Special Relativity and Enganglement

[bobc2]

Here is an attempt at representing a two-photon enganglement situation as analyzed in spacetime for two observers (red and black in sketch below) moving in opposite directions at the same relativistic speeds with respect to the black rest system shown in the sketch.

Let's say that the photon moving to the left is found to be in the UP state at event A by an observer at rest in the red frame. Then the photon moving to the right snapes to the DOWN state at event B. I have the following puzzling questions:

1) If the right photon is in a DOWN state at event B, then in the blue coordinate system that would seem to snap the left photon into an UP state at event C. But that event precedes event A, implying a reverse causality, that is event A has caused the past event C.

2) Once event A has snapped the left photon into UP, how does nature decide which observer's frame of reference to snap the right photon into? The black reference frame would have the right photon snapping to DOWN at event D.

3) Would a chain of events be released, i.e., event C causes the right photon to snap to DOWN at event E, etc.?

 

[Dale]

Let's say that there was a measurment at B. Then (according to my knowledge) in the blue frame the wavefunction of the other photon collapses at C and in the red frame the wavefunction of the other particle collapses at A.

 

[Calrid]

Yeah as long as the time line doesn't show a simultaneous or reverse causality and I can't see how it does here then that looks pretty much like the correct transform in that situation. I suppose technically the speed of transfer of information would have to be shown as less than c but I'm sure that would be a semantic issue unless the distance between entanglement was extremely large.

 

[bobc2]

Let's say that there was a measurment at B. Then (according to my knowledge) in the blue frame the wavefunction of the other photon collapses at C and in the red frame the wavefunction of the other particle collapses at A.

Your analysis seems right, DaleSpam. But when the two-particle system wave function collapses snapping the left photon into an UP state at C, then wouldn't that cause the right photon to snap into the DOWN state at E? But, that would be a reverse causality with the measurement at B causing the event E (before B had yet happened)?

 

[Dmitry67]

Yes, yes.
So if you accept Block Time, you have to abandon realism.

 

[bobc2]

Yes, yes.
So if you accept Block Time, you have to abandon realism.

Dmitry67, could you explain that a little more?

 

[Dale]

Your analysis seems right, DaleSpam. But when the two-particle system wave function collapses snapping the left photon into an UP state at C, then wouldn't that cause the right photon to snap into the DOWN state at E? But, that would be a reverse causality with the measurement at B causing the event E (before B had yet happened)?

Not according to my understanding (which is admittedly superficial on this topic). My understanding is that it is the interaction with the measuring device at B which causes the collapse. There is no measurement performed at C, so the wavefunction would not collapse at E in either frame. Due to the measurement at B the wavefunction collapses at C in the blue frame and at A in the red frame, and that is all.

 

[bobc2]

...My understanding is that it is the interaction with the measuring device at B which causes the collapse.

You are definitely correct about that.

There is no measurement performed at C, so the wavefunction would not collapse at E in either frame.

You bring up a very important point here, DaleSpam. My understanding would be that once the measurement is made at B (DOWN state) then the state of the left photon at C would instantly snap to UP. That would mean that the wave function for the two-photon system in the red frame of event C would require the right photon at E to be in the DOWN state.

Now, the only argument I can think of to avoid the state change at E would be the following (and I haven't found literature on this): Once the state is set for the two-photon system to UP and DOWN, coherence is destroyed so that the two photons are no longer entangled. Without specifying details of the measurement device at B, the photon is perhaps absorbed after detection.

Someone told me that Griffith's book (either the QM or QFT book) resolves this problem, but I wasn't told what the resolution was).

Due to the measurement at B the wavefunction collapses at C in the blue frame and at A in the red frame, and that is all.

I agree that once the measurement is made at B the wave function collapses. But once the wavefunction collapses, it's collapsed, and the photon at C is the UP state. But, that collapse event is also in the red frame at red's time of t1''. That's one of the fundamental problems I'm having here.

And by the way, thanks for your ideas and help in sorting this out.

