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Fundamental notions of QM have to do with observation, a major example being The Uncertainty Principle.

  1. What is the technical definition of an observation/measurement?

  2. If I look at a QM system, it will collapse. But how is that any different from a bunch of matter "looking" at the same system?

  3. Can the system tell the difference between a person's eyes and the bunch of matter?

  4. If not, how can the system remain QM?

  5. Am I on the right track?

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This is a very broad question, with overlap with other questions. You should look at the Heisenberg Pieirls analysis of tracks in a bubble chamber to understand the entanglement apparent collapse of a wavefunction, and then the philosophical problem of turning apparent collapse (decoherence) into collapse, and whether this is philosophy or not. There is no simple answer, and it is hard to not refer you to other questions on the site (although precisely which ones, I can't really be sure without more detail on what you are asking, like a thought experiment) –  Ron Maimon Nov 4 '12 at 4:54
    
Related: physics.stackexchange.com/q/1353/2451 –  Qmechanic Nov 4 '12 at 16:51
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For additional research, you should review and dig into the Mott problem and its resolution. Note that there is link to spontaneous symmetry breaking in the article. –  Hal Swyers Nov 5 '12 at 14:24
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6 Answers 6

up vote 7 down vote accepted

An observation is an act by which one finds some information – the value of a physical observable (quantity). Observables are associated with linear Hermitian operators.

The previous sentences tautologically imply that an observation is what "collapses" the wave function. The "collapse" of the wave function isn't a material process in any classical sense much like the wave function itself is neither a quantum observable nor a classical wave; the wave function is the quantum generalization of a probabilistic distribution and its "collapse" is a change of our knowledge – probabilistic distribution for various options – and the first sentence exactly says that the observation is what makes our knowledge more complete or sharper.

(That's also why the collapse may proceed faster than light without violating any rules of relativity; what's collapsing is a gedanken object, a probabilistic distribution, living in someone's mind, not a material object, so it may change instantaneously.)

Now, you may want to ask how one determines whether a physical process found some information about the value of an observable. My treatment suggests that whether the observation has occurred is a "subjective" question. It suggests it because this is exactly how Nature works. There are conditions for conceivable "consistent histories" which constrain what questions about "observations" one may be asking but they don't "force" the observer, whoever or whatever it is, to ask such questions.

That's why one isn't "forced" to "collapse" the wave function at any point. For example, a cat in the box may think that it observes something else. But an external observer hasn't observed the cat yet, so he may continue to describe it as a linear superposition of macroscopically distinct states. In fact, he is recommended to do so as long as possible because the macroscopically distinct states still have a chance to "recohere" and "interfere" and change the predictions. A premature "collapse" is always a source of mistakes. According to the cat, some observation has already taken place but according to the more careful external observer, it has not. It's an example of a situation showing that the "collapse" is a subjective process – it depends on the subject.

Because of the consistency condition, one may effectively observe only quantities that have "decohered" and imprinted the information about themselves into many degrees of freedom of the environment. But one is never "forced" to admit that there has been a collapse. If you are trying to find a mechanism or exact rule about the moments when a collapse occurs, you won't find anything because there isn't any objective rule or any objective collapse, for that matter. Whether a collapse occurred is always a subjective matter because what's collapsing is subjective, too: it's the wave function that encodes the observer's knowledge about the physical system. The wave function is a quantum, complex-number-powered generalization of probabilistic distributions in classical physics – and both of them encode the probabilistic knowledge of an observer. There are no gears and wheels inside the wave function; the probabilistic subjective knowledge is the fundamental information that the laws of Nature – quantum mechanical laws – deal with.

