Where does non-locality originate in dBB theory?

[inflector]

Yeah, we definitely need Demystifier and Zenith8 to help us out here.

You might find this thread from earlier this year:

https://www.physicsforums.com/showthread.php?t=366994

interesting. The latter part of the thread is a fairly deep discussion of the nonlocality of dBB and relativity of simultaneity.

 

[nismaratwork]

You might find this thread from earlier this year:

https://www.physicsforums.com/showthread.php?t=366994

interesting. The latter part of the thread is a fairly deep discussion of the nonlocality of dBB and relativity of simultaneity.

Thanks Inflector, I'll give that a read!

 

[ThomasT]

LukeD, I noticed this statement by you:

So to me, this is "non-local" in the sense that it is local, but that the field propagates infinitely fast.

Then I said:

This doesn't make any sense to me.

Then you said:

Well Poisson's Equation in free space (Laplace's Equation)
{\nabla}^2 \varphi = 0

Can be seen to be the limit of the Wave Equation
{ \partial^2 u \over \partial t^2 } = c^2 \nabla^2 u
as the right side becomes much larger than the left (or as c^2 goes to infinity). So in free space, the Newtonian gravitational potential obeys a wave equation with infinite propagation speed.

Essentially, the Newtonian gravitation field looks just like the Electric Field if we take c->infinity and change some signs around so that the field is always attractive.

And I noticed that you also said:

If what I have said is accurate (and I have my doubts), then I see no problem with calling dBB local (but with infinite propagation speed)

So is dBB local or nonlocal or both or what? If it formalizes infinite propagation speeds (ie., simultaneous formal transformations), then it's nonlocal. Period. I think. But I await clarification by you and Demystifier and any other dBB experts.

 

[ThomasT]

This paper doesn't at all treat entanglement (though it conjectures that entanglement propagates as a field) and only notes that there is no non-locality when we have no entanglement. However, his explanation of why this occurs is very similar to my thinking about dBB. I am a disappointed though that he doesn't back up his explanation with some math.

I wonder what our dBB experts think about the idea that non-locality is due to propagation of correlations through a field in configuration space.

Well, I was hoping that you would explain exactly what Khrennikov is saying. Clarify it and refute it if necessary. I thought you were an expert on dBB.

I've emailed some guys, maybe they'll contribute maybe not.

Nobody cares about these discussions. You and Demystifier and, I almost forgot, Maaneli, and maybe a few others here know about this stuff. We're depending on you.

 

[zenith8]

'Fraid Demystifier's been .. disposed of by a gang of humiliated many worlds theorists. So you'll have to make do with me.

Yeah, we definitely need Demystifier and Zenith8 to help us out here.

Aww.. I love it when people remember me. It makes all the abuse seem worthwhile.

OK - it's late and I'm massively busy. Let's do one question at a time (nonlocality later - those threads do go on don't they?)

Let's start with this one:

Q2: As I understand, the Born rule is the 'mechanism' behind probabilities in QM measurements <\psi|P_i|\psi>. Is there any explanation in dBB to the Born rule, to make it deterministic?

Yes. Take a look at the attached picture (which I've taken from Towler's talk "The origin of the Born rule: dynamical relaxation to quantum equilibrium" in the recent deBB conference that Demystifer and Maaneli apparently were lucky enough to be invited to (http://www.vallico.net/tti/deBB_10/conference.html" ). Unlike some people I could mention. Not that I'm sulking.)

The top three images show the time-dependence of the square of the wave field (taken to be the physical object mathematically represented by the Schroedinger wave function).

The bottom three images show the time-dependence of the density \rho of particles (deliberately taken to be NOT equal to the square of the wave function, at least initially). The trajectories of these particles are being influenced by the changing shape of the wave field.

Note how the particle density evolves in the course of time.

There is a prize for the first person who posts telling me how that explains the Born rule. No clues now, it's not easy.

 

[LukeD]

So is dBB local or nonlocal or both or what? If it formalizes infinite propagation speeds (ie., simultaneous formal transformations), then it's nonlocal. Period. I think. But I await clarification by you and Demystifier and any other dBB experts.

Ah, I'm not a dBB expert. I'm afraid I don't think I even understand Quantum Mechanics that well. What I meant is that I have no reason to believe that the propagation speed (of the field in configuration space) remains infinite in the fully relativistic theory, and that such a theory would be local.