 

[DrGreg]

Like Dale, my knowledge of quantum theory is limited too, but it is wrong to think that measuring one photon causes the other one to change its state in some way. "Collapse of the wavefunction" refers to the knowledge that an observer has of the system. The result of an experiment causes the observer's knowledge to change and therefore the wavefunction has to be replaced by another wavefunction. (Note there is a single wavefunction that describes both photons, and the before-measurement wavefunction specifies that the probability of two UPs is zero.) Measurement of one photon doesn't cause the other photon's state to change, it causes the observer's knowledge of the other photon's state to change.

When two experiments independently measure the UP/DOWN state of each photon, the temporal order of those experiments depends on the choice of inertial frame (assuming spacelike separation of the two measurement events) so that makes even less sense in terms of one measurement influencing the other. Don't confuse correlation with causation.

 

[Dmitry67]

Dmitry67, could you explain that a little more?

Based on the Bell's theorem, realism can't be local.

If you accept realism, in EPR you have to ask weird questions like "does Alice affect Bob's measurement or vice versa" knowning that in different frames order of measurements is different. In Block Time (wiki it) there is no difference between FUTURE and the PAST, everything is just a static solution in 4D spacetime. Hence it is meaningless to ask if Alice affects Bob or Bob affect Alice.

P.S. I assume you are also aware that 'wavefunction collapse" is an abandoned concept since min 90x, so you had used it as just an example/simplification.

 

[Dale]

P.S. I assume you are also aware that 'wavefunction collapse" is an abandoned concept since min 90x, so you had used it as just an example/simplification.

I was not aware of that. What has replaced the concept or how has it been modified or superceded?

 

[Dmitry67]

Quantum Decoherence
http://en.wikipedia.org/wiki/Quantum_decoherence
had replaced the "mysterious" collapse.
Copenhagen Interpretation is dead 15 y already...

 

[bobc2]

Yes, yes.
So if you accept Block Time, you have to abandon realism.

I'm thinking you may have intended to say it the other way around. If you accept the block universe model (All 4 dimensions of the universe exist as a real material space/structure) then you can't have the picture I've presented representing the entanglement dilemma. In other words you have to abandon EPR (at least the mechanism depicted here) if you are to retain the block universe with all of the photon world lines in place as static 4-dimensional objects.

 

[Dale]

I have not yet finished reading about quantum decoherence, so my comments may be outdated.

You bring up a very important point here, DaleSpam. My understanding would be that once the measurement is made at B (DOWN state) then the state of the left photon at C would instantly snap to UP.

In the blue frame, yes.

That would mean that the wave function for the two-photon system in the red frame of event C would require the right photon at E to be in the DOWN state.

No, in the red frame the collapse of the other photon occurs at A, not C.

I agree that once the measurement is made at B the wave function collapses. But once the wavefunction collapses, it's collapsed, and the photon at C is the UP state.

In the blue frame, yes.

But, that collapse event is also in the red frame at red's time of t1''. That's one of the fundamental problems I'm having here.

But it doesn't collapse until A in the red frame.

 

[bobc2]

I was not aware of that. What has replaced the concept or how has it been modified or superceded?

I think "collapse" is still used, but the context has to be understood. If one has a precise context in mind, then the concept is used with refinement and the "collapse" term might not be used. That is, the electron, in the time neighborhood of the measurement apparatus, participates in a more global wavefunction along with elements in its measurement environment.

If you were able to follow a very slow motion movie of the electron as it participates in an ever larger encompasing time varying system wave function as it approaches close proximity to the measurement system and ultimately interacts with it, you would see that the contribution of the original electron pair coupling becomes small compared to the new evolving coupling to the larger system having a more global wave function. This means that at some point the two original electrons are decoupled--or coherence is lost (decoherence).

You can actually demonstrate an analogous situation classically with vibrating structures. Start with a cantelever beam vibrating in an eigenstate corresponding to its first resonance frequency. Then have a second very complex system of many vibrating masses and springs, and first couple the two systems together with a light spring so that there is very slight coupling (the first cantelever frequency shifts just a little). Then progressively connect more and more springs of increasing stiffness between the two systems until the identity of the original cantelever eigenstate is completely buried in the new global modes of vibration.

