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The tensor product, demystified (2018)

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Re: The tensor product, demystified (2018)

#31

Earlier quoted context omitted.

> No, that's not what superposition means a priori. The word was originally used to describe the decomposition of waveforms into sums of sinusoids, which is as canonical an example of a linear system as you can get. > the idea of a system being in "two states at the same time", apart from vector addition. But that's not what's going on. A system is only ever in one state at a time: the ability to treat it as a sum (m…

> > No, that's not what superposition means a priori. > The word was originally used to describe the decomposition of waveforms into sums of sinusoids, which is as canonical an example of a linear system as you can get. You are right, I was being a bit too sloppy with my usage of the term "superposition". I guess once people realized that a QM system being in "two states at the same time" is just a linear sum like fo…

A useful illustration: polarized light can be considered to be in a superposition if you use a basis rotated 45 degrees to the polarization axis. So whether or not polarized light is in a superposition depends entirely on how you choose to look at it. It's not a reflection of the underlying physical reality.

Re: The tensor product, demystified (2018)

#32
post #31

Earlier quoted context omitted.

> > No, that's not what superposition means a priori. > The word was originally used to describe the decomposition of waveforms into sums of sinusoids, which is as canonical an example of a linear system as you can get. You are right, I was being a bit too sloppy with my usage of the term "superposition". I guess once people realized that a QM system being in "two states at the same time" is just a linear sum like fo…

A useful illustration: polarized light can be considered to be in a superposition if you use a basis rotated 45 degrees to the polarization axis. So whether or not polarized light is in a superposition depends entirely on how you choose to look at it. It's not a reflection of the underlying physical reality.

I think we're talking past each other. :) I fully agree with your comment. However, I was addressing your original comment[0] about the naturalness of the tensor product. My whole point was merely (and maybe I didn't phrase it particularly well) that you need to assume all the stuff we (now) know about quantum mechanics (vector space structure etc.) in order to conclude that the tensor product is pretty much the only option you have. Your comment didn't mention this and seemed to make a much broader claim. That was all.

(EDIT: I think your other comment[1] fully resolves any gripe I had with your original comment. :))

[0]: https://news.ycombinator.com/item?id=37363347

[1]: https://news.ycombinator.com/item?id=37372225

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