There is a prize for the first person who posts telling me how that explains the Born rule. No clues now, it's not easy.

On the top, we have |\psi|(t)^2 and on the bottom with have an actual probability distribution Q that starts off away from |\psi|(t)^2. If we propagate Q with the velocity given by dBB, then it eventually converges to |\psi|(t)^2.
As far as how this "proves" the Born rule... If we assume that the wavefunction \psi exists and determines the probability distribution's velocity, but the probability distribution does not start off obeying the Born rule, then the probability distribution eventually resembles the Born distribution. so the Born distribution is an equilibrium distribution

 

[ThomasT]

'Fraid Demystifier's been .. disposed of by a gang of humiliated many worlds theorists. So you'll have to make do with me.


Aww.. I love it when people remember me. It makes all the abuse seem worthwhile.

OK - it's late and I'm massively busy. Let's do one question at a time (nonlocality later - those threads do go on don't they?)

Let's start with this one:


Yes. Take a look at the attached picture (which I've taken from Towler's talk "The origin of the Born rule: dynamical relaxation to quantum equilibrium" in the recent deBB conference that Demystifer and Maaneli apparently were lucky enough to be invited to (http://www.vallico.net/tti/deBB_10/conference.html" ). Unlike some people I could mention. Not that I'm sulking.)

The top three images show the time-dependence of the square of the wave field (taken to be the physical object mathematically represented by the Schroedinger wave function).

The bottom three images show the time-dependence of the density \rho of particles (deliberately taken to be NOT equal to the square of the wave function, at least initially). The trajectories of these particles are being influenced by the changing shape of the wave field.

Note how the particle density evolves in the course of time.

There is a prize for the first person who posts telling me how that explains the Born rule. No clues now, it's not easy.

Well, rho|psi|² has to be the initial density, afaik. But I'm not sure how to read these pictures.

 

[zenith8]

Well, rho|psi|² has to be the initial density, afaik. But I'm not sure how to read these pictures.

No prize.

Think in deBB terms, not in orthodox QM. Particles and waves exist. The particle distribution and the wave field are now logically separate entities. In principle their shapes do not have to be related to each other. If I want to start with them being different, then I can.

Anyone else?

 

[ThomasT]

Ah, I'm not a dBB expert. I'm afraid I don't think I even understand Quantum Mechanics that well. What I meant is that I have no reason to believe that the propagation speed (of the field in configuration space) remains infinite in the fully relativistic theory, and that such a theory would be local.

Don't sweat it. We're all novices here wrt dBB except Demystifier and Zenith8, and maybe a few others, I think. Now, if the experts will just come back, we can listen and learn. And of course Google and Yahoo and arxiv.org, etc.

 

[nismaratwork]

It should be noted that the status of the Born rule has been a contentious issue
in quantum theory generally, perhaps most notably in the many-worlds formulation
of Everett (Deutsch 1999; DeWitt & Graham et al. 1973; Wallace 2004). Some
recent authors (Barnum et al. 2000; Caves et al. 2002) base their justification of the
Born rule on Gleason’s theorem (Gleason 1957), which states that the Born rule is
the unique probability assignment satisfying ‘non-contextuality’—the condition that
Proc. R. Soc. A (2005)
Downloaded from rspa.royalsocietypublishing.org on October 3, 2010
Dynamical origin of quantum probabilities 271
the probability for an observable should not depend on which other (commuting)
observables are simultaneously measured. However, as pointed out by Bell (1966),
Gleason’s non-contextuality condition is very strong, as it amounts to assuming that
mutually incompatible experimental arrangements yield the same statistics for the
observable in question. A recent ‘operational’ derivation of the Born rule by Saunders
(2004) assumes that probabilities are determined by the quantum state alone;
while Zurek (2003) appeals to ‘environment-assisted invariance’ to derive the Born
rule. Other recent derivations of the Born rule arise from novel axioms for quantum
theory (Clifton et al. 2003; Hardy 2002a,b).
Like Euclid’s axiom of parallels in geometry, the Born rule seems to stand apart
from the other axioms of quantum theory, and there have been a number of attempts
to derive it either from the other axioms or from something else. We have argued in
this paper that, in the de Broglie–Bohm formulation of quantum theory, the Born rule
has a status similar to that of thermal equilibrium

from: http://rspa.royalsocietypublishing.org/content/461/2053/253.full.pdf

Is the Born rule truly helpful here?

