hi guys, i just have a quick question concerning the Copenhagen interpretation of things.
say there is a star, very far away (perhaps 1 billion light-years from Earth) that for the sake of this idea, has never been observed, by any intelligent being, anywhere. we happen to turn our telescope or observational instrument in the direction of this star and observe it for the very first time. The light that we are observing took one billion years to travel to us from the star and the act of observing this star collapses its wave function into one reality (the reality that the star exists, at this location, at this time 1 billion years before observing it).
Now because this light is essentially 1 billion years old, and by observing it, we collapsed its wave function and 'crystallized' its place in reality, are we changing the past of the star itself? (since the star is 1 billion years ahead of time of when we observed it)
i don't think that came out as coherent as i would have wished but if you need me to explain more please ask. thanks in advance, Michael.
Interesting question... , challenging also!
Anyway,I think that has to do with the problem of definition of measurement.At first we should know what is observation?...What must happen to cause wave function collapse.
As far as I know, that is still in debate and so your question should wait for an answer.
But considering the theory of Quantum Decoherence,any interaction with outside world can affect the wave function of an object and so even if the star is not observed by any human till now,its interaction with other parts of the universe can cause processes like wave function collapse(I'm saying this because in Quantum Decoherence things are a little different).
There's nothing in quantum mechanics that suggests that what happens to the light after it has left the star will affect the star in any way.
Well,when you want to measure a property of a system at time t,there is again a delay between observation time and time t because of the finite speed of light,delay in devices and many other things.So you always have the delay,here we're only making that delay very very longer which means what you said can be said about all quantum systems not only this one!
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@ Nugatory
but doesn't the fact that we observed or 'interacted' with the light confirm that there exists a star at this location, at that time. And this knowledge 'forces' the star to have one single wave function, not a superposition of all the different possible states it could be in. so by observing the light, this forces the star into one particular state.
@ Shyan
i know this is all a bit unrealistic since in a star there are interactions between particles within itself that establish its own reality and its place in existence. but for the thought experiments sake let's not talk about a star, but rather a photon that does not interact with any other particle (and hence is not decohered... until we the observer, interacts with it).
also, out of interest, does anyone know if the delayed choice experiment has been performed with an electron, rather than a photon. and if it has been performed, what was the outcome?
For me this kind of paradoxes leads to the simple conclusion that there is no collapse of the state as assumed in some flavors of the Copenhagen interpretation. I also never understood, why one should postulate such a collapse, because it's not necessary to connect the QT formalism with observations. That's why I prefer the minimal statistical interpretation over all kinds of interpretations containing the collapse hypothesis.
but doesn't the fact that we observed or 'interacted' with the light confirm that there exists a star at this location, at that time.
For the life of me I can't see how you can draw that conclusion.
The star emitted the photon from a definite position. Its wave-function spreads out with an unknown momentum. The thing that emitted it can cease existing - no problem - it will continue to spread. When we observed it we gave it a definite position and its momentum is now unknown - if it wasn't destroyed by the observation - and will continue to spread as before.
Yes, this is a famous and old problem. John Bell wrote it in a memorable way, "It would seem that the theory [quantum mechanics] is exclusively concerned about "results of measurement", and has nothing to say about anything else. What exactly qualifies some physical systems to play the role of "measurer"? Was the wavefunction of the world waiting to jump for thousands of millions of years until a single-celled living creature appeared? Or did it have to wait a little longer, for some better qualified system ... with a Ph.D.? If the theory is to apply to anything but highly idealized laboratory operations, are we not obliged to admit that more or less "measurement-like" processes are going on more or less all the time, more or less everywhere. Do we not have jumping then all the time?" http://www.tau.ac.il/~quantum/Vaidman/IQM/BellAM.pdf
The Copenhagen interpretation does not answer this question. In Copenhagen, one divides the universe into classical and quantum realms. The classical realm contains you and your measuring apparatus, and quantum mechanics is just a way of calculating the probabilities for various results that your apparatus measures.
The problem is solved by de Broglie-Bohm theory and its variants for non-relativistic quantum mechanics. Another approach that seems very promising is the many-worlds interpretation of quantum mechanics.
@ Nugatory
but doesn't the fact that we observed or 'interacted' with the light confirm that there exists a star at this location, at that time. And this knowledge 'forces' the star to have one single wave function, not a superposition of all the different possible states it could be in. so by observing the light, this forces the star into one particular state.
I thought that might be what you were getting at when I read the words "observed, by any intelligent being" in your original post. The idea that consciousness causes collapse is not part of the Copenhagen interpretation, which instead makes a (somewhat arbitrary, hence problematical) distinction between classical things and quantum things. He's not around to ask, but I expect that Bohr himself would have relegated an entire star to the classical side without much hesitation.
A more modern treatment would say that the star is made up of an enormous number of particles each behaving according to the laws of quantum mechanics. However, their interactions with one another (google around for "quantum decoherence") cause the entire mass to behave like a classical star (this is somewhat analogous to the way that ##PV=nRT## for an ideal gas emerges from the motions of each individual particle in the gas); thus, there's no observation needed for the star to be there.
Either way, what we do with the photons that left the star a billion years ago has no effect on the star.
Well,when you want to measure a property of a system at time t,there is again a delay between observation time and time t because of the finite speed of light,delay in devices and many other things.So you always have the delay,here we're only making that delay very very longer which means what you said can be said about all quantum systems not only this one!
In this thought experiment, we're observing light that's right under our nose. More generally, the measurement is always what happens at the measuring device, so there's never any lightspeed delay involved in measurement/interaction. There's no non-locality in a single measurement.
