Is entanglement just a mathematical construct or is it a real phenomenon?

[Ken G]

Thus I agree that science does not tell us how reality really works but it may provide only a mental/mathematical model for reality at a certain level of abstraction.

Right, this is the crucial recognition that seems surprisingly rare among those who discuss science.

Although this "deliberately neglecting noise" is inherent to classical physics too, this is not a conceptual principal firewall within the terminology of the theory itself.

The firewall is not the concept of neglecting noise, it is the application of that concept. We choose when to apply it, and the choice is the firewall. What is normally meant by a "pure state" in quantum mechanics is one where the choice has not been made, and the mysterious "collapse" people debate endlessly is simply the place where that choice got made.

The question of "how science works" is the subject of "philosophy of science" . Thus in truth it is the CI that destroys the boundary between science and philosophy of science by creating a vague mixture of terminologies (mathematical/physical on one hand and epistemological on the other hand).

I think a perfectly valid way to study how science works is to look at the examples of how scientific theories were supported or refuted. In all cases, you will find confrontation with classical-acting systems, meaning, systems that we know we can successfully treat by making the choice to average over the noise we cannot explicitly track. This is very much a step of "translation" from reality to what fraction of it can actually fit in our heads, yet causes so much confusion about "what is really happening in reality".

A scientific theory may cover the phenomenon of "how science works" by incorparating how human mind works and interacts with external reality however it cannot be allowed to do this by a mixed terminology.

I don't see where Bohr is "mixing terminology", it is all just describing the method-- you look at the imprint of various physical phenomena on instruments you can rely on to behave classically. The latter behavior is the logic of our experience, what shaped our minds into tools for doing science. To ignore the role of our classical notions in science and mathematics would be to imagine that a brain is something other than what the evidence says it is-- a tool for organizing macroscopic phenomena. Bohr isn't mixing anything, he is recognizing the mixture that is inherent when a mind that evolved to create concepts like logic and geometry and macroscopic objects is used to study a microscopic realm it never directly experiences. Science is always a translation into what we can understand, Bohr is not introducing that basic truth, just building an interpretation that reflects it faithfully.

For a good scientific theory it is not sufficient to be a recipe for evaluating experiments. It should provide a consistent firewall-less model for the whole range of phenomena that are implicitely in its claim-area.

But the result must fit in our brains at the end, this is the crucial requirement that forces a firewall-full approach. Science is like a function, and it is not just the domain space that is handed to us (reality), but also the image space (our minds). All we can do is find the function, that is what we are learning about-- not the domain space. The "firewall" is between the domain space and the image space, and those who seeks a "firewall-free" result are ignoring the role of the image space. They are not finding an experimentally constrained function, they are finding an unconstrained and untestable philosophy.

If the theory, (when applied to the combined system of "measured particle + measuring device + observer" which are all made up supposedly by elements that qm pretends to describe), predicts a continuous evolution of superpositions, whereas experience tells otherwise.

But we already agreed the theory does no such thing, because all theories involve choices of simplifications, idealizations, and identifications of what will be treated as relevant and explicitly tracked, and what will be treated as irrelevant and ignored or averaged over. Those who treat science as a completely axiomatic process, well, I just don't know what scientific papers they have been looking at-- purely abstract ones I guess. But science can never be purely abstract and still be science-- it will only be mathematics. A useful component of science to be sure, when one remembers what it actually is.

The only conclusion is that there is a scientific not philosophical problem namely that QM cannot describe certain type of interactions between a single particle and a many particle system.

QM cannot and does not completely describe those interactions, and it was never intended to. It describes whatever element of that interaction we choose to track, and that is what it was intended to do. It's all a question of the experimental setup what data we need to track and what data we need to average over or ignore. That is how science has always been, we seem in a rush to pretend it is something else out of sheer hubris, it seems to me.

Thus since obviously, measuring devices, human eye, human brain etc are all made up of elements that are within the claim domain of quantum mechanics, QM should be regarded as incomplete unless it provides a firewall-less description of transition from quantum behavior to classical behavior.

This is the crux of the matter. The problem is your identification of a "claim domain", but science just doesn't work that way. It is not the domain that defines science, it is its various image spaces. We choose these images, this is the point. Science is about finding ways to get the only domain that matters, reality, to leave an imprint on an objective image space that we choose via our experiments and modes of inquiry. Thus you should be speaking of "claim images" not "claim domains". That's the brilliance of the CI in a nutshell. That's why Bohr isn't introducing the firewall, the scientist is, when he/she chooses an image space to couple to the domain of reality.

I have nothing against CI, I am against the claim that the problem is not scientific but it is merely philosophical .

That again sounds like a kind of modified CI that perhaps was popularized by Heisenberg, though I don't even know if he actually thought that way. To me, CI in its "pure" (Bohring, if you will) form has zero philosophical content outside of simply registering the process of how science defines itself. One cannot scientifically "investigate" the CI, one can only choose to do science differently somehow. But so far, no such alternative has been suggested or attempted! The method I've described is always used, with no exception, other than purely abstract mathematical journeys that are not by themselves science. When the results of those journeys are tested as science, the tests always look exactly the way I (and Bohr) have described them.

Thus it can be studied scientifically. Zurek's idea of decoherence for example is a scientific approach to try to describe this transition from quantum to classical by scientific theoretical methods from within the theory.

If someone wishes to interject new image spaces between the domain and previously used image spaces, they are more than welcome to do so, more power to them. But don't be surprised when the way they do it is still exactly the way the CI describes it! There is no way around it, the final step must couple to a classical-type image space. It can certainly be a transitional image space, as I said, in the sense of doing less averaging and more explicit tracking, but that won't separate it from the CI understood in its proper form.

Whether it solves the problem or not is another issue. If we would accept your approach then we should regard all the theoretical scientific work on decoherence to create a scientific modell for measurement as purely philosophical.