 

[inflector]

The top three images show the time-dependence of the square of the wave field (taken to be the physical object mathematically represented by the Schroedinger wave function).

The bottom three images show the time-dependence of the density \rho of particles (deliberately taken to be NOT equal to the square of the wave function, at least initially). The trajectories of these particles are being influenced by the changing shape of the wave field.

Note how the particle density evolves in the course of time.

There is a prize for the first person who posts telling me how that explains the Born rule. No clues now, it's not easy.

It sure looks like the density matching the square of the wave function simply emerges from the dynamics of the effects of the wave field. The densities go from one that doesn't match the wave function squared at all to one that closely tracks by the third column. Which means that the Born Rule is emergent in dBB. Right?

 

[LukeD]

Anyone else?

What about my try?

My only disagreement with this viewpoint that it is a proof of the Born rule is that if we have the wavefunction, then we already have the distribution. Instead, I like to view this result about the Born distribution being an equilibrium as beig in terms of a distribution and a conservative velocity field (the 2 things we need to get the wavefunction and describe the dynamics of dBB). Then, if we have a small rouge sample (a small sample of the total distribution that does not obey the |\psi|^2 statistics) and if it is so small that it's existence doesn't effect the dynamics of the larger distribution, the "rouge sample"'s statistics eventually approach that of the larger distribution.

In other words, perturbations on the |\psi|^2 distribution get smoothed out until they have no effect if the perturbations are small enough that we can use the unperturbed \frac{\nabla S}{m} velocity

 

[Demystifier]

I haven't been here for a couple of days. Many questions have been asked during this time, and some of them have been answered. Unfortunately, I don't have time to answer all these questions by myself. So please, if you still want me to answer some PARTICULAR questions, draw my attention to them again.

Thanks!

 

[ThomasT]

I haven't been here for a couple of days. Many questions have been asked during this time, and some of them have been answered. Unfortunately, I don't have time to answer all these questions by myself. So please, if you still want me to answer some PARTICULAR questions, draw my attention to them again.

Thanks!

Thank you. Just point us to the best sources that you know for learning dBB, especially for non-experts if possible, and then you probably won't have to, er, endure, any of our questions for at least a few days. Possibly weeks, who knows.

 

[ThomasT]

It sure looks like the density matching the square of the wave function simply emerges from the dynamics of the effects of the wave field. The densities go from one that doesn't match the wave function squared at all to one that closely tracks by the third column. Which means that the Born Rule is emergent in dBB. Right?

This seems generally/essentially right to me. But I'm generally/essentially ignorant about this stuff, so hopefully Zenith8, or Demystifier, or DA, or nismaratwork, or Maaneli, or LukeD ... or somebody, will give the definitive answer.

My two cents, on looking at this again, is that it's assumed, via Bohmian mechanics, that the evolution of the wave field is determining the particle density. Particle density, ie., the probabiltiy of detection, is directly proportional to wave amplitude. The Born rule in qm says that the probability of a particular detection at a particular position at a particular time is the square of the amplitude of the wavefunction at that position at that time. At t - 4pi the particle density evolution matches the wave field evolution. Hence, the Bohmian mechanical evolution has reproduced, in a more 'natural' way equivalent to the evaluation of qm wavefunctions via the Born rule in standard qm, the probability of detection at a particular position and time.

I think this is essentially equivalent to what LukeD said. But I'm not sure, so hopefully LukeD will clarify.

Edit: I thought I might add that, apparently, the Born rule is a very deep physical insight. And the fact that it emerges more or less 'naturally' in dBB is, well, sort of exciting.

 

[zenith8]

It sure looks like the density matching the square of the wave function simply emerges from the dynamics of the effects of the wave field. The densities go from one that doesn't match the wave function squared at all to one that closely tracks by the third column. Which means that the Born Rule is emergent in dBB. Right?

Correct! If you happen to live in the same country as me, then I'll send you a coconut.

If the electron density distribution is not equal to the square of the wave field, and the system is evolving according to the laws of QM, then it will become so distributed over the course of time. Once so distributed, it will stay like that for ever. Psi^2 is the only distribution with this property.