You may be trying to think of the photon and the star as an entangled system possessing a single wave function? That's a different topic than OP's question about Copenhagen, but lightspeed limits don't apply to that form of non-locality.
The idea that consciousness causes collapse is not part of the Copenhagen interpretation, which instead makes a (somewhat arbitrary, hence problematical) distinction between classical things and quantum things.
If its the consciousness thing that's the issue, Copenhagen specifically postulated the existence of a commonsense classical world independent of us. QM is a theory about marks left by quantum systems in such a world.
How a classical world emerges from a theory that postulates its existence beforehand is the real issue with QM - not what Einstein and Bohr used to go on about:
http://scitation.aip.org/content/aip/magazine/physicstoday/article/58/11/10.1063/1.2155755
'Bohr’s version of quantum mechanics was deeply flawed, but not for the reason Einstein thought. The Copenhagen interpretation describes what happens when an observer makes a measurement, but the observer and the act of measurement are themselves treated classically. This is surely wrong: Physicists and their apparatus must be governed by the same quantum mechanical rules that govern everything else in the universe. But these rules are expressed in terms of a wavefunction (or, more precisely, a state vector) that evolves in a perfectly deterministic way. So where do the probabilistic rules of the Copenhagen interpretation come from?
Considerable progress has been made in recent years toward the resolution of the problem, which I cannot go into here. It is enough to say that neither Bohr nor Einstein had focused on the real problem with quantum mechanics. The Copenhagen rules clearly work, so they have to be accepted. But this leaves the task of explaining them by applying the deterministic equation for the evolution of the wavefunction, the Schrödinger equation, to observers and their apparatus. The difficulty is not that quantum mechanics is probabilistic—that is something we apparently just have to live with. The real difficulty is that it is also deterministic, or more precisely, that it combines a probabilistic interpretation with deterministic dynamics.'
For me this kind of paradoxes leads to the simple conclusion that there is no collapse of the state as assumed in some flavors of the Copenhagen interpretation. I also never understood, why one should postulate such a collapse, because it's not necessary to connect the QT formalism with observations. That's why I prefer the minimal statistical interpretation over all kinds of interpretations containing the collapse hypothesis.
Well, the reason people think in terms of collapse is through the following argument process:
In an EPR-type twin particle experiment, either the measurement of the spin of one particle tells you something about the results of distant measurements on the other particle, or it doesn't. I think there is a sense in which, according to the Many-Worlds Interpretation, the spin of one particle doesn't tell you anything about distant measurements. But let's ignore MWI for now, and assume that measurements here give you information about distant measurements.
So if a measurement here let's you know something about measurements there, then it seems that either (1) there is a causal influence--the one measurement affects the other measurement results (i.e., "collapse"), or (2) the measurement here simply reveals a pre-existing fact about the distant measurement.
Bell's theorem seems to rule out the possibility that measurements are simply revealing pre-existing facts.
So that's the problem, it seems to me. Quantum measurements seem to force us into one of two unpalatable alternatives: (1) Many-Worlds, (2) nonlocal influences. The "minimalist statistical interpretation" refuses to choose between those possibilities, but I don't see how it allows a third possibility that is more palatable.
In this thought experiment, we're observing light that's right under our nose. More generally, the measurement is always what happens at the measuring device, so there's never any lightspeed delay involved in measurement/interaction. There's no non-locality in a single measurement.
You may be trying to think of the photon and the star as an entangled system possessing a single wave function? That's a different topic than OP's question about Copenhagen, but lightspeed limits don't apply to that form of non-locality.
Light speed limit was one of the reasons I mentioned.You can't tell when we measure a property at time t, we perceive its value exactly at the same moment.There is always a delay,the most obvious reason is the delay of our brain in interpreting the data.Lots of other things can cause the delay.
And in a world where particles can come into existence,travel some meters and be destroyed in fractions of a second which are much less than our blinking time,I think those delays I mentioned can mean "a future time" for the system under consideration!
As noted above, this is an issue of interpretation. If you think in terms of Consistent Histories or Time Symmetric interpretations, the answer may well be "Yes". (Not that you would know any different.)
Well, the reason people think in terms of collapse is through the following argument process:
In an EPR-type twin particle experiment, either the measurement of the spin of one particle tells you something about the results of distant measurements on the other particle, or it doesn't. I think there is a sense in which, according to the Many-Worlds Interpretation, the spin of one particle doesn't tell you anything about distant measurements. But let's ignore MWI for now, and assume that measurements here give you information about distant measurements.
So if a measurement here let's you know something about measurements there, then it seems that either (1) there is a causal influence--the one measurement affects the other measurement results (i.e., "collapse"), or (2) the measurement here simply reveals a pre-existing fact about the distant measurement.
Bell's theorem seems to rule out the possibility that measurements are simply revealing pre-existing facts.
So that's the problem, it seems to me. Quantum measurements seem to force us into one of two unpalatable alternatives: (1) Many-Worlds, (2) nonlocal influences. The "minimalist statistical interpretation" refuses to choose between those possibilities, but I don't see how it allows a third possibility that is more palatable.
This is only a problem, if you interpret the quantum state (statistical operator) as some physical entity (like a classical point particle or a classical em. field, etc.). According to the Statistical Interpretation it's a description of probabilistic knowledge I have about the system because of the knowledge about a preparation procedure for this state (or through observations on the system determining its (pure or mixed) state).
