EPR & SR

[sethoflagos]

Recent discussions in the thread https://www.scienceforums.net/topic/128407-the-nature-of-time/ have got me scratching my head again over the relationship between past-present-future in both the quantum and classical realms.

My starting point is case 1 of Bohm's variant of the Einstein-Podolsky-Rosen paradox in which Charlie at point C will operate a gadget to launch an entangled spin singlet along the x axis: an electron leftward towards Alice at point A and a positron towards Bob at point B. At some point Charlie will simultaneously release the pair and broadcast a light speed timing signal to alert Alice and Bob of when they should measure the z-spin of their respective particles. As the tests are made Alice and Bob similarly broadcast the results of their measurements. For simplicity's sake Alice, Bob and Charlie are all stationary within their common inertial reference frame, but sufficiently distant for the two measurements to be non-local.

Consider what is recorded by independent observers in arbitrary inertial reference frames. Am I correct in thinking that:

a) all observers will agree that Charlie's timing signal occurred before either of Alice and Bob's measurement signals.

b) irrespective of the actual distance between point A and point B, some will observe Alice make the first measurement, some Bob.

c) some few observers may observe simultaneous measurement signals from Alice and Bob and have no problem interpreting this as instantaneous collapse of the wave function at point of measurement.

d) other observers may deduce that wave function collapse must have occurred before Alice's measurement; others that it occurred before Bob's.

e) there are apparently different 'histories' being observed by different observers suggesting that there are different timelines of the wave function in play. 

And now we get into the speculative rabbit hole.

f) if there are different histories being observed does this not imply that different observers are seeing different stages in a dynamic editing process of the wave function - ie that history is undergoing a transformation from a superposition of possible futures to a classically deterministic past for example.

g) the paradoxes chiefly arise from seeing entanglement as some sort of physical link stretching across space, rather than connections within the complex vector space in which the wave function is set.

h) for 'reasons' linkages within this complex vector space between 'gadget' at t=0 (specifically!) and electron-positron pair at t>0 are not unreasonable in themselves, and being unobservable, cannot pass real information to the past, and therefore do not conflict with causality.

i) therefore an interpretation of the commencement of Alice's measurement process of a z+ electron inducing an overwrite of its wavefunction back to the gadget, and forwards again as an unambiguous z- positron for Bob would seem to resolve the paradox.

j) simultaneous measurements by Alice and Bob imply the need for some sort of handshaking back and forth until the wave function resolves to a consistent solution.

I stress that these are just general impressions of subjects that I find challenging, that have sunk in over the years and must surely break down at some point in the reasoning. But I'd be most grateful to find out where they do actually begin to collapse.    

[Lorentz Jr]

If by "back to the gadget" you mean time travel, then you lost me. I'm sure "complex vector space" is very nice math, but it's not my idea of an underlying mechanism or ultimate explanation.

So, as I see it, there are two possibilities:

• The universe is Newtonian (not Galilean), Lorentz was right, there's no such thing as particles, everything is waves, there's some legitimate reason the vacuum's state of motion hasn't been detected (because of some kind of dynamical principle (e.g. it minimizes some kind of action) that keeps it hidden), entanglement is superluminal communication, and Bell/EPR is a tempest in a teapot because it's based on fundamental misconceptions.
• The universe is relativistic, Einstein was right, space itself is some kind of illusion, we're all living in some kind of weird simulation, and Bell/EPR is a tempest in a teapot because how can you make sense of anything if the world is just the output of Universe.exe running on some superintelligent being's PC? 😧

In other words, it's either/or. Either completely Lorentzian or completely batshit, and by "batshit" I don't mean to suggest that it's not a viable answer to your questions. Because there's no law that says the universe has to conform to our intuitions or expectations. The only thing I believe with conviction is that 20th-century physics only scratches the surface of a very bizarre, complicated world, and there must be more to it than "it's all relative" and "it's inherently random".

If you want a more scientific answer than that, you might read up on loop quantum gravity, but I know next to nothing about it except that it doesn't seem blatantly wrong to me the way string theory does.

