Exploring Non-Locality in dBB Theory: Insights from EPR and Bell's Inequalities

[nismaratwork]

I mean the latter.

OK, understood... that's what I believed dBB proposed in the first place, and much of what makes it a distinct theory that hasn't been culled along with everything except QM.

 

[DevilsAvocado]

heh... ok I get it, big picture

No worries mate. It’s just that my new 142" LED display isn’t delivered until Monday and my arm just give up scrolling infinitely horizontal... ()

@All you guys:
Even though I had Polar Bear for breakfast, it’s time for a refill. I think its Polarizer Bear on the menu. (Buuuhhhh :/)

Be back later... lot to answer.

 

[nismaratwork]

No worries mate. It’s just that my new 142" LED display isn’t delivered until Monday and my arm just give up scrolling infinitely horizontal... ()

@All you guys:
Even though I had Polar Bear for breakfast, it’s time for a refill. I think its Polarizer Bear on the menu. (Buuuhhhh :/)

Be back later... lot to answer.

Salt... in... wounds... *gasp* So cruel!

Now man up and buy this! http://www.gizmag.com/toob-dome-screen/12635/

 

[DevilsAvocado]

Now man up and buy this! http://www.gizmag.com/toob-dome-screen/12635/

Cool!

I’m canceling my order!

When thinking more about it... a Swedish guy has come up with an even simpler solution, the retail will be approx 200 bucks:

https://www.youtube.com/watch?v=<object width="640" height="385">
<param name="movie" value="http://www.youtube.com/v/rNsFSVhZi9w&fs=1&amp;hl=en_US&amp;rel=0&amp;color1=0x3a3a3a&amp;color2=0x999999"></param>
<param name="allowFullScreen" value="true"></param>
<param name="allowscriptaccess" value="always"></param>
<embed src="http://www.youtube.com/v/rNsFSVhZi9w&fs=1&amp;hl=en_US&amp;rel=0&amp;color1=0x3a3a3a&amp;color2=0x999999" type="application/x-shockwave-flash" allowscriptaccess="always" allowfullscreen="true" width="640" height="385"></embed>
</object>

 

[DevilsAvocado]

Yes, that interests me very much, because it helps me to understand why many people don't like dBB.

I especially like your point:
"from a perspective "outside math", dBB looks like maybe the most complex thing one can ever think of"

Cool if I can help you in any way. (As I said, PF never stops to surprise me! )

Now I perfectly understand what makes you think so. Yet, when dBB is viewed from a mathematical point of view, it looks remarkably simple. In fact, all except one equations in
http://xxx.lanl.gov/abs/1002.3226
are equations of "standard" purely probabilistic QM. Relativistic dBB adds ONLY ONE equation, which is the last equation, Eq. (23).

That’s very interesting. I must tell you that to a layman there is some "lingual confusion" regarding dBB. It is called the de Broglie–Bohm theory, the Pilot-wave theory, Bohmian mechanics, and the Causal interpretation. So what is it, theory or interpretation...?
(When it comes to MWI, it’s 'just' an interpretation = no physical evidence [yet ].)

I wish I could understand the full extent of Eq. (23), I’m just guessing, but it looks like
(X1(s), . . . ,Xn(s))
is about "a statistical ensemble of particles", right?

Q1: Is your solution to making nonlocal reality compatible with relativity, unconditionally depending on a statistical ensemble of particles?
(Explanation to why this has caught my interest in next post.)

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?

Because it is MUCH EASIER to construct a nonlocal (Bohmian) superdeterministic theory that agrees with predictions of QM, than a local one. There are people who struggle with construction of an explicit local superdeterministic theory (like 't Hooft), but it is much more difficult to do it, even if possible in principle.

(I have to take one step back and reconsider this)

Do we really have to bother with nonlocal/local if we explain the world in superdeterministic terms? What’s the problem? We run "ordinary" QM and conclude that the only reason we see entangled correlations between Alice & Bob is because everything we did in the EPR-Bell experiment was already settled from the Big Bang = no spooky action at a distance, just "plain & simple" superdeterminism?