My point is, in spite of this, the entanglement phenomena are well established, and when the measurement is made on the first electron, it's state is established and the other electron snaps to the opposite state (in my example the original coupled electron pair system spin was zero, so the final states had to take on + and - to conserve the original two-particle system state). So, your original language is really understood and doesn't really affect your analysis.

 

[bobc2]

But it doesn't collapse until A in the red frame.

Please don't take this to be argumentative. I'm still struggling with the concept that when an event occurs in 4-dimensional space, it is there as a 4-dimensional event and is not subject to moving to different 4-D positions. That's how an event is described. We can identify the event, C, in our case using a 4-vector (a displacement vector), call it C. Then that is the same 4-D object (vector), no matter whose coordinates are used:

Cred = Cblue

The X1 and X4 components are different, but the vector is the same, and that 4-D event for the left photon changing to the DOWN state is the same event for both red and blue coordinates.

The photon at event C cannot simultaneously have two different definite states of UP and DOWN. It can only be one or the other. And that state exists in both the blue coordinate system and the red coordinate system at event C.

Now, Dimitry67 may be telling us that the event C cannot exist as a real event. That's another ball of worms that might push us over to a QM thread. It's been a long time since I've studied Bell's theorem, so I'll have to do some side bar on that.

 

[Dale]

Please don't take this to be argumentative. I'm still struggling with the concept that when an event occurs in 4-dimensional space, it is there as a 4-dimensional event and is not subject to moving to different 4-D positions. That's how an event is described. We can identify the event, C, in our case using a 4-vector (a displacement vector), call it C. Then that is the same 4-D object, no matter whose coordinates are used:

Cred = Cblue

The X1 and X4 components are different, but the vector is the same, and the 4-D event for the left photon changing to the DOWN state is the same event for both red and blue coordinates.

I don't think that the collapse of the wave function is an event in this sense. It is not something that can be observed or recorded on its own in any way. It is only something which you can get by comparing data after the fact.

You see similar things in other situations, e.g. when you are doing EM in a gauge other than the Lorentz gauge. You can get dramatic changes in the potentials in one frame that do not happen in another frame. If you called the change in the potential an event, then you might suffer this same confusion. But the potential is not observable, nor is the collapse.

You may want to ask this in the QM section, I am way beyond the limits of my understanding here, and I could very well be completely wrong.

 

[bobc2]

Based on the Bell's theorem, realism can't be local.

If you accept realism, in EPR you have to ask weird questions like "does Alice affect Bob's measurement or vice versa" knowning that in different frames order of measurements is different. In Block Time (wiki it) there is no difference between FUTURE and the PAST, everything is just a static solution in 4D spacetime. Hence it is meaningless to ask if Alice affects Bob or Bob affect Alice.

P.S. I assume you are also aware that 'wavefunction collapse" is an abandoned concept since min 90x, so you had used it as just an example/simplification.

Thanks a lot for your input, Dmitry67. Good work. I answered your earlier post a while ago, and thought you may have communicated the opposite of what you intended, but now I see that I misinterpreted your meaning. I see what you are saying now and will review Bell's theorem since it has actually been at least three years since I've thought about it.

And yes, I was aware of the decoherence considerations and the imprecision in using "wavefunction collapse" (you are of course correct with that).

I'm still troubled with the apparent conflict between QM and special relativity on this entanglement issue, notwithstanding Bell's theorem. I don't see how you deny realism in QM (but then maybe that's the essense of QM) and yet we would still like to include elementary particle world lines in the spacetime diagrams--we would like for them to be real (should we instead have wave functions in the spacetime diagrams?). Feynman diagrams seem close to a representation of reality (being sure to include the W boson in the beta decay pictures, etc.).

Spacetime pictures are consistent with tracks in particle accelerators. And the entanglement phenomena are adequately demonstrated experimentally. So, where are we?