I hope I have clarified why that does not follow from my position, nor from the CI. What makes something science versus philosophy has nothing to do with the model that is being created, it is all about the method being used.

It is interesting that if you group the terminologies you put scientific on one side and mathematical/philosophical on the other side. I would group it like mathematical/scientific and philosophical because theory (mathematics) and experiment is two aspects of the science that go hand in hand.

I do not doubt that theory and experiment go hand in hand, while philosophy has a more distant relationship. But both philosophy and mathematics are formal exercises of thought, so that is why they are logically grouped together, whereas experiment is how we couple to reality. In the domain/image language, I would say that experiment describes the image space and reality determines the function. Mathematics only gives us a language to understand the function, and philosophy plays no role at all after it has been used to recognize that this is the structure we are using.

 

[Ken G]

The cavity quantum electrodynamics (an atom and a photon in a micro cavity) has created in my opinion new possibilities to trace the time evoultion of the wave function with extraordinary time resolutions that were unthinkable in the past. We can observe a photon actually during the process of emission/absorption while it is half/emnitted absorbed. Of course this information is obtained ultimately by statistical avaraging over many detections using an ordinary photon detector and calculating back the wave function.

Right, that is the point-- it's still a situation where the CI is appropriate and applicable.

I think in future we will be able to trace how a collapse-like evolution actually occurs as a continuous time evolution of the wave function.

I agree, that will be interesting-- but note that at every stage of the process, they will have a perfectly CI-compatible interpretation of what is happening, because they will still be using standard scientific methodology. That which they track explicitly will behave quantum mechanically just as the CI allows, and that which they decide not to track they will neglect or average over, defining the classical claim-image, also allowed by the CI. Much will be learned about how the decoherence of measurement works, but nothing new will be learned about the CI if the proper (i.e., non-philosophical) version is being envisioned-- expressly because quantum mechanics will work fine. Of course if it does not, all the "I's" will be out the window equally. I guess one could summarize my position by pointing out that Bohr's approach to the CI is compatible with all other interpretations of quantum mechanics-- all perceived incompatibilities stem from either unfairly interpreting Bohr's CI as a philosophical statement about reality rather than a recognition of how science works, or from extraneous elements of some of the interpretations (like many worlds) that fall outside of any remotely possible or suggested scientific methodology.

 

[erastotenes]

Right, that is the point-- it's still a situation where the CI is appropriate and applicable.
I agree, that will be interesting-- but note that at every stage of the process, they will have a perfectly CI-compatible interpretation of what is happening, because they will still be using standard scientific methodology. That which they track explicitly will behave quantum mechanically just as the CI allows, and that which they decide not to track they will neglect or average over, defining the classical claim-image, also allowed by the CI. Much will be learned about how the decoherence of measurement works, but nothing new will be learned about the CI if the proper (i.e., non-philosophical) version is being envisioned-- expressly because quantum mechanics will work fine. Of course if it does not, all the "I's" will be out the window equally. I guess one could summarize my position by pointing out that Bohr's approach to the CI is compatible with all other interpretations of quantum mechanics-- all perceived incompatibilities stem from either unfairly interpreting Bohr's CI as a philosophical statement about reality rather than a recognition of how science works, or from extraneous elements of some of the interpretations (like many worlds) that fall outside of any remotely possible or suggested scientific methodology.

As I said, I don't say that CI is wrong in its predictions. My objection to CI is that in order to avoid the questions and conflicts with special relativity regarding a dynamical mathematical description of detection process in terms of wave function time evolution, it declares the wave function to be a just only mathematical function for predicting the statistical distribution of the outcomes of the measurement adn nothing else.

However if we can describel measurement really in terms of dynamic time evolution of the wave function (even if its by back tracing the wave function a procedure in accordance with CI) , it would not be necessary to declare wave function as something less real then any classical entity. But as experimental violation of Bell inequality shows this would mean that a conflict with relativity is unavoidable. Because such a dynamical process if possible at all, must involve superluminal wave-function currents as the measurement on distant entagled particles shows.

Thus even the hope I described above conflicts with relativity.

Since decoherence implies the slicing of the wave function of 3n dimensional configurations space of the measuring device consisting of n particle into n 3dimesional noninterfering subspaces each describing a different classical reality corresponding a different outcome, I wonder how it guaranties that the the correct correlated outcomes on entangled particles on distant locations remain within the same "slice" of macroscopical reality. Since the decoherence is a mechanism within the known time evolution of the wave function in accordance with relativity I have doubts that decoherence alone can correctly describe time evolution of wave function during measurement on entangled distant particles dynamically.

If so then there must be another mechanism. In my opinion it can be the effect of radiation reaction (self field) during interaction that may destroy the Lorentz invariance (namely the relativistic compliance) of the equations of time evolution of the system.

 

[Ken G]

However if we can describel measurement really in terms of dynamic time evolution of the wave function (even if its by back tracing the wave function a procedure in accordance with CI) , it would not be necessary to declare wave function as something less real then any classical entity.

I have no doubt at all that the wave function can be used to describe the measurement process as a dynamical time evolution for as far as we care to treat it that way and have the experimental apparatus capable of tracing that evolution. I further see not the least contradictions with CI to make that statement. It will require an experimental apparatus that makes the connection with classical instruments in some "transitional phase" of the evolution of the wave function, and the predictions for the outcomes during that transitional phase will come perfectly well from the CI. There just isn't any evidence of any problems with CI, because it is a misinterpretation of the CI to say that it "declares what is unphysical". What it does is say what the wave function is for, quite clearly and specifically, and in all the situations we have been talking about that is indeed just what it is for.