Then there is no problem whatsoever with EPR-like paradoxes, faster-than-light signal propagation, etc. Let's take the famous Aspect experiment, where one prepares an entangled photon pair (e.g., by parametric downconversion on a non-linear cyrstal). We consider only the polarization state of this "biphoton". Let's assume, it's in the singlet state
\hat{R}=|\Psi \rangle \langle \Psi| \quad \text{with} \quad |\Psi \rangle =\frac{1}{\sqrt{2}} (|HV \rangle-|V H \rangle).
Then you might ask, how to describe the polarization state of one of the photons. According to the rules of quantum theory (which in this case follow from the general rules of probability theory) you have to "trace out" the other photon. This gives you the single-photon state
\hat{R}_1=\frac{1}{2} \hat{1}.
Thus it is in the mixed state representing maximum entropy, i.e., least possible knowledge about the photon's polarization. Preparing many photons in this way you simply have unpolarized light.
Now you can wait for some time t \simeq L/c and register one of the photons at a place very far away from registering the other photon (usually the two observers are called Alice and Bob) letting both go through a polarization filter in H-orientation.
Now, according to the laws of quantum mechanics, the probability that Alice measures a H-polarized photon (her filter let's it through) is 1/2 as well as is Bob's probability to find it.
Now you can ask, what's the probability that Alice and Bob find their photons in any possible combination. According to the rules of quantum theory you get
Code:
Alice's photon Bob's photon Probability
---------------------------------------------------
H H 0
H V 1/2
V H 1/2
V V 0
as one can easily calculate from taking the appropriate scalar products of |\Psi \rangle with the appropriate product states for these four cases.
That reveals that, despite the complete indeterminism of the single-photon polarization states, a 100% correlation between the polarizations of the photons: As is also easily calculated you get probabilities 0 and 1 for the conditional probabilities:
If Alice measures her photon to be H-polarized then the probability that Bob's photon is V-polarized is 100% and that it is H-polarized is 0 etc.
Does this now mean that Bob's photon got into a definite polarization state by Alice's measurement? The answer, according to the Minimal Statistical Interpretation, as spelled out above is clearly no! At no point I have said, who measures her or his photon first! Who measures the photon first is simply a matter of distance from the biphoton source. Even when Alice is way farer away from the source than Bob and thus measures her photon way later than he does, we will observe the 100% correlations and vice versa. In our current understanding the registration of Alice's photon polarization is due to a local interaction of her photon with the polarization foil and detector and doesn't affect Bob's photon in any way and vice versa. The 100% correlations of the totally undetermined single-photon polarization states are due to the polarization state of the two-photon system as a whole and is thus inherent in this state, i.e., and thus due to the preparation of the biphoton pair as an entangle pair via parametric down conversion. In this minimal interpretation there is thus no "spooky action at distance" or a "collapse of the state" necessary to explain the 100% correlation of the photons' polarization since this 100% was already prepared when the photons were created by parametric down conversion and not by Alice's and/or Bob's measurement of the polarization state of their single photons.
In the whole description of this EPR experiment nowhere a collapse assumption or action at a distance is necessary and thus there's no EPR paradox. That's why I never understood what the collapse assumption is good for. Of course, adapting the Minimal Interpretation, we must give up the idea that quantum theory is a direct description about physical entities. It is rather a description about the (fundamentally maximal possible!) knowledge about a quantum system given a preparation procedure or previous observations of observables of this system.
In the whole description of this EPR experiment nowhere a collapse assumption or action at a distance is necessary and thus there's no EPR paradox. That's why I never understood what the collapse assumption is good for. Of course, adapting the Minimal Interpretation, we must give up the idea that quantum theory is a direct description about physical entities. It is rather a description about the (fundamentally maximal possible!) knowledge about a quantum system given a preparation procedure or previous observations of observables of this system.
It is true that the EPR experiment does not need a collapse. However, it is not universally agreed that denying the realism of the wave function allows one to deny Bell nonlocality. http://arxiv.org/abs/0901.4255 Denying the reality of the other observer does allow one to deny Bell nonlocality. http://arxiv.org/abs/quant-ph/0509061
Neither collapse nor Bell nonlocality are at odds with special relativity. Although different observers may assign wave function collapse to different spatial hypersurfaces, the experimental results they predict are related by Lorentz transformation. http://arxiv.org/abs/0706.1232 Operations that violate special relativity do non-trivially turn out to be forbidden in relativistic gauge theories. http://arxiv.org/abs/hep-th/0110205
Collapse is needed as a postulate in interpretations such as Copenhagen and the ensemble or minimal statistical interpretation for describing filtering measurements as a means of state preparation. If one does not do that, then it is true that one only needs completely positive trace preserving maps, which can be thought of as arising from unitary evolution of a larger system and decoherence of the subsystem. But when using filtering measurements for state preparation, the operation is a completely positive trace non-increasing map. This is why Hardy includes completely positive trace non-increasing operators in his derivation of finite dimensional quantum mechanics. http://arxiv.org/abs/quant-ph/0101012
One possibly misleading idea about collapse is the idea that it is the only way to describe things like quantum teleportation or steering. It isn't, but it is one useful way of describing such things. http://arxiv.org/abs/quant-ph/0612147 A second possibly misleading idea about collapse is to take it as the root of the problem, whereas wave function collapse is a symptom, and not the root of the problem. The root is the cut between the macroscopic and quantum realms, where the macroscopic realm is the realm with definite events. Once the macroscopic/quantum cut is made, there is no problem with collapse, since the theory is instrumental or operational anyway.