 

[bobc2]

I don't think that the collapse of the wave function is an event in this sense. It is not something that can be observed or recorded on its own in any way. It is only something which you can get by comparing data after the fact.

You see similar things in other situations, e.g. when you are doing EM in a gauge other than the Lorentz gauge. You can get dramatic changes in the potentials in one frame that do not happen in another frame. If you called the change in the potential an event, then you might suffer this same confusion. But the potential is not observable, nor is the collapse.

You may want to ask this in the QM section, I am way beyond the limits of my understanding here, and I could very well be completely wrong.

Thanks a lot for your thoughts. I'll do some Bell's theorem study and also reflect on your well reasoned analysis. And that might be good advice, carrying the topic over to the QM guys.

One critical point you've put your finger on turns on the question of whether, at the instant of measurement of photon 1, does photon 2 change state, regardless of whether it is observed or not? I take it that is really your key point--and a very good one. I've been assuming the answer to that is yes--and maybe that's out of my tendency to find as much realism in spacetime as possible (as opposed to being informed about QM theory). Of course the Aspect experiments always validated EPR by making that measurement on particle no. 2 and finding that sure enough it was opposite to particle no. 1. So, if he had not made the measurement of particle 2, how could he have known if its state had actually changed (although I've been betting on maintaining original system spin = zero, and how could that be maintained if particle 2 did not change even though it was not measured?).

 

[Dmitry67]

At first, I wanted to add that historically Von Neumann had recognized the problem you are talking about. He developed his own 'flavor' of Copenhagen Interpretation, where "collapse" was just an information update, not a physical process, avoiding issues with relativity.

I'm still troubled with the apparent conflict between QM and special relativity on this entanglement issue, notwithstanding Bell's theorem. I don't see how you deny realism in QM (but then maybe that's the essense of QM) and yet we would still like to include elementary particle world lines in the spacetime diagrams--we would like for them to be real (should we instead have wave functions in the spacetime diagrams?). Feynman diagrams seem close to a representation of reality (being sure to include the W boson in the beta decay pictures, etc.).

After the death of Copenhagen Int. (and also Transaction Int) there are 3 viable Int, and they approach this issue differently.

Stochastic Mechanics - macroscopic, not microscopic events are atomic. particles, fields etc are "just the math" to explain the correlations between the macroscopic events. So in SM it is non-issue: math gives you the formula which is in agreement with the reality - then shut up and calculate. Dont think how some weird stuff "propagates" from Alice to Bob. Neither real nor virtual particles exist in that Int - they are just math. On the contrary, particles tracks in cameras are real.

Bohmian Mechanics - is non-local. Some versions even have a hidden preferred frame. Note that no matter how far particles are in real space, they can be very close in some other configurational space. So BM can be local - but not in our space :) BM also has some weird definition of reality, so I don't want to go further.

MWI - is local, nonrealistic (becased on the commonly accepted definition of realism) but is realistic in a wider sense, because the global wavefunction of the universe is well defined in any point of spacetime. Also, in EPR experiment at least 2 copies of Alice and Bob are created independently. Later they synchronize their data using slow than light channels, and reveal the correlations. Nothing is transferred FTL in such case and ordering of events is well defined.

In MWI there is just a unitary evolution of the wavefunction. There are no particles - just waves (even measurement create an illusion of them and even tracks). Ultimately, the whole world is just one big unbound Feynman diagram

Personally, for me by EPR nature is crying that MWI is true, but not all people agree with me, of course. MWI is also deterministic, so God does not play dice after all..

 

[Calrid]

As long as any interpretation fails to distinguish itself beyond talk, in any way, none of them will either be alive or dead, but somewhere in between.

This is after all science not what I like best because of my pet theory du jour.

Put up or shut up is probably the best way of saying this, talk is cheap.

MWI is eternally unprovable so it tends to be one of those interpretations you like if you don't want to be too troubled by evidence, it is of course scientifically speaking completely indistinguishable from any other philosophical interpretation and likely always will be. Unless of course we find ways of proving other dimensions exist and these other wave functions are played out in them as one is selected in ours. Which to me seems intrinsically impossible, maybe in a few tens or hundreds of million years if we are still around and have transcended beyond our conscious limitations?