Afaict, we can run the good old 1927 Copenhagen interpretation without any modification, and wind up with an "add-on" for the superdeterministic part (that 'acts' in a probabilistic way), sometime in the future (like http://arxiv.org/abs/0903.3680" ) ...

What am I missing?

 

[DevilsAvocado]

Do you actually ask "What is the Lorentz frame with respect to which the Bohmian force is instantaneous?". If THAT is your question, then the answer in the relativistic-covariant version of dBB is simple: If you repeat the experiment many times, then each time it will probably be ANOTHER Lorentz frame, because it (the Lorentz frame) is determined by initial conditions on Bohmian spacetime positions, which are usually different in each repeat of the experiment.

According to Special Relativity, depending on which frame of reference you are, you will see Alice first performing her measurement and thereby decohere the shared wavefunction, and decide what Bob will measure. In another frame of reference you will see the opposite, Bob will decide what Alice will measure. And in a third frame of reference, all will be simultaneous.

See #33, and a quote from the paper:
R: "... However, due to the superluminal influences, 'prior' does not always need to mean 'at an earlier time'."

The following quotes may also help:

On nonrelativistic BM:
No one can understand this theory until he is willing to think of psi as a real objective field rather than just a 'probability amplitude'.
John S. Bell

On relativistic BM:
No one can understand this theory until he is willing to think of x as a position in a 4-dimensional space, rather than just a collection of two conceptually different entities: 3-space position and 'time'.
H.N.

Let’s take it conceptually step by step. This is the setup:

• A laser source produces entangled pairs of photons through a BBO crystal.
  
  
• There measuring polarizers are separated by 20 km, and it takes light 66 microseconds (10^-6) to travel 20 km (in vacuum) from Alice to Bob.
  
  
• The total time for electronic and optical processes in the path of each photon at the detector is calculated to be approximately 100 nanoseconds (10^-9).
  
  
• The settings of the polarizers at Alice & Bob are independently and randomly chosen every 100 nanosecond (10^-9).
  
  
• Type II PDC crystal is used, yielding anti-correlated photon pairs.
  
  
• When the polarizers are aligned parallel (0º/0º), the result will be [0, 1] or [1, 0] unconditionally, so-called perfect correlations.
  
  
• When the polarizers are aligned anti-parallel (0º/180º), the result will be [0, 0] or [1, 1] unconditionally, so-called perfect correlations.

EPR-Bell experiment according to traditional QM + Superdeterminism (yet to be discovered):

• Alice, Bob & Chris diced to run an EPR-Bell experiment to verify Bell's theorem. They think that it’s their own decision, when in fact all has been settled from the Big Bang.
  
  
• They "diced" to let the two polarizers vary randomly and independent between the two fixed values 0º & 180º. (They don’t know that there is nothing random in the universe.)
  
  
• They have setup two big laser beams to signal high in the air when an entangled photon hits the measuring apparatus. (This is a 'futuristic function', only possible when we get a 100% 'clean' entangled source.)
  
  
• Alice & Bob travel to their polarizer & measuring apparatus.
  
  
• Chris starts the laser source, and immediately he sees the two laser beams in the sky, simultaneously.
  
  
• Alice will see her laser beam light up the sky before Bob’s laser beam light up.
  
  
• Bob will see his laser beam light up the sky before Alice’s laser beam light up.
  
  
• They all get together to verify the results, and they see that there is a perfect correlation between Alice & Bob. There is no disagreement about that.
  
  
• But then they start analyze in what order things happened, and a big quarrel starts. They can’t agree on the order, and they know that the shared wavefunction for the entangled pair can only decohere/collapse ONCE! And they know that if Alice was first she would have settled the outcome unconditionally for Bob, and if Bob was first he would have settled the outcome unconditionally for Alice!? Total confusion arises...
  