Edited December 29, 2022 by Lorentz Jr

[sethoflagos]

1 hour ago, Lorentz Jr said:

If by "back to the gadget" you mean time travel, then you lost me.

That's a valid and honest response. Thank you.

[Genady]

10 hours ago, sethoflagos said:

the paradoxes chiefly arise from seeing entanglement as some sort of physical link stretching across space

The link is "physical" as it can be measured. And it "stretches" across space. The paradoxes arise from seeing something else, I guess.

[Mordred]

One thing I've always found annoying about how entanglement is described in numerous papers involving the various paradoxes and interpretations is that very few of the papers ever mention that the entangled particle pair had a causal past connection at the moment of entanglement. That causal connection also prepares the allowable states in accordance to the conservation laws. (charge,energy-momentum, flavor, color, isospin, lepton number ) etc.

 So lets examine that using the parametric down conversion of a monochrome light beam through the beam splitter common to the EPR experiment. As photons are used were dealing with polarity states (left and right circular polarity states). 

 Ok so we don't know the which particle is which so naturally we have a superposition probability state that will be common to both wavefunctions as its fired to the detectors. (treat as one state shared by both) or treat as two identical states. (seems to me shouldn't matter which descriptive is used in this case. The probability is further increased by the detector alignment at detector A and B in so far as the angle is concerned. That gets factored into the correlation function. 

 Now lets stop for a second and think about this. The state sent to each detector is a probability state. It is not the physical state. We do not know the physical state so we can only describe the probability state. Once you observe/measure (in QM measure is identical to observe), you have determined the physical state so naturally the probability state is no longer required. Applying the previous conservation laws the person at detector A will automatically know wheat state should be detected at detector B as being the opposite polarity. 

There is no cause or communication needed beyond the original preparedness of the entangled particle pair. The very act of generating an entangled particle pair in the first place requires a causal connection. (the two particles must interact in order to become entangled).

the particles themselves do not communicate between each other nor change states as a result of the superposition wavefunction collapse. The communication that occurs is when you go to communicate the results of one detector to the other detector or for timing purposes.

if for example observer at detector A does their measurement. detector B doesn't know the results until detector A informs them. Until detector B gets the results that detector will still treat the state as a superposition state.  A probability state isn't a physical measured state.  Any measured stated is a determined state.

 

A key note you can have a superposition of waveforms that are physical (ie a collective of different frequencies in the same space) thats a bit different than the entangled superposition state which is a probability function. 

Edited December 29, 2022 by Mordred

[sethoflagos]

5 hours ago, Genady said:

The link is "physical" as it can be measured. And it "stretches" across space. The paradoxes arise from seeing something else, I guess.

Are you saying the paradoxes don't truly exist? In particular, that different observers may disagree on whose measurement collapsed the wave function.

That's not to mention the superluminal implications.

[Genady]

1 minute ago, sethoflagos said:

Are you saying the paradoxes don't truly exist?

Yes.

[sethoflagos]

4 hours ago, Mordred said:

... There is no cause or communication needed beyond the original preparedness of the entangled particle pair. The very act of generating an entangled particle pair in the first place requires a causal connection. (the two particles must interact in order to become entangled).

the particles themselves do not communicate between each other nor change states as a result of the superposition wavefunction collapse. The communication that occurs is when you go to communicate the results of one detector to the other detector or for timing purposes.

Now that response I did not expect. 

If there is no communication between the particles post preparation, then how are they able to self-correlate when one or other is measured? 

9 minutes ago, Genady said:

Yes.

So my logic breaks down at step d)? Really?

[Genady]

3 minutes ago, sethoflagos said:

So my logic breaks down at step d)? Really?

No. Different observers can deduce different things. Especially, since wave function is not an observable.

[sethoflagos]

4 minutes ago, Genady said:

No. Different observers can deduce different things. Especially, since wave function is not an observable.

How about some observers knowing the result of Alice's measurement before she's made it, and other's having similar foreknowledge of Bob's result? These are observables aren't they?

[Genady]

1 minute ago, sethoflagos said:

How about some observers knowing the result of Alice's measurement before she's made it, and other's having similar foreknowledge of Bob's result? These are observables aren't they?

