Why there isn't missing information in QM

[jackle]

Why there isn't "missing information" in QM

First of all, can I ask you to be a little patient, because my years of performing quantum
calculations are well and truly over. I write computer software for an insurance company now!

I have noticed that every so often, a member of the public who is trying to understand quantum physics will ask something about "missing information" and I have also noticed that every time the response from those who do know quantum physics is always "There isn't any missing information". I have slowly got used to this and started to accept this answer without questioning it...

The problem I have never removed from the back of my mind is that quantum mechanics does contain unpredictabilty. eg. in the double slits experiment, the sequence that individual electrons will arrive at on different points on the screen is unpredictable. Surely the information about where the individual electrons will arrive is in some sense "missing" (until the measurements are actually made?) I recall that the position of a single electron on the screen can not be calculated beforehand (although the final pattern they make is predictable). Also, it seems to me that this idea of "missing information" is intuitive to the public and I have forgotten why we don't call it "missing information".

Sorry if I have posted this before (I couldn't see one), it comes back to haunt me occasionally.

 

[ice109]

in all sense of the word qm makes very good predictions, they're just not deterministic predictions

 

[peter0302]

Surely the information about where the individual electrons will arrive is in some sense "missing" (until the measurements are actually made?) I recall that the position of a single electron on the screen can not be calculated beforehand (although the final pattern they make is predictable). Also, it seems to me that this idea of "missing information" is intuitive to the public and I have forgotten why we don't call it "missing information".

I think the reason saying "missing" or "hidden" information is disfavored is because just saying this implies that it _exists_ (we just can't obtain it). But we've seen, for example with entanglement, that quanta don't simply behave as though the information is "there" but "hidden." Rather, they behave as though the information is _not_ there until measured, and then, once measured, they behave as we would expect.

So saying there is "missing" or "hidden" information has led to false predictions (i.e. Bell's Inequality which is found not to hold up in entanglement). Assuming the information truly isn't there until measured leads to the correct ones.

 

[vanesch]

I think the reason saying "missing" or "hidden" information is disfavored is because just saying this implies that it _exists_ (we just can't obtain it). But we've seen, for example with entanglement, that quanta don't simply behave as though the information is "there" but "hidden." Rather, they behave as though the information is _not_ there until measured, and then, once measured, they behave as we would expect.

So saying there is "missing" or "hidden" information has led to false predictions (i.e. Bell's Inequality which is found not to hold up in entanglement). Assuming the information truly isn't there until measured leads to the correct ones.

One should put the caveat that what you say is only correct if we want information to be transmitted only locally (and a few other constraints). After all, BM is an example of a view where exactly this kind of information is "present but hidden" (in the statistical distributions of the particle positions in the initial state). But BM has the problem of needing internal mechanisms where particles have immediate effects upon other particles, potentially lightyears away from there, and undiminished with distance.

 

[peter0302]

Good point, though I never quite understood how Bohmian theories account for entanglement. Is the Bohmian view that the photons do have defined polarizations before measurement?

 

[vanesch]

Good point, though I never quite understood how Bohmian theories account for entanglement. Is the Bohmian view that the photons do have defined polarizations before measurement?

The idea is that a "spin measurement" will ultimately be a "position measurement", in the sense that we will hit one detector or another for instance, at different locations. As such, the setting of one polarizer and the answer you get on one side, will be present in the position of the detected photon on that side. As the "quantum potential" of the OTHER particle is not only a function of the wavefunction, but also of the instantaneous exact positions of ALL other particles, one sees that one can relay the setting and outcome on the first side immediately to the other side. In other words, the tiny difference in position of the first detected particle has a major influence on the quantum potential felt by the other, and hence on its ultimate position (and thus outcome) as a function of the second setting.

In other words, through the dependence of the quantum potential for particle A on the immediate position of ALL other particles, this is the famous "spooky action at a distance" explicitly.

 

[peter0302]

Ok gotcha. So there really is this idea not just of "hidden" information but also some kind of instantaneous "transmission" (and I know that's a loaded word but I use it only in the broadest sense) of that information to the rest of the system as soon as something is measured?

Which of course presents just as many problems as it solves, because as we all know from special relativity, in the frame of the particles themselves (say we're using electrons), neither will agree on which one is the first to be measured, thereby imparting that position information to the rest of the system.