  
• They can’t find a solution to the problem, and starts writing https://www.physicsforums.com/showthread.php?t=395509".
  
  
• What they don’t know is that there is no nonlocal-relativity-correlation-problem at all, because absolutely everything was settled from the beginning! Every atom and photon in the experiment was predestinated, including the "random" polarizers. There was no superluminal collapse of the shared wavefunction. All they saw was an ordinary relativity experiment, where observers do have different experience of the ordering of events, i.e. perfectly normal.

EPR-Bell experiment according to the de Broglie–Bohm theory:
(Due to my lack of understanding, this is obviously wrong and needs to be CORRECTED.)

• Everything is the same as in the first example, until Alice, Bob & Chris gets together to analyze the experiment.
  
  
• They come to the conclusion that even though the polarizers are randomly set at very high speed, in the last nanosecond when the polarizer is fixed, a superluminal pilot-wave is sent out to ensure that the two entangled photons shows a perfect correlation when measured. All this happens in the very last nanosecond, when the two entangled photons are "in flight".
  
  
• First they get a little confused... why a pilot-wave if everything including the outcome is already settled by superdeterminism? But they decide to leave this problem for now, because there are worse things...
  
  
• They realize that "the last nanosecond" is dependent on relativity. Alice before Bob, or vice versa? They know that there is no "voting facility" in the pilot-wave, one has to decide, but whom!?
  
  
• They all go crazy and decide to start terrorizing Demystifier on Physics Forum.

P.S. Both experiments were repeated with only ONE photon pair measured and then a pause for 1 hour, for 10 hours/day, during 100 days, to avoid any "ensemble interpretations" – with exactly the same outcome and problems.

 

[nismaratwork]

Let’s take it conceptually step by step. This is the setup:

• A laser source produces entangled pairs of photons through a BBO crystal.
  
  
• There measuring polarizers are separated by 20 km, and it takes light 66 microseconds (10-6) to travel 20 km (in vacuum) from Alice to Bob.
  
  
• The total time for electronic and optical processes in the path of each photon at the detector is calculated to be approximately 100 nanoseconds (10-9).
  
  
• The settings of the polarizers at Alice & Bob are independently and randomly chosen every 100 nanosecond (10-9).
  
  
• Type II PDC crystal is used, yielding anti-correlated photon pairs.
  
  
• When the polarizers are aligned parallel (0º/0º), the result will be [0, 1] or [1, 0] unconditionally, so-called perfect correlations.
  
  
• When the polarizers are aligned anti-parallel (0º/180º), the result will be [0, 0] or [1, 1] unconditionally, so-called perfect correlations.

EPR-Bell experiment according to traditional QM + Superdeterminism (yet to be discovered):

• Alice, Bob & Chris diced to run an EPR-Bell experiment to verify Bell's theorem. They think that is their own decision, when in fact all has been settled from the Big Bang.
  
  
• They "diced" to let the two polarizers vary randomly and independent between the two fixed values 0º & 180º. (They don’t know that there is nothing random in the universe.)
  
  
• They have setup two big laser beams to signal high in the air when an entangled photon hits the measuring apparatus. (This is a 'futuristic function', only possible when we get a 100% 'clean' entangled source.)
  
  
• Alice & Bob travel to their polarizer & measuring apparatus.
  
  
• Chris starts the laser source, and immediately he sees the two laser beams in the sky, simultaneously.
  
  
• Alice will see her laser beam light up the sky before Bob’s laser beam light up.
  
  
• Bob will see his laser beam light up the sky before Alice’s laser beam light up.
  
  
• They all get together to verify the results, and they see that there is a perfect correlation between Alice & Bob. There is no disagreement about that.
  
  
• But then they start analyze in what order things happened, and a big quarrel starts. They can’t agree on the ordering, and they know that the shared wavefunction for the entangled pair can only decohere/collapse once! And they know that if Alice was first she would have settled the outcome unconditionally for Bob, and if Bob was first he would have settled the outcome unconditionally for Alice!? Total confusion arises...
  