This is entirely analagous to the usual approach to thermal equilibrium, which is why one talks about 'quantum equilibrium' and 'quantum-nonequilibrium'

The reason why the Born rule seems to be true whenever we make a measurement now is that the universe has a long and violent astrophysical history and it has had plenty of time to come into equilibrium. The current state of the universe is analagous to the the usual thermodynamical `heat death' - except it's just happened quicker.

Note that this has potential observable consequences. Look far back in time enough (e.g. by looking at the cosmic microwave background) and maybe you'll find something that isn't in equilibrium yet..

Just to make this result aesthetically pleasing, look at http://www.tcm.phy.cam.ac.uk/~mdt26/raw_movie.gif" from the same site I gave earlier. This shows the whole process of approaching equilibrium for a system in a 2D box. The cool thing is effect of nodes. Do you see all those little vortices moving around, stirring everything up? Those are the nodes - the singularities in the velocity field where the wave field goes to zero.. The more of them you have, the more chaotic the system, and the quicker the approach to equilibrium. Cool, or what?

from: http://rspa.royalsocietypublishing.o...3/253.full.pdf

Is the Born rule truly helpful here?

Good link. Indeed, as far as I know, Valentini and Westman were the first people to do calculations like the above..

My only disagreement with this viewpoint that it is a proof of the Born rule is that if we have the wavefunction, then we already have the distribution.

No you don't. That's a postulate of orthodox QM, not of de Broglie-Bohm..

Thank you. Just point us to the best sources that you know for learning dBB, especially for non-experts if possible, and then you probably won't have to, er, endure, any of our questions for at least a few days. Possibly weeks, who knows.

The http://www.tcm.phy.cam.ac.uk/~mdt26/pilot_waves.html" has a full graduate lecture course, popular lectures, links to pretty much every deBB paper ever published including lots of review articles. I would start there.

Start with the `Supplementary Popular Lecture' called 'The return of pilot waves, or why Bohr, Heisenberg, Pauli, Born, Schrödinger, Oppenheimer, Feynman, Wheeler, von Neumann and Einstein were all wrong about quantum mechanics' - very funny.

By the way, a good intro into the relativistic non-locality stuff that this thread is supposed to be about is in Lecture 5 of the course.

OK - next question. Demystifier's turn, I think. I have to go away for the day.

 

[Demystifier]

Thank you. Just point us to the best sources that you know for learning dBB, especially for non-experts if possible, and then you probably won't have to, er, endure, any of our questions for at least a few days. Possibly weeks, who knows.

In my opinion, the best source is the book by P. Holland. But if it is too much for a start, then you can start, e.g., with these two reviews:
http://www.tcm.phy.cam.ac.uk/~mdt26/local_papers/bohm_hiley_kaloyerou_1986.pdf
http://www.tcm.phy.cam.ac.uk/~mdt26/local_papers/passon_2006.pdf

 

[nismaratwork]

Thank you to both Zenith8, and Demystifier... I have a lot of reading to do.

 

[unusualname]

For those interested in the historical origins and early objections to de Broglie's pilot wave idea you shouldn't miss:

Quantum Theory at the Crossroads: Reconsidering the 1927 Solvay Conference (pdf)

this is a draft of the 533 page book published recently by Cambridge University press

 

[inflector]

Correct! If you happen to live in the same country as me, then I'll send you a coconut.

Just credit me one virtual coconut and I'll be fine. I spent 6 years in the U.S. Virgin Islands so I have had my share of the real ones.

What I find remarkable is how this is the first time I have heard of this result. Seriously? The Born Rule just falls out of the dynamics of dBB? That is an astounding result. The fact that I haven't heard of this before despite my interest in dBB for at least 18 months is just testimony to the effects of the status quo on people's thinking.

 

[unusualname]

I fail to see what is surprising about deterministic particle trajectories guided by a Schrodinger Equation having (and evolving to) an invariant probability density given by |Psi|^2. Since we already know that |Psi|^2 is the conserved probability density for the SE!

 

[inflector]

I fail to see what is surprising about deterministic particle trajectories guided by a Schrodinger Equation having (and evolving to) an invariant probability density given by |Psi|^2. Since we already know that |Psi|^2 is the conserved probability density for the SE!

What's surprising is NOT the result

\rho = |\psi|^2

which is, as you stated, what we already knew.

What is surprising is how this behavior—which we already know is true through experimental observation—emerges from the equations for the dynamic guidance of the particles.

