# second quantization and elementary questions

I want your opinions on how useful it is to throw second quantization at students when they have not understood first quantization. I tend to add a simpler answer when I see this.

Also the emphasis on second quantization and statements of the type "all space is filled with electron fields /particle fields etc" instead of "one can describe mathematically that the ground state of the electron wave function covers all space" gives a false "aether type" impression . False because if there is no electron at (x,y,z,t) the ground state gives zero probability of finding one, and the impression given is that there exists something there except zero. It is a similar conceptual problem as with virtual versus real. Creating this aether of all fields in mathematics does not mean a real physical existence.

One can fit the shape of my computer with a Fourier series expansion or another complete mathematical series expansion from here to infinity. This does not mean that part of my computer is at infinity. It makes mathematics as a reality, which is not the current physics point of view imo.

• Careful about filling your computer with Fourier expansions, I say the reason you can't is because it is assumed that the computer is discrete and hence contains discontinuities that can't be addressed (well) by a Fourier expansion. If you could actually fill it then, part of it would indeed be at infinity or rather right on the edge of acceptable solutions (like the FT of a cosine). – Mikhail Dec 14 '15 at 5:49
• So... how is this about the site? It sounds like a physics education question. I assume that's not what you meant, but in that case I don't see what you did mean to ask, so maybe some clarification might help? – David Z Dec 14 '15 at 6:24
• @DavidZ It is about the content of the answers to the site questions. I thought it was to be a repository of answers using the accepted physics pov – anna v Dec 14 '15 at 6:36
• Which site questions? If you're asking about specific questions on the main site, it would be useful to link to them. – David Z Dec 14 '15 at 8:42
• @DavidZ a number of people are all all for talking about "the whole spoace is filled with fields", it is not one or two questions . the last one was here physics.stackexchange.com/q/223899 . – anna v Dec 14 '15 at 15:46
• @Mikhail My point is that even an electron IS NOT at infinity. It is whole, it just has a probability of being at infinity, which is a completely different story. QFT is a clever way of describing this, and very useful, but it is a mathematical tool, not reality in the sense of measurement . – anna v Dec 14 '15 at 15:53
• First quantization is a very limited concept that misrepresents most of physics. It may be necessary for the beginner to get their feet wet in QM (I am beginning to even doubt that), but it causes more conceptual problems than it answers. You can see this in endless questions about problems of foundations of QM that may have been acute in 1923-1927 and that all went up in white smoke as soon as field quantization was somewhat understood. Quantum fields do cover the entire vacuum, just like the em field does. There is nothing particularly aether like about that. – CuriousOne Dec 27 '15 at 12:00
• @CuriousOne I think that you, as well as many other theoretically inclined physicists, tend to forget on what all those creation and annihilation operators operate. They operate on basic wave functions called ground state, that are the solutions of the appropriate quantum mechanical equations. The vacuum where there are no potentials has zero expectation value when operated upon, so quantum fields do not cover the entire vacuum except ideologically. QFT IS a great "invention", it is similar to what Fourier tranforms and Bessel functions and all the other complete sets to functional analysis. – anna v Dec 27 '15 at 12:30
• continued : But, imo, it is just that, mathematics convenient for many body quantum mechanical problems. Unless the student has an intuition about quantum mechanical solutions with and without potentials, throwing second quantization on his/her head is meaningless, again imo. – anna v Dec 27 '15 at 12:33

With respect to answers to questions on this site, I think that as long as the answer addresses the concerns of the OP, it is okay to use language & mathematics beyond their ken. You probably won't get terribly many upvotes or accepted answers doing that, but I don't think that's a bad thing1.

Remember that the answers we post here aren't necessarily for the actual OP, they're for the 100 people who wonder the same question at another point in time (~45 min lecture by SE founder Joel Spolsky; the hypertext phrase is a paraphrase of something he says in the video). So your answer, while likely advanced for the OP, could actually be beneficial to someone else at another point in time, which is a good thing.

1 I mean that, since reputation isn't really useful outside of some privileges, not gaining more doesn't do anything bad.