 

[bobc2]

At first, I wanted to add that historically Von Neumann had recognized the problem you are talking about. He developed his own 'flavor' of Copenhagen Interpretation, where "collapse" was just an information update, not a physical process, avoiding issues with relativity.



After the death of Copenhagen Int. (and also Transaction Int) there are 3 viable Int, and they approach this issue differently.

Stochastic Mechanics - macroscopic, not microscopic events are atomic. particles, fields etc are "just the math" to explain the correlations between the macroscopic events. So in SM it is non-issue: math gives you the formula which is in agreement with the reality - then shut up and calculate. Dont think how some weird stuff "propagates" from Alice to Bob. Neither real nor virtual particles exist in that Int - they are just math. On the contrary, particles tracks in cameras are real.

Bohmian Mechanics - is non-local. Some versions even have a hidden preferred frame. Note that no matter how far particles are in real space, they can be very close in some other configurational space. So BM can be local - but not in our space :) BM also has some weird definition of reality, so I don't want to go further.

MWI - is local, nonrealistic (becased on the commonly accepted definition of realism) but is realistic in a wider sense, because the global wavefunction of the universe is well defined in any point of spacetime. Also, in EPR experiment at least 2 copies of Alice and Bob are created independently. Later they synchronize their data using slow than light channels, and reveal the correlations. Nothing is transferred FTL in such case and ordering of events is well defined.

In MWI there is just a unitary evolution of the wavefunction. There are no particles - just waves (even measurement create an illusion of them and even tracks). Ultimately, the whole world is just one big unbound Feynman diagram

Personally, for me by EPR nature is crying that MWI is true, but not all people agree with me, of course. MWI is also deterministic, so God does not play dice after all..

Good stuff, Dimitry67. Thanks a lot for your summary of interpretations of QM. I do get the impression there are still a lot of Copenhgen physicists around (not necesarily the ones who are actively involved with QM though).

 

[bobc2]

As long as any interpretation fails to distinguish itself beyond talk, in any way, none of them will either be alive or dead, but somewhere in between.

This is after all science not what I like best because of my pet theory du jour.

Put up or shut up is probably the best way of saying this, talk is cheap.

MWI is eternally unprovable so it tends to be one of those interpretations you like if you don't want to be too troubled by evidence, it is of course scientifically speaking completely indistinguishable from any other philosophical interpretation and likely always will be. Unless of course we find ways of proving other dimensions exist and these other wave functions are played out in them as one is selected in ours. Which to me seems intrinsically impossible, maybe in a few tens or hundreds of million years if we are still around and have transcended beyond our conscious limitations?

Interesting comments, Calrid. Do you have a preferred interpretation of QM?

 

[Dmitry67]

1 As long as any interpretation fails to distinguish itself beyond talk, in any way, none of them will either be alive or dead, but somewhere in between.

2 MWI is eternally unprovable so it tends to be one of those interpretations you like if you don't want to be too troubled by evidence, it is of course scientifically speaking completely indistinguishable from any other philosophical interpretation and likely always will be.

1 Copenhagen is dead not because it was falsified by some experiment, but because it is, mathematically speaking, self-inconsistent. The show stopper for CI is “what is a measurement device”? When devices were huge, it was silently ignored. However, now we are able work with quantum computers, where “measurement devices” are only few atoms large. So it raises unavoidable questions like ‘why these 10 atoms are measurement device while these 10 are not?” or “why the same media (glass, mirror) is not a measurement device for visible light but measures the gamma rays?”. Ultimately, CI fails to provide M(x) – a function, which for every system x returns 0 or 1 if it is a measurement device or not.

