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We've learned that the wave function of a particle collapses when we measure a particle's location. If it is found, it becomes more probable to find it a again in the same area, and if not the probability to finding it in the place that was checked decreases dramatically.

My question is about the definition of measurement. What makes a measurement different from any other interaction between two particles (gravity and EM fields for example)?

In reality, almost every particle interacts with any other particle, so shouldn't there be constant collapse of the wave function all the time? If this happens we're right back in classical mechanics, aren't we?

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Reading about Rydberg Atoms may help you understand how different quantum states are produced experimentally. In order to produce a quantum state that has a probability function that is diffuse spatially or in terms of energy it is often necessary to limit it's interaction to the outside world to a large degree. The measurement is preformed between these diffuse states and some probe which is produced to have a well defined quantum states. –  Davorak Nov 2 '10 at 22:45
I have heard that wavefunction collapse is just a symptom of an incomplete theory, and if you consider the detector along with the particle as a composite quantum system, the "collapse" turns out to be just decoherence, which is a fully sensible process. But I don't know enough about that area of research to say anything more definitive. –  David Z Nov 15 '10 at 5:07
By the way, in quantum field theory, gravity and EM interactions are also represented by particles (or at least they have as much right to be called particles as the things you normally think of as being particles). So I think any interaction can be thought of as a measurement and vice-versa, but again, I'm not completely clear on the details of the interpretation. –  David Z Nov 15 '10 at 5:10
And (sorry to keep commenting), I wondering about the [epistemiology] tag - it feels like [philosophy] under a different name, and I've already stated my objections to the latter. Make no mistake, I like this question, I'm just not quite sure what the proper tag for the "interpretation" aspect of it is. (I'm not going to retag it, I just wanted to mention my thought) –  David Z Nov 15 '10 at 5:18
@DavidZaslavsky Only amplifications count as measurements. –  joseph f. johnson Dec 18 '11 at 5:35

10 Answers 10

up vote 15 down vote accepted

What you describe in your question is the "Copenhagen interpretation" of quantum mechanics. There are more nuanced views of this nowadays that don't treat "measurements" quite so asymmetrically, see e.g. sources that talk about decoherence.

I recommend watching the classic lecture "Quantum Mechanics in your face" by Sidney Coleman for a nice take on this sort of thing.

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Penrose suggests (controversially) that decoherence could happen when gravity becomes a relevant force. It could be verified by experiment but such experiments are at the limit of what we can currently do. –  Ebenezer Sklivvze Nov 3 '10 at 13:36
@Skliwz: Decoherence obviously can happen when gravity becomes relevant. Decoherence should happen in any interpretation of QM. The controversial aspect is that he suggests that objective wave function collapse happens precisely when gravity becomes relevant. –  wnoise Apr 4 '11 at 16:06
I finally had the time to watch the Sidney Coleman lecture. Although I didn't understand everything - it's great and provided good insights regarding this question. Highly recommended. (wish there was a youtube link because that player sucks) –  Uri May 8 '11 at 18:54
I watched the Coleman lecture. It doesn't seem to me to address the OP's question. Coleman sets out to prove that quantum mechanics isn't classical mechanics. That's true, but it has very little to do with the OP's question, which is about the Copenhagen interpretation. Coleman discusses the CI only obliquely, and only at the very beginning and end of the talk. –  Ben Crowell Nov 5 '12 at 3:30

Interactions merely involve a correlation developing. For example, if an electron is put through a Stern-Gerlach apparatus, a correlation develops between the distance travelled in the x direction and the distance deviated in the y direction. It is reversible. The measurement which occurs when the particle hits the photographic plate is irreversible. It is associated with irreversible dissipation, i.e. entropy generation.
This approximation can itself be dissected further, but it gets very tricky.

A really good (1983) book is by Wheeler and Zurek, "The quantum theory of measurement" available as a djvu file at http://www.4shared.com/get/vw66Qp70/Wheeler_JA_Zurek_WH_eds_Quan.html (8 MB, wait 30 sec for the download). [Now if I can only figure out how to work a reader for a Mac ...]

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+1 for Wheeler and Zurek. For Mac OSX try djvu.sourceforge.net/djview4.html –  j.c. Nov 5 '10 at 14:50
I just want to add a comment in support of this answer. Measurements are absolutely not related to physics other than ordinary unitary quantum evolution, and in particular there is no such process as nonunitary wavefunction collapse. Decoherence is the key. –  Matt Reece Nov 12 '10 at 23:28

Much has been covered in these answers, but one aspect has been left out. The actual physics going on in any measurement process includes amplification. Feynman thought this was significant. Here is a perhaps little-known quotation of his:

We and our measuring instruments are part of nature and so are, in principle, described by an amplitude function [the wave function] satisfying a deterministic equation [Schrodinger's equation]. Why can we only predict the probability that a given experiment will lead to a definite result? From what does the uncertainty arise? Almost without a doubt it arises from the need to amplify the effects of single atomic events to such a level that they may be readily observed by large systems.