  
• They can’t find a solution to the problem, and starts writing https://www.physicsforums.com/showthread.php?t=395509".
  
  
• What they don’t know is that there is no nonlocal-relativity-correlation-problem at all, because absolutely everything was settled from the beginning! Every atom and photon in the experiment was predestinated, including the "random" polarizers. There was no superluminal collapse of the shared wavefunction. All they saw was an ordinary relativity experiment, where observers do have different experience of the ordering of events, i.e. perfectly normal.

EPR-Bell experiment according to the de Broglie–Bohm theory:
(Due to my lack of understanding, this is obviously wrong and needs to be CORRECTED.)

• Everything is the same as in the first example, until Alice, Bob & Chris gets together to analyze the experiment.
  
  
  [*]They come to the conclusion that even though the polarizers are randomly set at very high speed, in the last nanosecond when the polarizer is fixed, a superluminal pilot-wave is sent out to ensure that the two entangled photons shows a perfect correlation when measured. Al this happens in the very last nanosecond, when the two entangled photons are "in flight".
  
  
  [*]First they get a little confused... why a pilot-wave if everything including the outcome is already settled by superdeterminism? But they decide to leave this problem for now, because there are worse things...
  
  
  [*]They realize that "the last nanosecond" is dependent on relativity. Alice before Bob, or vice versa? They know that there is no "voting facility" in the pilot-wave, one has to decide, but whom!?
  
  
• They all go crazy and decide to start terrorizing Demystifier on Physics Forum.

P.S. Both experiments where repeated with only ONE photon pair measured and then a pause for 1 hour, for 10 hours/day, during 100 days, to avoid any "ensemble interpretations" – with exactly the same outcome and problems.

@Bolded portion... That's what really confuses me about dBB, and I also suspect it's a lack of knowledge on my part. To me, the concept of a Pilot Wave sounds like the hand of god, in the shape of the Schrodinger equation.

 

[DevilsAvocado]

@Bolded portion... That's what really confuses me about dBB, and I also suspect it's a lack of knowledge on my part. To me, the concept of a Pilot Wave sounds like the hand of god, in the shape of the Schrodinger equation.

Yeah agree, it will be very interesting to hear what DeM has to say...

 

[nismaratwork]

Yeah agree, it will be very interesting to hear what DeM has to say...

From what little I understand, Schrodinger 'trajectories' replace the standard QM sum over paths, and it's the pilot wave that causes interference... it still sounds odd to me. Then again, it's clear Demystifier is very familiar with this theory, and I know I'm not.

 

[DevilsAvocado]

From what little I understand, Schrodinger 'trajectories' replace the standard QM sum over paths, and it's the pilot wave that causes interference... it still sounds odd to me. Then again, it's clear Demystifier is very familiar with this theory, and I know I'm not.

Yeah that’s my understanding too. There’s only one problem – as soon as you start involving "superluminal stuff" – you will have trouble in SR. And this goes for all, including Schrödinger wavefunction, or Pilot wave, or Little Green Men working very fast...

It’s predestinated to be messy, just because there is ONE thing that settles the outcome for TWO, and Einstein won’t let go on this situation just that easy.

You can start speculate about foliation of space-time, or holographic, or any other complicated solution.

Or you can just say that Special Relativity is wrong.

Both options are extremely tough.

 

[inflector]

They realize that "the last nanosecond" is dependent on relativity. Alice before Bob, or vice versa? They know that there is no "voting facility" in the pilot-wave, one has to decide, but whom!?

@Bolded portion... That's what really confuses me about dBB, and I also suspect it's a lack of knowledge on my part. To me, the concept of a Pilot Wave sounds like the hand of god, in the shape of the Schrodinger equation.

I understand it this way (but please feel free to correct me Demystifier if I get this wrong): once you invoke the idea of superluminal communication, "the last nanosecond" is not dependent on relativity that is constrained to lightspeed. In normal relativity, due to the speed of light limit, you have different "time" for each particle as they are separated.

