This forum gives conflicting info on the HUP

[Fredrik]

The notion of state survival is not well defined. For example, even when the photon is destroyed, you can say that the state survives because you still have some state of quantum electrodynamics. A state with zero number of photons is still a state.

Good point, but I would choose to call state survival "theory-dependent" (as in "it depends on whether you're using a theory with a fixed number of particles"), rather than "ill-defined".

If we accept only the first requirement above (that outcomes need to be given by the Born rule), then "my" simultaneous measurement of non-commuting observables is "accurate".

Then how do you measure $S_z$ and $S_x$ (in the quantum theory of a single spin-1/2 particle with a magnetic moment) simultaneously? You can't put two Stern-Gerlach devices in the same place, because (if they each have a detector screen) the first one you put there physically prevents you from putting another one there. I suppose that a Stern-Gerlach device would still be considered a Stern-Gerlach device if we replace the detector screen with two small detectors at the appropriate locations. Then you could actually put two in devices in the same place. Now you have four detectors but they will never signal detection because the particles will miss them all. So two measuring devices in the same place equals no measuring device at all. You could also try to combine two Stern-Gerlach devices into one, by using one detector screen and the magnets from both, but this combination device would (presumably, because I haven't done the math) be a measuring device that's suitable for a measurement of $(S_z+S_x)/\sqrt 2$. You could interpret the position of the dot as a simultaneous measurement of $S_z$ and $S_x$, but then the results wouldn't be consistent with the Born rule (imagine doing a measurement on a particle prepared in an eigenstate of $S_x$).

Pretend that you know nothing about quantum theory, and just use two sophisticated gadgets for which you were told that they measure position and momentum. You don't even need to know how the gadgets work. All you need to know is how to use them, by pressing appropriate buttons. When you do that, the displays on the gadgets show some digital numbers which, you are told, are the measured position and momentum.

So when you turn on both gadgets at the same time, what do you expect to see? Do you expect that only one of the gadgets will display a number? If so, then which one?

No, you should not expect such a thing. There is no doubt that both gadgets will show some numbers. As long as you think like an experimentalist without any theoretical prejudices, there is nothing more natural than to interpret these two numbers as simultaneous measurement of position and momentum. That is all.

My comments about Stern-Gerlach devices apply to this as well. I described a scenario in which the gadgets wouldn't show any numbers at all, so I would say that there's plenty of doubt. I also described a scenario where "numbers" are shown, but it's not at all natural to interpret them as results of simultaneous measurements of non-commuting observables.

 

[Fredrik]

I think a few general comments are in order. A theory of physics can't be defined by mathematics alone. We also need correspondence rules, i.e. statements that tell us how to interpret the mathematics as predictions about results of experiments. The correspondence rules must describe the devices that we're supposed to use to test the predictions. (It is possible to do this without using the theory, but this isn't the topic of this post, so I'll put the explanation in a footnote*).

If we try to put two measuring devices that are represented by non-commuting self-adjoint operators A and B at the same place, we're typically going to find one of the following:

1. It's physically impossible to put them at the same place.
2. The result is a single device that isn't described by any correspondence rules.
3. The result is a single device that according to the correspondence rules is represented by a self-adjoint operator C, different from both A and B.

I haven't thought this through to the point where I can say that these are the only options, but at the moment, it seems to me that they are. Option 2 has a couple of sub-options: If you add a new correspondence rule that describes the device and tells you to use it for simultaneous measurements of A and B, will this make the theory worse?

Consider two compatible observables instead, like position components. You don't make a simultaneous measurement of position components by designing a device that only measures one component, and then using several such devices in the same place. I don't think it's even possible to measure only one component. The closest you can get is probably to measure one component more accurately than the others. If this is what we mean by only measuring one component, I don't think two measuring devices with different orientation can exist in the same place.

What you actually do to measure position is to use a particle detector. If it signals detection, then all components of position have been measured simultaneously. This makes me suspect that we need to think about simultaneous measurements of incompatible observables in the same way. It's not about putting two devices in the same place. It's about the possibility to build a new device that can be said to be measuring both observables simultaneously, in the sense that if we add a new correspondence rule to the theory, one that specifies the two observables and the situation in which the device is able to measure the observables simultaneously, we're not making the theory worse.