In a few days, I will write a blog entry about the fundamentally subjective nature of the observation in QM:

http://motls.blogspot.com/2012/11/why-subjective-quantum-mechanics-allows.html?m=1

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''My treatment suggests that whether the observation has occurred is a "subjective" question.'' - If this were really true, one still had to explain why we get objective science out of our subjective measurements. Therefore, there may not be more subjectivity than is in the error bars. –  Arnold Neumaier Nov 4 '12 at 15:37
    
No, Arnold, your question is very correct but the way how you reply to it is completely unscientific. You haven't tried to solve the exercise at all; instead, you decided to humiliate it. Indeed, one may also show why objective science emerges from quantum mechanics and the proof goes through - it requires some QM-type maths. But the proof does not assume that some information about the state of world at a given moment is objective because this is, according to QM, not true! –  Luboš Motl Nov 5 '12 at 7:15
    
-1: The state of an ideal quantum gas in equilibrium is objectively determined, to an accuracy of the square root of the inverse volume, by the measurable numbers P, T, and V. If it were otherwise, objective physics were impossible. –  Arnold Neumaier Nov 5 '12 at 9:44
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I am fairly certain that agreement of outcomes of joint observations are part of the point that is being made above. Entanglement will ensure agreement of joint observables. However each system will have information that can never be observed jointly. There is no inconsistency in saying that those states continue to evolve within their respective systems as long as the probability of joint measurement is effectively zero (or in fact effectively negative). This is captured in the use of complex amplitudes which can track the evolution of unphysical states. –  Hal Swyers Nov 6 '12 at 14:18
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Another way of thinking about this is that if you dream about observing a particle track, there is nothing wrong with someone saying the track did something different from what you dream, since there is no possible way for them to make an observation of what you dreamed. –  Hal Swyers Nov 6 '12 at 14:21
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Let me take a slightly more "pop science" approach to this than Luboš, though I'm basically saying the same thing.

Suppose you have some system in a superposition of states: a spin in a mix of up/down states is probably the simplest example. If we "measure" the spin by allowing some other particle to interact with it we end up with our original spin and the measuring particle in an entangled state, and we still have a superposition of states. So this isn't an observation and hasn't collapsed the wavefunction.

Now suppose we "measure" the spin by allowing a graduate student to interact with it. In principle we end up with our original spin and the graduate student in an entangled state, and we still have a superposition of states. However experience tells us that macrospcopic objects like graduate students and Schrodinger's cat don't exist in superposed states so the system collapses to a single state and this does constitute an observation.

The difference is the size of the "measuring device", or more specifically its number of degrees of freedom. Somewhere between a particle and a graduate student the measuring device gets big enough that we see a collapse. This process is described by a theory called decoherence (warning: that Wikipedia article is pretty hard going!). The general idea is that any system inevitably interacts with its environment, i.e. the rest of the universe, and the bigger the system the faster the interaction. In principle when our grad student measures the spin they do form an entangled system in a superposition of states, but the interaction with the rest of the universe is so fast that the system collapses into a single state effectively instantaneously.

So observation isn't some spooky phenomenon that requires intelligence. It is simply related to the complexity of the system interacting with our target wavefunction.

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Dear Johm, right, I agree we're saying pretty much the same thing. Still, I would probably stress that decoherence is just an approximate emergent description of the quantum evolution of systems interacting with the environment. Even if the density matrix for the observed system gets almost diagonal, it doesn't mean that one is "forced to imagine" that the system has already "objectively chosen" one of the states on the diagonal. Instead, one is only allowed to say such a thing because it no longer leads to contradictions. –  Luboš Motl Nov 4 '12 at 9:08
    
So, for a wavefunction to collapse it need only be able to interact with the rest of the universe? If so, I'm slightly confused. How can the wavefunction know when it has interacted with the "rest of the Universe"? When it is observed by the grad student, can't the student and in the room in which observation has taken place be taken as the rest of the Universe? –  ThisIsNotAnId Nov 7 '12 at 2:42
    
The phrase "the rest of the universe" just means everything that isn't part of the system being studied, so the grad student does count as "the rest of the universe". Have a read of the Wikipedia article I linked and see if that helps. –  John Rennie Nov 7 '12 at 6:58
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  1. A measurement is a special kind of quantum process involving a system and a measurement apparatus and that satisfies the von Neumann & Lüders projection postulate. This is one of the basic postulates of orthodox QM and says that immediately after measurement the system is in a quantum state (eigenstate) corresponding to the measured value (eigenvalue) of the observable.