In some sense, in dBB the entanglement ties together the time of the two frames such that they can been looked upon as if they were not separated by distance, or are separated by an arbitrarily small distance. So from the perspective of the two entangled particles there is never a question of which measurement takes place first since they share clocks for the duration of their entanglement. We may not be able to tell as observers which happened first, but the particles can tell.

In my mind's picture, I see two entangled particles running off with an invisible connection in the 4th dimension so they are always touching and therefore share the same time with respect to that connection no matter how far away they are separated. Thus a measurement of one particle is simultaneously a measurement of the two entangled (connected in a hidden dimension) particles at once even though they are separated spatially in our 3D slice of the world.

NOTE: This is just my own internal analogy for understanding one way this might be possible (like the balloon analogy in cosmology), I'm not proposing any idea or theory that this is the way it actually works.

So for me, the idea that in dBB the wave function for a particle is dependent on all the other particles in the universe, is just a way of saying that these sorts of nonlocal connections can exist, not that they always exist all the time between every particle.

 

[nismaratwork]

I understand it this way (but please feel free to correct me Demystifier if I get this wrong), once you invoke the idea of superluminal communication, "the last nanosecond" is not dependent on relativity that is constrained to lightspeed. In normal relativity, due to the speed of light limit, you have different "time" for each particle as they are separated.

In some sense, in dBB the entanglement ties together the time of the two frames such that they can been looked upon as if they were not separated by distance, or are separated by an arbitrarily small distance. So from the perspective of the two entangled particles there is never a question of which measurement takes place first since they share clocks for the duration of their entanglement. We may not be able to tell as observers which happened first, but the particles can tell.

In my mind's picture, I see two entangled particles running off with an invisible connection in the 4th dimension so they are always touching and therefore share the same time with respect to that connection no matter how far away they are separated. Thus a measurement of one particle is simultaneously a measurement of the two entangled (connected in a hidden dimension) particles at once even though they are separated spatially in our 3D slice of the world.

NOTE: This is just my own internal analogy for understanding one way this might be possible (like the balloon analogy in cosmology), I'm not proposing any idea or theory that this is the way it actually works.

So for me, the idea that in dBB the wave function for a particle is dependent on all the other particles in the universe, is just a way of saying that these sorts of nonlocal connections can exist, not that they always exist all the time between every particle.

I understand what you're getting at, but then you introduce foliation and dBB starts to look like string theory without the TOE promise. Where's Demyst and Zenith when you need 'em.

 

[ThomasT]

In what sense is dBB "non-local"? Is there any way of interpreting non-locality in dBB as being due to local, but non-realist, effects?

In case this hasn't already been cited, it does seem thematic, and since you're online:

How can one find nonlocality in Bohmian mechanics?
http://arxiv.org/PS_cache/quant-ph/pdf/0311/0311108v1.pdf
Andrei Khrennikov

 

[ThomasT]

... I also suspect it's a lack of knowledge on my part.

On all our parts, I suspect, except for Demystifier, and maybe a few others at PF. From only a cursory knowledge of dBB, and little-researched preconcieved notions about it, I've made some statements about it, all of which I should probably retract (even if some of them might be approximately correct) and start from scratch. So, after a morning of learning a bit more about the rationale for, and the formal construction of, dBB, I definitely know two things. 1) I would like to actually learn it as best I can given certain time constraints, and 2) I'm not going to argue with Demystifier (or any other Bohmians) about any dBB-related considerations, including nonlocality, until I actually do become much more approximately fluent wrt it than I am now (which will probably be a while).

I only have a couple of minor conceptual difficulties with it which, if they persist, I can always ask DeMystifier about. I would ask him in this thread, however, 1) I like to work these things out on my own, and 2) this thread is specifically about dBB and nonlocality.