2 I adhere to Max Tegmark’s MUH. Strictly speaking, his program is not 100% physics, but something with a high percentage of philosophy, but it is very constructive and it also gives some testable predictions – for example, that in TOE there will be no ‘non-physical axioms’ – just equations. So it will be purely mathematical system. For that reason I don’t like Bohmian Mechanics – because it contains some unavoidable blah-blah-blah stuff.

 

[Calrid]

Interesting comments, Calrid. Do you have a preferred interpretation of QM?

I'm afraid I'm quite vanilla Copenhagen, although I quite like relational quantum mechanics. That said they are all pretty much indistinguishable, I just kind of despair when people make completely unsubstantiated claims about such and such an interpretation being better or in this case on interpretation being dead. If it MWI is so shiny and good why is it still couched in the term interpretation, even the term sounds like its a matter of opinion. Nothing against people being a fan of an interpretation whatever it is. I might not like MWI except as a sort of descriptive form of Copenhagen, but I don't deny its popular atm.

 

[Calrid]

1 Copenhagen is dead not because it was falsified by some experiment, but because it is, mathematically speaking, self-inconsistent. The show stopper for CI is “what is a measurement device”? When devices were huge, it was silently ignored. However, now we are able work with quantum computers, where “measurement devices” are only few atoms large. So it raises unavoidable questions like ‘why these 10 atoms are measurement device while these 10 are not?” or “why the same media (glass, mirror) is not a measurement device for visible light but measures the gamma rays?”. Ultimately, CI fails to provide M(x) – a function, which for every system x returns 0 or 1 if it is a measurement device or not.

2 I adhere to Max Tegmark’s MUH. Strictly speaking, his program is not 100% physics, but something with a high percentage of philosophy, but it is very constructive and it also gives some testable predictions – for example, that in TOE there will be no ‘non-physical axioms’ – just equations. So it will be purely mathematical system. For that reason I don’t like Bohmian Mechanics – because it contains some unavoidable blah-blah-blah stuff.

So Copenhagen is not mathematically consistent then? Seriously doubt that is true.

I'm not sure I follow your logic, what does any of that have to do with the potential correctness of CI? I also don't think Copenhagen has any problems with explaining quantisation either in all mediums, or using 10 atoms. Clearly some lattices of atoms absorb some wavelengths because of their atomic configurations and some don't, this is the basis of QM or more particularly materials science. This isn't I don't think anything to do with interpretation issues which are about what we are measuring, information and perceptual/observational issues: what is really going on? Perhaps I'm missing something?

It's great you like these interpretations, I myself would like to see a more real approach, I just think we are kind of limited by the nature of the wave. But let's not get ahead of ourselves, they are still indistinguishable. We're still talking about philosophy here.

That's not a testable axiom btw, just because we find no black swans does not mean all swans are white. So even if a series of experiments turn up all white swans it doesn't fundamentally mean that they cannot or do not exist. It may well be a result of how you chose to meausre something an your biases, it may not, but saying something might be so does not distinguish anything.

What will decide an interpretations demise is purely its ability to model experiment or anothers to distinguish itself beyond it. Maths is irrelevant except as it describes a theoretical/experimental model it is as always subservient to reality not the other way around.

I tell you what is dead, absolute time, alchemy, the four element theory. What caused their demise? Experiment. It's a bit premature to call anything dead before the fat lady has sung. I think MWI is catching up to Copenhagen in terms of mainstream popularity, just because it is deeply unsatisfying. I don't think though reality is going to give much of a toss for hurt feelings or popularity..?

 

[Dmitry67]

In classical experiments made in CI era we knew in advance what was a measurement device and what was not. There was a huge gap between measurement devices (billions and billions of atoms) and QM world (few particles).

Recently that gap had been closed: at one side, we have 'measurement devices' mode of few atoms, on another side, we can put hundreds particles in superposition (Double slit experiment with C60 molecules) or even billions of electrons (experiment with superposition currents on the superconductive ring)

2 worlds collided. There is no anymore 'macroscopic world' and 'microscopic world'. hence, CI must explain the measurement
a) based on the intristic properties of QM stuff or
b) as something that emerges at some size or complexity.

a) can't be true because QM evolution without a measurement is unitary while measurement is not. So option b) is claiming that some NEW LAWS of physics emerge when the number of atoms reaches... reaches what?