Ozawa seems to have found a theorem that tells us that if A and B are non-commuting observables, there's a state $\psi$ such that if the system is prepared in that state, then we can "simultaneously measure" A and B. (See post #24, by atyy). But Ozawa's definition of "simultaneously measurable in state $\psi$" is purely mathematical, as it must be, since the term was meant to be used in a theorem. This means that we can't be sure that it's possible to build a measuring device that does the measurement just because two incompatible observables are "simultaneously measurable in state $\psi$" in the sense of Ozawa's definition.

I'm inclined to say that if it's not possible to build the device, then Ozawa's definition of "simultaneously measurable" is inappropriate and misleading. But if is possible to build the device (and make a new correspondence rule about it without making the theory worse), I would say that his definition is perfectly appropriate.

I don't think you can prove that the device can always be built, so my impression is that what Ozawa's theorem is really telling us is just this: Every time we figure out a way to build a device that can be used to do a (state-dependent) simultaneous measurement of two incompatible observables, add a new correspondence rule for this device, and verify (with experiments) that this hasn't made the theory worse, it will strengthen our opinion that his definition of "simultaneously measurable in state $\psi$" is appropriate. And every time we can't think of a way to do it, it will weaken this opinion. If we find a compelling argument against the possibility that the device can be built, then we will reject his definition.*) I have thought of a procedure that can at least in principle be used to ensure that the correspondence rules can be described without using the theory that they're a part of. You need to build a hierarchy of theories. In the level-0 theories, measuring devices are so simple that no theory is needed to describe how to build them. For example an hourglass for time measurements and a rope with knots for length measurements. For each positive integer n, the measuring devices in a level-n theory are described by assembly instructions that can be understood and carried out by someone who understands level n-1 theories and has access to level n-1 measuring devices.

 

[Demystifier]

Then how do you measure $S_z$ and $S_x$ (in the quantum theory of a single spin-1/2 particle with a magnetic moment) simultaneously?

As I explained in #29, I need at least 3 particles, the two of which can be thought of as "micro-detectors". So if you insist that I must use only one particle, then I cannot do that.

 

[Demystifier]

I would have to study those definitions to know what impact his theorems have on my conjecture that "simultaneous measurements are possible if and only if the measuring devices can exist in the same place without interfering with each other".

Why do you insist that simultaneous measurements are made in the same place?

In my three-particle method of simultaneous measurements in #29, the three particles are at the same place at the time of their mutual interaction, but at different places at the time of detection. Do you clasify this as being at the same place?

 

[atyy]

The notion of state survival is not well defined. For example, even when the photon is destroyed, you can say that the state survives because you still have some state of quantum electrodynamics. A state with zero number of photons is still a state.

If we accept only the first requirement above (that outcomes need to be given by the Born rule), then "my" simultaneous measurement of non-commuting observables is "accurate".

Yes, for the collapse rule more generally I should use that for a POVM, so that I can treat the collapse to zero photons.

But I'm still skeptical that you can measure accurately for arbitrary state.

For simultaneous measurements, why doesn't the impossibility proof given in section III of http://arxiv.org/abs/quant-ph/0310070 apply?

For sequential measurements, why don't the inequalities in http://arxiv.org/abs/1304.2071 (Eq 12) or http://arxiv.org/abs/1211.4169 or http://arxiv.org/abs/1306.1565 apply?

It seems that at best, one can make an accurate sequential measurement for some states.

 

[Fredrik]

Why do you insist that simultaneous measurements are made in the same place?

In my three-particle method of simultaneous measurements in #29, the three particles are at the same place at the time of their mutual interaction, but at different places at the time of detection. Do you clasify this as being at the same place?

I don't think this three-particle trick works, at least not in this case. I haven't been able to find a state vector with the appropriate entanglement. When I tried to write one down, I failed in ways that made me suspect that no such state vector exists. It seems to me that we need a sum of terms of the form $|x\pm,x\mp,\sigma\rangle$ and $|y\pm,\rho,y\mp\rangle$. But no matter what we choose $\sigma$ to be, a measurement of $S_y$ on particle C that yields +1/2 will not tell us that particle A is in state y-.

This may however be a problem that's specific to systems with 2-dimensional Hilbert spaces. I haven't tried to work out any other case. If the three-particle trick works in in other cases, then I agree that it's not true in general that simultaneous measurements are done at the same place.