It's great that you and DA seem, at least for the present, interested in whatever Demystifier might teach us also. Of course, most of it's on the web (I'm assuming). But, I'm hoping that Demystifier can point us to what he thinks are the best sources for teaching non-experts about dBB (no offense, but I'm assuming that you're also a non-expert, and if not then I apologize). I don't think it will require learning any new 'languages'. Just, perhaps, a slight shift in one's thinking and the blocking out of any prejudices that one might have had wrt dBB. And I'm also hoping that you and DA , with your youth and intelligence, will motivate me, for however long you stay interested in it, to study this stuff in order to keep up. I'm anticipating an intensive study program of about two to three weeks to get a good handle on this stuff. (By "intensive" I mean 12 to 16 hour days of looking at the dBB formulation, considering its relationship to standard qm, its possible implications, its possibilities, etc., etc., while, in my case at least, consuming copious amounts of popcorn and beer, my favorites, with an occasional break for pizza, and ... sleep?)

Bottom line for me is, Bohm was a really smart dude. I learned (what I can readily recall of) qm from the Dover edition of his 1950 textbook on quantum theory. And what I know of his philosophical/metaphysical worldview is very much in line with the way I've come to think about things.

To me, the concept of a Pilot Wave sounds like the hand of god, in the shape of the Schrodinger equation.

I don't think it's like that at all. But hopefully Demystifier will elaborate/explain.

 

[LukeD]

Wow, I haven't checked back on this thread in a little while. I wasn't expecting so much activity.

No!
Poisson equation is local, but acceleration of ONE particle CANNOT be calculated by knowing ONLY the solution of the of the Poisson equation and position of that particle. Instead, you must also know the positions of all other particles.

I believe I disagree with you on interpretation here.
Just because you need to know the positions of all other particles to calculate the gravitational field does not make Newtonian gravity non-local in my eyes.

The dynamics still arise from the Poisson eq, which is a local law. However, the Poisson equation's field propagates infinity fast, so we need to know all of the positions of each particle to calculate the dynamics accurately.
So to me, this is "non-local" in the sense that it is local, but that the field propagates infinitely fast.
And IMO, this is great because when we go from Newtonian Gravity to GR, the propagation speed changes from infinity to c. Clearly then, the gravitational field is local by just about anyone's definition.

Similarly, in dBB, we have that the dynamics of the theory (at least if we talk about the theory involving a wave function in configuration space), are local but propagate infinitely fast. Of course it is also strange that the wave function is defined not in space, but in configuration space.

--
Edit: I should mention that below I'm talking about vanilla relativistic QM, and that I haven't studied this myself, so my understanding is via small discussions with my roommate. That is to say, I have no reason to believe I haven't said something wrong.
--

If we change to the Klein-Gordon equation, we still have a local law with infinitely fast propagation, but if we use the Dirac equation(s), we have particles & anti-particles that travel no faster than speed c. We get multiple local disturbances that propagate at finite speed and conspire together to create a law that looks non-local.

So the way it looks to me is: in Schroedinger-dBB, we have non-local dynamics that arise from a local law with infinitely fast propagation. When we move to the relativistic limit with the Dirac equation, this propagation becomes only finitely fast.

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)

 

[ThomasT]

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

This doesn't make any sense to me.

 

[LukeD]

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.

 

[DevilsAvocado]

I understand it this way (but please feel free to correct me Demystifier if I get this wrong): once you invoke the idea of superluminal communication, "the last nanosecond" is not dependent on relativity that is constrained to lightspeed. In normal relativity, due to the speed of light limit, you have different "time" for each particle as they are separated.

In some sense, in dBB the entanglement ties together the time of the two frames such that they can been looked upon as if they were not separated by distance, or are separated by an arbitrarily small distance. So from the perspective of the two entangled particles there is never a question of which measurement takes place first since they share clocks for the duration of their entanglement. We may not be able to tell as observers which happened first, but the particles can tell.

. . .

Thanks for the reply inflector. Except for the pros, we’re probably all more or less stumbling in the dark with this enigma.

