is tagged, hence, there is only one 'real' outcome.

As I understand, dBB is self-consistent, even it uses some magical, non-physical axioms, and after death of CI and TI it is the 3rd alternative (SM, MWI and dBB - this is what is left). Personaly, I would be very dissapointed if dBB would appear to be true - the very idea of 'particles' looks sooooooooooooo human, using our common sense reasoning from the macroscopic world... The real explanation (based on a history of science) must be crazier, not simpler (this is why I like MWI).

 

[Fyzix]

As I understand, dBB is self-consistent, even it uses some magical, non-physical axioms, and after death of CI and TI it is the 3rd alternative (SM, MWI and dBB - this is what is left). Personaly, I would be very dissapointed if dBB would appear to be true - the very idea of 'particles' looks sooooooooooooo human, using our common sense reasoning from the macroscopic world... The real explanation (based on a history of science) must be crazier, not simpler (this is why I like MWI).

I won't join in this discussion too deeply, but I would like to point out a few things.

What you call a "magical/nonphysical axiom" doesn't nessicarily have to be viewed that way, you are aware that there is different Bohmian interpretations?

There is more interpretations left than just SM (Statistical/stochastic mechanics?), MWI and dBB.
Have you looked into the work of Gerard 't Hooft?
He is developing another realistic and deterministic interpretation of QM, you can get a gist of it from this article about it:

http://www.nature.com/news/2003/030108/full/news030106-6.html

There is also a very recent interpretation by Amit Hagar and Giuseppe Sergioli which also keeps realism and determinism:

http://mypage.iu.edu/~hagara/Steps.pdf

Also have a look at Travis Norsen's "Theory of Exclusive Local Be-ables"

To quote the author himself:
The goal is thus not to recommend the TELB proposed here as a replacement for ordinary pilot-wave theory (or ordinary quantum theory), but is rather to illustrate (with a crude first stab) that it might be possible to construct a plausible, empirically viable TELB, and to recommend this as an interesting and perhaps-fruitful program for future research.

http://arxiv.org/abs/0909.4553

Not to mention we do not have a Theory of Everything, so all the speculation might be premature...

You also got other interpretations (not that I'm very fond of them personally): GRW, Ensemble interpretation etc.

Now, over to your favorite interpretation MWI:

First, you yourself acknowledge that MWI as of now, can't make sense of probability and you just choose to BLINDLY believe that MWI somehow will make sense of it.
So your reason for prefering MWI isn't based in scientific reasoning, but rather personal preference.

On top of this, you have the preferred basis problem.
Someone actually made a thread about it on this very forum just a few weeks ago, but for some weird reason, NOONE responded to that thread...

Here you got 2 different papers from different authors touching on this subject:

Ilja Schmelzer
Why the Hamilton operator alone is not enough
http://arxiv.org/abs/arXiv:0901.3262

M. Dugic, J. Jeknic-Dugic
The quantum structures of the Universe: Questioning the Everett's Interpretation of Quantum Mechanics
http://arxiv.org/PS_cache/arxiv/pdf/1012/1012.0992v3.pdf[/URL]

So there are quite a few problems with MWI that doesn't seem to be "solvable" at all, unless you modify the interpretation a lot.

 

[Demystifier]

... Now change the foliation to s'=s=0 at particle one and s'=0,s=1 at particle 2.

Your "s'=s=0 at particle one and s'=0,s=1 at particle 2" specifies two points in spacetime. But it has nothing to do with foliation, because two points do not define a hypersurface.

The Lorentz violating factor is the fixed background telling what pairs of spacetime points in the worlds lines X_1 and X_2 correspond to a "simultaneous time".

But there is no FIXED background that tells it. Instead, it is told by the choice of initial conditions X_a(s=0), and initial conditions are not fixed by the theory. Of course, even in classical local mechanics, no initial condition is Lorentz invariant. For example, your screen (on which you just read this text) defines a particular Lorentz frame with respect to which this screen is at rest. Yet, this does not change the fact that your screen satisfies Lorentz invariant LAWS of motion.