Different observers, no contradictions.

The crucial fact here is that Alice does not know the result of her measurement before she makes the measurement. Same with Bob.

[sethoflagos]

5 minutes ago, Genady said:

Different observers, no contradictions.

The crucial fact here is that Alice does not know the result of her measurement before she makes the measurement. Same with Bob.

I'll need to have a good think about that one. Thank you.

[Mordred]

1 hour ago, sethoflagos said:

Now that response I did not expect. 

If there is no communication between the particles post preparation, then how are they able to self-correlate when one or other is measured? 

So my logic breaks down at step d)? Really?

The correlation function is determined at the preparedness of the entangled states and the experimental apparatus.

Before I go further you do know how a correlation function applies is statistical math correct. ? Any two variables can be tested for a correlation those two variables can be 100% unrelated to the other.

 It could be the number of accidents in Japan vs population growth in the US  if one value increases and so does the other then you a positive correlation.

 If one goes down while the other up then a negative correlation  if one  value changes while the other randomly goes up and down them no correlation.

Regardless of the correlation results no communication hidden variable or cause and effect or in this case shared causality need exist.

Here is a simple two possible analogy take a bag of apples and a bag of oranges. You have a statistical chance of getting either oranges or apples.

Alice opens her bag she has determined she has apples the probability becomes zero as she determined the physical state (apples) Bob knowing Alice got apples will automatically know he has oranges. The states of what were in the bag were not changed to get the results.

The same applies to particle entanglement measuring the (I will stress this the physical state) of one particle does not change the physical state of the other particle) the measurement only affects the probability states.

Ignoring the quantum uncertainty when applied to observational interference for the moment

 

 

Edited December 29, 2022 by Mordred

[swansont]

7 hours ago, Genady said:

The link is "physical" as it can be measured. And it "stretches" across space. The paradoxes arise from seeing something else, I guess.

The correlation exists, but saying it’s “physical” implies an interaction, and one needs to explain what that interaction is.

The alleged paradox arises from assuming QM is ultimately classical, which is a really bad assumption. 

[sethoflagos]

27 minutes ago, Mordred said:

Before I go further you do know how a correlation function applies is statistical math correct. ?

I hesitate to say 'yes' in case you're about to launch into a bunch of Green's functions. 

If it gets dense it'll take me a bit of time to get my head around it, though I will eventually.

Edited December 29, 2022 by sethoflagos
s

[Mordred]

lmao well if you think about it the Greens correlations is a good example with regards to creation and annihilation operators 

however I think you should instead refer to this for starters

https://en.wikipedia.org/wiki/Correlation_function note the specifications of autocorrelation 

https://en.wikipedia.org/wiki/Autocorrelation

 

[sethoflagos]

4 hours ago, Mordred said:

lmao

I'm familiar with the basics of these in as much as they apply to acoustics and process control theory amongst other fields, so fire away.

[MigL]

For some reason I could not get this to quote, but Markus' post, in the Crowded Quantum Information thread should be required reading for anyone confused about entanglement ...

 

"Let’s look at this whole quantum entanglement business systematically, because I really don’t think it requires 22 pages of discussion and argument to understand this. It may be counter-intuitive, but it really isn’t that complicated.

Suppose you have - to begin with - two completely separate particles, which aren’t part of a composite system; their states are thus entirely separate, and denoted by

 

|A〉,|B〉

Don’t mind the precise meaning of this mathematical notation; it simply denotes two separate particles being in two separate states, where the outcome of measurements are probabilistic, and not in any way correlated at all. No mystery to this thus far.