I asked Demystifier about this:

What is Nikolic saying? Is Alice incapable of reading the measurement of her polarizer? I don’t understand?? Or does he mean that that entangled photons exchange superluminal signals, but this is somehow "delayed" to non-superluminal before Alice can actually read the measurement...??

And the answer was:

Alice, of course, is capable of reading the measurement of her polarizer, but here the point is that she (as well as Bob) cannot CONTROL the reading of her/his measurement apparatus, in the sense that they cannot make the apparatus to be in the state they WANT. For that reason, they do not interpret nonlocal correlations as true exchange of information.

See, however, a way to (apparently) avoid this problem as well, leading to a possibility to use entanglement for an (apparent) superluminal communication:
http://xxx.lanl.gov/abs/1006.0338

I totally understand that there is NO way to use entanglement for true communication. The individual outcome is 100% random. But in the case of "perfect correlation" there will be a causal superluminal relation between Alice & Bob – cause & effect. And there can only be ONE cause and ONE effect, and they are NOT "relativity interchangeable". We can disagree on which occurs first of any two events that are spatially separated. This is perfectly OK according to by Einstein's theory of relativity. But we CANNOT disagree on cause & effect, because that would create unsolvable http://en.wikipedia.org/wiki/Grandfather_paradox" .

I think we can (without any doubts) interpret the answer from Demystifier on my (stupid ) question about a "delay" as negative (of course!). Thus, there will be a "DIRECT CONNECTION" to the superluminal (instantaneous?) "dBB signal" and Alice & Bob’s polarizer and measuring apparatus.

I have absolutely no problem with "Closed timelike curves" or "Wormholes", in fact they are valid solutions to the equations of General Relativity.

[PLAIN]http://upload.wikimedia.org/wikipedia/commons/a/af/Worm3.jpg

Normally there is no trouble with a disagreement on the orderings of events, if they are NOT causally connected. Causality is what causes all the trouble...

Personally, I just can’t see how one can "lift out" the superluminal "dBB signal" from the reality of Special Relativity. The measuring apparatus will be in a "frame of reference" that obeys Special Relativity, and that "frame of reference" will decide when NOW is, and what "the last nanosecond" will mean. The superluminal "dBB signal" just has to "wait" for the "Special-Relativity-Polarizer" to stop, to be able to "decide" what the "instantaneous" outcome will be. I can’t see any other solution...

And my stationary version of Alice & Bob is very "nice" in respect of Special Relativity. I’m pretty sure we can setup a complete "stretchy-rubber-spacetime-mess" of moving apparatus and observers that can’t agree on anything when it comes to distances, elapsed times, and orderings of events.

This http://en.wikipedia.org/wiki/Lorentz_transformation" shows events in spacetime of an accelerating observer:

[URL]http://upload.wikimedia.org/wikipedia/commons/e/e4/Lorentz_transform_of_world_line.gif[/URL]

Check out this picture of http://upload.wikimedia.org/wikipedia/commons/9/96/Einstein_train_relativity_of_simultaneity.png" for an explanation:

http://upload.wikimedia.org/wikipedia/commons/9/96/Einstein_train_relativity_of_simultaneity.png"

To put it short: The superluminal dBB signal obeys the rotating polarizer, and the polarizer obeys Special Relativity, therefore the superluminal dBB signal must obey Special Relativity!

I think...

 

[nismaratwork]

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

@ThomasT: I'm sure I must be wrong about the pilot wave, after all it's theory that matches the predictions of QM so "hand of god" can't be in it. I'd really like to learn more about spacetime foliation in dBB... that's the technical part that I find challenging, as opposed to conceptual challenges.

 

[LukeD]

In case this hasn't already been cited, it does seem thematic, and since you're online:

How can one find nonlocality in Bohmian mechanics?
http://arxiv.org/PS_cache/quant-ph/pdf/0311/0311108v1.pdf
Andrei Khrennikov

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.

 

[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.