 

[atyy]

The article by Ozawa that you linked to in #24 says this:

In fact, it is widely accepted nowadays that any observable can be measured correctly without leaving the object in an eigenstate of the measured observable; for instance, a projection $E$ can be correctly measured in a state $\psi$ with the outcome being 1 leaving the object in the state $M\psi/\|M\psi\|$, where the operator $M$ depends on the apparatus and satisfies $E=M^\dagger M$ (see, for example, a widely accepted textbook by Nielsen and Chuang [10]).
​

I'm going to have to read up on this, because I have no idea what he's talking about.

These are given in http://arxiv.org/abs/1110.6815 (p9, statements [II.1]-[II.5]). These axioms can deal with the case that Demystifier mentions about zero photons (p13, R2).

Maybe he's just talking about that. (He doesn't say if his $\psi$ is arbitrary). I will think about it.

Ozawa seems to have found a theorem that tells us that if A and B are non-commuting observables, there's a state $\psi$ such that if the system is prepared in that state, then we can "simultaneously measure" A and B. (See post #24, by atyy). But Ozawa's definition of "simultaneously measurable in state $\psi$" is purely mathematical, as it must be, since the term was meant to be used in a theorem. This means that we can't be sure that it's possible to build a measuring device that does the measurement just because two incompatible observables are "simultaneously measurable in state $\psi$" in the sense of Ozawa's definition.

I'm inclined to say that if it's not possible to build the device, then Ozawa's definition of "simultaneously measurable" is inappropriate and misleading. But if is possible to build the device (and make a new correspondence rule about it without making the theory worse), I would say that his definition is perfectly appropriate.

I don't think you can prove that the device can always be built, so my impression is that what Ozawa's theorem is really telling us is just this: Every time we figure out a way to build a device that can be used to do a (state-dependent) simultaneous measurement of two incompatible observables, add a new correspondence rule for this device, and verify (with experiments) that this hasn't made the theory worse, it will strengthen our opinion that his definition of "simultaneously measurable in state $\psi$" is appropriate. And every time we can't think of a way to do it, it will weaken this opinion. If we find a compelling argument against the possibility that the device can be built, then we will reject his definition.

My understanding is that these statements about the possibility of simultaneous or sequential measurements being possible only apply for very special states.

For example, sequential measurement of non-commuting observables A and B is possible if the state is an eigenstate of A, because measuring A leaves the state undisturbed, so that B can be measured accurately on the same state. But this procedure is very bad in general, since measuring A will cause the state to collapse to a completely different state, so that the subsequent "accurate" B measurement will be very inaccurate because it is carried out on the wrong state. In general, a more accurate procedure for all states is one that is not perfectly accurate for any state, but slightly inaccurate for all states.

The case of simultaneous accurate measurement that Ozawa discusses is basically an EPR-type argument that if the particles are appropriately entangled, a simultaneous measurement of A on particle 1 and B on particle 2 can give you an accurate measurement of B on particle 1. As he says, this is again a special case, and the procedure will fail for any other state.

 

[Demystifier]

I don't think this three-particle trick works, at least not in this case. I haven't been able to find a state vector with the appropriate entanglement. When I tried to write one down, I failed in ways that made me suspect that no such state vector exists. It seems to me that we need a sum of terms of the form $|x\pm,x\mp,\sigma\rangle$ and $|y\pm,\rho,y\mp\rangle$. But no matter what we choose $\sigma$ to be, a measurement of $S_y$ on particle C that yields +1/2 will not tell us that particle A is in state y-.

I understand your point, and mathematically you are right. However, there is a conceptual subtlety, which is best conveyed as a counter question: If you measure only one observable, say S_y, then what kind of measurement DOES tell you that the particle A is in state y?

If you try to answer it, you will see that your answer may be questioned by a different interpretation of QM. That's why, in a kind of a minimal interpretation, it may not be useful to think of a particle being in a state y. Instead, it may be more useful to concentrate only on the classical states of macroscopic pointers. It is only in this MACROSCOPIC CLASSICAL language that my three-particle trick makes sense.

 

[Demystifier]

But I'm still skeptical that you can measure accurately for arbitrary state.

For simultaneous measurements, why doesn't the impossibility proof given in section III of http://arxiv.org/abs/quant-ph/0310070 apply?