Now let’s take the next step - we combine the two particles into a composite system. The state function of that composite system is then the tensor product of the states of the individual particles, like so:

 

|ψ〉=|A〉⊗|B〉≡|AB〉

Again, don’t mind the precise definition of these mathematical operations; the idea here is simply that our two particles A and B form a composite system. Let’s, for simplicity’s sake, assume that each particle can only have two states, ‘0’ and ‘1’ - the physical meaning of the tensor product above is then that it combines each possible state of one particle with each possible state of the other, so the overall combined system can have four possible states:

 

|00〉,|01〉,|10〉,|11〉

Thus the overall combined state of the particle pair is (I will omit the coefficients here, as the precise probabilities aren’t important):

 

|ψ〉=|00〉+|01〉+|10〉+|11〉

This is an example of a system that is not entangled - the combined state function can be separated into the individual states of the constituents, and all combinations are possible (though not necessarily with equal probability). Non-entangled states are separable into combinations of states of the individual constituent particles - they are tensor products of individual states - which means physically that there are no correlations between outcomes of measurements performed at the constituent particles. If you get state ‘0’ for a measurement on particle A, then you can get either state ‘0’ or state ‘1’ for a measurement on B, and these outcomes are statistically independent from each other. Mathematically, the tensor product makes no reference to the separation of the particles, ie it is not a function of their position, hence neither is the overall combined state.

An entangled 2-particle state, on the other hand, looks like this:

 

|ψ〉=12–√(|01〉+|10〉)

Notice three things:

1. Compared to the non-entangled state, two of the possible measurement outcomes are missing; the set of possible outcomes is reduced

2. The combined state cannot be uniquely separated into tensor products of individual states; it is non-separable

3. The form of the combined state does not depend on the spatial (or temporal) position of the particles - it is purely a stochastic statement, not a function of spacetime coordinates.

What does this physically mean? Because the set of possible measurement outcomes in the overall state is reduced as compared to the unentangled case, there is now a statistical correlation between measurement outcomes - with emphasis being on the term statistical. There are now only two possible combinations, as opposed to four in the unentangled case. This is the defining characteristic of entanglement - it restricts the pool of possible combinations of measurement outcomes, because the overall state cannot be separated, due to there being extra correlations that weren’t present in the unentangled case. This is purely due to the form of the combined wave function - the outcome of individual measurements on each of the constituents is still purely stochastic, and not (!!!) a function of distant coordinates.

Because the outcome (statistical probability) of local measurements is not a function of coordinates or any distant states, it is completely meaningless to say that this situation is somehow non-local, or requires any kind of interaction, be it FTL or otherwise. The entire situation is fully about statistics and correlations, which is not the same as a causal interaction; in fact, any interaction between the constituents (including FTL ones) would change the combined wave function and preclude the possibility of there being a statistical correlation while at the same time maintaining the stochastic nature of the outcomes of individual measurements. This is evident in the fact that the entanglement property of the above state function isn’t encoded in any kind of coordinate dependence, but rather in a reduction of terms, ie in a reduced pool of possible outcomes. This hasn’t got anything to do with locality at all, but is purely a statistical phenomenon."

                                                                                                                                                                    Markus Hanke            Nov 21 / 22

Edited December 30, 2022 by MigL

[Lorentz Jr]

1 hour ago, MigL said:

any interaction between the constituents (including FTL ones) would change the combined wave function and preclude the possibility of there being a statistical correlation while at the same time maintaining the stochastic nature of the outcomes of individual measurements. This is evident in the fact that the entanglement property of the above state function isn’t encoded in any kind of coordinate dependence, but rather in a reduction of terms, ie in a reduced pool of possible outcomes. This hasn’t got anything to do with locality at all, but is purely a statistical phenomenon."

I'm sorry, but this is sheer nonsense. The first 99 percent of the post is a perfectly reasonable introduction to the subject, but then the last 1 percent literally says there's no physical basis for it at all (it's "purely statistical").

Math isn't a replacement for physics. Wave functions only describe physical systems, they don't explain why outcomes are correlated. Physics is not a purely a statistical phenomenon. Correlations may be caused by FTL communication, or they may be caused by what @joigus has called "beables" that were established when the particle was created, or they may be caused by something else. But they're caused by something. They don't happen by magic. Saying correlations in physical systems have no causal explanations is like saying human beings exist with no conscious thoughts.

Math is not physics.