  2. Measurement does not change by considering the pair system+apparatus or by considering the triple system+apparatus+observer, because the fundamental interaction happens between system and measurement apparatus, and the observer can be considered part of the environment that surrounds both. This is the reason why measuring apparatus give the same value when you are in the lab during the measurement that when you are in the cafeteria during the measurement.

  3. See 2.

  4. The system is always QM.

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''No elementary quantum phenomenon is a phenomenon until it is a registered ('observed', 'indelibly recorded') phenomenon, brought to a close' by 'an irreversible act of amplification'.'' (W.A. Miller and J.A. Wheeler, 1983, http://www.worldscientific.com/doi/abs/10.1142/9789812819895_0008 )

  1. A measurement is an influence of a system on a measurement device that leaves there an irreversible record whose measured value is strongly correlated with the quantity measured. Irreversibility must be valid not forever but at least long enough that (at least in principle) the value can be recorded.

  2. There is no difference.

  3. The system doesn't care. It interacts with the measurement device, while you are just reading that device.

  4. Quantum interactions continue both before, during and after the measurement. Only the reading from the device must be treated in a macroscopic approximation, through statistical mechanics. See, e.g., Balian's paper http://arxiv.org/abs/quant-ph/0702135

  5. Which track are you on?

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Well, except that irreversibility is always a subjective matter. Many subjects may agree it's irreversible for them but in principle, the situation is always reversible and an agent tracing the "irreversible" phenomena exponentially accurately could do it. –  Luboš Motl Nov 5 '12 at 7:18
    
@LubošMotl: The resuts of statistical mechanics resulting in equilibrium and nonequilibrium thermodynamics are extremely well established, and show that there is nothing subjective at all in irreversibility. We observe it every moment when we look at fluid flow of water or air. - If the basic laws are in principle reversible this has no bearing on the real universe as it is impossible in principle that an observer inside the universe can reverse the universe. The real universe as_observed_by_objects_inside is irreversible, and measurements are permanent records for these observers. –  Arnold Neumaier Nov 5 '12 at 9:42
    
The only problem with your assertion is that in the quantum framework, measurements and other "records" are subjective as well. Many people may agree about them, and they usually do, but in principle, others may disagree. The gedanken experiment known as Wigner's friend illustrates this clearly. A friend chosen in a box may "know" that some record of a measurement is already there and became a fact, but the physicist outside the box may choose a superior treatment and describe the physicist inside by linear superpositions of macro-different states. –  Luboš Motl Nov 5 '12 at 10:11
    
Irreversibility in Nature is never perfect, it's always a matter of approximations, and there's no objective threshold at which one could say that "now it's really irreversible". With a good enough knowledge of the velocities and positions, one may reverse some evolution and prepare a state whose entropy will decrease for a while. It's exponentially difficult but not impossible in principle. The same thing with decoherence. If one traces environmental degrees of freedom, and in principle he can, he may reverse certain amounts of decoherence, too. Decoherence is very fast but never perfect. –  Luboš Motl Nov 5 '12 at 10:13
    
@LubošMotl: ''Irreversibility in Nature is never perfect'' - only according to an idealized theoretical model that assumes (against better knowledge) that one can change something without having to observe the required information and without having to set up the corresponding forces that accomplish the change. This can be done in principle only for very small or very weakly coupled systems. –  Arnold Neumaier Nov 5 '12 at 12:25
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What is the technical definition of an observation/measurement?

A QM measurement is essentially a filter. Observables are represented by operators $\smash {\hat O}$, states or wave functions by (linear superpositions of) eigenstates of these operators, $|\,\psi_1\rangle, |\,\psi_2\rangle, \ldots$. In a measurement, you apply a projection operator $P_n$ to your state, and check if there is a non-zero component left. You ascertain you yourself that the system is now in the eigenstate $n$. Experimentally, you often send particles through a "filter", and check if something is left. Think of the Stern-Gerlach experiment. Particles that come out in the upper ray have spin $S_z = +\hbar/2$. We say we have measured their spin, but we have actually $prepared$ their spin. Their state now fulfils $\smash{\hat S} \,|\,\psi\rangle = +\hbar/2 \,|\,\psi\rangle$, so it is the spin-up eigenstate of $\smash{\hat S}$. This is physical and works even if no one is around.