Consider the second paper Demystifier linked to above:

http://www.tcm.phy.cam.ac.uk/~mdt26/local_papers/passon_2006.pdf

In this paper, it states three postulates for dBB theory. The third is:

3. The position-distribution, \rho, of an ensemble of systems which are described by the wave function, \psi, is given by |\psi|^2. This postulate is called the quantum equilibrium hypothesis.

So in dBB the Born rule is postulated.

Note from: http://www.math.ru.nl/~landsman/Born.pdf on the last page, the first two sentences of the last paragraph of the paper:

In most interpretations of quantum mechanics, some version of the Born rule is simply postulated. This is the case, for example, in the → Consistent histories interpretation, the → Modal interpretation and the → Orthodox interpretation.

I always found the mere postulation of the Born Rule to be unnatural and evidence of a weakness in the theories that required it.

So now with these results from Valentini et al. and Towler more recently, we have a deep and important postulate emerging from only the first two postulates of dBB thereby removing the need for the third postulate entirely. So now rather than relying on three postulates, dBB only requires two, the wave function and the guidance equation alone since the Born Rule emerges naturally from the first two postulates.

You don't find this surprising?

 

[zenith8]

I fail to see what is surprising about deterministic particle trajectories guided by a Schrodinger Equation having (and evolving to) an invariant probability density given by |Psi|^2. Since we already know that |Psi|^2 is the conserved probability density for the SE!

It might be obvious to you, Mr. name, but it sure isn't obvious to anyone else. Take the recently published "Compendium of Quantum Physics" (published by Springer in 2008) - available at Google books http://books.google.co.uk/books?id=...resnum=1&ved=0CC4Q6AEwAA#v=onepage&q&f=false". At the end of the article on the Born rule, the author states (p. 69):

"The conclusion seems to be that no generally accepted derivation of the Born rule has been given to date, but this does not imply that such a derivation is impossible in principle."

What he does not mean is "I've considered the deBB explanation of this but it's not generally accepted." He just (of course) doesn't mention it - though he mentions most of the other 'interpretations'. That a guy can do that in a well-researched Encyclopedia article is just scandalous but entirely typical.

So, if it's so obvious, can you derive it mathematically? How would you go about doing that?

So now with these results from Valentini et al. and Towler more recently, we have a deep and important postulate emerging from only the first two postulates of dBB thereby removing the need for the third postulate entirely. So now rather than relying on three postulates, dBB only requires two, the wave function and the guidance equation alone since the Born Rule emerges naturally from the first two postulates.

Inflector - I entirely agree with you. Funnily enough, even the guidance equation doesn't really have to be postulated (though there are some subtleties). If you simply state that probability means 'probability of a particle being at x' as opposed to 'probability of a particle being found at x in a suitable measurement' then the guidance equation is essentially just a transcription of the usual expression for the probability current (which is non-zero only in a non-stationary state with a moving charge distribution, obviously)...

Early presentations of the deBB theory did indeed include \rho = |\Psi|^2 as a postulate, but it is now widely understood that this is not necessary. That doesn't stop people still writing this in review articles though, as you've seen.

 

[inflector]

Take the recently published "Compendium of Quantum Physics" (published by Springer in 2008) - available at Google books http://books.google.co.uk/books?id=...resnum=1&ved=0CC4Q6AEwAA#v=onepage&q&f=false". At the end of the article on the Born rule, the author states (p. 69):

"The conclusion seems to be that no generally accepted derivation of the Born rule has been given to date, but this does not imply that such a derivation is impossible in principle."

The Born Rule chapter in that compendium appears to be the same as the one I quoted from and linked to earlier at http://www.math.ru.nl/~landsman/Born.pdf. The author must have posted an excerpt of his chapter separately.

Early presentations of the deBB theory did indeed include \rho = |\Psi|^2 as a postulate, but it is now widely understood that this is not necessary. That doesn't stop people still writing this in review articles though, as you've seen.

Interesting, I didn't know that. Thanks for the help and updates.

 

[zenith8]

The Born Rule chapter in that compendium appears to be the same as the one I quoted from and linked to earlier at http://www.math.ru.nl/~landsman/Born.pdf. The author must have posted an excerpt of his chapter separately.

Ah, sorry.. I didn't make that connection.

