- #36
Jilang
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I am interested in understanding more about whether there is anything special about a measurement. Does a measurement always involve an increase in entropy? Is that what makes it special?
Jilang said:I am interested in understanding more about whether there is anything special about a measurement. Does a measurement always involve an increase in entropy? Is that what makes it special?
What's "special" about a measurement is just that some kind record of the outcome is created, and isn't immediately destroyed. If you measure something, then the final state of the measuring device is such a record, and so is the memory of the result that's created in your brain.Jilang said:I am interested in understanding more about whether there is anything special about a measurement. Does a measurement always involve an increase in entropy? Is that what makes it special?
stevendaryl said:The difference with QM is that statements such as "The electron has spin-up in direction x" not only have an unknown truth value, but they don't have a truth value. They can't have a truth value--that would be a hidden variable, which Bell's theorem rules out (again, if we disallow nonlocal interactions). I don't see how probabilities in the QM can reflect ignorance of a truth value if the truth value doesn't exist. If you ask "What color is the real number pi?" there is no answer--pi doesn't have a color. It doesn't make sense to say that it has a 20% probability of being red.
stevendaryl said:That's my complaint about probabilities in QM. It doesn't make sense to say that probabilities reflect ignorance about system properties if our theory tells us that the system just doesn't HAVE those properties.
I know that after a measurement, it seems to be the case that "The electron was measured to have spin-up in direction x" is either true or false. So it seems that the statement has a definite truth value, afterward, so we can apply probabilities in the same way we do classically, to reflect our ignorance about the truth value of a statement that has (or will have) a definite truth value. But that's where the issue of whether there is something special about measurement comes in. If "The electron has spin-up in the x-direction" has no truth value before the measurement, and there is nothing special about measurements, then why should "The electron was measured to have spin-up in the x-direction" have a definite truth value?
vanhees71 said:The only difference between classical physics and quantum physics is that in classical physics all observables always have definite values, be they known or unknown to a physicist, while in quantum theory any observables can have a definite value or not, depending on how the system was prepared. It's of course a bit unintuitive in the beginning of learning quantum theory that observables can be indetermined, but that's how Nature is.
In principle, the time evolution of an isolated system is always reversible, but I think that the state of the environment (in which the record is stored) can't (even in principle) be reversed without also reversing the state of the measured object.Jilang said:Thanks. Would it be fair to say that the record made was non-reversible then?
Jilang said:I am interested in understanding more about whether there is anything special about a measurement. Does a measurement always involve an increase in entropy? Is that what makes it special?
Fredrik said:In principle, the time evolution of an isolated system is always reversible, but I think that the state of the environment (in which the record is stored) can't (even in principle) be reversed without also reversing the state of the measured object.
I think that division is what's misleading. It suggests that measuring devices are fundamentally different, when in fact they're not.atyy said:in Copenhagen and the Ensemble interpretation, one has to divide the universe into a classical part and a quantum part.
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(Ballentine, as far as I can tell, fails to mention this classical/quantum division, which is foundational for the Ensemble interpretation. It's unclear whether he even knows it, which is why his discussion on measurement and wave function collapse is so misleading. Landau and Lifshitz, and Weinberg make this point clear.)
That sort of record is certainly impossible to reverse in practice. And it wouldn't do you any good, since records of the result of the measurement tend to be stored all over the place: on the plate, in your brain, and even in the air.Jilang said:I am wondering how you could remove the remove the record on a photographic film for example. Is that what you are saying?
Fredrik said:I think that division is what's misleading. It suggests that measuring devices are fundamentally different, when in fact they're not.
The idea that measurements must have results doesn't belong to any particular interpretation. It's part of the definition of science. Scientific theories must be falsifiable. To be falsifiable they must assign probabilities to specific final states of interactions such that several humans can agree that the final state has been obtained.
If you succeed at putting a two-detector measuring device in a superposition of "left detector clicked" and "right detector clicked", then you haven't produced a final state that a human is capable of interpreting as a result of a (position) measurement. One reason is that the interaction that stores the memory of the observed result in your brain is subject to decoherence. If you're the person making that observation, then from my point of view, your state almost instantly decoheres from "superposition of remembering left and remembering right" to the mixed state "either left or right".
Why would we need to assign a wavefunction to the universe? I agree that we can't, but I don't see a reason to think of that as a problem. We're talking about a generalized probability theory. All it does is to assign probabilities to results of measurements, so we can't expect it to be useful in scenarios where measurements aren't possible in principle.atyy said:But that assumes that "the wave function of the universe" (system + measurement device + environment) makes sense.
Fredrik said:Why would we need to assign a wavefunction to the universe? I agree that we can't, but I don't see a reason to think of that as a problem. We're talking about a generalized probability theory. All it does is to assign probabilities to results of measurements, so we can't expect it to be useful in scenarios where measurements aren't possible in principle.
