# re-defining the question, field quanta size in field theory? [duplicate]

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confusion on quantum field theory

I asked are field quanta infinite in extent and I keep getting back that its the probabibility distribution. But this is a normal quantum mechanics answer. In terms of quantum field theory, what is meant by saying a field quanta of an electron field is infinite in extent? does it mean the quanta is infinite in size? Art Hobson has said its energy can be spread across light years which surely means the field quanta of the field is massive in size?

if we assume the wavefunction is real and doesn't collapse then each quanta is a wave spread across the whole of space, correct?

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## marked as duplicate by Manishearth♦Jan 12 '13 at 16:29

I know the question is similar but I have asked a new bit at the end, about if the wavefunction is real and doesnt collapse is a field quanta extended accross all of space, an answer to this, as with my original question would be greatly appreciated –  lee hudson Jan 12 '13 at 14:19
Links to the earlier questions: Confusion on quantum field theory and Field quanta- infinite in extent?. I still think you shouldn't ask pretty much the same question 3 times in one hour. –  Wouter Jan 12 '13 at 14:20
im sorry wont happen again. I have altered it slightly –  lee hudson Jan 12 '13 at 14:27

The answer is simple: quantum field theory is not divorced from quantum mechanics. Any mathematical solutions pertaining to wave functions are probability wave descriptions.

See this simplified description:

it is possible to approach their quantum counterparts from a purely mathematical view using similar techniques as before. The equations governing the quantum fields are in fact PDEs (more precisely, relativistic wave equations (RWE)s). Thus one can speak of Yang-Mills, Dirac, Klein-Gordon and Schroedinger fields as being solutions to their respective equations. A possible problem is that these RWEs can deal with complicated mathematical objects with exotic algebraic properties (e.g. spinors are not tensors, so may need calculus over spinor fields), but these in theory can still be subjected to analytical methods given appropriate mathematical generalization.

PDE=Partial Differential Equation.

QFT uses equations for defining the wave functions that are relativistically correct.

There is no way out of it. There are no "matter waves" and whoever says so is wrong.

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Anna that has not answered my question, are field quanta of a field infinite in size and what does he mean by saving there energy is spread out over light years... –  lee hudson Jan 12 '13 at 14:48
and "if we assume the wavefunction is real and doesn't collapse then each quanta is a wave spread across the whole of space, correct?" whats the answer please? –  lee hudson Jan 12 '13 at 14:50
Forget about "him", ( you have not given a link). This is elementary quantum mechanics. It has differential equations the solutions squared describe the probability of finding a particular quantum in a specific (x,y,z,t) space time point. These solutions sometimes have a sinusoidal variation in space , but for finite boundaries . For infinite boundaries the square of the solutions which give the real probability, will be exponentially small, unmeasurable. The only real thing in the mathematical analogue of reality is the probability distribution. That is where mathematics and reality meet. –  anna v Jan 12 '13 at 15:16
anna so field quanta are not infinite in extended in space then? but you said the probability is small, so they could be... –  lee hudson Jan 12 '13 at 15:20
physics.uark.edu/hobson/pubs/11.10.TPT.pdf "each quantum is an energy increment of the entire space filling field" –  lee hudson Jan 12 '13 at 15:22

Position is not an observable in quantum field theory; as explained in textbooks and papers $x$ in quantum field theory is an dummy parameter without physical meaning.

Asking about the position, size, or extension of "field quanta" is meaningless in quantum field theory.

As said in your other question, the article by Art Hobson is full of misconceptions and mistakes.

No, we cannot assume that the wavefunction is real:

1. The wavefunctions of quantum mechanics are not waves but unobservable functions.

2. Wavefunctions are not even defined in ordinary space

3. Quantum field theory does not use wavefunctions; that is why the Dirac and Klein Gordon equations of relativistic quantum mechanics had to be reinterpreted as mathematical identities for field operators.

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as I said though, supposing the wavefunction is real and doesnt collapse(just supposing these are true) are the field quanta literally spread everwhere –  lee hudson Jan 12 '13 at 16:10
any answer juanrga or anyone else? –  lee hudson Jan 12 '13 at 16:30
@leehudson you cannot suppose "real" something that does not exist physically. The question about the "field quanta" was already answered above. –  juanrga Jan 12 '13 at 17:06
but thats your opinion, mwi says it is real, so the question was under mwi, are they spread infinitely everywhere? –  lee hudson Jan 12 '13 at 17:43
@leehudson It is not an opinion but a basic fact explained in virtually any textbook on Quantum Mechanics. MWI has been proven wrong many times... in any case you continue ignoring what I have said about quantum field theory. –  juanrga Jan 12 '13 at 20:43