Tag: quantum

Wigner’s Friend

If we define both the observer and the “observed” as both being part of say an even bigger system, would the wave function still collapse in this system?

This conundrum is known as the Wigner’s Friend problem, though it is also often asked with reference to Schrodinger’s cat.

In my opinion its best resolution is in the understanding that the wave function or quantum state is not a property of the system itself but of its relationship to an observer, and I think this view is a better reading of what Hugh Everett was describing in his “Relative State” interpretation of quantum mechanics [which was re-presented later (mostly by others) as a “Many Worlds” interpretation where observations (and other interactions) continually cause the creation of new “branches” (in a way that Everett himself apparently once described as “bullshit” in a marginal note on someone else’s elaboration of the MWI)].

Source: (1001) Alan Cooper’s answer to Is the collapse of the wave function in Quantum Physics based on a system frame of reference? If we define both the observer and the ‘observed’ as both being part of say an even bigger system, would the wave function still collapse in this system? – Quora

Is observation required for collapse? 

Whether or not observation is the only way in which a wave function can collapse depends on what you mean by “collapse”, and that word is used by various people in reference to different aspects of the measurement and observation process – which can be considered as happening in two stages.

The setting involves a system in a pure quantum state which may have been prepared as an eigenstate of some observable (such as spin relative to a particular direction), and so is a nontrivial superposition of eigenstates of some other observable (such as spin relative to a different axis) which we now want to measure.

In the first stage, the system of interest interacts with a larger more complex system which is not fully known and so is in a statistical mixture of pure states (represented by a density matrix rather than a single state vector). If the larger system is suitably designed as a measuring apparatus, then the interaction leads to the state of the combined system approaching a statistical mixture of states in which the subsystem of interest is in an eigenstate of the observable and the measurement apparatus is in a related state which involves some macroscopic feature (such as a pointer, a readout panel, or a bright spot on a phosphor screen) which has a corresponding humanly visible value. Henceforth the system acts as if it is in just one eigenstate which is not yet known but is subject to classical probabilities. This process eliminates the possibility of future interference between the eigenstates that was possible while the state of the system was in a pure state (represented by a coherent wave function) and so is often called “decoherence”; and since it reduces the system to being effectively in just one eigenstate it is often identified with “collapse of the wave function”. It actually happens in almost any interaction with a complex system (even when there is no humanly visible related macroscopic property of the system). So, for those who identify decoherence as collapse, it is indeed possible for collapse to occur without observation.

But after this kind of “collapse” we still don’t know what the measured value actually is, even though we can think of it as having just one of several precise values – each with some known probability.

The second stage of the observation process is where the conscious observer notices which value is present. Some people think of this as where the “collapse” happens, but here it is not really collapse of the wave function but rather of the classical probability distribution (similar to the case of a coin toss which starts of in a stochastically mixed state and collapses to just one case when we see the result).

The difference from a coin toss is that in that case we assume that all along the system was really in whatever particular state we eventually observe, and that state could have been determined with certainty just by making more observations at the start; whereas in the quantum situation the uncertainty seems to be essential until we actually experience the result. This leads to a philosophical problem for those who think that the quantum state is a property of the system itself rather than of its relation to the observer as it seems to imply that the experience of a conscious observer has some physical effect on the universe and raises the problem of Wigner’s friend who watches an experiment before Wigner does and seems to collapse the wave function even though the friend is himself just a complex quantum system who Wigner sees with a wave function that does not collapse until the information reaches his (Wigner’s) own mind.

To my mind this is resolved by seeing the quantum state as a description not of the universe but of its relationship to the observer; and I think this view is a better reading of what Hugh Everett was describing in his “Relative State” interpretation of quantum mechanics which was re-presented later (mostly by others) as a “Many Worlds” interpretation where observations (and other interactions) continually cause the creation of new “branches” (in a way that Everett himself apparently once described as “bullshit” in a marginal note on someone else’s elaboration of the MWI).

Source: (1001) Alan Cooper’s answer to Is observation the only way in which a wave function can collapse? – Quora

Does an observer modify the observed?

What many people misunderstand is that in quantum theories the “state” of a system is not a property of the system itself but rather of how it appears to an observer.

There are actually at least two stages to the observation process. One is when the system of interest interacts with the much more complex system of a measurement apparatus whose precise quantum state is too complex for the observer to keep track of and so has to be expressed as a statistical mixture. This can have the effect of causing the combined system, in which the observed subsystem was initially in a pure “coherent” superposition state (with interference still being possible between different possible observed eigenvalues), to end up very close to a statistical mixture in which each possible measured value of the observed quantity has a well defined value with no interference between them. This “decoherence” process can be caused by interaction with any sufficiently complex system (even, as Viktor Toth notes, just a brick) and it does modify the observed (as does any interaction with anything – even just another simple quantum system). But it still leaves the actual value of the observation unspecified. The “collapse” process, which identifies which particular value has occurred, only happens in the mind of the observer whose conscious experience corresponds to just one of many possible histories of the universe. But this doesn’t modify the observed – at least no more than it modifies everything in the universe that is dependent on that observed value. (For example if we are in a room together and I see a red flash then the you that I see will also see a red flash, but if you see a blue flash then the I that you see will also have seen a blue flash.)