Does BM address this or is the whole thing just considered non-causal?

 

[vanesch]

Ok gotcha. So there really is this idea not just of "hidden" information but also some kind of instantaneous "transmission" (and I know that's a loaded word but I use it only in the broadest sense) of that information to the rest of the system as soon as something is measured?

Which of course presents just as many problems as it solves, because as we all know from special relativity, in the frame of the particles themselves (say we're using electrons), neither will agree on which one is the first to be measured, thereby imparting that position information to the rest of the system.

Does BM address this or is the whole thing just considered non-causal?

BM is not relativistically invariant in its mechanism. It is its principal problem. However, as its predictions are the same as those of normal QM, the statistical predictions themselves ARE Lorentz invariant of course (if the interactions are lorentz invariant). But BM can only be compatible with an ether-theory of relativity, with a preferred reference frame.

 

[kdv]

One should put the caveat that what you say is only correct if we want information to be transmitted only locally (and a few other constraints). After all, BM is an example of a view where exactly this kind of information is "present but hidden" (in the statistical distributions of the particle positions in the initial state). But BM has the problem of needing internal mechanisms where particles have immediate effects upon other particles, potentially lightyears away from there, and undiminished with distance.

I am still bugged by the question of information in the context of the Copenhagen interpretation. I know what the lore is: there is no faster than light transmission of information since the two observers may only compare their results after they get in touch. And yet, when Bob measures the spin of its electron to be up, he knows that the wavefunction went from, say the linear combination |up, down> + |down up> to the state |up down>. How can he conclude that his measurement does not have a nonlocal effect on the state of the other electron?

 

[peter0302]

Well, that's basically the pre-Bell view of entanglement. Take a quarter and slice it in half on the long end, and separate the halves by light years. One person then looks at his quarter and sees tails. He then "knows" that the other's is heads. The "wavefunction" in that case changed but there was no transmission of information necessary at the time of observation because the "information" making his half "heads" and the other's half "tails" was actually always in their respective pieces to begin with, i.e., "hidden information."

But Bell proved that that view is too naive in entanglement. It works fine for mutually exclusive variables like "heads" vs. "tails." It even works fine for "spin up at 0 degrees" versus "spin up at 90 degrees" - also two mutually exclusive conditions. That's why it took people so long to realize the error. It was when people started doing experiments with properties that were NOT mutually exclusive, such as "spin up at 0 degrees" versus "spin up at 22.5 degrees" where bizarre correlations showed up which simply cannot be explained without non-local information transfer OR abandoning deterministic reality.

 

[colorSpace]

Which of course presents just as many problems as it solves, because as we all know from special relativity, in the frame of the particles themselves (say we're using electrons), neither will agree on which one is the first to be measured, thereby imparting that position information to the rest of the system.

Does BM address this or is the whole thing just considered non-causal?

BM considers itself "causal" and explicitly "non-local", yet compatible with relativity due to what I think are called "equilibrium" effects (or something like that).

Independently of the interpretation (BM or not), the question which measurement comes first in a specific reference frame, doesn't pose a real problem since the cause-effect relations are symmetric in this regard.

 

[kdv]

Well, that's basically the pre-Bell view of entanglement. Take a quarter and slice it in half on the long end, and separate the halves by light years. One person then looks at his quarter and sees tails. He then "knows" that the other's is heads. The "wavefunction" in that case changed but there was no transmission of information necessary at the time of observation because the "information" making his half "heads" and the other's half "tails" was actually always in their respective pieces to begin with, i.e., "hidden information."

But Bell proved that that view is too naive in entanglement. It works fine for mutually exclusive variables like "heads" vs. "tails." It even works fine for "spin up at 0 degrees" versus "spin up at 90 degrees" - also two mutually exclusive conditions. That's why it took people so long to realize the error. It was when people started doing experiments with properties that were NOT mutually exclusive, such as "spin up at 0 degrees" versus "spin up at 22.5 degrees" where bizarre correlations showed up which simply cannot be explained without non-local information transfer OR abandoning deterministic reality.

Nice summary.
Yes, I agree completely. But I want to focus on your very last line. I am not sure about the "OR" part. You are saying that the violation of bell's theorem implies that we either have non-local information transfer and deterministic relatity or local information transfer but no deterministic reality?