On the other hand, whether or not the label "physical" applies is a matter of taste, as with all things physical, and although CI proponents may have used that language to clarify how they are describing the action of the wave function, that language is not an important part of the CI. The problem is, if you want it to be physical, it will have some properties we normally think of as aphysical. That's not a problem for the CI, it's a problem for the people who like to imagine that a wave function is "physically real". The CI doesn't care if someone says a wave function is physical or not, it just says what the wavefunction does, along the lines of "it is as it does", and sure enough, that is just what a wavefunction does, in practice.

But I do think you are welcome to view that as "physical" if you choose, just as you are welcome to view an "electron" as physical even though it is an identical subset of all electrons and therefore never actually possesses a "single particle wavefunction" in some real or absolute sense. It's all a useful construct, there is no such thing as "something physical" that science can define in an absolute way, we choose what is physical just as we choose our claim-images (to reinterpret your claim-domains). And we pay the price for those choices, if we don't like the ramifications. Don't blame the CI-- that's shooting the messenger!

But as experimental violation of Bell inequality shows this would mean that a conflict with relativity is unavoidable. Because such a dynamical process if possible at all, must involve superluminal wave-function currents as the measurement on distant entagled particles shows.

No such "currents" are required, this is the whole point of treating the wave function as what it is-- instructions for making predictions that work. That's what it is, that's what is testable. There's no reason to try and equip the wave function with a superluminal mechanism if it is information in your head-- that's the beauty, not the weakness, of the CI.

Since decoherence implies the slicing of the wave function of 3n dimensional configurations space of the measuring device consisting of n particle into n 3dimesional noninterfering subspaces each describing a different classical reality corresponding a different outcome, I wonder how it guaranties that the the correct correlated outcomes on entangled particles on distant locations remain within the same "slice" of macroscopical reality. Since the decoherence is a mechanism within the known time evolution of the wave function in accordance with relativity I have doubts that decoherence alone can correctly describe time evolution of wave function during measurement on entangled distant particles dynamically.

I think you will find the problem goes away if you stop imagining that a "wave function" is a unique entity "possessed" by the particles. We already know this is not true, a wave function is just an expression of what we can know about the particles given a particular assumed environment. If we are wrong about the environment, we are using the wrong wave function, and if there is a history to the particle that we are not privy to, we must either neglect or average over what we don't know.

So it is with all things probabilistic, this is not new to quantum mechanics. Even classical concepts like "position" work that way-- there was never any such thing as a definite position, even if we have measured it. There is only a Gaussian position uncertainty, that is all that science would ever have access to. If someone else had a spectacularly more accurate representation of the particle position, neither would be the "real" one. Science is about organizing and handling information, the connection to reality we may imagine as we like.

If so then there must be another mechanism. In my opinion it can be the effect of radiation reaction (self field) during interaction that may destroy the Lorentz invariance (namely the relativistic compliance) of the equations of time evolution of the system.

I have no doubt that this kind of thinking can inspire good science-- so make a testable prediction, expressed in terms of accessible information, not a philosophical model of reality.

 

[erastotenes]

I think you will find the problem goes away if you stop imagining that a "wave function" is a unique entity "possessed" by the particles. We already know this is not true, a wave function is just an expression of what we can know about the particles given a particular assumed environment. If we are wrong about the environment, we are using the wrong wave function, and if there is a history to the particle that we are not privy to, we must either neglect or average over what we don't know.

In order to explain why the problem does not go away, I have to express it in more clear semi-mathematical terms. The discussion is namely not a verbal one about our taste what we consider as physical.

As you know the following continuity equation is valid for probability density for a single particle(By the way I am aware that for n particles we don't have n wave functions but a a single wave function of 3n variables(I mean spatial part) . However I don't know at the moment which form the equation below takes in the 3n dimensional configurations space therefore I take the simple example of single particle ) .

d/dt(volume integral over probability density) = surface integral (QM-current density)

where:
the surfece is the closed surface
probability density = psi-square .
QM-current density = psi*grad(psi) - psi grad(psi*)

This can be deduced directly from Schrödinger equation. It tells us that if the probability density decreases at some region it can happen only through a leak on the surface that closes the region. It tells us namely that if it increases at some space region and decreases at some other distant lreqion (preserved normalization) then it can happen only by a current between these regions.

Of course since Schrödinger equation is nonrelativistic , there is no limit for how fast this process can happen. But if we would write down the continuity equation using the relativistic expressions for the currrent density and probability density consistent with Dirac equation (I don't know at the moment how they look like) then certainly the fact that Dirac equation is relativistic would impose an upper limit to the velocity of probability flow (that must be related some howe to the expression for current density) from one region to another region.

This is one thing.

The other thing is the following:

We know that for example during the measurement of position after an interference experiment the wave function (as it manifests itself only over large number of measurements undertaken on an ensemble of particles with "almost" identically prepared intial states) is widely spread over the whole screen just immediately prior to the measurement and it is localized to a tiny region of space immediately after detection(as a second measurement immediately after the first one would verify).

However it seems this process of "probability density decreasing at far regions and increasing at the detected location" happens so fast that if the flow of probability density "would" be decribed as a continuous time evolution mathematically it would require superluminal density currents.

This was only suspected in 1920's (and it is one of the reasons why Schrödinger had to give up his wave-only viewpoint. ) but Aspects experiments and other similar ones on entangled particles verfied that if the change of the probability density is a result of very fast but continuous time evolution of the wave function during the measurement on one location then this must involve superluminal quantum mechanical current between distant locations (The propagation of the effect of the first measurement to the location of the other measurement device ) to guarantee that the result of the other location is correlated with the first one.

This is experimental fact . Please notice that I nowhere refer to how "physically real" the probability density , or quantum mechanical current density is. I just say experiment shows that if we consider the measurement on first location as a dynamical evolution of the whole wavefunction of the two particle system(+ measuring device + environment) , then we must assume that the propagation of the effect of the change of the probability density at first location to the other location must be superluminal. Thus either continuity equation is violated where increase at some region and decrease at some other can happen without a flow of current between them, or continuity equation holds but currents are superluminal. Thus if there is an equation that can correctly describe this process as a continuous process (if at all) then this equation cannot be Lorentz invariant.