Source: (1001) Alan Cooper’s answer to In the quantum mechanical idea that the observer modifies the observed, can the observer be an insect? – Quora

In QM, how can all people see something and all report the same thing? Wouldn’t 1 person’s observation cause their reality to branch off?

Quantum physics, without any additional “interpretation”, is just a tool for predicting the probabilities of various possible future observations from knowledge of other observations we have made in the past. To do so, it summarizes the observer’s previous observations (up to the point of the observer’s last interaction with the system) in what is called the “state” of the system relative to that observer. Any new observation ends the period of isolation of the system from the observer and so requires that a new relative state be defined taking into account the result of the most recent observation.

(Actually the “observer” of the system here doesn’t have to be a person or any other conscious entity. Any other physical system that it could interact with will do – with observations just corresponding to changes of the state of the observing system relative to any other “external” observer.)

It turns out that all observers who are isolated from the system during an experiment, and who start with the same information about the system, can use the same mathematical object to represent its relative state and for making predictions about the outcome; and this has led to the idea that the state is somehow completely independent of the observer – with various convoluted “interpretations” being added to “explain” what is “really” going on. But none of these adds anything in the way of useful predictions, and they all lead to various kinds of seeming paradox which get seriously multiplied if you mix different “interpretations” (as pointed out in Johann Holzel’s answer ).

Actually, if some friend, or other observers, (or just other physical systems) observe (or just interact with) the system before you do, then the states of the system relative to them “collapse” in the sense that after the observation (or other interaction) the probabilities of future observations are changed (with some becoming no longer possible and others more likely). But the state of the system relative to you does not collapse until you interact with it – either directly (eg by observing it yourself), or indirectly (eg by observing or communicating with your friend).

Usually it is quite hard to keep things isolated, and so just by being in the same room and sharing contact with the same air and ambient radiation you are effectively always interacting with your friend; so even without consciously learning what the friend has observed you have access to that information and so the collapse occurs for you too at the same time as for the friend. But if we were to keep the friend completely isolated in a pure quantum state (which is not possible for a real person, or even a cat, but might be possible for another microscopic system as the “observer”), then the combination of experimental system and “friend” could be in a pure state relative to you which remains uncollapsed until you actually learn the outcome (either by observing the system directly or by checking with your friend).

But as soon as we have been in contact with one another, the you that I see will agree with me about the experiment, and the me that you see will agree with you.

Source: (250) Alan Cooper’s answer to Quantum physics question If reality or superposition is fixed at observation or measurement, how can all people see something and all report the same thing? Would 1 person obseving something different cause their reality to branch off? – Quora

Michael Price’s answer to How does the Many Worlds Interpretation of Quantum Mechanics explain the emergence of probabilities according to the Born rule? – Quora

Source: (1001) Michael Price’s answer to How does the Many Worlds Interpretation of Quantum Mechanics explain the emergence of probabilities according to the Born rule? – Quora

3ntangled

Can three or more particles be quantum entangled? And if they can, what will the two particles opposite state, like opposite spin, translate to for three (or more) entangled particles?

Certainly! Any n-particle state that cannot be written as a pure tensor product of n one-particle states is “entangled” to some extent, though in many cases the entanglement may be “partial” in the sense of only involving some of the particles, and the question probably wants a state which is “fully” entangled in the sense that there is no way of writing the state as a pure tensor product of states for any partition of the n particles into subsets. [Note: I am using “partial” and “full” here to refer to the breadth or scope of the entanglement rather than to some measure of its pairwise strength or depth.]

A system of three spin 1/2 particles is in a completely unentangled state if and only if the state vector can be written as a pure tensor of the form [math]|\Psi\rangle =|\Psi_1\rangle \otimes |\Psi_2\rangle \otimes|\Psi_3\rangle[/math] where each [math]|\Psi_i\rangle [/math]is a pure state of the one particle system (which may or may not be an eigenstate of some spin direction). The reason for this definition is because if a state can be written this way, then the effective state of the remaining particles after measurement of any one of them can be shown to always be independent of the measurement value obtained on the observed particle.

Note: A state that is given as a sum of several pure tensors may nonetheless be rewritable as a pure tensor and so be unentangled. For example, if [math]|\uparrow\rangle[/math] and [math]|\downarrow\rangle[/math] are the eigenstates for spin up and down in, say, the z-direction, then [math]\begin{align}|\Psi\rangle &=\frac{1}{\sqrt{2}}(|\uparrow, \downarrow ,\uparrow \rangle +|\uparrow ,\downarrow ,\downarrow \rangle)\\ &=\frac{1}{\sqrt{2}}(|\uparrow\rangle \otimes |\downarrow\rangle \otimes |\uparrow \rangle +|\uparrow \rangle \otimes |\downarrow \rangle \otimes |\downarrow \rangle) \\ &=|\uparrow\rangle \otimes |\downarrow\rangle \otimes(\frac{|\uparrow\rangle +|\downarrow\rangle}{\sqrt{2}})\end{align}[/math]

And this is unentangled because it can be written as a pure tensor and we can see that measurement of spin 3 can “collapse” the [math]|\Psi_3\rangle[/math] factor to either [math]|\uparrow\rangle[/math] or [math]|\downarrow\rangle[/math] without affecting either of the others.