For sequential measurements, why don't the inequalities in http://arxiv.org/abs/1304.2071 (Eq 12) or http://arxiv.org/abs/1211.4169 or http://arxiv.org/abs/1306.1565 apply?

Different conclusions concerning whether something can or cannot be measured accurately depend on different DEFINITIONS of "accurate measurement" one adopts. In classical mechanics it is quite clear what an accurate measurement is, but in QM it is not. Essentially, that's because in QM it is not clear what is the reality or ontology the accurate measurement is supposed to be about. In other words, whether something can or cannot be measured accurately depends on the interpretation of QM.

For example, in one interpretation of QM, measurements (either accurate or inaccurate) do not exist at all. That is, experiments do not "measure" reality, but create it.

Of course, nobody is obligued to accept such an interpretation, but then one needs to carefully explain what interpretation one does adopt, and according to it, what exactly one means by a "measurement".

 

[atyy]

Different conclusions concerning whether something can or cannot be measured accurately depend on different DEFINITIONS of "accurate measurement" one adopts. In classical mechanics it is quite clear what an accurate measurement is, but in QM it is not. Essentially, that's because in QM it is not clear what is the reality or ontology the accurate measurement is supposed to be about. In other words, whether something can or cannot be measured accurately depends on the interpretation of QM.

Yes, what definition are you using? If I understand correctly, these papers define an accurate measurement of A as one that produces the same distribution of outcomes as a projective measurement of A.

 

[Demystifier]

Yes, what definition are you using? If I understand correctly, these papers define an accurate measurement of A as one that produces the same distribution of outcomes as a projective measurement of A.

If so, then their definition is fine, but different from the one I used. I used a definition natural to a naive experimentalist, for whom the measurement is a procedure that would correspond to a standard notion of measurement of classical quantities.

Clearly, there are well defined procedures for simultaneous measurement of classical quantities such as position and momentum. Whatever such a procedure is, a naive experimentalist may apply the same procedure to ANY system (classical or not) and see what he will get.

 

[Ken G]

Does the definition in that paper that atyy quotes seem a bit troublesome to anyone else? First of all, the word "measurement" is used twice, which is a bit like defining something by that something. I believe what this must really mean, if one removes that circularity, is an accurate measurement is one that agrees with quantum mechanics theory. Now that is a fine way to define measurements if one has already used some other meaning of measurement to establish the value of quantum theory, but my question is, what was the definition of that other kind of measurement that was used to verify quantum theory in the first place? I believe one will then arrive at a meaning close to what Demystifier is talking about.

 

[Demystifier]

Now that is a fine way to define measurements if one has already used some other meaning of measurement to establish the value of quantum theory, but my question is, what was the definition of that other kind of measurement that was used to verify quantum theory in the first place? I believe one will then arrive at a meaning close to what Demystifier is talking about.

Again, I agree with you.

 

[atyy]

If so, then their definition is fine, but different from the one I used. I used a definition natural to a naive experimentalist, for whom the measurement is a procedure that would correspond to a standard notion of measurement of classical quantities.

Clearly, there are well defined procedures for simultaneous measurement of classical quantities such as position and momentum. Whatever such a procedure is, a naive experimentalist may apply the same procedure to ANY system (classical or not) and see what he will get.

Does the definition in that paper that atyy quotes seem a bit troublesome to anyone else? First of all, the word "measurement" is used twice, which is a bit like defining something by that something. I believe what this must really mean, if one removes that circularity, is an accurate measurement is one that agrees with quantum mechanics theory. Now that is a fine way to define measurements if one has already used some other meaning of measurement to establish the value of quantum theory, but my question is, what was the definition of that other kind of measurement that was used to verify quantum theory in the first place? I believe one will then arrive at a meaning close to what Demystifier is talking about.

Naively, I don't see how the classical definitions can be "right", since one can prove that in some sense the classical definitions don't exist. For example, there is in general no joint distribution of the values of conjugate observables.

But I do agree that there may be different definitions that are reasonable, so perhaps simultaneous accurate measurements of conjugate observables could be possible with a different definition of "accurate". Could you provide an explicit example?

 

[atyy]

In a "classical" measurement scheme, I would further say again - the theory determines what you can measure. So if one would like a classical measurement theory, one should use Bohmian mechanics.