In short, the LAWS of motion are covariant and do not involve a preferred Lorentz frame. Yet, the SOLUTIONS of these laws are not (and do not need to be) Lorentz invariant. This refers to both classical relativistic mechanics and Bohmian relativistic mechanics.

 

[JesseM]

dBB does not use any new ideas to solve the first part of the measurement problem - it uses the quantum decoherence approach.

dBB solves the second part of the measurement problem, which is not solved by decoherence. Decoherence just shows how interaction effectively splits system into pairs like happy observer-alive cat and sad observer-dead cat. Based on dBB only one pair is tagged, hence, there is only one 'real' outcome.

"Effectively" is an important word here, since from what I've read the off-diagonal interference terms never entirely disappear even with decoherence, so it is never exactly correct to view a quantum superposition as having turned into an ordinary statistical mixture due simply to decoherence. Whereas Bohmian mechanics does allow quantum probabilities to be derived from an ordinary statistical ensemble of different possible exact trajectories for the positions of the parts of the system. So it seems to me that decoherence in a MWI framework only comes suggestively close to solving the measurement problem without actually explaining where precise probabilities come from, whereas the Bohmian approach resolves it exactly, though as I said earlier there are other aspects of the Bohmian approach that may seem contrived or unappealing for various reasons (for these reasons my intuition is that the MWI approach is ultimately more promising than the Bohmian approach, but it seems like we should be realistic about the fact that in its current form the MWI doesn't provide a clear resolution to these problems). And for this reason I doubt that what you say above--that Bohmian mechanics can be viewed as equivalent to MWI + decoherence, just with one outcome "tagged" as real--could really be backed up in any precise mathematical sense. Can you point to any papers or textbooks that justify your argument rigorously?

 

[Demystifier]

"Effectively" is an important word here, since from what I've read the off-diagonal interference terms never entirely disappear even with decoherence, so it is never exactly correct to view a quantum superposition as having turned into an ordinary statistical mixture due simply to decoherence. Whereas Bohmian mechanics does allow quantum probabilities to be derived from an ordinary statistical ensemble of different possible exact trajectories for the positions of the parts of the system. So it seems to me that decoherence in a MWI framework only comes suggestively close to solving the measurement problem without actually explaining where precise probabilities come from, whereas the Bohmian approach resolves it exactly, though as I said earlier there are other aspects of the Bohmian approach that may seem contrived or unappealing for various reasons (for these reasons my intuition is that the MWI approach is ultimately more promising than the Bohmian approach, but it seems like we should be realistic about the fact that in its current form the MWI doesn't provide a clear resolution to these problems). And for this reason I doubt that what you say above--that Bohmian mechanics can be viewed as equivalent to MWI + decoherence, just with one outcome "tagged" as real--could really be backed up in any precise mathematical sense. Can you point to any papers or textbooks that justify your argument rigorously?

Your way of thinking is very close to mine.

I would like to see what do you think about my recent alternative to Bohmian mechanics
http://xxx.lanl.gov/abs/1102.1539 ?
Would you find it less contrived and more appealing than BM?
(In short, the equations for particle trajectories are local, but the physical time is a non-classical time non-locally related to the classical one, which provides a form of nonlocality simpler and more elegant than that in BM.)

 

[Dmitry67]

And for this reason I doubt that what you say above--that Bohmian mechanics can be viewed as equivalent to MWI + decoherence, just with one outcome "tagged" as real--could really be backed up in any precise mathematical sense. Can you point to any papers or textbooks that justify your argument rigorously?

I am not dBB proponent :)
It is not an argument, it is my understanding.

Based on MY understanding, only one, tagged observer is consicous. It is not derived from anything: it is dBB axiom. This axiom is not physical: it is not a formula or any kind a physical law: it is pure handwaving, it is expressed in words, and can't be put into mathematical framework.