 

@MigL The equation for the entangled state is something like

[math]\displaystyle{|\psi> = \frac{1}{\sqrt{2}}\left(|01>+|10>\right>}[/math]

[math]\displaystyle{|\psi> = \frac{1}{\sqrt{2}}\left(|01>+|10>\right>}[/math]

You have to right-click the equation, copy the TeX, and paste it in as text surrounded by the math codes in your own post.

EDIT: From Markus's post, the code is

|\psi \rangle  =\frac{1}{\sqrt{2}}\left(|01\rangle +|10\rangle \right)

 

Edited December 30, 2022 by Lorentz Jr

[Markus Hanke]

57 minutes ago, Lorentz Jr said:

Saying correlations in physical systems have no causal explanations

I never ever said or implied anything about there not being a causal explanation or physical basis. The causal link between a pair of entangled particles is their past interaction, which is when the entanglement relationship becomes first established. That’s the causal explanation. This is not in contention, and it’s not a mystery. You don’t get entangled pairs unless they first interact in certain ways to set up this relationship, and no one here has claimed otherwise.

But the meaning of “entanglement” is nevertheless a statistical correlation of measurement outcomes, as I have attempted to explain. The thing is that, if you look at just one of these particles and perform a local (!) measurement there, then each outcome (‘0’ or ‘1’) will appear with equal probability of 0.5. The same is true for local measurements on the other particle - each outcome will appear with equal probability of 0.5 to that local observer. Neither observer can predict the outcome of his own local measurements, he can only define probabilities for them, and these probabilities are identical whether or not the particles are entangled.

To put this differently - there is no local experiment you can perform that will tell you whether the single particle you have in front of you is entangled or not. Entanglement is meaningless when only a single particle is considered. 

It is only when you compare the outcomes of the two measurements on the two constituents of the system that you will find the overall two-particle state to be either |01> or |10> (with equal probability!), but never |11> or |00>. This is in contrast to unentangled particle pairs, which can yield any of the four possible states. So entanglement means you reduce the pool of possible global states by introducing a statistical correlation.

So yes, entanglement is defined to be a statistical correlation between measurement outcomes. There’s nothing unphysical about statistics at all, it’s a straightforward description of what we actually see when we perform these experiments in the real world.

1 hour ago, Lorentz Jr said:

But they're caused by something.

Yes, of course - they’re caused by the initial interaction that sets up the correlation. This then persists until the entanglement is broken again, which happens if and when any of these two particles is interacted with in any way. 

1 hour ago, Lorentz Jr said:

it's "purely statistical"

There are plenty of concepts in physics that are statistical in nature, and don’t make sense for systems that have only one state, or only one constituent. Obvious examples that come to mind are things like temperature, and entropy. You cannot meaningfully apply these to a single particle - and the same is true for entanglement.

[Mordred]

1 hour ago, Markus Hanke said:

I never ever said or implied anything about there not being a causal explanation or physical basis. The causal link between a pair of entangled particles is their past interaction, which is when the entanglement relationship becomes first established. That’s the causal explanation. This is not in contention, and it’s not a mystery. You don’t get entangled pairs unless they first interact in certain ways to set up this relationship, and no one here has claimed otherwise.

But the meaning of “entanglement” is nevertheless a statistical correlation of measurement outcomes, as I have attempted to explain. The thing is that, if you look at just one of these particles and perform a local (!) measurement there, then each outcome (‘0’ or ‘1’) will appear with equal probability of 0.5. The same is true for local measurements on the other particle - each outcome will appear with equal probability of 0.5 to that local observer. Neither observer can predict the outcome of his own local measurements, he can only define probabilities for them, and these probabilities are identical whether or not the particles are entangled.

To put this differently - there is no local experiment you can perform that will tell you whether the single particle you have in front of you is entangled or not. Entanglement is meaningless when only a single particle is considered. 

It is only when you compare the outcomes of the two measurements on the two constituents of the system that you will find the overall two-particle state to be either |01> or |10> (with equal probability!), but never |11> or |00>. This is in contrast to unentangled particle pairs, which can yield any of the four possible states. So entanglement means you reduce the pool of possible global states by introducing a statistical correlation.

So yes, entanglement is defined to be a statistical correlation between measurement outcomes. There’s nothing unphysical about statistics at all, it’s a straightforward description of what we actually see when we perform these experiments in the real world.