To be taken seriously, CI should provide a function which must in advance tell us if something is a measurement device or not. Problem with collapse would be the second step. But clearly, CI fails to do that first step and is abandoned (in QM forum I don't see any proponents of CI anymore, the last one was I guess 3 years ago)

Of course, for all practical work when measurement devices are big enough CI is good and works as a rule of thumb, but it can’t be used to understand the fundamental properties of nature.

 

[Calrid]

Copenhagen doesn't make any of these claims it merely says the wave function is undefined without measurement, it's purely about what we can known about an unmeasured quantity and what happens on measurement and how our bias might effect how we interpret results. I don't think anything has been decided. Any interpretation is not really concerned with issues outside of what is going on at or before the point of measurement. CI does tell us what a measurement device is, its anything which we use as part of the experimental set up but that's all it has to say in the context you mention. Copenhagen is fundamentally agnostic about what is the nature of things that are not measured. I agree it can't be used to tell us what the fundamental property of a photon is, but then neither can any other interpretation, none of them have gotten around the problem in a demonstrable way, so talk is cheap.

Maths or postulating about maths and unitary constructs is not going to win a Nobel prize. I'm not really sure about what you mean by unitary in this context anyway? If you mean the measurement produces different results than non measurement, well sure, but then that's just a fact one that can be explained in about a dozen different ways, none of which really distinguishes itself.

The explanation of two worlds is that quantum events are fragile and likely to collapse (or at least are effectively different after they are interfered with) so they are seldom observed at any but the smallest scales. I don't think there is anything that really says the two worlds are different or detached in some way. Only that quantum effects can impinge on the large scales but such an effect is rare and its probability approaches 0 at the limit of the lifespan of the Universe. The boundary is not a real boundary it is about probabilities of measurement, it's not physical and it's not discreet.

 

[Dmitry67]

it merely says the wave function is undefined without measurement

Very good then.
Now define, what is a measurement :)

 

[Calrid]

Very good then.
Now define, what is a measurement :)

Well it does depend, but in this context it is anything that is set up to find something out at a given point in our experiment, that actively impinges on our photon by imparting energy to the system.

 

[Dmitry67]

Well, it is a wordy stuff, which defines the word 'measurement' besed on some human concept of 'an experiment', 'find something'. It is poetry, not physics.

I need a binary-valued predicate, IsMeasurementDevice(system).

 

[bobc2]

Dmitry67 and Calrid,

Does the measurement have to be observed by a conscious being in order for the two-photon system to snap into a definite eigenstate of UP and DOWN, or can the measurement apparatus itself perform adequately as the observer?

 

[Dmitry67]

If you adhere to the flavor where wavefunction is not real and collapse is just an information update, you can't avoid issues with the early universe: as 'wavefunction is underfined without measurement' (c) Calrid, and the very first measurement devices were possible only when Universe had cooled down enough so the information could be preserved in some system and there was a possibility for the systems, isolated from the environment to some extent, then the whole history of the early Universe appears to be non-realistic. Wavefunction was not defined at all in early Universe (?) until the very first measurement device had formed (magically from non-existent wavefunction?) when (?)

In a flavor where wavefunction is real, you have issues with relativity, described in the original post.

 

[bobc2]

If you adhere to the flavor where wavefunction is not real and collapse is just an information update, you can't avoid issues with the early universe: as 'wavefunction is underfined without measurement' (c) Calrid, and the very first measurement devices were possible only when Universe had cooled down enough so the information could be preserved in some system and there was a possibility for the systems, isolated from the environment to some extent, then the whole history of the early Universe appears to be non-realistic. Wavefunction was not defined at all in early Universe (?) until the very first measurement device had formed (magically from non-existent wavefunction?) when (?)

In a flavor where wavefunction is real, you have issues with relativity, described in the original post.

This is a fun discussion for sure, Dmitry67. Thanks for sharing.