Every time you listen to dBb proponent you get some inconsistent picture:
- Is wavefunction real? Yes, it is
- Are particles real? Yes, but they are undetectable
- Are 'empty' worlds real?
- No
- But how? They are described by wavefunction, and as you say, wavefunction is real.
- Hmm... Well, to be real, it must have particles inside
- So wavefunction is real, but it is not enough to be effectively real?
- Yes, non-empty branch is much more real :)

To avoid confusion, when I discussed it with Demystifier, we agreed to call branches 'tagged' to avoid using different 'flavors' of being real.

 

[Demystifier]

Every time you listen to dBb proponent you get some inconsistent picture:
...
- Are particles real? Yes, but they are undetectable

No, this is not what dBB proponents say. In fact, according to dBB, particle positions are THE ONLY THING that is directly detectable.

However, the source of confusion is the fact that, even though the particle positions are detectable, the particle trajectories predicted by dBB theory are not. But how that can be? This is because, in order to measure the trajectory, you actually need to measure the position MANY TIMES. And whenever you do that, you disturb the wave function in a way which you cannot control (i.e., decoherence takes place), which disturbs the trajectory as well, so that the measured trajectory is not the same as the one predicted by dBB in the absence of measurements. In fact, due to decoherence, the measured trajectory looks stochastic to an experimentalist, even though it is deterministic at the fundamental microscopic level.

If one could do a measurement without decoherence, then one could actually observe the Bohmian trajectories (or prove that the Bohmian theory is wrong). Unfortunately, nobody knows how to make a measurement without decoherence. Decoherence seems to wash out all the differences between various interpretations of QM.

 

[Dmitry67]

Good example

particle positions are THE ONLY THING that is directly detectable.

To clarify your statement

particle positions are THE ONLY THING that is directly detectable by a tagged observer

Tagged observers observe tagged things, empty observers observe empty things... So you must accept the handwavy axiom to get rid of the addition I highlighted with bold

 

[JesseM]

I am not dBB proponent :)

Well, I didn't say you were, and neither am I.

It is not an argument, it is my understanding.

But your understanding here is nonmathematical, correct? Do you agree that because decoherence never causes interference terms to go to zero exactly, the MWI cannot quite be viewed as an ordinary statistical ensemble of different "worlds" or "branches", so that it cannot be exactly correct to say that the dBB is simply taking a "branch" of the MWI and tagging it as conscious? Or are you claiming that dBB itself contains different "branches" and one is tagged in this way? If the latter can you point to some reference that shows that the pilot wave is mathematically equivalent to some sort of sum of different branches?

 

[JustinLevy]

Your "s'=s=0 at particle one and s'=0,s=1 at particle 2" specifies two points in spacetime. But it has nothing to do with foliation, because two points do not define a hypersurface.

Demystifier, please be reasonable.
As I said,
The Lorentz violating factor is the fixed background telling what pairs of spacetime points in the worlds lines X_1 and X_2 correspond to a "simultaneous time". This is provided by the foliation given by s. The evolution equation is only invariant to foliations that don't change this pairing

So yes, what I specified was not a unique foliation since it only gave two points. It specified a class of foliations. The point still remains that the predicted evolution changed with the choice of foliation.

But there is no FIXED background that tells it.

How can you deny this? You are not making sense.

Look at the initial value problem. If you are given a slice of spacetime with the wavefunction, its derivatives, and particle positions, can one use your evolution equation to answer whether this is enough to determine the derivatives of the particle positions? The answer is no. You need ADDITIONAL INFO. You need to know whether that slice matches with the pairings of simultaneous time defined by the structure you give in the scalar s.

There is information IN ADDITION to the wavefunction and particle positions that is needed. You must provide a FIXED background.

Furthermore, to get the full evolution (not just the particle derivative at one slice) it is not even enough to give an INITIAL pairing (ie. given where in spacetime s=0 for particle 1 and particle 2), you need to specify ALL the pairings, because changing the foliation so that s'=s at particle one and at particle two s'=2s will change the pairing and therefore effect the evolution, even though the INITIAL pairing is the same.