Collapse is needed as a postulate in interpretations such as Copenhagen and the ensemble or minimal statistical interpretation for describing filtering measurements as a means of state preparation.
Not really - its a simple by-product of continuity as has been discussed in previous threads.
But since it only occurs with filtering type measurements, which are equivalent to state preparation procedures, then you can actually associate the state with the preparation procedure avoiding this whole collapse thing entirely - which is what I think you are getting at anyway.
But even if you allow collapse its a total non issue - in Copenhagen and the Ensemble interpretation it, just like probabilities are, is simply an aid to calculating the frequencies of outcomes. As I often say - you have a dice with a probability of 1/6 attached to each side - throw it - one side gets a probability 1 and the others 0. Your state vector (a vector with 6 entries) suddenly changed. My god there is a problem with probability theory - we urgently need to explain this collapse of a probability vector issue - its vitally important - better rush out immediately and have this published - wow - might even get a Fields medal
Of course totally tongue in cheek - but I am sure you get the drift.
And the analogy isn't that far fetched, because as the paper I often post shows, QM is simply a variation of probability theory that allows for continuous transformations between pure states, or, equivalently, entanglement. It's what's known these days as a generalized probability model, of which standard probability theory is the simplest case. They all have states that change when you do a trial, observation, whatever you want to call it depending on the application, and its of zero concern because its simply an aid to calculation - a theoretical construct.
That's why I never understood what the collapse assumption is good for.
It's not good for anything.
As Ballentine says it harks back to the idea, because it is fundamental to QM, like the EM field in Electrodynamics, you tend to think its real.
But its purpose is entirely different, and when you understand its similar to probabilities in standard probability theory, your whole view changes and you scratch your head why people worry about it.
It is true that the EPR experiment does not need a collapse. However, it is not universally agreed that denying the realism of the wave function allows one to deny Bell nonlocality. http://arxiv.org/abs/0901.4255 Denying the reality of the other observer does allow one to deny Bell nonlocality. http://arxiv.org/abs/quant-ph/0509061
Neither collapse nor Bell nonlocality are at odds with special relativity. Although different observers may assign wave function collapse to different spatial hypersurfaces, the experimental results they predict are related by Lorentz transformation. http://arxiv.org/abs/0706.1232 Operations that violate special relativity do non-trivially turn out to be forbidden in relativistic gauge theories. http://arxiv.org/abs/hep-th/0110205
Collapse is needed as a postulate in interpretations such as Copenhagen and the ensemble or minimal statistical interpretation for describing filtering measurements as a means of state preparation. If one does not do that, then it is true that one only needs completely positive trace preserving maps, which can be thought of as arising from unitary evolution of a larger system and decoherence of the subsystem. But when using filtering measurements for state preparation, the operation is a completely positive trace non-increasing map. This is why Hardy includes completely positive trace non-increasing operators in his derivation of finite dimensional quantum mechanics. http://arxiv.org/abs/quant-ph/0101012
One possibly misleading idea about collapse is the idea that it is the only way to describe things like quantum teleportation or steering. It isn't, but it is one useful way of describing such things. http://arxiv.org/abs/quant-ph/0612147 A second possibly misleading idea about collapse is to take it as the root of the problem, whereas wave function collapse is a symptom, and not the root of the problem. The root is the cut between the macroscopic and quantum realms, where the macroscopic realm is the realm with definite events. Once the macroscopic/quantum cut is made, there is no problem with collapse, since the theory is instrumental or operational anyway.
I like to avoid the notion of "realism" in the discussion of the foundations of quantum theory. It's pretty unsharply defined.
The point is that, within the Minimal Statistical Interpretation (MSI) just takes the state as encoding the probabilistic statements inherent in Born's rule. This is sometimes called "unrealistic". That's ironic, because that's what all experiments tell us to be right.
Further, nobody denies the "nonlocal correlations" known as entanglement. The point is that these are correlations but not nonlocal interactions. To the contrary, the most successful theories, like the Standard Model of elementary particles, are local relativistic quantum field theories. This precisely resolves the EPR paradox as explained in my previous posting. The correlations are already there from the very beginning of the experiment, i.e., due to the preparation of the two photons in the entangled polarization state and it's not caused by the measurement of one of the photon's polarization. So there is no need for an action at a distance of the far-distant photon with the apparatus located where the other photon is registered. Thus, to explain the nonlocal correlations due to entanglement no collapse argument is necessary, but are well explained for local interactions of the photon's with their measurement apparati. The violation of Bell's inequality is validated by numerous experiments with high statistical significance, and various loop holes have been closed in the recent years. I don't think that there's any reason to deny these features of quantum theory.
I like to avoid the notion of "realism" in the discussion of the foundations of quantum theory. It's pretty unsharply defined.
The point is that, within the Minimal Statistical Interpretation (MSI) just takes the state as encoding the probabilistic statements inherent in Born's rule. This is sometimes called "unrealistic". That's ironic, because that's what all experiments tell us to be right.
I don't think that the idea of realism is so fuzzy. Realism is the belief that there is a world and that it has properties and that when we perform experiments, we are learning about those properties. In contrast, in some flavors of interpretations of quantum mechanics, the properties simply don't exist prior to the measurement.
Further, nobody denies the "nonlocal correlations" known as entanglement. The point is that these are correlations but not nonlocal interactions. To the contrary, the most successful theories, like the Standard Model of elementary particles, are local relativistic quantum field theories. This precisely resolves the EPR paradox as explained in my previous posting.