\dots In what way is only the probability of a future event accessible to us, whereas the certainty of a past event can often apparently be asserted? \dots Obviously, we are again involved in the consequences of the large size of ouselves and of our measuring equipment. The usual separation of observer and observed which is now needed in analyzing measurements in quantum mechanics should not really be necessary, or at least should be even more thoroughly analyzed. What seems to be needed is the statistical mechanics of amplifying apparatus.

R. Feynman and A. Hibbs, Quantum Mechanics and Path Integrals, New York, 1965, p. 22.

This is quoted and discussed in my The Axiomatisation of Physics, see http://www.mast.queensu.ca/~jjohnson/HilbertSixth.pdf and http://arxiv.org/abs/0705.2554

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Much of how you answer this question comes down to your view of the wavefunction or state. If you think that the quantum state is a state of reality (that is, an ontic state), then you must either reproduce the predictions of orthodox (Copenhagen) QM without the measurement postulate or you must explain why nature provides two forms of evolution. The former view is basically the Many Worlds Interpretation, which I feel a great degree of attraction to, as it postulates only unitary evolution, and explains measurement as being an emergent, rather than fundamental, effect.

On the other hand, if you hold that the wavefunction is a state of knowledge (epistemic) about some other underlying ontic state, then measurement collapse represents not a true evolution, but a discontinuous change in your knowledge about a system. Alternative formulations of quantum mechanics, such as Bohmian mechanics, explain this in a mathematically rigorous way, but that some find unsatisfying.

Each of these approaches (and the many more I didn't mention) suggests where to look for the next physical theory, and so the question should eventually be experimentally decidable. For now, though, we must rely on mathematics, physical intuition and rational argument.

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Both explanations that you give seem to only rename the problem, without addressing it. In the many worlds interpretation, why are we perceiving only one of the possible outcomes of a measurement and why that particular one? In the other approach, how do you define knowledge? –  Ebenezer Sklivvze Nov 3 '10 at 13:55
We're only perceiving one of the outcomes because only one of the outcomes exists in the universe 'we' inhabit. Another version of us exists in another universe, and that one gets a different outcome. –  Grant Crofton Nov 12 '10 at 17:33

It is the case that all measurements proceed via the exploitation of the natural interactions that we understand theoretically. But once the measurement is completed and the result in hand, the QM analysis of the subsequent evolution of just those systems that yielded that particular result can no longer employ the original state function (which allows for all the different possible results), but must then employ just that part of the original state function that corresponds to the particular result. This 'sudden' change in the state function used is called state function collapse. Many physicists regard this change as corresponding to nothing more than the change in the experimenter's knowledge once the result is in hand. This is the epistemological interpretation of the state function. But many regard the change as also reflecting a genuine physical change in the state of those systems that came through the measurement yielding the particular result. This is the ontological interpretation of the state function and it has many variations. Still many others hold an ontological interpretation of the state function while denying that collapse happens at all.

These latter views, which also have many versions, have given rise to various interpretations of and/or alternatives to QM that go by names such as Pilot wave, deBroglie-Bohm, Modal interpretations, Relative state, Many Worlds, Many Minds, Consistent Histories, Decoherence theoretic, Information theoretic etc. Collectively these are all called NO-Collapse theories.

The champions of real, physical collapse have also been at work creating alternative theories of their own that replace the collapse postulate by evolutions that generate collapse dynamically. These theories go by the names of their authors, Ghirardi-Rimini-Weber-Pearl, Karolahazy, Penrose, Gisin, Percival, etc. Collectively these are the Collapse theories.

The difficulty in deciding among these many and still proliferating alternatives is due to the incredible success of standard QM. All the alternatives must, at least, reproduce the corroborated results of QM while possibly allowing for deviations in, as yet, untested waters. Some of them offer no deviations from QM, whatsoever! So deciding between them and QM must be a matter of philosophy or aesthetics. In any case, the days of the hegemony of the Copenhagen interpretation, if they ever really existed, are gone forever.

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You talk about QM interpretations as if they were not QM :-)) –  Anixx Feb 20 '11 at 13:37

There is no clearly definable distinction between measurement and any other process. This is one of the reasons why (a) the distinction only occurs in the Copenhagen interpretation (CI), and (b) the CI is only an interpretation, not a theory that makes predictions different from those of other interpretations of quantum mechanics. Another reason why the CI clearly can't be taken as a physical theory is that it treats time in a manner that violates time-reversal symmetry, whereas CPT is a perfect symmetry of the actual quantum-mechanical theory.

What makes the Copenhagen interpretation useful is that it accurately describes the psychological experience of making a measurement. Similarly, we don't expect Maxwell's equations to explain the rules of color mixing; this is because the rules of color mixing are psychological, not physical -- they have to do with the fact that we've evolved as trichromats. That doesn't mean the rules of color mixing aren't useful. They're very useful.