If you want to claim a dBB state now include the following elements:
- wavefunction
- particle positions
- s structure on spacetime

then fine, you can call those 'initial conditions' in a limited sense (limited, because you can predict the evolution of the first two state pieces, but not s). But you are claiming instead that the evolution in invariant to choice in foliation. That is clearly false.

Arguing your theory is then Lorentz invariant is the same as attempting to argue that modern Aether theories are lorentz invariant, because one can claim the background field is merely specifying the vacuum state's initial condition. While I can see what you mean by that, it is not what people mean by Lorentz invariance. You cannot change the meaning of Lorentz invariance to suit your needs. Your theory, undeniably, requires a foliation structure on spacetime which violates lorentz invariance.

 

[JesseM]

Your way of thinking is very close to mine.

I would like to see what do you think about my recent alternative to Bohmian mechanics
http://xxx.lanl.gov/abs/1102.1539 ?
Would you find it less contrived and more appealing than BM?
(In short, the equations for particle trajectories are local, but the physical time is a non-classical time non-locally related to the classical one, which provides a form of nonlocality simpler and more elegant than that in BM.)

Thanks, but the problem is that as I mentioned to JustinLevy I have only a layman-level understanding of Bohmian mechanics, I haven't actually studied the math! So I would need more study to understand your paper, but I'll save a copy and hopefully come back to it sometime when I get around to reading up on the details of dBB.

 

[Dmitry67]

Do you agree that because decoherence never causes interference terms to go to zero exactly, the MWI cannot quite be viewed as an ordinary statistical ensemble of different "worlds" or "branches", so that it cannot be exactly correct to say that the dBB is simply taking a "branch" of the MWI and tagging it as conscious? Or are you claiming that dBB itself contains different "branches" and one is tagged in this way? If the latter can you point to some reference that shows that the pilot wave is mathematically equivalent to some sort of sum of different branches?

If there are some non-zero interferation terms of wavefunction (weird combinations of an observer observing 2 fuzzy images of both cats) then in dBB particles have non-zero probability of 'leaking' into these areas. As a result, there is (a very low) chance of observing these things. So in that sense there I absolutely no difference between dBB and MWI. Otherwise one would be able to tell what theory is right using the 'partial' measurements.

 

[JesseM]

If there are some non-zero interferation terms of wavefunction (weird combinations of an observer observing 2 fuzzy images of both cats)

What do interference terms have to do with "weird combinations of an observer observing 2 fuzzy images of both cats"? I don't think that's what they'd mean in orthodox QM, I suspect they would just mean that the probabilities of different outcomes on measurement of the cat cannot be calculated in terms of a weighted sum of different classical histories, and isn't MWI intended to duplicate the predictions of orthodox QM?

then in dBB particles have non-zero probability of 'leaking' into these areas.

What do you mean by "areas"?

 

[Dmitry67]

Lets begin from the first part.
In "Ortodox" (Copenhagen) QM measurement is 100% final and irreversible, hence the following

decoherence never causes interference terms to go to zero exactly

does not happen. So modern (decoherence) based QM is slightly different from the "Ortodox" one, even the difference (for macrocopic measurement devices) is far beyond any experimental ability.

It does not include interaction-free measurements (I wonder how that types of measurements were explained in CI era)
(is my understanding correct)?

 

[JesseM]

does not happen. So modern (decoherence) based QM is slightly different from the "Ortodox" one, even the difference (for macrocopic measurement devices) is far beyond any experimental ability.