I think you mean something different by "resolve".
The correlations are already there from the very beginning of the experiment, i.e., due to the preparation of the two photons in the entangled polarization state and it's not caused by the measurement of one of the photon's polarization.
It's not the correlation, it's the information about the result of a distant measurement. A twin pair of photons are produced, and one is sent to Bob and the other is sent to Alice. Assume that Bob uses a horizontally-polarized filter and Alice uses a vertically-polarized filter. When Bob detects a photon passing through his filter, he knows with certainty that Alice does not detect a photon. So the state of his knowledge about Alice and her observations changes when Bob makes his observation:
After Bob has made his observation, he knows with certainty that Alice's photon is horizontally polarized and will not pass Alice's vertical filter. This seems to be a fact about the state of Alice + polarizing filter + detector + electromagnetic field. So the issue is whether this fact was true before Bob made his observation, or whether it became true when he made his observation.
If F is the statement "Alice will not detect a vertically polarized photon", then it seems to me that there are three possibilities: (1) It's not really a fact about Alice, even after Bob makes his observation. (2) It is a fact about Alice, and it was true (though Bob didn't know it) before Bob made his observation. (3) It is a fact about Alice, and it became true when Bob made his observation. The paradox is that there seems to be only 3 possibilities, and none of the 3 is very satisfactory. That's the issue, and I don't see how the minimal interpretation resolves it.
In my experience with these forums, this line of discussion will eventually lead to the closing of the thread by the moderators, so everybody has to get in their last digs. One other comment: a lot of people seem to act as if puzzling over the interpretation of quantum mechanics is a sign that you don't understand the proper way of using and thinking about the theory. I have to strongly disagree with that. I believe that I understand quantum mechanics pretty well, and I think I could give the pitch that there's nothing at all mysterious about it as well as anyone.
The paradox is that there seems to be only 3 possibilities, and none of the 3 is very satisfactory. That's the issue, and I don't see how the minimal interpretation resolves it.
May I suggest that one avoids making statements about what is subjectively satisfactory or not? In that way, maybe we could have objective discussion about interpretations. Thus we only discuss whether something is objectively satisfactory or not. For example - an interpretation can be judged objectively satisfactory if it reproduces all the predictions of quantum mechanics and it is logically consistent.
It's not the correlation, it's the information about the result of a distant measurement. A twin pair of photons are produced, and one is sent to Bob and the other is sent to Alice. Assume that Bob uses a horizontally-polarized filter and Alice uses a vertically-polarized filter. When Bob detects a photon passing through his filter, he knows with certainty that Alice does not detect a photon. So the state of his knowledge about Alice and her observations changes when Bob makes his observation:
After Bob has made his observation, he knows with certainty that Alice's photon is horizontally polarized and will not pass Alice's vertical filter. This seems to be a fact about the state of Alice + polarizing filter + detector + electromagnetic field. So the issue is whether this fact was true before Bob made his observation, or whether it became true when he made his observation.
This is precisely what a correlation means! Bob's measurement of his photon's polarization state implies immediately what Alice will find but not because of Bob's measurement but because of the entangled two-photon state, prepared in the very beginning. The only thing you have to know is that you have been send one of the such entangled photons and that there was no decoherence through interactions with the environment on one or both photons travel to Alice and Bob.
If F is the statement "Alice will not detect a vertically polarized photon", then it seems to me that there are three possibilities: (1) It's not really a fact about Alice, even after Bob makes his observation. (2) It is a fact about Alice, and it was true (though Bob didn't know it) before Bob made his observation. (3) It is a fact about Alice, and it became true when Bob made his observation. The paradox is that there seems to be only 3 possibilities, and none of the 3 is very satisfactory. That's the issue, and I don't see how the minimal interpretation resolves it.
No, it's a fact about the entangled photon pair due to it's preparation in this state. There is nothing mysterious if you accept the minimal interpretation. The resolution by the minimal interpretation simply is that there is nothing to resolve ;-)).
In my experience with these forums, this line of discussion will eventually lead to the closing of the thread by the moderators, so everybody has to get in their last digs. One other comment: a lot of people seem to act as if puzzling over the interpretation of quantum mechanics is a sign that you don't understand the proper way of using and thinking about the theory. I have to strongly disagree with that. I believe that I understand quantum mechanics pretty well, and I think I could give the pitch that there's nothing at all mysterious about it as well as anyone.
Well, the debate about the interpretation of quantum theory is very often drifting towards useless debates about purely metaphysical issues, making additional assumptions concerning the ontology implied by the physical theory and thus leaving the strict realm of the natural sciences, which by definition restricts itself to objectively observable properties of Nature and their description in terms of fundamental laws expressible in quantitative predictions about Nature's behavior in terms of mathematical theories.
If this realm is left too far towards metaphysics or even esoterics, it's very appreciable if you have a good moderation closing such threads to keep the forum useful as a discussion forum on science rather than fruitless philosophy or esoterics. I think the moderators do this job very well, keeping the forum on the one hand open enough for such discussions which are puzzling particularly for students starting to learn quantum theory and the more for interested laymen and on the other hand avoid it to be swamped by crackpot contributions making such forums pretty easily useless for scientific discussions!
May I suggest that one avoids making statements about what is subjectively satisfactory or not?
I thought you were making claims about how satisfactory the minimal interpretation was, and I was disagreeing. If you're not making such a claim, then nevermind.
No, it's a fact about the entangled photon pair due to it's preparation in this state.