1. Please notice also that a possibility of a dynamical description of for example localization during posisiton measurement by an equation on time evolution of wave function is equivalent to a claim that this process must be deterministic intrinsically and that the apparently probabilistic behavior must be related to uncontrollable initial small differences of the whole system ( measured particle + detector + environment) as it is in classical (only apparently but not intrinsically) probabilistic behavior of a dice.

Please notice that the argument of CI to avoid a conflict with special relativity regarding measurement on entangled particles is the following:

"Since the outcome of each individual measurement is ultimately probabilistic and since the correlations between distant measurement become evident only after we bring the results by normal means together and compare them, there is no "information flow" from some location to other location during the measurement so the relativity is not violated."

Thus because of (1) the idea that the collapse process can be described by a condinuous time evolution, is inconsistent whit these arguments of reconciliation between QM-measurement on entangled particles and relativity.

 

[Ken G]

d/dt(volume integral over probability density) = surface integral (QM-current density)

This is a cute way to express the situation, but like you point out, the choice of a concept of "current" is an arbitrary one and in no way invokes relativistic limits, necessarily. There are many ways of thinking about physics where things are happening faster than c, but whenever we do that, it magically turns out that no real (i.e., information carrying) effects ever do. This is just one more example.

Of course since Schrödinger equation is nonrelativistic , there is no limit for how fast this process can happen. But if we would write down the continuity equation using the relativistic expressions for the currrent density and probability density consistent with Dirac equation (I don't know at the moment how they look like) then certainly the fact that Dirac equation is relativistic would impose an upper limit to the velocity of probability flow (that must be related some howe to the expression for current density) from one region to another region.

Leaving out the demonstration of this is a crucial weakness. I would not anticipate any such requirement on the relativistic wave function, and indeed it is easy to think of experiments that violate it. That's what I meant when I said that your problem derives not from the equations, but rather from your desire to think of the wave function as something real that the particle "possesses". If it's real, then a "current" of it shouldn't go faster than c, but if it's a mathematical function in your head that you give values to at distant locations, there is no such constraint.

The same problem exists classically, it's just that there we do get away with imagining the information is something the particle "possesses" (even though we had no way to prove it). If I take two distinguishable cards and don't look at them, put one on a spaceship for alpha Centauri, wait a few years, and then look at the other card, I instantly know what the card on the ship is. Instantly. Now that's pure classical information there, but the "faster than light" problem is exactly the same as in quantum mechanics. We just resolve it differently-- classically we get away with imagining that the card "was always that", so no information actually propagated faster than c. That resolution doesn't work with quantum mechanics, but so what? We just find a different resolution, involving correlations in the joint wave function. Why were we so unbothered classically but get all in a fret quantum mechanically? We already have many examples of joint wave function phenomena, like white dwarfs and exchange energies.

This was only suspected in 1920's (and it is one of the reasons why Schrödinger had to give up his wave-only viewpoint. ) but Aspects experiments and other similar ones on entangled particles verfied that if the change of the probability density is a result of very fast but continuous time evolution of the wave function during the measurement on one location then this must involve superluminal quantum mechanical current between distant locations (The propagation of the effect of the first measurement to the location of the other measurement device ) to guarantee that the result of the other location is correlated with the first one.

Do you see how you bias your own picture by choosing the word "propagation" here? What if I said, when I look at my classical card, that the knowledge of what that card is has to "propagate" to the spaceship? We don't think about it as a propagation classically, we think the card was always that. So why would we think of it as a propagation quantum mechanically, simply because there we cannot say "it was always that"? Chuck local realism, it's clunky in quantum mechanics. It's all a question of where the wave function "lives"-- you imagine it lives in real space, but it lives in your mind, and you imagine it spread over space because sometimes it helps to do that (and other times it just confuses you).

A good example here might be to think about a satellite photo of a forest. You could look at the tree density in various parts of that forest, and there it's clear you are dealing with a local variable-- those trees are really there and in some sense really have that density (it doesn't matter what this means). But if you instead asked, which trees are prettier, and came up with a "beauty function", it too would have a value spread over the locations of the forest, but there it is more clear that the beauty function lives in your head, it's your beauty function. I'm not saying the analogy is close, but it's a way to see what I mean by "where a function lives", even a function that takes on values over space.

Another way to look at this is, it's the fallacy of the excluded middle-- we imagine that either we have local realism, as in classical thinking where particles "possess" all the information that relates to them, or we have information "spread out" over a wave function which has to "propagate" to get somewhere else. The wave function is in your head (is it not? I mean, we can debate if it is real, but we know for sure that you have a mental picture of it), so it doesn't necessarily have to propagate anywhere, even if you want to picture its time evolution as a divergence of a current. You are "shooting the messenger" when you object to superluminal properties of wave functions!

Please notice that I nowhere refer to how "physically real" the probability density , or quantum mechanical current density is.

Yes, this is an important point, but you actually did just that in subtle ways when you chose words like "current", "leak", and "propagation". The mathematics requires none of those concepts, they are useful analogies when picturing what is happening. Specifically, there is no FTL limitations in the mathematics, and I doubt they appear in Dirac's formulation either except when applied to actual information propagation between observers (i.e., affecting predictions that would be made by uncausally connected physicists).

I just say experiment shows that if we consider the measurement on first location as a dynamical evolution of the whole wavefunction of the two particle system(+ measuring device + environment) , then we must assume that the propagation of the effect of the change of the probability density at first location to the other location must be superluminal.

I hope it's clear now the refutation of this claim-- I do see the evolution as being one of the whole wavefunction and I do not see the need to interpret its changes as a propagation of anything but a mathematical construct, though I see that as a useful picture as long as we don't take it too literally.