But decoherence can be modeled in the orthodox version, and indeed I think this is the way it's usually done, it's not like decoherence is characteristically associated with MWI or non-collapse interpretations in general (though certainly it strengthens the case for dropping the idea of collapse from QM). To model it using orthodox QM, the idea as I understand it is that you use the standard QM rules to model a system composed of both some subsystem S and the remainder of the system which constitutes its "environment"...then if S interacts with the environment at time T0, and if you later measure S at time T1 and model this as "collapsing the wavefunction", you can show that the probabilities of finding different outcomes for S at T1 will be nearly identical to what you'd predict if you had modeled the earlier interaction with the environment as causing another "collapse" at T0, even though in fact you modeled it using the standard deterministic rules of wavefunction evolution where the interaction of S with its environment simply resulted in their becoming entangled. Someone correct me if I'm wrong, but I think this is one valid way of understanding the meaning of decoherence and its relevance to the measurement problem.

 

[Demystifier]

Look at the initial value problem.

Yes, that is the right way of looking at it.

If you are given a slice of spacetime with the wavefunction, its derivatives, and particle positions, can one use your evolution equation to answer whether this is enough to determine the derivatives of the particle positions? The answer is no. You need ADDITIONAL INFO. You need to know whether that slice matches with the pairings of simultaneous time defined by the structure you give in the scalar s.

My claim is the following. If I know the particle positions X^{\mu}_a(s=0) and if I know the wave function and its derivatives at these positions, then my evolution equation is sufficient to determine the derivatives (with respect to s) of the particle positions at s=0. Indeed, this is exactly what Eq. (23) in my
http://xxx.lanl.gov/abs/1002.3226
says. Don't you agree with that?

 

[JustinLevy]

Demystifier,
You seem to be ignoring the points. This is math, there should be no confusion. The s-structure is needed to evaluate your equations, in contrast to what you were claiming before.

Don't you agree with that?

There, you specified an intial foliation as well. So yes, you can obtain the derivative at s=0 then. The point is you need to specify this foliation, since the solution depends on the foliation.

Nothing you said is disproving my point. In fact you seem to have just ignored it completely.

It is not clear from your response if you are still incorrectly claiming that your formulation is independent of the foliation (since you again, require one to specify an initial pairing for "s simultaneity"). So are you still claiming your formulation is independent of the s structure or not?

Another thing you avoided from the previous post.
Are you claiming a dBB state now includes the following elements?
- wavefunction
- particle positions
- s structure (a "folliation" on spacetime)

To make this even more clear to you, consider a slice of spacetime with the wavefunction, its derivatives, and particle positions. If we choose this slice as s=0, and solve for the evolution, you now have the wavefunction and particle paths in a chunk of spacetime. Now it is possible to take a different slice in this solution, and decide THAT as you initial conditions (with s=0 on this slice), you will get a DIFFERENT solution. Because, as already noting several times, the solution depends on the s structure.

Either your equations demand a preferred foliation, or they are inconsistent mathematically.

 

[Demystifier]

There, you specified an intial foliation as well. So yes, you can obtain the derivative at s=0 then. The point is you need to specify this foliation, since the solution depends on the foliation.

It seems that we don't understand each other. To repeat, I specified:
a) The spacetime positions at s=0
b) The wave function and its derivatives at these positions.
That is all that I specified, nothing more and nothing less. So are you claiming that a) also specifies a foliation?

Assuming that your answer is - yes, then my response is:
1. Although it is not strictly a foliation that a) specifies, for 2 particles it does specify a particular Lorentz frame. So you are more right than wrong about that. However,
2. This specification of the Lorentz frame is encoded in the specification of the INITIAL CONDITION. The EQUATIONS OF MOTION themselves do not specify a Lorentz frame. Consequently, the theory is still covariant, because covariance is a property of the equations of motion, not of the initial conditions.

In other words, even if one can say (by using an imprecise language) that the theory specifies a foliation, it is simply totally wrong to say that this specification of the foliation ruins the covariance. One who says that this ruins the covariance does not understand what covariance is. Covariance is a property of the equations of motion (which do not specify a foliation or anything like that). Covariance is not a property of initial conditions (which do specify something like that).