However, do "Hamiltonian conjugate observables" exist in Bohmian theory?

Given that there isn't (yet due to the incompetence of experimentalists) a unique Bohmian dynamics, wouldn't the notion of accurate measurement depend on which Bohmian dynamics one chose?

 

[Ken G]

Naively, I don't see how the classical definitions can be "right", since one can prove that in some sense the classical definitions don't exist. For example, there is in general no joint distribution of the values of conjugate observables.

The classical definitions I'm talking about (I won't speak for Demystifier) are not definitions of the obervables, but rather definitions of the observations, and then the observations provide operational definitions of the observables (all quantities in science are just proxies for acts of observation, after all). In other words, if I say I have this apparatus, and I will claim that it "observes x", then I have a classical definition of what I mean by x based on that apparatus. If I have an apparatus that I say "observes p", same story. Now if I have an apparatus that I say "observes p and x simultaneously", then we will need to look at the ramifications of my claim.

Above I said that these claims can make good on several different levels. The weakest level is that they can agree with the predictions I used some theory to make, but they destroy the system for the purposes of further replication of my result. Since they destroy the system, they cannot be said to "confer knowledge" about the state of the system after the measurement, only about the state of the system prior to measurement (by "state" I mean "everything I can possibly need to know about the preparation of that system in order to predict subsequent behavior"). The next strongest level is an apparatus that conveys knowledge about the state going forward, but only if I already know certain things about the preparation prior to the measurement, so the apparatus is not a "complete" or self-contained measurement. Finally, the strongest level is an apparatus that conveys knowledge of the state going forward even if I know nothing about the history of that system.

Given that we can recognize three separate types of measurement, it seems natural that each might obey a different set of constraints, in particular, different versions of a HUP. If we look at EPR systems, we see that we do need past knowledge of the system, it's not a completely WYSIWYG kind of measurement. It also destroys the entanglement, so the results cannot be used to make predictions going forward that involve knowledge of the x and p of both particles. Can we say that it is the weakest type though, the type that confers knowledge about the past preparation of that system, given knowledge that we have a momentum-conserving entanglement? Yes, we can use our x and p results on an ensemble to recover completely the preparation of that system, given that prior knowledge.

But here's my point there: the information in the preparation of that system, given its entanglement, involves only the same amount of information as is in a single particle, but it is in some sense "spread out" over two particles. Hence, the past knowledge can only be the same as a wave packet of a single particle, and that knowledge is governed by the HUP of a single particle. To treat the x and p measurements on the two particles as simultaneous knowledge of x and p, one must then treat the particles as two separate systems, which involves breaking the entanglement, which means we are talking about the post-measurement preparation, not the pre-measurement preparation. It is not surprising that classical observables can impart knowledge of the post-measurement x of one particle, and the post-measurement p of another particle.

 

[atyy]

@Ken G, I think I agree to the extent I understand what you are saying. Just one question: are you agreeing with Demystifier that simultaneous or successive measurements on the same state are possible, for some definition of "accurate"? Edit: And for any state - the definition I was using means it is possible for some special states, but not for any state, at least not by the procedures considered in those papers.

Regarding EPR, if one accepts that as an accurate measurement, then it clearly is not a measurement procedure that can be defined classically. And if one needs the measurement to give accurate information about the post-measurement state, then clearly one can't do those simultaneous or joint measurements in quantum mechanics, because that is using the measurement to prepare a state, and so the preparation HUP must hold, which is just the textbook HUP.

 

[Ken G]

@Ken G, I think I agree to the extent I understand what you are saying. Just one question: are you agreeing with Demystifier that simultaneous or successive measurements on the same state are possible, for some definition of "accurate"? Edit: And for any state - the definition I was using means it is possible for some special states, but not for any state, at least not by the procedures considered in those papers.

I think your interest is in the possibility of simultaneous or successive measurements of complementary observables? If that's what you are asking, I do not think such measurements convey "observed properties" of that system, no. I think that a system is defined in part by the apparatus that it is encountering. I feel it is not even enough to say that the apparatus changes the system, I feel one must say that the apparatus is part of how we define the system. To me, the lesson of the HUP is we must get away from the classical model that systems "carry around with them" certain observables, things that in some sense "the universe already knows", and our job is to use an apparatus to figure those things out. Instead, the system is defined by both the apparatus that prepared it, and the apparatus that is measuring it, because we want to think of a system as something "real", and that means we need to be able to give it real attributes, and that means we need to be able to observe it, so that must involve both a preparation that we can know things about (by observing them or inferring them from other things we can observe), and an outcome we can know things about.

