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If we experimentally proved that superposition exists, why can't we test if anything is in a superposition state? This seems like a contradiction because one would think that, if superposition exists, we should we able to find something in that state.

For example, as a proof of existence of the superposition, the double slit experiment is often given. But if double slit experiment shows that particles are in superposition, then it could show when superposition collapse, but this is seemingly not the case.

What is the explanation for this?

knzhou
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Łukasz Zaroda
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3 Answers3

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We do measure superpositions all the time.

  • We can measure if light is diagonally polarized with a polarizing filter, but diagonal polarization is an equal superposition of horizontal and vertical polarization.
  • We can measure the momentum of a particle, but a definite momentum state is a superposition of infinitely many definite position states.
  • We can measure if a spin 1/2 particle has its spin pointing to the right, but this state is an equal superposition of spin up and spin down.
  • We can measure if a spot on the screen in the double slit experiment is dark. This means the amplitude there is an equal and opposite superposition of the amplitudes from each slit.

These are all superpositions, in every sense of the word, even if they don't all make it into pop-sci.

I think you're looking for a situation where your measuring apparatus both "clicks and doesn't click" at the same time, but this is the wrong thing to look for. Measurements have definite results.

knzhou
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  • I was referring to the "collapse of the wave function", I don't have much knowledge on the matter, but I thought that we cannot really measure if the particle have it's wave function collapsed or not (so if it is in the superposition or not), because if we could, it seems to open a lot of loopholes for FTL communication. – Łukasz Zaroda Aug 21 '16 at 00:23
  • @ŁukaszZaroda But a wavefunction isn't "either" collapsed/in superposition or not. Just think about ordinary vectors. Northeast is a superposition of north and east. But it's also just an ordinary vector on its own. Similarly, north is a definite direction, but it's a superposition of northeast and northwest. – knzhou Aug 21 '16 at 00:25
  • Totally analogously, quantum measurements will give you definite results. But the wavefunction after a measurement can still be considered a superposition of some other set of states. – knzhou Jun 23 '19 at 22:28
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Superposition does not "exist," as much as it is a mathematical tool that we use to describe the world that does exist. We can't measure it because its not something to be measured.

Superposition is a concept in mathematics. A function has the property of superposition iff:

$$f(x_1+x_2) = f(x_1) + f(x_2)$$ $$f(ax) = af(x)$$

Any system which satisfies this property is said to have superposition. That's all.

The quantum physics principle you are referring to is that the quantum states of the system have superposition. This lets me say things like "The spin of the electron is a superposition of spin up and spin down." What experiments like the double-slit experiment show is that intuitive explanations which assume the spin is either up or down fail to properly predict what we show experimentally. We see experimental evidence that suggests that theories which assume the spin is either up or down yield incorrect results, as does the assumption that its spin is the "average" of spin up and spin down. We then show that the behavior is well predicted by the quantum mechanics, and that behavior has the property of superposition.

You can actually "solve" quantum mechanics waveforms without using the principle of superposition. You don't have to use that property at all. However, it becomes intractable very quickly. The fact that the equations of quantum mechanics permit us to treat a state as a superposition of several states simplifies the mathematics for us dramatically.

Cort Ammon
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  • So, if I think correctly, you would say that the "collapse of the wave function" doesn't refer to any actual physical event, it's just the weird way of describing a measurement? Am I right? :) – Łukasz Zaroda Aug 21 '16 at 00:37
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    That is true. In fact, the concept of "collapsing the waveform" does not appear in all interpretations of quantum physics. From what I have read, the concept of quantum dechoherence seems to be more universal to all interpretations of quantum physics. – Cort Ammon Aug 21 '16 at 00:49
  • I feel like the quantum physics vocabulary is the source of most of the confusion. I mean, how can we use the term "collapse of the wave function" if it doesn't mean anything more than the measurement mean? And if you also know that Copenhagen interpretation was developed by the pretty intelligent people, you are even more confused about it :/ . – Łukasz Zaroda Aug 21 '16 at 09:14
  • Something which helps me is to dig into the philosophy of science. Science is an epistemological philosophy: it is a study of what we can know. Along the way, it became so successful that we started treating it as an ontological philosophy, one that could actually speak to what reality "is." Quantum mechanics is a region where science has to remind itself that it's really all about what we can know, because QM is all about what we can know about the world and what we cannot. Unfortunately, by the time we got there, ontological phrasings had become the norm, so it gets confusing. – Cort Ammon Aug 21 '16 at 15:11
  • All scientific theories, from Newton's gravitation to relativity to quantum mechanics, are just models which we can use to predict something about the future using what we know about the present. In most of these theories, it appears the only limit on the accuracy of our predictions is our ability to measure the present state, and we can simply spend more effort to measure better. In the case of QM, the models predict a hard line that says "you cannot measure state any better than this, so you cannot perfectly predict the future." This makes every QM theory slightly further from... – Cort Ammon Aug 21 '16 at 15:20
  • ... ontological truth than other theories have been in the past. The interpretations are the attempts of, as you put it, "pretty intelligent people" trying to bridge that gap between what we know of reality and reality itself. – Cort Ammon Aug 21 '16 at 15:21
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Usually, when we express a quantum state as a superposition, we expand the state $|\psi\rangle$ in terms of a set of orthogonal basis states $|n\rangle$: $$ |\psi\rangle=\sum_n \alpha_n |n\rangle . $$ We can choose any set of orthogonal basis states. Different sets are related to each other via unitary transformations $$ |n\rangle=U|m\rangle . $$

Now the important thing to realize is that when we make measurements, our measurement setup dictates which set of basis states we should use. During the measurement process the quantum state (according to particular interpretations of quantum mechanics) collapses to one particular element of that set of basis states, which means that it is now not in a superposition of that set anymore, but consists of only one of the elements. However, we can now go and expand that state in a different set of basis states and again get a superposition. This can be confirmed by doing another measurements where the setup dictates a different set of basis states.

flippiefanus
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