• Wow, two downvotes...either or f you care to inform me what is to disagree here? – Kyle Kanos Dec 14 '15 at 12:09
• Why not do both high and lowlevel in the same answer? or even in 2 answers (or is that discouraged?) – innisfree Dec 14 '15 at 12:18
• BTW I wasn't a downvoter – innisfree Dec 14 '15 at 12:19
• @innisfree: this is of course also an option. My point here was to focus on the should I answer a question above the level of the OP aspect of anna's question. – Kyle Kanos Dec 14 '15 at 12:23
• I agree that all answers are relevant for a repository. But maybe the OP's question should also be addressed , particularly if it is a student. (I did not downvote) – anna v Dec 14 '15 at 15:48
• @annav: I agree, the answers should answer the question; I just don't think there is an issue with "talking over their heads" with them as well. One could do what innisfree suggested and answer both levels, but this may be too time consuming for some people to do. – Kyle Kanos Dec 14 '15 at 15:54
• I didn't downvote. Here's an upvote to prove it. – John Duffield Dec 16 '15 at 13:51

I want your opinions on how useful it is to throw second quantization at students when they have not understood first quantization.

My opinion is that it might not be very useful, but you do need to give a correct answer.

I tend to add a simpler answer when I see this.

That's understandable. If it's a simpler version of the correct answer who could possibly object? I think the issue comes if you start getting sucked into "lies to children".

Also the emphasis on second quantization and statements of the type "all space is filled with electron fields/particle fields etc" instead of "one can describe mathematically that the ground state of the electron wave function covers all space" gives a false "aether type" impression.

It isn't false. Einstein talked of space as the aether of general relativity, check out the arXiv, and see what Robert B Laughlin said here about quantum vacuum:

"About the time relativity was becoming accepted, studies of radioactivity began showing that the empty vacuum of space had spectroscopic structure similar to that of ordinary quantum solids and fluids. Subsequent studies with large particle accelerators have now led us to understand that space is more like a piece of window glass than ideal Newtonian emptiness. It is filled with 'stuff' that is normally transparent but can be made visible by hitting it sufficiently hard to knock out a part. The modern concept of the vacuum of space, confirmed every day by experiment, is a relativistic ether. But we do not call it this because it is taboo."

False because if there is no electron at (x,y,z,t) the ground state gives zero probability of finding one, and the impression given is that there exists something there except zero.

There is something there. Space is not nothing. What's false is the notion that the electron is a point particle located at (x,y,z,t). It just doesn't match the hard scientific evidence of electron diffraction etc.

It is a similar conceptual problem as with virtual versus real. Creating this aether of all fields in mathematics does not mean a real physical existence.

But space exists, gravitational fields exist, electromagnetic fields exist, and so on. It doesn't mean to say that electric fields and magnetic fields exist as separate unrelated things. Or that photon fields and electron fields and gluon fields etc all exist as separate unrelated things. But something exists. See Einstein talking about electromagnetic and gravitational fields in 1929: "It can, however, scarcely be imagined that empty space has conditions or states of two essentially different kinds". According to Einstein, a field is a state of space. And how many states of space are there where an electron is? One. IMHO little things like this are the key to unification, and the multiple fields of QFT are pulling in the wrong direction.

One can fit the shape of my computer with a Fourier series expansion or another complete mathematical series expansion from here to infinity. This does not mean that part of my computer is at infinity. It makes mathematics as a reality, which is not the current physics point of view imo.

IMO some people elevate mathematics above reality, and don't pay enough attention to the scientific evidence.

• I didn't downvote, but Meta isn't really the pace to discuss physics per se, just site policies and such. If you deleted the irrelevant aspects to this answer, I'd be willing to upvote it. – Kyle Kanos Dec 16 '15 at 15:28
• There's nothing irrelevant above. I go through the OP step by step responding point by point, with references. – John Duffield Dec 17 '15 at 8:26
• Even on meta, you find a way to satisfy your need for Einstein quotes, complaining about gauge theories etc! It's quite laughable, at this point. – Danu Dec 22 '15 at 23:01
• @Danu : there's nothing laughable about answering the question point by point and telling the OP about fields according to relativity. – John Duffield Dec 22 '15 at 23:10