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very nice answer, such nice analogy at the end too. +1 I really wish you'd write more on this with your answer :(( –  user929304 Dec 10 at 12:36

This is a question that philosophers of physics try to answer now, not physicists (even if most of the times the border is not really sharp). So if you are looking for a more detailed discussion (and ressources), you should have a look at this article of the Stanford Encyclopedia of Philosophy: http://plato.stanford.edu/entries/qt-measurement/

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There is a problem with the literature of philsophy--- its mechanisms of peer review are not moderated by neither experimental input nor rigorous proof, so the methods of evaluation are entirely political. The history of thought does not suggest that political competition of ideas without external moderation using experiments or rigor can ever be successful. –  Ron Maimon Aug 15 '11 at 5:28

It seems that this question is regarding Copenhagen interpretation (and other related interpretations with collapse and one observer) solely, because it uses the term "measurement" which has no special position in other interpretations.

So assuming this is about the Copenhagen interpretation, yes, the measurement is different from any other interaction. The difference is in that the quantum system interacts with the observer, a person who has special physical properties of having ability to trigger the wave function collapse. There is only one such person and the QM provides the theoretical possibility to unambiguously determine who is it based on his special abilities of interacting with matter.

This constitutes the main problem of Copenhagen interpretation, and the reason why other interpretations were proposed (Relational, MWI) which are observer-agnostic, do not include special, chosen personalities and symmetric across all people. This does not mean however that still there should not be a person apparently having special properties at least in the observable universe.

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The agent doesn't have to be a person--- it's a sort of disembodied consciousness, and it could even be a collective. This doesn't have any bearing on the issue of whether consciousness is computation because a computer interacting with a quantum system is just as mysterious as a person collapsing the wavefunction. A computer can't compute in quantum mechanics without doing a measurement at the end to see what was computed. If we think the computer somehow has a "sense" of what its memory is, this leads to a collapse of the wavefunction relative to this sense. –  Ron Maimon Aug 15 '11 at 5:26
What you said is secondary to the fact that there is only one special observer. Yes, a computer makes measurements and a collapse of a wave function, so does a collective of researches but in both cases only because they are thermodynamically (through the environment) are connected to the distinguished observer. A properly isolated computing device (called a quantum computer) does not make measurements in the same sense as classical computer does and does not trigger a collapse. A properly isolated physicist is probably quite impossible because proper isolation means near-zero temperature. –  Anixx Mar 25 '12 at 23:48

The measurement happens at the end of time for our universe as a collapse in the form of post-selection as in the two-state formalism. Read the papers by Aharonov and Vaidman for more details. There is a theorem in quantum mechanics to the effect that we can always push the measurement collapse into the future without any observable consequences.

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The short answer is that measurement and interactions are two different animals in Quantum Mechanics. In reality measurements are performed using one of the fundamental interactions (usually EM), but this does not enter the framework of QM.

The long answer is that you will not receive a satisfying answer to your question. First, because physicists don't know the answer, and second, because physicists don't care.

Physics is concerned with understanding nature, in so far as making predictions regarding measurements. If we have a theory of what happens between measurements (things like Lagrangians and forces) and a theory of measurements (a postulate in Quantum Mechanics that wave functions collapse, plus the probabilistic interpretation of the abs.square of the wave function), and this framework works to the desired accuracy, then the philosophical implications of trying to unite the two are of no interest to physicists, unless they bring about a deeper understanding of nature, in so far as making more precise or more general predictions regarding measurements.

In practice, the line of questioning you pose has been investigated ever since the advent of Quantum Mechanics, but to my knowledge, nothing ever came of it regarding unification of forces and measurements ("don't know"), so the mainstream has lost interest a long time ago ("don't care"). (As an interesting side-note, one important result to come out of related type of inquiry is the Bell inequality.)

Sorry if this answer seems negative. To quote David Mermin [corrected] regarding the philosophical issues regarding Quantum Mechanics, the pragmatic thing to do is to "shut up and calculate!"

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I strongly disagree that physicists don't care. The whole field of of quantum foundations is based on trying to answer this and other questions about quantum mechanics. QF is a rich field of study that gives us clues as to what the next theory should look like and how we should expect to go about finding it. –  Chris Granade Nov 3 '10 at 13:21
Let me add that the quote you ascribe to Feynman is actually due to David Mermin en.wikiquote.org/wiki/David_Mermin –  j.c. Nov 3 '10 at 14:02
Thanks for the correction. –  mtrencseni Nov 4 '10 at 17:15
I think this answer is unduly negative with respect to the foundations of quantum mechanics. While physicists "don't know" still is an apt description of the various interpretations of QM, some classes of them i.e. using local hidden variables have been ruled out experimentally beginning with Alain Aspect in the 1980s. The fact that anyone would go to such trouble very much reveals the lie to your assertion that mainstream physicists "don't care". –  user756 May 17 '12 at 4:28

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