The preparation is thus just one part of that system, and determines what we call the "state" of the system, but the apparatus that is measuring that system is also part of the system, because it determines what aspects of that system are actualized. A state, or a preparation, only produces tendencies for actualizations, often expressed in terms of an "ensemble" to make it more concrete. To be considered something actual, and not just a set of tendencies, one must include the measuring device in the meaning of "the real system." The thing that Demystifier is saying that I do agree with is that the apparatuses are always classical, somewhere along the way (since ultimately, our brains are), so no quantum system is "real" until one can associate it with a set of classical pointers. The realness is in some sense the "closure" or "actualization" of that quantum system. I believe this is also what Bohr meant when he said "there is no quantum world"-- the realness comes from a system that is complete, all the way from preparation to measurement. What I don't like about the Bohmian picture is the desire to add extraneous elements to the preparation+actualization such that the classical pointers can refer to attributes that the system has all the time, and not just at the end of the closure process.

Regarding EPR, if one accepts that as an accurate measurement, then it clearly is not a measurement procedure that can be defined classically.

You can do measurements that you can define classically on the two particles, like you can measure x and p. The issue is, if when you measure the p of one particle, and know by momentum conservation it is the p of the other particle, does that then allow you to know x and p of the other particle? I say no, because the instant you think you know both the x and p of the particle, you have broken the entanglement that let you know p in the first place. I'm sure Demystifier agrees that you don't know x and p any more, after the measurement, but he holds that the particle had an x and p instantly before the measurement, and that's how you can know it. I hold that you cannot know anything without specifying the apparatus that let's you know it, and no apparatus let's you know x and p before the apparatus let's you know x and p!

And if one needs the measurement to give accurate information about the post-measurement state, then clearly one can't do those simultaneous or joint measurements in quantum mechanics, because that is using the measurement to prepare a state, and so the preparation HUP must hold, which is just the textbook HUP.

Yes, I think a key point is recognizing the difference between measurement as knowledge of a system that still exists, versus measurement as knowledge of a system just before you measured it but no longer exists in that state. I don't think of measurement as how we get knowledge of the properties of systems, I see measurement as part of the meaning of the properties of a system. So I reject the whole concept of using measurements to know the properties of a system prior to the measurement, but I do think measurements can be used to characterize the state of a system, i.e., everything we need to know about the preparation of that system to able to predict what properties it may have when those properties are actualized by measurements.

 

[DevilsAvocado]

I'm sure Demystifier agrees that you don't know x and p any more, after the measurement, but he holds that the particle had an x and p instantly before the measurement, and that's how you can know it.

(I’ve only skimmed the posts since my last post, so I trust on you that this is what he is saying)

Gentlemen, if I may: Einstein and Bohr debated x and p for 20 years (albeit without Bell) and the 'measurements' I have done all point in the direction that they both were smarter than any of us in this forum...

Therefore: My humble 'proposal', to get a better grip on EPR-Bell, is to use photon polarization instead of momentum and position, as it's easier to handle IMHO.

In the case of entangled photons, it gets instantly clear – there is no possibility of preexisting (real) values kept unchanged all the way from the source to measurement.

Why?

It's a mathematical impossibility, having 3 hidden variables A, B and C for the settings 0°, 120° and 240°. I'll use binary representation to make it even clearer (excludes 'impossible' 0 and 7):

The Yellow and Purple group are XOR mirrored (i.e. 001 XOR 111 = 110, or decimal 1 XOR 7 = 6), and since the actual values are trivial, 001 and 110 are the same when it comes to correlated hits. A hit is defined as the same values for Alice and Bob (i.e. [1, 1] or [0, 0]).

The correlation is cos²(120°) = 25% for all (relative) settings, thus we must have a minimum of 4 runs to get 25%, and the 3 hidden variables must be able to handle all three combinations of AB, AC and BC, that Alice and Bob could get jointly, and 25% are equal to one hit and three misses.