But [math]|\Psi\rangle =\frac{1}{\sqrt{2}}(|\uparrow\rangle \otimes |\uparrow\rangle +|\downarrow\rangle \otimes |\downarrow\rangle)\otimes(\frac{|\uparrow\rangle +|\downarrow\rangle}{\sqrt{2}})[/math] is partially entangled because of the connection between the first and second spins. It is not fully entangled though, since we can measure the third spin without affecting the other two.

The state [math]|\Psi\rangle=\frac{1}{\sqrt{2}}(|\uparrow,\uparrow,\uparrow\rangle +|\downarrow,\downarrow,\downarrow\rangle )[/math] is fully entangled because finding any of its spins forces both of the others to be the same. This isn’t the only way to achieve full entanglement though, and it is not necessary to force the other spins to all be the same as the one measured (though of course, as mentioned in the question, more than two can’t all be “opposite” to one another).

For example [math]|\Psi\rangle=1/2(|\uparrow,\uparrow,\uparrow\rangle +|\downarrow,\downarrow,\uparrow\rangle +|\uparrow,\downarrow,\downarrow\rangle +|\downarrow,\uparrow,\downarrow\rangle)[/math] is a fully entangled state because “collapsing” onto the part with any one of the [math]|\Psi_i\rangle=|\uparrow\rangle[/math] gives only cases with [the other two parallel, whereas [math]|\Psi_3\rangle=|\downarrow\rangle[/math] corresponds to them being anti-parallel.

P.S. There are various ways of defining the “amount” or “strength” of entanglement between two particles; and it turns out for some of these measures that in a large class of systems of many particles, the strength of entanglement between any two particles is never more than it could be if they were only entangled with one another. One thing that may have given rise to this question is the unfortunate use of “entanglement monogamy” to refer to this phenomenon. (But as Percy Bridgeman points out in answer to another question, the fact that being fully polygamous reduces the amount of time available for marital relations with any one partner does not actually in any way enforce monogamy.)

fromQuora: Isn’t a ‘probability wave’ simply a statistical function and not a real wave? Does it no more ‘collapse’ than me turning over a card and saying that the probability ‘wave’ of a particular deal has collapsed?

Well, as other answers have noted, the wave function of quantum mechanics is not a probability wave as its values are complex and it is only the squared amplitude that gives a probability density. But the process of “collapse” involved in a quantum measurement does involve something like your playing card analogy.

There are actually two stages in the measurement and observation process. One is the interaction with an incompletely known measurement apparatus which reduces or eliminates the prospects for future interference and basically turns the previously pure state of the isolated system (considered as a subsystem of the larger world) into a statistical mixture. And the second is the collapse of that statistical mixture by observation – with the result that, from the observer’s point of view, of the many possible alternatives only one is actually true.

And if this makes it seem to you that the “state” of the system actually depends on the observer then you are on the right track. (But it is nothing special about the “consciousness” of the observer that is relevant here. Almost any localized system could play the same role relative to the rest of the universe.)

Any configuration history of any physical system can be considered as “seeing” the rest of the universe in a “relative state” which “collapses” when the configuration history in question passes a point beyond which the configuration includes information about that particular measurement value.

Source: (255) Alan Cooper’s answer to Isn’t a ‘probability wave’ simply a statistical function and not a real wave? Does it no more ‘collapse’ than me turning over a card and saying that the probability ‘wave’ of a particular deal has collapsed? – Quora

Entanglement

Entanglement is just a word we can use to describe a situation where knowledge of some property of one object gives us information about some (possibly different) property of another.

The term is rarely used in the classical case, because we take it for granted. If we separate a pair of gloves for example and pack them up in identical boxes and then choose by a coin toss to send each in one of two opposite directions, then we are not surprised by the fact that if someone who knows how they started out but does not know the result of the coin toss opens one box and sees a left glove, he or she knows immediately that whoever opens the other box will see a right glove.

There is often similar classical chance-based uncertainty in our knowledge of quantum systems; but for such systems, even in the most precisely prepared “pure” states the knowledge of some properties makes it impossible for us to know others. This residual uncertainty is expressed by representing the state of the system by a “state vector” in a Hilbert space and the “mystery” of quantum entanglement is that the correlations between systems (like the gloves) that were once together but are now far apart can sometimes be greater than would be possible for any way of randomly assigning the properties at the outset.

The reason this extra correlation is sometimes considered “spooky action at a distance” is because the change of state vector (often called “collapse”) that occurs when we open one box seems to trigger a simultaneous collapse at the other box – and in a way that can change what the remote observer will see when looking at different properties from the one that obviously has to be opposite. At first sight it may seem that this effect might be used to send a signal where what the second observer sees might depend on what the first one chose to measure, but that turns out not to be the case.

Whether or not this bothers you may depend on whether you consider the state vector to be a property of the system itself or rather of the way it appears to a particular class of observers.