So I am guessing that you would characterize the Copenhagen interpretation as being of the second type? But this is what confuses me: to me it seems that there is something nonlocal going on, even in the Copenhagen interpretation. After all, once Bob has measured the spin of one electron, he knows that the wavefunction has collapsed to a specific state.

I know that people say that there is no transfer of information in the sense that this can't be used for BOB to tell Sally who won the Super Bowl, but still the state of the far away particle has been altered in a well defined way. It bothers me that this collapse of the wavefunction is brushed aside as being inconsequential because no information is transmitted. To me, it feels like a cop-out. And I do know that because the events are spacelike, depending on your frame it may be Bob or it may be Alice who makes the first measurement which makes it clear that the question "who collapsed the wavefunction" is meaningless. But, again, it feels to me lik echeating to brush aside the whole issue because no information is transmitted. It seems to me that the whole issue points to a need to modify something fundamental in our understanding of nature.

 

[kdv]

BM considers itself "causal" and explicitly "non-local", yet compatible with relativity due to what I think are called "equilibrium" effects (or something like that).

Independently of the interpretation (BM or not), the question which measurement comes first in a specific reference frame, doesn't pose a real problem since the cause-effect relations are symmetric in this regard.

But that means that the very notion of cause vs effect has to be drastically modified in QM. The very notion of cause vs effect implies an symmetry. If we start talking about a symmetry cause-effect, we have to modify drastically what is meant by a causal relationship or time.

 

[peter0302]

Heh, you just noticed that? :)

 

[vanesch]

And I do know that because the events are spacelike, depending on your frame it may be Bob or it may be Alice who makes the first measurement which makes it clear that the question "who collapsed the wavefunction" is meaningless.

Yes, in CI, the "collapse of the wavefunction" and even the wavefunction itself, is not considered physical, but just a conceptual tool to help us know what will happen to the classical world. In between "preparation of experiment" and "irreversible measurement" which are both "interfaces to the classical world", we are, in CI, not supposed to know or even to consider what is going on. Particles are classically prepared, then "dive into the black box of quantum chimera" and pop up again in a classical existence at the moment of measurement. The wavefunction is then just a tool that helps us link the statistics of the measurement with the initial setup, but has no physical description pretention. At least, that's how I understand CI, but it is not easy to know what exactly is meant with it :-)

 

[Fra]

About CI, I think the best simple statement that illustrates the philosophy of CI is that of Niels Bohr.

"It is wrong to think that the task of physics is to find out how Nature is. Physics concerns what we say about Nature."

I think we've all heard that over and over again now, but it seems to never get out of faishon. It's probably my favourite physics quote all times.

In my view, Bohr's state put strong emphasis of questions, questioners and what _the questioner_ say about the possible answers. What questioner2 says about questioner1's questions is obviously a _different_ question.

An experimental setup kind of corresponds to a question. But if we are trying to ask what happen in between the question is posed and we have the answer, then we are actually modifying the original question. In the CI view, I don't think it has to be more complicated than that.

In between experiments we may still have expectations of what could be answers, IF the questions were posed. But if we do, we are obviously changing the conditions implicit in previously asked questions.

In my thinking, in which I also felt reasonably close to CI even though I'm not faithful supporter, the schrödinger equation describes how the observers expectations evolves - until new information arrives - at which point the the conditions changes, which of course also perturbs the evolution of the expectations.

To try to predict when and what NEW information will arrive, and thus the perturbations, doesn't make sense to me at least! The whole notion of intristic information is that, that's all you've got, wether you like it or not. And if this new information COULD be predicted, then it would mean we would in a certain sense already know everything of the future, which is twisted, because you the notion of expectation would make not sense. If you knew everything already, then any questions would be redundany because you already have all answers to all possible questions. One has expectations of the environment, but the accuracy of these are always under remodelling in the course of our interactions.

/Fredrik

 

[CaptainQuasar]

The last time I read through the Bell's Inequalities tests stuff, I remember getting the impression that it seemed to be more concerned with proving that QM isn't equivalent to classical physics, rather than trying to prove that QM is non-deterministic and non-causal in general. Does that make sense to anyone?

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