We start by picking the first three in order (i.e. decimal 1 to 3) and there are no problems in the Yellow group, it's safe regarding all possible combinations (i.e. one hit and two misses for all three AB, AC and BC settings).

But the forth pick – that must be a miss in all three combinations – is a mathematical dead end! There is no viable number left to pick, since the Purple group is a mirror of the Yellow. Fait accompli...

I would love to hear DM explain how there could be any useful (local) information there for us to know?? ()

 

[Demystifier]

I would love to hear DM explain how there could be any useful (local) information there for us to know?? ()

Your picture is a bunch of 0's and 1's, each being written at a definite position in space. And this picture, I think, is useful. Therefore, the picture itself presents a useful local information.

 

[Ken G]

Isn't it true that Bohmian mechanics allow Bell-type correlations to be true via the pilot wave? That was my impression, that if you are committed to letting systems have classical attributes all the time, not just as outcomes of measurements but also as "properties" of the system prior to measurement, you can get it with the pilot wave. You basically just take all the outcomes of the measurements you need to agree with, and reverse-engineer a pilot wave that does not itself have observable consequences, but makes the classical "properties" act quantum mechanically. You need a HUP? The pilot wave does it. You need Bell correlations? Pilot wave.

Note there is nothing wrong with this-- it agrees with the observations. It's all just a question of how badly do you want the system to maintain classical properties all the time, and if you really want that, you can get it with an invisible scaffolding that does not obey the properties assumed in von Neumann's no-go theorem. Does it seem artificial? To me, yes, but to someone committed to those classical properties, it is a requirement for getting the behavior we see-- but it does get the behavior we see (if Demystifier is right about how to make it work relativistically).

 

[Demystifier]

Naively, I don't see how the classical definitions can be "right", since one can prove that in some sense the classical definitions don't exist. For example, there is in general no joint distribution of the values of conjugate observables.

Ah, now I think I see the source of confusion. One should distinguish two things:
1) SINGLE measurement, from which no information about probability distribution can be extracted (except that the obtained value has probability larger than one).
2) Statistical ENSEMBLE of similar measurements, from which the probability distribution can be extraced.

I was talking about the former, while it seems that you are talking about the latter. If I simultaneously measure position and momentum ONLY ONCE, I cannot extract any information about the joint probability distribution.

But then again, even in classical mechanics I can repeat many times the simultaneous measurement of position and momentum. From such a measurement I CAN extract the joint distribution. Moreover, by using the theory called classical STATISTICAL mechanics I can even predict or explain the joint distribution I measured. So your claim that "classical definitions for joint distribution don't exist" is certainly wrong.

 

[Demystifier]

... but it does get the behavior we see (if Demystifier is right about how to make it work relativistically).

Even if I am wrong about that, there are also other ways to make Bohmian mechanics compatible with predictions of relativistic quantum theory. For example, one can always use a Bohmian theory with a preferred Lorentz frame at the level of hidden variables, which leads to Lorentz invariant measurable predictions. (It's only that I don't particularly like such a variant of Bohmian mechanics, because it looks somehow too cheap for me.)

 

[Demystifier]

What I don't like about the Bohmian picture is the desire to add extraneous elements to the preparation+actualization such that the classical pointers can refer to attributes that the system has all the time, and not just at the end of the closure process.

I'm sure Demystifier agrees that you don't know x and p any more, after the measurement, but he holds that the particle had an x and p instantly before the measurement, and that's how you can know it.

Note that I don't consider the Bohmian interpretation to be the only viable interpretation. What I like even more is to view the things from the point of view of DIFFERENT interpretations. In particular, I have constructed a hybrid between Copenhagen and Bohmian interpretation
http://lanl.arxiv.org/abs/1112.2034 [Int. J. Quantum Inf. 10 (2012) 1241016]
according to which only the particles of the observer are real in a Bohmian-like sense, while the observed particles are never real in that sense, not even when they are observed.

 

[Ken G]

Yes, I agree there is value in being able to see the elephant from all possible angles. There is little point in debating which is the perspective that gives us a truer look!

 

[DevilsAvocado]

Note that I don't consider the Bohmian interpretation to be the only viable interpretation. What I like even more is to view the things from the point of view of DIFFERENT interpretations. In particular, I have constructed a hybrid between Copenhagen and Bohmian interpretation

This is just great!