If I look at a QM system, it will collapse. But how is that any different from a bunch of matter "looking" at the same system? Can the system tell the difference between a person's eyes and the bunch of matter?

There are two different things going on, knowledge update (subjective), and decoherence (objective).

First the objective part: If you have a quantum system by itself, it's wave function will evolve unitarily, like a spherical wave for example. If you put it in a physical environment, it will have many interactions with the environment, and its behavior will approach the classical limit.

Think of the Mott experiment for a very simple example: Your particle may start as a spherical wave, but once it hits a particle, it will be localized, and have a definite momentum (within $\Delta p \,\Delta x \geq \hbar/2$). That's part of the definition of "hits a particle". The evolution will then continue from there, and it is very improbable that the particle has the next collision in the other half of the chamber. Rather, it will follow its classical track.

Now the subjective part: If you look at a system, and recognize that it has certain properties (e.g. is in a certain eigenstate), you update your knowledge and use a new expression for the system. This is simple, and not magical at all. There is no change in the physical system in this part; a different observer could have different knowledge and thus a different expression. This subjective uncertainty is described by density matrices.

Sidenote on density matrices:

A density matrix says you think the system is with probability $p_1$ in the pure state $|\,\psi_1\rangle$, with probability $p_2$ in the pure state $|\,\psi_2\rangle$, and so on. (A pure state is one of the states defined above and can be a superposition of eigenstates, where as a mixed state is one given by a density matrix.)

Pure states are objective, if I have a bunch of spin-up particles from my Stern-Gerlach experiment, my colleague will have to agree that they are spin-up, no matter what. They all go in his experiment to the top, too. If I have a bunch of undetermined-spin particles, $$|\,\psi\rangle_\mathrm{undet.} = \frac{1}{\sqrt{2}} (|\,\psi_\uparrow\rangle + |\,\psi_\downarrow\rangle)\,,$$ they will turn out 50/50, for both of us.

Mixed states are different. My particles could be all spin-up, but I don't know that. Someone else does, and he uses a different state to describe them (e.g. see this question). If I see them fly through a magnetic field, I can recognize their behavior, and use a new state, too.

And note that a mixed state of 50% $|\,\psi_\uparrow\rangle$ and 50% $|\,\psi_\uparrow\rangle$ is not the same as the pure state $|\,\psi\rangle_\mathrm{undet.}$ defined above.

If not, how can the system remain QM?

Technically, it remains QM all the time (because classical behavior is a limit of QM, and physics always has to obey QM uncertainties). Of course, that's not what you mean. If a system is to stay in a nice, clean quantum state for a prolonged time, it helps that it is isolated. If you have some interaction with the environment, it will not neccessarily completely decohere and become classical, but a perfect QM description will become impractically complicated, as you would have to take the environment and the apparatus into account quantum mechanically.

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First, wow really nice reply. Thanks! If I read correctly, are you saying that a QM system can decohere differently for different observers? If so, what is the limit to this subjectivity? For example, can two observers view a particle going in opposite directions at the same time? –  ThisIsNotAnId Feb 3 '13 at 0:18
    
As far as I understand, decoherence is objective, so no, two observers can't disagree. They can disagree over wheter a system is in a pure or a mixed state. Maybe my use of 'observer' is confusing here. I don't mean something deep like different frames of reference, just that different people (experimentators) have different incomplete knowlege, and that is expressed through their density operators / mixed states. Its like statistical mechanics, but QM. –  jdm Feb 3 '13 at 12:32
    
That clears things up nicely, thanks! –  ThisIsNotAnId Feb 6 '13 at 23:35
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Nothing exists until it is measured and observed.

the Copenhagen consensus

Everything in this universe universally obeys the Schrodinger equation. There's no special measurement objective collapse.

So, there are no measurements. There are no observers either. Ergo, nothing exists. The false assumption nearly everyone makes is something exists.

Can you prove something exists? You can't!

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protected by Qmechanic Jan 30 '13 at 8:19

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