I think I can make this position more clear with an example. We can just use a single particle and put it in a huge box, and prepare its wave function so that it is much more likely to be at either end of the box than anywhere near the center (perhaps with a potential barrier over much of the middle of the box). Now imagine coupling the system to a classical measuring device on one side of the box, so it ends up telling you if the particle is on that side or not. Whether or not that coupling could ever be diluted down to the action of an interaction Hamiltonian on the particle, let's imagine it can, so that the action of the measurement on the wave function will still satisfy the Schrodinger equation and your expression at all times, and will ultimately result in either raising or lowering the amplitude at the other end of the box. This can be set up so that the raising or lowering appears to be due to a superluminal current, as you describe. Is this a relativity problem?

No, it's just another example of how actual signals are subluminal even when at first glance it looks like they are superluminal. You can interpret the measurement on one end of the box as either causing the "other half" of the particle to tunnel over to the side of the measurement, or the "first half" to tunnel over to the far side, depending on the result of the measurement. But neither of those interpretations run afoul of relativity. Let's say they have equal probability (1/2). A person on the other side of the box will never need to know that you did your measurement-- their results are still 1/2 if they do the measurement. You'll know what their outcome will be, but they won't-- no signal, no violation of relativity.

 

[erastotenes]

I think I can make this position more clear with an example. We can just use a single particle and put it in a huge box, and prepare its wave function so that it is much more likely to be at either end of the box than anywhere near the center (perhaps with a potential barrier over much of the middle of the box). Now imagine coupling the system to a classical measuring device on one side of the box, so it ends up telling you if the particle is on that side or not. Whether or not that coupling could ever be diluted down to the action of an interaction Hamiltonian on the particle, let's imagine it can, so that the action of the measurement on the wave function will still satisfy the Schrodinger equation and your expression at all times, and will ultimately result in either raising or lowering the amplitude at the other end of the box. This can be set up so that the raising or lowering appears to be due to a superluminal current, as you describe. Is this a relativity problem?

No, it's just another example of how actual signals are subluminal even when at first glance it looks like they are superluminal. You can interpret the measurement on one end of the box as either causing the "other half" of the particle to tunnel over to the side of the measurement, or the "first half" to tunnel over to the far side, depending on the result of the measurement. But neither of those interpretations run afoul of relativity. Let's say they have equal probability (1/2). A person on the other side of the box will never need to know that you did your measurement-- their results are still 1/2 if they do the measurement. You'll know what their outcome will be, but they won't-- no signal, no violation of relativity.

Your description contains the following subtle contradiction between 2 paragraphs:

If we can describe the first measurment according to Schrödinger equation(SE) , this means we have a deterministic description of the time evolution of the wave function. This means that we in principle would be able to "predict" the outcome of the measurement if we could have enough information on the initial conditions(which are the state of the environment and fluctuations of radiation fieldf etc.) This means also that, we could not only predict, but also influence the outcome in a desired direction, by modifying the initial conditions in the environment, although this may be near to impossible practically (but this is another matter) .

This would then mean that we could influence the outcome on the other end in desired direction by playing with the conditions of environment at this end, which means we could transmit information to the other end superluminally.

As you see, since a dynamical description means automatically a deterministic description of time evolution of the wave function, such a possibility would automatically violate relativity.

 

[Ken G]

If we can describe the first measurment according to Schrödinger equation(SE) , this means we have a deterministic description of the time evolution of the wave function. This means that we in principle would be able to "predict" the outcome of the measurement if we could have enough information on the initial conditions(which are the state of the environment and fluctuations of radiation fieldf etc.)

Agreed.

This means also that, we could not only predict, but also influence the outcome in a desired direction, by modifying the initial conditions in the environment, although this may be near to impossible practically (but this is another matter) .

Not agreed. Define what you mean by "influence the outcome". That is the crux of the matter-- you will not be able to give meaning to that phrase without adding philosophical baggage not in evidence in the experiment.

This would then mean that we could influence the outcome on the other end in desired direction by playing with the conditions of environment at this end, which means we could transmit information to the other end superluminally.

I explained, in my example, why we could not do that. If you think we could, then you'll have to work up an example of how that would work.

As you see, since a dynamical description means automatically a deterministic description of time evolution of the wave function, such a possibility would automatically violate relativity.

My central point is that this does not follow, and indeed, it doesn't even follow classically. (Say in a "shell game" setup where the shells are carried far apart and one is looked at.) But even if one restricts to quantum mechanics and Bell-type problems, any violations of relativity are resolved by simply thinking of the wave function as not a "real attribute possessed by the system" (because that is no part of how it is used), but rather as a means used by a physicist to make a prediction. Note this latter approach shows that the wave function need not be unique to be useful (as is in fact the case in practice). So if one person uses some information to do a deterministic calculation and make predictions, someone else could also successfully apply quantum mechanics using a different wave function of the same system, based on different information. In that light, it is simply untrue that "a deterministic description violates relativity", because your determinism does not leave any detectable imprint on the independent observations of someone else.

 

[erastotenes]

Agreed.
But even if one restricts to quantum mechanics and Bell-type problems, any violations of relativity are resolved by simply thinking of the wave function as not a "real attribute possessed by the system" (because that is no part of how it is used), but rather as a means used by a physicist to make a prediction. Note this latter approach shows that the wave function need not be unique to be useful (as is in fact the case in practice). So if one person uses some information to do a deterministic calculation and make predictions, someone else could also successfully apply quantum mechanics using a different wave function of the same system, based on different information. In that light, it is simply untrue that "a deterministic description violates relativity", because your determinism does not leave any detectable imprint on the independent observations of someone else.