Or if you still don't get it, let me also quote from wikipedia
http://en.wikipedia.org/wiki/Bohmian_quantum_mechanics#Relativity
which says the same, but in different words:
"The relation between nonlocality and preferred foliation can be better understood as follows. In de Broglie–Bohm theory, nonlocality manifests as the fact that the velocity and acceleration of one particle depends on the instantaneous positions of all other particles. On the other hand, in the theory of relativity the concept of instantaneousness does not have an invariant meaning. Thus, to define particle trajectories, one needs an additional rule that defines which space-time points should be considered instantaneous. The simplest way to achieve this is to introduce a preferred foliation of space-time by hand, such that each hypersurface of the foliation defines a hypersurface of equal time. However, this way (which explicitly breaks the relativistic covariance) is not the only way. It is also possible that a rule which defines instantaneousness is contingent, by emerging dynamically from relativistic covariant laws combined with particular initial conditions. In this way, the need for a preferred foliation can be avoided and relativistic covariance can be saved."

Yet another way to explain that is to exploit the analogy with spontaneous breaking of symmetry (which many physicists are familiar with). The equations of motion for such a theory still obey the symmetry. Yet, a solution (more precisely - the vacuum solution - but this is not important here) does not obey the symmetry. With an abuse of terminology, one could say that relativistic Bohmian mechanics is a Lorentz invariant theory with a spontaneous breaking of Lorentz invariance.

 

[Demystifier]

So are you still claiming your formulation is independent of the s structure or not?

Actually yes, because, as long as the only goal is to calculate the trajectories in spacetime, the parameter s can be eliminated from the equations. In this sense, s is only an auxiliary parameter. If you don't see how s can be eliminated, see
http://xxx.lanl.gov/abs/quant-ph/0512065
Eq. (30).

 

[JustinLevy]

It seems that we don't understand each other. To repeat, I specified:
a) The spacetime positions at s=0
b) The wave function and its derivatives at these positions.
That is all that I specified, nothing more and nothing less. So are you claiming that a) also specifies a foliation?

Yes, more precisely, you specified:
1] the particle positions
2] the wavefunction and its derivatives (at the particle positions)

(the typical bohmian mechanics state, at least at the particle positions)
AND

3] the "simultaneity pairing structure" / foliation / s structure (at least for s=0)

If you only gave the state of the Bohmian mechanics system on a slice of spacetime (ie. not specifying 3), you could NOT solve for the dynamics.

You can ONLY consider specifying the "pairing structure" as an initial condition, if you decide that you have now added an additional structure to the state of bohmian mechanics: wavefunction, particles, and pairing-structure. You have stated otherwise, so your further statements on initial conditions are wrong, and pointless to debate until we can agree on this simple math.

I'll ignore your issues with Lorentz invariance (since they are based on misunderstanding the intial conditions situation) until we can at least agree on the math.

So are you still claiming your formulation is independent of the s structure or not?

Actually yes, because, as long as the only goal is to calculate the trajectories in spacetime, the parameter s can be eliminated from the equations. In this sense, s is only an auxiliary parameter. If you don't see how s can be eliminated, see
http://xxx.lanl.gov/abs/quant-ph/0512065
Eq. (30).

Please stop introducing new ways to write the same dynamics. You are making a similar error in that paper. We are having enough trouble agreeing on the math, that I don't want to branch out into discussing other errors at this time. Let's focus on one math error at a time.Defining the s-structure as well as the wavefunction and particle positions is clearly necessary as shown back in post 24. Unless it is always the case that
\partial^\mu_1 \partial^\nu_2 \mbox{Arg}\left[ \psi(X_1,X_2) \right] = 0
then clearly changing the foliation will change the evolution.

Put another way, and as I explained earlier:
Consider a slice of spacetime with the wavefunction, its derivatives, and particle positions. If we choose this slice as s=0, and solve for the evolution, you now have the wavefunction and particle paths in a chunk of spacetime. Now it is possible to take a different slice in this solution, and decide THAT as you initial conditions (with s=0 on this slice), you will get a DIFFERENT solution.

Either your equations demand a background s-structure to be specified, or they are inconsistent mathematically.