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This question is based on a fundamental misunderstanding of superposition. Every state is a single state and, at the same time, a superposition of other states.

Essentially a state is a vector and a vector, as you know, is a single vector and linear combination of other vectors.

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I'm sorry I did not understand that.This question is based on a fundamental misunderstanding of superposition. Every state is a single state and, at the same time, a superposition of other states.

Essentially a state is a vector and a vector, as you know, is a single vector and linear combination of other vectors.

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I would say it is one of the most common misconceptions about superposition. Also, "collapse" is a really misleading word, IMHO. In the Copenhagen interpretation, the state changes suddenly after a measurement to the relevant eigenstate of the observable.I'm sorry I did not understand that.

This "collapsed" state is just as much a state as any other. In fact, in terms of position, say, the eigenstates are not

physically realisable, so after a position measurement the state "collapses" into a continuous distribution of position eigenstates - which is sometimes known as a "wave-packet". THis is just a regular state, albeit localised about a particular point.

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So essentially the superposition only "collapses" after a specific measurement to the particle. Is that how it works?I would say it is one of the most common misconceptions about superposition. Also, "collapse" is a really misleading word, IMHO. In the Copenhagen interpretation, the state changes suddenly after a measurement to the relevant eigenstate of the observable.

This "collapsed" state is just as much a state as any other. In fact, in terms of position, say, the eigenstates are not

physically realisable, so after a position measurement the state "collapses" into a continuous distribution of position eigenstates - which is sometimes known as a "wave-packet". THis is just a regular state, albeit localised about a particular point.

- #6

Nugatory

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It's analogous to the way that I can describe the position of something as "one kilometer to the north and one kilometer to the east" or as "1.414 kilometers northeast, zero kilometers northwest". The first description is more convenient if I'm looking at a map with north up and north/south and east/west gridlines on it; the second is more convenient if I'm in a city whose streets are laid out in a grid pattern with downtown/uptown avenes running from southwest to northeast and crosstown streets at right angles to the avenues. One way, my basis vectors are north/east, the other ways they're uptown/crosstown. But it's the same point with the same physical relationship to me either way.I'm sorry I did not understand that.

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That's the Copenhagen interpretation. There are other interpretations, but to get you started on QM Copenhagen is as good as any. So, yes, a measurements "collapses" the system into an eigenstate of the observable, with the eigenstate correspondiong to the eigenvalue returned by the measurement.So essentially the superposition only "collapses" after a specific measurement to the particle. Is that how it works?

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The Copenhagen interpretation says that we can never find out why it "collapses", right?That's the Copenhagen interpretation. There are other interpretations, but to get you started on QM Copenhagen is as good as any. So, yes, a measurements "collapses" the system into an eigenstate of the observable, with the eigenstate correspondiong to the eigenvalue returned by the measurement.

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Yes, there's no why in that sense.The Copenhagen interpretation says that we can never find out why it "collapses", right?

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Thank you

Thank you as wellYes, there's no why in that sense.

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Physics Footnotes

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Taken at face value (which may not be quite what you meant, as I'll explain shortly), @PeroK gives the correct answer, which I quote again because this fact can never be repeated too much:When measured/viewed particles in superposition collapse and take the form of one state. So how do we know they are in superposition in the first place.

However, here is a modification of your question which I think you may have intended (and if not, I'm pretty sure it will teach you something useful anyhow!).This question is based on a fundamental misunderstanding of superposition. Every state is a single state and, at the same time, a superposition of other states. Essentially a state is a vector and a vector, as you know, is a single vector and linear combination of other vectors.

Suppose we have an observable ##A## which has two eigenstates ##|a\rangle## and ##|b\rangle## corresponding to eigenvalues ##a## and ##b##, respectively. We now make a series of ##A##-measurements on a beam of particles and get a series of readings like this:$$aababaabbbbaababaabbaaaabbbaba$$ Your teacher says that the particles in the beam have all been prepared in a superposition state of the form ##\alpha|a\rangle + \beta|b\rangle## and that upon measurement each particle's state 'collapses' randomly to either ##|a\rangle## or ##|b\rangle## with probabilities ##\alpha^{2}## and ##\beta^{2}##, respectively, resulting in the observed series of ##a## and ##b## values.

The

Forgetting any quibbles about how you've phrased the question, the answer is, no we don't.And do we know why they collapse into one state?

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Is that where the interpretations of QT come in, like the Many Words interpretation?Forgetting my quibbles about how you've phrased the question, the answer is, no we don't.