Example:

We have a beam of electrons and double slit interference and two personA and B. If A makes n detections and calculates the wave function by extrapolating the result and calculates the wavelength of the beam. Then comes person B and makes also n measurements and therefore calculates a slightly different wave function by same procedure. Of course the two will differ slightly because of finite number of measurements. However If A comes and makes another set of n measurements and B comes and makes another set of n measurements and if bothe make their calculation using the results of 2n measurements , it is obvious that their results come closer. The more they increase the number of their measurements the closer the results come. (We assume that there is no systematic change of the process about how the coherent beam is produced)

Since ( if there is no systematic change in the preperation of the beam throughout the process), the results of the two independent extrapolations would converge to the same limit, if we increase the number of measurements , we have every right to assume that this limit is the inseperable part of the measured system that is the function of preparation conditions and not our actual measurement.

Thus the concept of wave function itself does not refer to the actually collected information which is always limited but it refers to the theoretical entity justifiedly (above paragraph) assumed to exist prior to any measurement, about which we gather information at a level of desired accuracy if one makes sufficiently large number of measurements.

Consider that the value of any classical physical variable in an experiment is obtained by a statistical process after number of measurements to eliminate random errors. That the value fluctuates does not lead us to strange discussions whether the measured variable is something physically real or not.

So why do we do this if the subject of interest is not a classical variable in a classical experiment but the quantum wave function?

Because we on one hand succesfully calculate its time evolution and compare the results with experiment (although statistically) which gives us the confidence "we know how it evolves". On the other hand we suspect, our equations are unable to explain the apparently immeately(?!) occurring change during measurement. So instead of being humble and admitting that "something must be missed in our equation to describe this process", we choose the easy way to ignore the problem by declaring "the wave function not being something real but rather merely a mathematical construct, just representing our limited information on the system" because we know as you said that if we assume it to be ""real attribute possessed by the system" we are in danger of conflicting with relativity.

 

[Ken G]

We have a beam of electrons and double slit interference and two personA and B. If A makes n detections and calculates the wave function by extrapolating the result and calculates the wavelength of the beam.

But the wave function is not calculated from data-- it is calculated from knowledge of the experiment. The data is only used to test that wavefunction, and assert its predictive power. This is exactly what science is doing, we should not pretend it is doing something different. The example you gave is a trivial case because both A and B have the same knowledge of the experiment-- our discussion becomes relevant when you have physicists with different knowledge of the experiment, and therefore are using different wave functions. That's what is at issue in quantum entanglement experiments, for example. Their information is not contradictory, just incomplete (do we ever have complete information of our reality?), so they construct different wave functions, test them, and their wave functions come through with flying colors. Quantum mechanics works.

A good way to say this is, quantum mechanics is not a process of "determining the wave function that the particle has", because a particle doesn't have a wave function (or at least, no one has ever demonstrated that it does). Quantum mechanics is a prescription for mapping knowledge of an experiment into knowledge of a wave function, and then using the time evolution of the wave function to predict statistical outcomes, again based on knowledge of the experiment. It is not the knowledge itself, it is the mapping between knowledge and prediction. The mapping, the experiment, and the data, can all be the same even when the knowledge, wave functions, and predictions are all different for two observers. That dichotomy sorts between what lives "in reality" and what lives "in the mind of the physicist", and it is constructed simply by noticing how quantum mechanics is actually being used. The rest is philosophical baggage we add because we like to imagine we are doing something other than what we are-- it gibes better with our experiential prejudices. That's fine, but we should not be surprised when paradoxes emerge-- we put them there by forgetting what we were actually doing.

So why do we do this if the subject of interest is not a classical variable in a classical experiment but the quantum wave function?

The data is a classical variable, the wave function is a means for understanding and predicting it. Again, the dichotomy between what is observed and what is just mental bookkeeping.

On the other hand we suspect, our equations are unable to explain the apparently immeately(?!) occurring change during measurement.

Our equations are not asked to "explain" this, merely to reproduce what happens in the experiments. There is no problem with what is "immediate" when it is in our heads, this is the key point.

So instead of being humble and admitting that "something must be missed in our equation to describe this process", we choose the easy way to ignore the problem by declaring "the wave function not being something real but rather merely a mathematical construct, just representing our limited information on the system" because we know as you said that if we assume it to be ""real attribute possessed by the system" we are in danger of conflicting with relativity.

But the "easy way" is the easy way because it is true to itself. Adding philosophical baggage just introduces paradoxes that have no business being there in the first place, because they appear nowhere in the scientific methodology. Yes we'd like to understand as much as we can, but if we try to understand more than is there, we reach an impasse of our own making. We need to get out of the way of science, and let it do its job of elucidating natural mechanisms, rather than us deciding in advance what kinds of mechanisms we should be looking for.

 

[erastotenes]

But the wave function is not calculated from data-- it is calculated from knowledge of the experiment. The data is only used to test that wavefunction, and assert its predictive power. .

Since the term "information" in your message was obscure whether it refers to setup of the experiment or whether it refers to "collected data" by measurement, I assumed you refer by the term information to the "data collected by measurement" and accordingly I meant by "calculating" the "curve fitting" procedure based on the available data not the theoretical calculation acording to the Schrödinger equation. This is why I use the term "preperation conditions" which refers to setup of the experiment in order to prevent confusion. This misunderstanding removed, of course there is no difference of opinions considering the above.

This is exactly what science is doing, we should not pretend it is doing something different. The example you gave is a trivial case because both A and B have the same knowledge of the experiment-- our discussion becomes relevant when you have physicists with different knowledge of the experiment, and therefore are using different wave functions. That's what is at issue in quantum entanglement experiments, for example. Their information is not contradictory, just incomplete (do we ever have complete information of our reality?), so they construct different wave functions, test them, and their wave functions come through with flying colors. Quantum mechanics works.

The question is not whether we have "ultimately complete information of reality" or not. Nobody claims that. In fact by saying "incomplete" information you implicitely mean that there is a reference point that defines whether an information is complete or not. Obviously this reference point is assumed objective reality. I am not talking on an "ultimately complete information on the objective reality" but I am just talking about the comparison between two set of information where one set can be more complete(closer to reality) then the other one.