I don't think that's correct. The fact that the two photons are entangled is a fact about the preparation--I agree with that. But the fact that "Alice will not detect a vertically polarized photon" is not implied by that fact. It's an additional fact.
There is nothing mysterious if you accept the minimal interpretation.
I don't know why you say that. The issue is whether the statement "Alice will not detect a vertically polarized photon" is true before Bob's observation, or does it become true when Bob makes his observation. The minimal interpretation doesn't say.
Well, the debate about the interpretation of quantum theory is very often drifting towards useless debates about purely metaphysical issues, making additional assumptions concerning the ontology implied by the physical theory and thus leaving the strict realm of the natural sciences, which by definition restricts itself to objectively observable properties of Nature and their description in terms of fundamental laws expressible in quantitative predictions about Nature's behavior in terms of mathematical theories.
I find this attitude annoying. Basically, what it amounts to is saying: we can avoid arguments over metaphysics if we all agree on metaphysics. If everybody agreed with you about ontology and what natural science is all about, then there wouldn't be any arguments about it.
I find this attitude annoying. Basically, what it amounts to is saying: we can avoid arguments over metaphysics if we all agree on metaphysics. If everybody agreed with you about ontology and what natural science is all about, then there wouldn't be any arguments about it.
In other words, if we all thought the same way, there wouldn't be any arguments.
I find this attitude annoying. Basically, what it amounts to is saying: we can avoid arguments over metaphysics if we all agree on metaphysics. If everybody agreed with you about ontology and what natural science is all about, then there wouldn't be any arguments about it.
stevendaryl said:
In other words, if we all thought the same way, there wouldn't be any arguments.
It's been a good thread, but I got to say... It's drifting towards the point of diminishing returns.
I don't think that's correct. The fact that the two photons are entangled is a fact about the preparation--I agree with that. But the fact that "Alice will not detect a vertically polarized photon" is not implied by that fact. It's an additional fact.
I don't know why you say that. The issue is whether the statement "Alice will not detect a vertically polarized photon" is true before Bob's observation, or does it become true when Bob makes his observation. The minimal interpretation doesn't say.
This shows how difficult it is to communicate this issue. I try again!
Before Bob measures the polarisation of his photon, he doesn't know it, and the polarizaton is not determined at all. He also doesn't know anything about Alice's photon, and it's indetermined as well. Now at the moment when Bob measures his photon's polarization, he also knows Alice's photon's polarization. The reason for this correlation between Alice's and Bob's photon polarization is, however not Bob's measurement but the preparation in the entangled state by the parametric down conversion in the very beginning.
Actually, is there really a way to describe the EPR experiment using only unitary time evolution (say within an interpretation which does have collapse such as Copenhagen, not an interpretation without collapse like many-worlds)?
Why shouldn't this be possible? Of course the time evolution of any free two-photon system is unitary and can be done analytically, or do I misunderstand your question?
Why shouldn't this be possible? Of course the time evolution of any free two-photon system is unitary and can be done analytically, or do I misunderstand your question?
Let's say, from your example, the state is ##|\Psi \rangle =\frac{1}{\sqrt{2}} (|HV \rangle-|V H \rangle)##.
Let's say Alice measures her photon to be H, the state collapses to ##|\Psi \rangle = |HV \rangle##.
The collapse is non-unitary, and affects Bob's density matrix. Can we describe this situation without collapse? I have seen examples for teleportation, which was initially worked out with collapse, and unitary descriptions were later found. Is there a unitary description here?
Can you prove somehown that the state collapses? I cannot, and I don't see why it should. When Alice's photon is measured, it's usually absorbed in the photo multiplier used to register it. So why should there be a two-photon state after her measurement at all?
The only thing you can say is that when Alice measures a horizontally polarized photon (condition), Bob must necessarily find a vertically polarized photon.
In other words: The conditional probability for Bob to find hi photon to be vertically provided Alice's photon is measured to be horizontally polarized is 1 (and that it's horizontally polarized is necessarily 0) of course.
If you want to know, from quantum theory, what's going on at the measurement, you have to solve the very complicated interaction of the photons with Alice's and/or Bob's measurement apparati. This is, however not necessary to understand the conditional probabilities described above. They follow simply from Born's rule and elementary probability theory.
Can you prove somehown that the state collapses? I cannot, and I don't see why it should. When Alice's photon is measured, it's usually absorbed in the photo multiplier used to register it. So why should there be a two-photon state after her measurement at all?
The only thing you can say is that when Alice measures a horizontally polarized photon (condition), Bob must necessarily find a vertically polarized photon.
In other words: The conditional probability for Bob to find hi photon to be vertically provided Alice's photon is measured to be horizontally polarized is 1 (and that it's horizontally polarized is necessarily 0) of course.
If you want to know, from quantum theory, what's going on at the measurement, you have to solve the very complicated interaction of the photons with Alice's and/or Bob's measurement apparati. This is, however not necessary to understand the conditional probabilities described above. They follow simply from Born's rule and elementary probability theory.
Let's say Alice does a non-demolition measurement.
If I'm understanding you, I've read (e.g. Vaidman) that this can't be done because such a non-demolition measurement would violate Einstein causality.
There are some non-demolition measurements that are impossible, and I'm not sure the exact one I wrote is possible. For example, the non-demolition measurement of a non-Abelian Wilson loop is not possible, as shown in http://arxiv.org/abs/hep-th/0110205 following Vaidman, Aharonov and Albert.