Yes, of course - they’re caused by the initial interaction that sets up the correlation. This then persists until the entanglement is broken again, which happens if and when any of these two particles is interacted with in any way. 

There are plenty of concepts in physics that are statistical in nature, and don’t make sense for systems that have only one state, or only one constituent. Obvious examples that come to mind are things like temperature, and entropy. You cannot meaningfully apply these to a single particle - and the same is true for entanglement.

I fully agree with the above its literally the same as I have come to understand what is involved in entanglement and the nature of the correlation function Though when you get right down to it QM is entirely probabilistic

Edited December 30, 2022 by Mordred

[Lorentz Jr]

1 hour ago, Markus Hanke said:

I never ever said or implied anything about there not being a causal explanation or physical basis.

You said "purely a statistical phenomenon". "purely" means "with nothing else", and a causal explanation or physical basis would count as something else. You can define the word "entanglement" statistically if you want (although I'm not sure it was originally intended that way), but extending that description to the phenomenon itself implies a lack of causation.

1 hour ago, Markus Hanke said:

So yes, entanglement is defined to be a statistical correlation between measurement outcomes.

Right. That's the way the word "entanglement" is commonly used. I would say it's informally suggestive of some kind of interaction, but that's okay. It's commonly used to imply correlation, with no additional implications either way.

1 hour ago, Markus Hanke said:

There are plenty of concepts in physics that are statistical in nature, ... Obvious examples that come to mind are things like temperature, and entropy.

Sure, but there's no correlation in temperature. No cause, no correlation.

And entropy is one of the great mysteries of physics. No one understands how the universe can be in a state of such low entropy when thermodynamics tells us it shouldn't be. One would expect that it should have a cause.

Anyway, I'm not criticizing your whole post, Markus. (And of course you didn't post it in this thread.) Most of it is very good. Just the combination of "purely statistical" and "phenomenon". Semantically speaking, I think it goes a little too far towards suggesting a lack of causation.

Edited December 30, 2022 by Lorentz Jr

[sethoflagos]

4 hours ago, Markus Hanke said:

Yes, of course - they’re caused by the initial interaction that sets up the correlation. This then persists until the entanglement is broken again, which happens if and when any of these two particles is interacted with in any way. 

I'm seeing the initial correlation created as the point exp(i * pi / 4) on a unit circle. (That's not so much of an issue).

Then I'm seeing a local observation as this correlation being multiplied globally by exp(+/- i * pi / 4), thus selecting |0 1> or |1 0> at random.

It's this second global transformation that is problematic. Parsimony would suggest to me some mechanism whereby a 'request for clarification' is sent (yes, ok, backwards in time) to the source which then applies the requisite 45 degree twist one way or the other to its correlation initiating the collapse. This would seem to solve a couple of issues:

1) It removes any possibility of simultaneous measurement by Alice or Bob yielding uncorrelated results that might result if either of them initiated the collapse. If the collapse is executed back at the source, it can only occur once and the correlation must hold. 

2) Having two distinct timelines, one overwriting the other would appear to cover all possibilities of observations made from other reference frames where the apparent order of events may vary. 

3) No 'spooky action at a distance', just a brief time reversal. Nothing is exceeding c. 

Edited December 30, 2022 by sethoflagos
spooky action

[Genady]

15 minutes ago, sethoflagos said:

some mechanism whereby a 'request for clarification' is sent (yes, ok, backwards in time) to the source

Perhaps one could think about a "communication" going back and forth in time, just like one could think about positrons being electrons moving backwards in time. It might help one heuristically, albeit not adding anything to physics.

[sethoflagos]

13 minutes ago, Genady said:

Perhaps one could think about a "communication" going back and forth in time, just like one could think about positrons being electrons moving backwards in time. It might help one heuristically, albeit not adding anything to physics.

I don't have quite enough hubris to imagine that I can advance physics, but I would like to have at least a consistent picture in my head of what might be going on. Isn't there an 'advanced wave' available in the wave equation that might assist with the time reversed signalling?