The question is following: After we have established that there has been an entanglement by comparing the measurement outcomes later, can we deny the fact that the entanglement has been already there as an objective fact as a consequence of the physical process that creates the particles. That for an observer, his/her wave function correctly predicted the statistical distribution of his/her measurements despite this missing information merely means that his/her measurements were not able to distinguish between both cases. It is nothing surprising about a case where a particular experiment may give you only a partial aspect of the reality. So if your incomplete model works well with the experiment you conduct, you may be satisfied. However after you get information on some other aspect of the same reality, namely if you acess to the data collected by B, you cannot avoid the conclusion "I had all the time the wrong wave function, althoug there was a better one(that was closer to the "reality"), the only reason I couldn't realize this was that my measurements were insufficient to distinguish between my incomplete and a possible more complete information on the system."

A good way to say this is, quantum mechanics is not a process of "determining the wave function that the particle has", because a particle doesn't have a wave function (or at least, no one has ever demonstrated that it does).

By the way I never say "A particle has a wave function". In my opinion there is no particle. The wave function is the theoretical entity that is our modell for the quantum system. Thus according to the modell the wave function "IS" the quantum system. The question is whether our modell is good enough to describe the observed reality or not. In my opinion there is no room for "particles" in the modell. The concept particle as used generally is only an inappropriate projection of our macroscopic concepts(billiard balls) on quantum level. Many questions asked by layperson in this forum reflect this misconception.

Quantum mechanics is a prescription for mapping knowledge of an experiment into knowledge of a wave function, and then using the time evolution of the wave function to predict statistical outcomes, again based on knowledge of the experiment. It is not the knowledge itself, it is the mapping between knowledge and prediction. The mapping, the experiment, and the data, can all be the same even when the knowledge, wave functions, and predictions are all different for two observers. That dichotomy sorts between what lives "in reality" and what lives "in the mind of the physicist", and it is constructed simply by noticing how quantum mechanics is actually being used.

The rest is philosophical baggage we add because we like to imagine we are doing something other than what we are-- it gibes better with our experiential prejudices. That's fine, but we should not be surprised when paradoxes emerge-- we put them there by forgetting what we were actually doing.

Is the "entanglement" , that reflects,manifests itself in correlation of the results, something that "lives in reality" , or is it something "that is in the mind of physicists" to use your own words.

That is the question.

 

[Ken G]

The question is not whether we have "ultimately complete information of reality" or not. Nobody claims that.

On the contrary, I find that people who tend to think of the wavefunction as "real", and thus requiring "physical influences" to "change it" in a real way, very much take the perspective that the wave function is describing reality completely. As soon as we allow different wave functions to pertain to a particular situation, merely reflecting different information about the situation, we see the wavefunction for what it is-- a bookkeeping device in someone's mind. And at that same moment, the mysterious "instantaneous influences" of entanglement disappear in a puff of over-interpreted philosophical smoke.

I am not talking on an "ultimately complete information on the objective reality" but I am just talking about the comparison between two set of information where one set can be more complete(closer to reality) then the other one.

Actually, I believe this is what I am saying. We don't have reality, we have descriptions of reality, and if one person's description must change with new information, another's might not have to at all. So it is with entanglement-- it is only when we force there to be a "single reality" at every step that we run into trouble. The single reality only appears as a constraint that we must not be led to contradictory predictions, not that we must make the same predictions.

The question is following: After we have established that there has been an entanglement by comparing the measurement outcomes later, can we deny the fact that the entanglement has been already there as an objective fact as a consequence of the physical process that creates the particles.

There is no need for any such denial, nor was it included in any stage of my argument. I simply do not accept as true the idea that when I make a measurement that changes the wave function I'm using, that this effect manifests physically elsewhere in the universe. It does not, the objective fact is the entanglement, and that is the only thing that is physically manifested. The rest are just questions I pose to that manifestation, based on the information I include.

That for an observer, his/her wave function correctly predicted the statistical distribution of his/her measurements despite this missing information merely means that his/her measurements were not able to distinguish between both cases. It is nothing surprising about a case where a particular experiment may give you only a partial aspect of the reality. So if your incomplete model works well with the experiment you conduct, you may be satisfied.

That is indeed what I have been saying.

However after you get information on some other aspect of the same reality, namely if you acess to the data collected by B, you cannot avoid the conclusion "I had all the time the wrong wave function, althoug there was a better one(that was closer to the "reality"), the only reason I couldn't realize this was that my measurements were insufficient to distinguish between my incomplete and a possible more complete information on the system."

It is not at all necessary for me to conclude I had the "wrong wave function", my wave function was fine for the purposes I put it to. That's the "right wave function". To argue that there can be only one "right" wave function in a given situation is to attribute the very reality to the wavefunction that is no part of the science it is used for, and leads to nothing but problems. The wave function is tailored to the question being asked, and the information available in answering it.

By the way I never say "A particle has a wave function". In my opinion there is no particle. The wave function is the theoretical entity that is our modell for the quantum system. Thus according to the modell the wave function "IS" the quantum system.

I pretty much agree, except I would not say that the quantum system is our model. We have a quantum system, defined by its behavior, and we have a model, defined by its axioms. The goal is to achieve a close connection between the two, tailored to the information we have on the system, and the prescription for doing that is the construction of a wave function according to the axioms and the information. "Reality" just isn't in there, that's all on the experimental side of the comparison.

The question is whether our modell is good enough to describe the observed reality or not. In my opinion there is no room for "particles" in the modell. The concept particle as used generally is only an inappropriate projection of our macroscopic concepts(billiard balls) on quantum level. Many questions asked by layperson in this forum reflect this misconception.