Fredrik said:The idea that measurements must have results doesn't belong to any particular interpretation. It's part of the definition of science. Scientific theories must be falsifiable. To be falsifiable they must assign probabilities to specific final states of interactions such that several humans can agree what final state has been obtained.
Fredrik said:Why would we need to assign a wavefunction to the universe? I agree that we can't, but I don't see a reason to think of that as a problem. We're talking about a generalized probability theory. All it does is to assign probabilities to results of measurements, so we can't expect it to be useful in scenarios where measurements aren't possible in principle.
Right, these theories describe fictional universes with properties in common with our own. (If you prefer, they are approximate descriptions of our universe). But when you think about what a theory must be like in order to be falsifiable, you see that it doesn't need to describe a universe. It just needs to assign probabilities to possible results of measurements.atyy said:Well, the idea is that in classical physics, we don't talk about measurements in formulating a theory. We write down eg. an action specifying the fields and their interactions. We assume that the whole universe can be described by the theory, and because the measurement device is in the universe it is also described by the theory.
Yes, but there's no need to, if you just stop thinking of QM as a theory of the first kind, and accept that it's a theory of the second kind. The problem that you're referring to, and all the other "problems" with QM, are consequences of the unnecessary assumption that I'm rejecting.atyy said:However, in quantum theory, we seem to have a problem in extending the wave function to the whole universe.
All we have to do is to say which measuring device is supposed to tell us the result of the experiment. I wouldn't describe this as a classical/quantum cut.atyy said:Because of this, in Copenhagen and Ensemble interpretations we do have to make this classical/quantum cut.
If what you mean by a classical realm is something like semi-stable records of the results of certain interactions, then yes. If you mean something truly classical, then no.atyy said:It is true that in decoherence we can shift the classical quantum cut so that the environment+measuring device+system are quantum, but then we still need a classical realm outside of that, unless the wave function of the universe makes sense.
stevendaryl said:then why would theory specifically describe probabilities for results of measurements, and not describe other sorts of interactions.
I didn't say that reality is a certain way because of science. I only said that a scientific theory needs to be falsifiable. It's the idea that a good theory has to be more than that that's wishful thinking. QM is a perfectly fine generalized probability theory, but people are still looking for ways to interpret it as a description of a universe, presumably because they really want QM to be a description of a universe.stevendaryl said:To me, that seems kind of weird reasoning, to say such and such must be true, because otherwise, we would have a hard time doing science. The world isn't required to accommodate our needs.
The theory has to assign probabilities to something that people can think of as "results", in order to be falsifiable. (A "theory" that doesn't do that isn't a theory). Some interactions produce "results", and some don't. OK, strictly speaking, none of them does, but some interactions produce states that are for practical purposes indistinguishable from classical superpositions. This is the sort of interaction I have in mind when I (somewhat sloppily) say that some interactions produce results. The ones that do can be considered measurements. So in that specific sense, measurements are "special", but they're not fundamentally different. We just put the "measurement" label on those interactions that are the most useful when we test the theory.stevendaryl said:If measurement is not special, then why would theory specifically describe probabilities for results of measurements, and not describe other sorts of interactions.
Fredrik said:Right, these theories describe fictional universes with properties in common with our own. (If you prefer, they are approximate descriptions of our universe). But when you think about what a theory must be like in order to be falsifiable, you see that it doesn't need to describe a universe. It just needs to assign probabilities to possible results of measurements.
Fredrik said:Yes, but there's no need to, if you just stop thinking of QM as a theory of the first kind, and accept that it's a theory of the second kind. The problem that you're referring to, and all the other "problems" with QM, are consequences of the unnecessary assumption that I'm rejecting.
To clarify: The unnecessary assumption is the identification of pure states with possible configurations of the system. This assumption takes a theory of the second kind (an assignment of probabilities) and pretends that it's a theory of the first kind (a description). And the result is a disaster. Suddenly we have a "measurement problem", and a need to be able to associate a pure state with the universe. This leads inevitably to many worlds. (As I mentioned in a previous post, I don't think we can avoid many worlds by adding a collapse axiom. That just makes everything even worse).
Fredrik said:All we have to do is to say which measuring device is supposed to tell us the result of the experiment. I wouldn't describe this as a classical/quantum cut.
Fredrik said:If what you mean by a classical realm is something like semi-stable records of the results of certain interactions, then yes. If you mean something truly classical, then no.
vanhees71 said:The only difference between classical physics and quantum physics is that in classical physics all observables always have definite values, be they known or unknown to a physicist, while in quantum theory any observables can have a definite value or not, depending on how the system was prepared. It's of course a bit unintuitive in the beginning of learning quantum theory that observables can be indetermined, but that's how Nature is.