 

[unusualname]

It might be obvious to you, Mr. name, but it sure isn't obvious to anyone else. Take the recently published "Compendium of Quantum Physics" (published by Springer in 2008) - available at Google books http://books.google.co.uk/books?id=...resnum=1&ved=0CC4Q6AEwAA#v=onepage&q&f=false". At the end of the article on the Born rule, the author states (p. 69):

"The conclusion seems to be that no generally accepted derivation of the Born rule has been given to date, but this does not imply that such a derivation is impossible in principle."

What he does not mean is "I've considered the deBB explanation of this but it's not generally accepted." He just (of course) doesn't mention it - though he mentions most of the other 'interpretations'. That a guy can do that in a well-researched Encyclopedia article is just scandalous but entirely typical.

So, if it's so obvious, can you derive it mathematically? How would you go about doing that?

No I probably couldn't derive it, but I'm pretty sure that this type of result is common in ergodic dynamical systems, admittedly the general mathematical theorems from that subject aren't always easily applicable to real-world examples (or in fact even to many simple toy systems), but it's often difficult to get analytic rigour in theoretical physics (these days)

By "not surprising" I just mean it's common with chaotic deterministic dynamics to have the phase space trajectories evolve to an invariant probability density, but I may have misunderstood the technicalities which are being addressed here with regard to specifying the problem. I do agree that mathematically it is a difficult result to derive, but it sounds a bit like the proof that the Lorentz Attractor exists (Tucker ~1999) which was difficult but no one was really surprised.

 

[DevilsAvocado]

So now rather than relying on three postulates, dBB only requires two, the wave function and the guidance equation alone since the Born Rule emerges naturally from the first two postulates.

You don't find this surprising?

Yes I do. I find it very surprising, but maybe in a 'slightly' different manner...

Postulate 3
. . .
However, while it is ensured that the quantum equilibrium hypothesis is satisfied for a configuration which is |ψ|² distributed once, it is by no means clear why any configuration should be accordingly distributed initially.
. . .
However, there exists a more convincing approach to justify the quantum equilibrium hypothesis. Work by Dürr/Goldstein/Zanghi (1992) shows, that the quantum equilibrium hypothesis follows by the law of large numbers from the assumption that the initial configuration of the universe is "typical" for the |\Psi|^2 distribution (with \Psi being the wavefunction of the universe).
. . .
According to this view the quantum equilibrium hypothesis is no postulate of the de Broglie-Bohm theory but can be derived from it.

??

The initial configuration of the universe is "explained" by the law of large numbers?

The law of large numbers: The expected value of a single die roll is 3.5, with the accuracy increasing as more dice are rolled.

I have to tell you that chance that the initial configuration of the universe can be "explained" by the law of large numbers, is the same as a dice will actually show 3.5, if you just roll it long enough...

This does not look like derivation, but a mathematical variant of the dreadful http://en.wikipedia.org/wiki/Antropic_principle" .

 

[DevilsAvocado]

For those interested in the historical origins and early objections to de Broglie's pilot wave idea you shouldn't miss:

Quantum Theory at the Crossroads: Reconsidering the 1927 Solvay Conference (pdf)

this is a draft of the 533 page book published recently by Cambridge University press

THANKS unusualname! Extremely interesting, goes straight into the HDD archive!

 

[DevilsAvocado]

I’ll be back later, h**l of a lot to read...

 

[zenith8]

Yes I do. I find it very surprising, but maybe in a 'slightly' different manner...??

The initial configuration of the universe is "explained" by the law of large numbers?

The law of large numbers: The expected value of a single die roll is 3.5, with the accuracy increasing as more dice are rolled.

I have to tell you that chance that the initial configuration of the universe can be "explained" by the law of large numbers, is the same as a dice will actually show 3.5, if you just roll it long enough...

This does not look like derivation, but a mathematical variant of the dreadful http://en.wikipedia.org/wiki/Antropic_principle" .

There are two 'schools of thought' on this in the deBB community.

(1) Sheldon Goldstein's crew believe that the initial conditions of the universe were such that, because our universe is 'typical', the particles were distributed as \Psi^2 right from the Big Bang. They aggressively promote the view that anyone who believes otherwise is an idiot.

(2) Almost everyone else (including, for what it's worth, me) believes that one should show that \rho=\Psi^2 arises dynamically, irrespective of the initial conditions. This is what Valentini, Westman, Towler et al. appear to have done.

To me it's completely obvious that the second view is the correct one - assumptions about initial conditions can always be wrong.

You seem to be mixing up these two diametrically opposed point of view.