I'm just a bum layman, but sometimes (correct me if I'm wrong) I get a slight feeling that "interpretational fundamentalism" stands over everything else, i.e. some are willing to "look the other way", in cases which is not 'favorable' to their personal interpretation... but I could be wrong.

I'm not a scientist, but from what I know, your open-minded stance must be the correct way forward – to bend and twist this question from all angles possible.

DM, I sincerely hope that you will be successful in this work, good luck! :thumbs:

 

[DevilsAvocado]

You basically just take all the outcomes of the measurements you need to agree with,

Just to avoid any 'misunderstanding' – there is no possibility to cover all possible outcomes in EPR-Bell in preexisting hidden variables. From my picture above, it may look like we have 6 unique binary values (excluding 0 and 7), but the truth is; there are only 2 x 3 'mirrored' values, which reduces to the indisputable fact that 1/3 ≠ 1/4.

We need one more binary value to get 1/4, which the axioms of mathematics will never let us have, no matter what...

 

[DevilsAvocado]

Your picture is a bunch of 0's and 1's, each being written at a definite position in space. And this picture, I think, is useful. Therefore, the picture itself presents a useful local information.

Thanks DM, I don't understand Bohmian mechanics. What happens in an EPR-Bell experiment? You have (real) hidden variables going out from the source, and then what?

Does the pilot wave 'scan' the (space-like separated) settings and 'calculate' the correlation needed, and then 'send' this info to the hidden variables so that they can 'adjust' their values for the actual measurement?

Or, did I get this completely wrong...

 

[DevilsAvocado]

Even if I am wrong about that, there are also other ways to make Bohmian mechanics compatible with predictions of relativistic quantum theory. For example, one can always use a Bohmian theory with a preferred Lorentz frame at the level of hidden variables, which leads to Lorentz invariant measurable predictions. (It's only that I don't particularly like such a variant of Bohmian mechanics, because it looks somehow too cheap for me.)

Have you seen Lee Smolin's latest book Time Reborn? Our choice, according to Smolin, is epistemic/statistical QM or Aristotle was right!

Could there be a hidden-variables theory compatible with the principles of relativity theory? We know that the answer is no. If there were such a theory, it would violate the free-will theorem—a theorem implying that there’s no way to determine what a quantum system will do (hence no hidden-variables theory) as long as the theorem’s assumptions are satisfied. One of those assumptions is the relativity of simultaneity.

The aforementioned theorem of John Bell also rules out local hidden-variable theories—local in the sense that they involve only communication at less than the speed of light. But a hidden-variables theory is possible, if it violates relativity.

As long as we’re just checking the predictions of quantum mechanics at the level of statistics, we don’t have to ask how the correlations were actually established. It is only when we seek to describe how information is transmitted within each entangled pair that we need a notion of instantaneous communication. It’s only when we seek to go beyond the statistical predictions of quantum theory to a hidden-variables theory that we come into conflict with the relativity of simultaneity.

To describe how the correlations are established, a hidden-variables theory must embrace one observer’s definition of simultaneity. This means, in turn, that there is a preferred notion of rest. And that, in turn, implies that motion is absolute. Motion is absolutely meaningful, because you can talk absolutely about who is moving with respect to that one observer—call him Aristotle. Aristotle is at rest. Anything he sees as moving is really moving. End of story.

In other words, Einstein was wrong. Newton was wrong. Galileo was wrong. There is no relativity of motion.

This is our choice. Either quantum mechanics is the final theory and there is no penetrating its statistical veil to reach a deeper level of description, or Aristotle was right and there is a preferred version of motion and rest.

I like this book anyway...

 

[Ken G]

Just to avoid any 'misunderstanding' – there is no possibility to cover all possible outcomes in EPR-Bell in preexisting hidden variables. From my picture above, it may look like we have 6 unique binary values (excluding 0 and 7), but the truth is; there are only 2 x 3 'mirrored' values, which reduces to the indisputable fact that 1/3 ≠ 1/4.

I can't say I am following that logic, but I'm pretty confident that Bohmians are not such fools that they can't see their interpretation can be refuted by well known EPR-type observations! All the interpretations yield all the same experimental outcomes at this point, and people are trying very hard to try and find observations that can distinguish them, without a lot of success so far it seems to me.