However, there should be systems for which it is possible to do a non-demolition measurement on one particle in an EPR experiment. For example, http://arxiv.org/abs/0706.1232 (p3) give the example where the state is ##|\Psi \rangle =\frac{1}{\sqrt{2}} (|10\rangle-|01\rangle)##. After Alice measures her particle to be 1, the state collapses to ##|\Psi \rangle = |10\rangle##
Well, but this state collapse then is just the adaption of Alice's knowledge from her non-demolition measurement. Nothing has instantaneously happen with Bob's photon, at least as long standard QED is right, according to which the interaction of Alice's photon with her measurement apparatus is local. To let Bob know her measurement Alice needs to send the information to him, which signal takes at least the time L/c, when Bob is at a distance L from Alice. So there is no FTL communication possible by just doing the local measurement at Alice's photon, and no violation of the causality structure of SRT is implied.
Well, but this state collapse then is just the adaption of Alice's knowledge from her non-demolition measurement. Nothing has instantaneously happen with Bob's photon, at least as long standard QED is right, according to which the interaction of Alice's photon with her measurement apparatus is local. To let Bob know her measurement Alice needs to send the information to him, which signal takes at least the time L/c, when Bob is at a distance L from Alice. So there is no FTL communication possible by just doing the local measurement at Alice's photon, and no violation of the causality structure of SRT is implied.
I agree that wave function collapse does not lead to any FTL communication of classical information, and there is no violation of special relativity.
At any rate, I take back my claim in post #16 that in interpretations with a classical/quantum cut, EPR can be described without collapse or non-unitary time evolution of the wave function.
What I find unsatisfactory about the interpretation of quantum mechanics as a probabilistic theory is that probabilities are probabilities of events. Either it's a probability of something being true, or its a probability of something happening. In the case of quantum mechanics, it's not clear what the probabilities are probabilities for. Associated with a wave function \Psi, an observable \hat{O}, and an eigenvalue o_i of \hat{O}, there is a corresponding probability p_i. But is this a probability that something is true? Is there a probability of p_i that the observable has value o_i? I would say no, that is not a correct interpretation. Observables don't have definite values in quantum mechanics until they are measured (or prepared to have those values). If you prepare a spin-1/2 particle so that it is spin-up in the z-direction, it has a 50% probability associated with having spin-up in the x-direction. But it doesn't actually have a spin in the x-direction prior to measuring it. (If it did, that would be a hidden variable, which is ruled out by Bell-type inequalities.)
So the probabilities for quantum mechanics are not associated with a probability of something being true. Then what are they probabilities for? They are probabilities of measuring something. The probability p_i is the conditional probability that you will measure \hat{O} to have value o_i, given that you choose to measure that observable. That's fine as a heuristic, but what does it really mean? The difficulty for me is that measurements themselves are physical interactions, presumably described by quantum mechanics. There is no more reason for the statement "The measurement of \hat{O} produced value o_i" to have a definite truth value than "\hat{O} has value o_i". I feel that a theory is still at the ad hoc stage if it must rely on the distinction between measurements and other interactions.
The closest thing to a objective interpretation of quantum mechanics that does not rely on ad hoc nonlocal interactions of ad hoc distinctions between measurements and other interactions is the "consistent histories" interpretation (which I think of as a variant of the Many-Worlds Interpretation). The wave function of the universe evolves continuously according to Schrodinger's equation (or the quantum-field theoretic generalization) until decoherence splits it into effectively disjoint parts. At that point, we can choose to interpret the wave function probabilistically, as an ordinary probability distribution on alternative histories.
But I find that not completely satisfying either. For one thing, the notion of "effectively disjoint alternative histories" is fuzzy. It depends on the likelihood of being able to observe interference effects between alternatives. For another thing, it seems weird that we have to wait for decoherence to do its thing before we can interpret what is going on.
I feel that a theory is still at the ad hoc stage if it must rely on the distinction between measurements and other interactions.
Yes, it is widely agreed that quantum mechanics has a measurement problem, which within Copenhagen is rooted in the need to make a classical/quantum cut, with the measuring apparatus on the classical side.
Also I agree that attempts to say that in interpretations with a classical/quantum cut, that wave function collapse is exclusively updating of knowledge, and that the physical system is not evolving, are so far not convincing. If it were, then quantum theory in such interpretations would be standard probability theory, and it isn't.
#41
Jilang
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72
Why do we refer to a quantum/classical cut rather than a boundary condition? Is that what measurement effectively is?
Why do we refer to a quantum/classical cut rather than a boundary condition? Is that what measurement effectively is?
We do have boundary conditions on the wave function, but quantum mechanics is not a theory like classical field theory, which also has boundary conditions. In classical field theory, the field potentially includes everything in the universe, including the measuring apparatus. The field is a model in which there is a single reality that changes with time. In classical field theory, we don't think there is any fundamental problem with including the measuring apparatus or the whole universe in the field, although it may be inconvenient. However, in quantum mechanics, if we try to put the measuring apparatus or the whole universe into the wave function, we get time evolution into superpositions which are not observed. To make the match to observation, we have to introduce the notion of measurement as a distinct postulate, as something that produces definite outcomes.
It may be possible to avoid the classical/quantum cut by using an interpretation such as many-worlds. However, at least for non-relativistic quantum mechanics, one can also avoid the classical/quantum cut by de Broglie-Bohm theory and its variants. Since there is not one unique way of avoiding the classical/quantum cut, and since quantum mechanics with the cut is working just fine for the moment, we can use it and are agnostic about the underlying interpretation.