Jilang said:Thanks. Would it be fair to say that the record made was non-reversible then?
Nugatory said:It describes probabilities that particular states will be reached after an interaction. Those states that are especially useful to us, we call "measurement results".
vanhees71 said:Within the minimal interpretation, there is no problem, because you take the Born interpretation of states really seriously, i.e., before Alice's measurement the spin-z component of both the electron and the positron were (even maximally) undetermined, but due to the preparation in an entangled state, the correlations are already implemented when the electron-positron pair were prepared. Of course, such a thing is not describable with local deterministic hidden-variable theories, and as long as nobody finds a consistent non-local deterministic theory which is as successful as QT, I stick to (minimally interpreted) QT :-).
stevendaryl said:So the probability distribution is "entangled".
Fredrik said:I didn't say that reality is a certain way because of science. I only said that a scientific theory needs to be falsifiable. It's the idea that a good theory has to be more than that that's wishful thinking.
vanhees71 said:(I think, the assumption of a spontaneous collapse, which is outside of the dynamics of quantum theory is inconsistent with Einstein causality as is a "cut" between a quantum and a classical world; everything is quantum, the appearance of a classical behavior is due to a coarse grained observation of macroscopic observables of objects of macroscopic scales and well-understood from quantum-many body theory). If you assume that it's Alice's measurement which causes Bob's positron to spontaneously get a determined spin-z component, you indeed violate Einstein causality, because no signal can travel faster with the speed of light to make Bob's spin determined although initially it was completely indetermined. Within the minimal interpretation, there is no problem, because you take the Born interpretation of states really seriously, i.e., before Alice's measurement the spin-z component of both the electron and the positron were (even maximally) undetermined, but due to the preparation in an entangled state, the correlations are already implemented when the electron-positron pair were prepared. Of course, such a thing is not describable with local deterministic hidden-variable theories, and as long as nobody finds a consistent non-local deterministic theory which is as successful as QT, I stick to (minimally interpreted) QT :-).
bhobba said:Standard provability theory does not exhibit entanglement - it fact QM's ability to do that is what distinguishes it from probability theory:
http://arxiv.org/pdf/0911.0695v1.pdf
Thanks
Bill
stevendaryl said:I believe that the use of the word "entangled" in QM is such that it always means a composite state that cannot be factored into a product of component states.
bhobba said:Standard proability theory does not exhibit entanglement - it fact QM's ability to do that is what distinguishes it from probability theory:
http://arxiv.org/pdf/0911.0695v1.pdf
Thanks
Bill
We call the pure state entangled if it is not a product state.
It would be wishful thinking to believe that science can find all the answers, but I haven't advocated that view. There's no wishful thinking involved in thinking that QM makes very accurate predictions about results of experiments, or in explaining what a theory must do in order to be falsifiable. But there's wishful thinking involved in thinking that QM must be "more than that" (in the sense discussed above). It doesn't bother me that people are interested in exploring that option too, but it should be viewed as a long shot.stevendaryl said:You are making the distinction between science as a means of making predictions, and science as something more than that. You're calling the second "wishful thinking". But both are wishful thinking, in the sense that there is no necessary reason for nature to be humanly comprehensible, or predictable, at all.
Fredrik said:It would be wishful thinking to believe that science can find all the answers, but I haven't advocated that view. There's no wishful thinking involved in thinking that QM makes very accurate predictions about results of experiments, or in explaining what a theory must do in order to be falsifiable. But there's wishful thinking involved in thinking that QM must be "more than that" (in the sense discussed above). It doesn't bother me that people are interested in exploring that option too, but it should be viewed as a long shot.
stevendaryl said:But using the word "wishful thinking" is just not helpful. Given any unsolved problem, it's wishful thinking to a certain extent to believe that we will ever solve it. So whether something is wishful thinking is not much of a guide to what we should be working on in science.
I assume that what you mean by "everything is quantum" is that every physical system is such that a pure state (a mathematical thing) can represent what you previously called the system's "real state" (a real-world thing). Since the universe is a physical system, it follows that we can assign a state to the universe. But to me, "everything is quantum" just means that there's no experiment in which QM will not work, and that doesn't imply that we can assign a state to the universe.atyy said:If everything is quantum and there is only unitary evolution, then there would be unitary evolution of the wave function of the universe.
If someone who advocates a minimal interpretation disagrees with this, it's not because they're making some huge assumption. It's because they disagree with you about the meaning of concepts like "collapse" or "classical/quantum cut", as I did above.atyy said:The "minimal interpretation" without collapse and without a classical quantum cut is not minimal - it is making a huge claim - that the unitary evolution of the wave function of the universe makes sense. If this were true, the minimal interpretation would have solved the problem that the many-worlds approach investigates.