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Having read Art Hobsons paper on Quantum field theory, he states " the field collapses into a field of atomic size" This seems to be stating that each field quanta is a different quantum field? Like 2 electrons are 2 electron fields, rather than the 2 electrons come from the same field. I thought they all emerged from the same field rather than 2 of them have there own/be there own seperate field.

Also he say field quanta are infinitly extended and has its energy spread over light years. This has confused me also, I havent seen any infintely sized electrons about, and as electrons are field quanta, how can field quanta be countable, yet infinite in size?

please help...

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arxiv.org/abs/1204.4616 is the link to it. can someone clear up my confusion please –  lee hudson Jan 12 '13 at 12:32
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You shouldn't spend too much time thinking about the paper, it doesn't deserve it. It's full of crap. You're of course right that all electrons are excitations of the same field. The paper talks about some collapses but it's so vague and confused that it doesn't seem to distinguish the wave function for the center of mass of an electron from the internal structure of an electron - which are totally different things. –  Luboš Motl Jan 12 '13 at 12:35
    
Also I've never heard "collapse" used in connection with a field - it's usually used in connection with a state –  twistor59 Jan 12 '13 at 12:37
    
thankyou, what about the statement that each quanta is spatially extended and infinite in extent? –  lee hudson Jan 12 '13 at 13:30
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Lee, please edit this question with clarifications/etc instead of re-asking modified versions of this. Thanks. –  Manishearth Jan 12 '13 at 16:30
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closed as off topic by user1504, Waffle's Crazy Peanut, Manishearth Apr 13 '13 at 14:44

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1 Answer

What the author said was

Eq. (3) implies that a single mode's spatial dependence is sinusoidal and fills all space, so that adding a monochromatic quantum to a field uniformly increases the entire field's energy (uniformly distributed throughout all space!) by hf.

meaning presumably that if I create a state with a single monochromatic quantum, i.e. $$a^{\dagger}(k)|0\rangle $$ then its energy content, represented by the 00 component of the energy momentum tensor, (or the Hamiltonian if you like) is a function of the whole field. In the position representation you would have to integrate over all x to get the total energy. Given that the state $a^{\dagger}(k)|0\rangle $ is uniformly spatially distributed in the position representation, he talks of the energy in this state also being uniformly spatially distributed.

You could ask the same thing about the electron charge - what is the charge distribution of an electron in this momentum eigenstate? Again, it's uniformly distributed over all space.

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and what does that mean in laymans terms, the energy of the quantum is spread over all of space? –  lee hudson Jan 12 '13 at 15:42
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In classical mechanics, a point particle has a trajectory, meaning that at any instant of time, it has a definite position and a definite velocity. In quantum mechanics this is no longer true, it doesn't possess these attributes simultaneously. If an electron is given a perfectly well defined momentum (think velocity), then its position is completely undefined, i.e. if you were to try to locate it, it could be anywhere in space. It just doesn't possess a definite position property when in this state. –  twistor59 Jan 12 '13 at 15:50
    
so it isnt literally spread over space like its energy is physically everywhere –  lee hudson Jan 12 '13 at 16:08
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Ah, now in QM you have to be very careful with words like "literally" and "is physically". What I mean is that all you're allowed to do is to talk about what would happen if you made a measurement. To get an answer to this question you would have to describe a measurement which would verify, to your satisfaction, that the energy was literally spread over space. I'm not being evasive, it's just that to answer these questions in QM, you really do have to say how you intend to perform the measurement to verify what you want. Then you can apply the principles to predict what you'd see. –  twistor59 Jan 12 '13 at 16:17
    
in general then, field quanta are not thought of though us having there energy spread over all of space? –  lee hudson Jan 12 '13 at 16:20
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