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#43
Jilang
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72
Thanks atyy, my question is more along the lines of why we regard the preparation of the state as an initial boundary condition for the wavefunction, but why we don't talk of the measurement as being a final boundary condition.
Thanks atyy, my question is more along the lines of why we regard the preparation of the state as an initial boundary condition for the wavefunction, but why we don't talk of the measurement as being a final boundary condition.
There is one formulation of quantum mechanics in which something like this is the case, if I understand it correctly: http://arxiv.org/abs/0706.1232. I believe it is more a calculational method, like the path integral, than it is an interpretation. I think Dr Chinese has read this article quite carefully, so he could answer questions on it. But if you would like to disucss this, perhaps it'd be better to start a new thread.
In the more textbookish way of thinking, a measurement causes the wave function to collapse, and collapse is not governed by the Schroedinger equation, so if the particle still exists after the measurement, it isn't enough to set the measurement as a boundary condition, since unitary evolution is violated.
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#45
Jilang
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72
Thanks atyy. I will read the article and I might start a new post.
#46
DevilsAvocado
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[my bolding]
vanhees71 said:
In this minimal interpretation there is thus no "spooky action at distance" or a "collapse of the state" necessary to explain the 100% correlation of the photons' polarization since this 100% was already prepared when the photons were created by parametric down conversion and not by Alice's and/or Bob's measurement of the polarization state of their single photons.
In the whole description of this EPR experiment nowhere a collapse assumption or action at a distance is necessary and thus there's no EPR paradox.
vanhees71 said:
Further, nobody denies the "nonlocal correlations" known as entanglement. The point is that these are correlations but not nonlocal interactions. To the contrary, the most successful theories, like the Standard Model of elementary particles, are local relativistic quantum field theories. This precisely resolves the EPR paradox as explained in my previous posting. The correlations are already there from the very beginning of the experiment, i.e., due to the preparation of the two photons in the entangled polarization state and it's not caused by the measurement of one of the photon's polarization. So there is no need for an action at a distance of the far-distant photon with the apparatus located where the other photon is registered.
vanhees71 said:
Before Bob measures the polarisation of his photon, he doesn't know it, and the polarizaton is not determined at all. He also doesn't know anything about Alice's photon, and it's indetermined as well. Now at the moment when Bob measures his photon's polarization, he also knows Alice's photon's polarization. The reason for this correlation between Alice's and Bob's photon polarization is, however not Bob's measurement but the preparation in the entangled state by the parametric down conversion in the very beginning.
This is confusing...? Are you talking about the 1935 EPR picture??
What you are saying is obviously not true after 1964, and Bell's groundbreaking paper "On the Einstein Podolsky Rosen paradox". The 1935 picture is only valid for prefect alignments/perfect correlations; i.e. it does not work for any other settings...
[my bolding]
This is confusing...? Are you talking about the 1935 EPR picture??
What you are saying is obviously not true after 1964, and Bell's groundbreaking paper "On the Einstein Podolsky Rosen paradox". The 1935 picture is only valid for prefect alignments/perfect correlations; i.e. it does not work for any other settings...
There's a confusion about the meaning of "indeterminate". If you say that before Bob detects the photon, its polarization is indeterminate, you could be making an epistemological statement, that Bob doesn't know the polarization. Or you could be making a statement about the photon---that it doesn't have a polarization. After Bob does detect a horizontally-polarized photon, the state of Alice's photon + filter + detector becomes determined: She will definitely not measure a vertically-polarized photon. There are similarly two interpretations to this "becomes determined": (1) Bob learns about Alice's situation, or (2) Alice's situation changes to a situation in which the polarization is definite.
The two interpretations of the words "indeterminate" and "determined" are both unsatisfactory, in my opinion. If you view them as purely epistemological, so it's just a matter of Bob learning facts that are already true, then that would seem to imply a "hidden variables" model, which is ruled out by Bell's inequality. If you view them as not purely epistemological, but as actually about the state of the photons, then it would seem that Bob's measurement has an effect on the distant photon. Which is the "spooky action at a distance". Neither alternative is very attractive.
#49
DevilsAvocado
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bohm2 said:
The interesting question is what is responsible for the EPR correlations. I mean how does nature do that 'trick'?
I have absolutely no idea, and as a petite 'remedy' – we are in good company of über-smart people like Anton Zeilinger...
I think that Bohmian mechanics has some sort of "real explanation" (do you know?), but not in detail how the non-locality is 'implemented', and anyhow, there are serious trouble with RoS as soon as you make "real stuff" being there and influencing other distant "real stuff".
As Lee Smolin writes in his latest book:
Lee Smolin – Time Reborn said:
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.
It's hard and very interesting – I'm glad to live in these interesting times! ;)
#50
DevilsAvocado
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stevendaryl said:
There are similarly two interpretations to this "becomes determined": (1) Bob learns about Alice's situation, or (2) Alice's situation changes to a situation in which the polarization is definite.
The two interpretations of the words "indeterminate" and "determined" are both unsatisfactory, in my opinion.
I agree, there is no satisfactory explanation for EPR-Bell. You could refer to MWI to get rid of the whole problem, but to me this is at the same level as superdeterminism or the anthropic principle.
Basically, you could introduce even more weirdness to get rid of the EPR-Bell weirdness, or you could just "give up" and say - Shut up and calculate! ;)
P.S: My 'objection' to vanhees's posts was that it looks like he's talking about the 1935 picture of "gloves in a box", and of course this picture make it possible to refer to a common source as an explanation of the correlations, whereas this breaks down as soon as you go one step further to the Bell picture.