I agree, though I would perhaps replace the word "particle" by the word "quantum". That more or less strips away the classical misconceptions, but still preserves the axiomatic structure that we do need to be treating quanta here, or we are not doing quantum mechanics.

Is the "entanglement" , that reflects,manifests itself in correlation of the results, something that "lives in reality" , or is it something "that is in the mind of physicists" to use your own words.

The entanglement is real, I never suggested otherwise. The issue at hand is whether or not we should be bothered if I make a measurement on A and "instantaneously change" the wavefunction I should use at B. The answer to that, is no, as it is classically. The tricky part comes in with Bell, where we say that what if the correlations I predict at B given my measurement at A are such that I cannot imagine the particle at B "carried with it" all the information I need to get that correlation. But my answer to that is, it still does not bother me, nor do I see a problem with relativity, because I have no reason to think the particle carries that information with it anyway-- the information is in the entanglement, and I can instantaneously extract it from my measurement at A without "affecting" B in a physical way.

 

[erastotenes]

The entanglement is real, I never suggested otherwise. The issue at hand is whether or not we should be bothered if I make a measurement on A and "instantaneously change" the wavefunction I should use at B. The answer to that, is no, as it is classically. The tricky part comes in with Bell, where we say that what if the correlations I predict at B given my measurement at A are such that I cannot imagine the particle at B "carried with it" all the information I need to get that correlation. But my answer to that is, it still does not bother me, nor do I see a problem with relativity, because I have no reason to think the particle carries that information with it anyway-- the information is in the entanglement, and I can instantaneously extract it from my measurement at A without "affecting" B in a physical way.

You can not extract the information about entanglement instantaneously by a single measurement at A . That there is entanglement becomes evident only by statistical evaluation of large number of measurements at A and B using Bell inequality test.

Thus if you assign only each individual measurements an ontological status and if you claim, the wave function is only a mathematical construct in my mind to evaluate the statistical result of large number of measurements, then entanglement is not something real because it is the property of this mathematical construct in your mind since it manifests only after this statistical evaluation.

Thus imo you are contradicting yourself when you on one hand say entanglement is real , but on the other hand you say (to avoid the "paradox" with relativity) that wave function is not something real but only a mathematical construct for statistical evaluation of measurements.

Thus the situation is similar to double slit experiment, where you can extract the information of "wavelength of the electron beam" only after you have enough (large) number of measurements, so that the interference pattern emerges.

Of course a purely philosophical debate about what is real or what is not real based on verbal arguments may seem in a sense meanngless. However it is imo relevant in the sense that it may influence our opinion regarding what is worth investigating or not.

This debate has been going on for 80 years. There have been and there still are many brillant physicists who were not satisfied with CI as an ultimate solution. So, I am aware that we cannot reach a consensus on the issue.

 

[Ken G]

You can not extract the information about entanglement instantaneously by a single measurement at A . That there is entanglement becomes evident only by statistical evaluation of large number of measurements at A and B using Bell inequality test.

I cannot extract complete information about that correlation without a statistical sample, that is true, but that is entirely consistent with my argument. The key issue is, the correlations require information from both measurements at A and B (and many of them, to get the full picture), so there is no problem with causality-- I will need to communicate between A and B to assemble that information, nothing is instantaneously affected except the wave function I carry in my head to perform the required calculation.

Thus if you assign only each individual measurements an ontological status and if you claim, the wave function is only a mathematical construct in my mind to evaluate the statistical result of large number of measurements, then entanglement is not something real because it is the property of this mathematical construct in your mind since it manifests only after this statistical evaluation.

Entanglement is real because it stems from the setup of the experiment and is evidenced in a measured correlation. How I describe the entanglement is indeed a construct of my mind-- such has always been my claim here.

Thus imo you are contradicting yourself when you on one hand say entanglement is real , but on the other hand you say (to avoid the "paradox" with relativity) that wave function is not something real but only a mathematical construct for statistical evaluation of measurements.

The point is, we have on one hand a bunch of measured correlations, and on the other hand, a mathematical theory to describe and understand them. So it is with science. The measured effects are what we normally call "what is real", because it is as close as we get (we can more precisely say it is the projection of what is real onto the objective measures we choose to probe it). On the other hand, the theory we construct in our mind is never "what is real", for it stems from axioms that are purely chosen by us. Then there is a step where we judge the value of our axiomatic structure, but at no time does that judgement process make the theory real, or the wavefunction, it just demonstrates its value to the scientist.

Thus the situation is similar to double slit experiment, where you can extract the information of "wavelength of the electron beam" only after you have enough (large) number of measurements, so that the interference pattern emerges.

I certainly agree with the idea that the concept of "wavelength of the electron beam" is something we construct in order to be consistent with a body of observational data, as is true for all scientific theory. But the theory does not come from the data, nor does the concept of the meaning of a wavelength of the electron, it comes from an axiomatic structure we build and then confront with that data to judge the concept.

Of course a purely philosophical debate about what is real or what is not real based on verbal arguments may seem in a sense meanngless. However it is imo relevant in the sense that it may influence our opinion regarding what is worth investigating or not.

If we can agree that "what is real" in science means "what leaves an objective footprint on our measurement devices", then we have no debate on the meaning of that word.

This debate has been going on for 80 years. There have been and there still are many brillant physicists who were not satisfied with CI as an ultimate solution. So, I am aware that we cannot reach a consensus on the issue.

I am not claiming CI is an "ultimate solution", for that would require prescience. I am merely saying that if we keep track of the process of doing science in regard to quantum mechanics, the CI is the description of that process. In some distant future we may use a different process, or even redefine what we mean by science, but the CI is the only one that is consistent with the process as it is actually done today, and the meaning of science that we use today. The other interpretations take science and add philosophical baggage, not with the proven advantage of doing better science, but merely to achieve cognitive resonance with certain prejudices about the kind of reality we "should be" looking for.