# Do Quantum Fields Move?

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• friend
In summary,Quantum fields do not move with respect to each other. What establishes the background spacetime for quantum fields is unknown, but it is usually assumed to be flat Minkowski spacetime. There is no way to reconcile two different frames of reference in QFT.f

#### friend

Do quantum fields move with respect to each other? If not, then what establishes the background spacetime for quantum fields? Is there a way in which to say that the particle wave in one field is stationary in another frame and the rest of the particles are moving with respect to it?

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Do quantum fields move with respect to each other?

Since a field is a mathematical object with a value at all points in time and space, it doesn't make sense to talk about it moving.

what establishes the background spacetime for quantum fields?

Which background spacetime you assume in your model. Usually it's flat Minkowski spacetime, but you can do QFT on any background spacetime you like (for example, in the usual treatment of Hawking radiation, QFT is done with Schwarzschild spacetime being the background spacetime).

Since a field is a mathematical object with a value at all points in time and space, it doesn't make sense to talk about it moving.
Thank you. But in empty space you can't say who is moving and how fast, how do you chose a frame of reference to establish your QFT? What one person says is moving, another person says it's still. Is each observer allowed to say he is still and establish his QFT in that frame? Is there any way in QFT to reconcile two different frames of reference? Does QFT assume a center of mass frame?

in empty space you can't say who is moving and how fast, how do you chose a frame of reference to establish your QFT?

You don't have to. You can describe a spacetime without choosing a frame of reference. You just have to write everything in terms of frame-independent quantities (which contain all of the actual physics anyway). In the same way, you can formulate QFT on a background spacetime without choosing a frame of reference.

In the same way, you can formulate QFT on a background spacetime without choosing a frame of reference.

I might be confused between two points of view. One, that particles are waves in the field, and a wave propagates through space with time. And second, the Feynman diagrams show interactions, but the lines being drawn are not with respect to actual space and time coordinates; they only represent interactions at some other point of space at some other place in time.

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I might be confused between two points of view.

Neither of the points of view you describe are correct.

You just have to write everything in terms of frame-independent quantities (which contain all of the actual physics anyway).

Thank you. But I'm having trouble being certain about the spacetime independent nature of QFT. Let me see if I got the idea: First quantization is with respect to spacetime. But second quantization is with respect to fields (at least in the path integral) which are not spacetime variables. So the variables of QFT are the number operator... what else, that are spacetime independent?

I'm having trouble being certain about the spacetime independent nature of QFT.

Who said QFT was "spacetime independent"? I said it was frame independent. Big difference.

Let me see if I got the idea

You don't. And I don't think your misunderstandings can be disentangled in a "B" level thread. You need to spend some time working through a QFT textbook, so that you can formulate questions at the "I" level which can be more rigorously discussed.

They don't move but they change with time.

They don't move but they change with time.
In whose frame of reference?

In whose frame of reference?
Typically in every frame of reference.

Typically in every frame of reference.
Yes, that's my sense of it, that each observer is allowed to consider him/herself inside a stationary field. Another way to ask this is how do quantum fields account for kinetic energy or relativistic mass?

each observer is allowed to consider him/herself inside a stationary field

There is no such thing as a "stationary field". What @A. Neumaier is saying is that in general, every observer will see a quantum field changing with time along his worldline--in other words, the field values he measures in his local vicinity will, in general, change with time. This is not the same as the field "moving" or "not moving"; the latter concepts have no meaning.

how do quantum fields account for kinetic energy or relativistic mass?

Neither of those concepts appear in quantum field theory. They only appear in the classical approximation (and aren't very useful even then--we've had plenty of past PF threads on why relativistic mass isn't a useful concept, we even have a FAQ on it).

Once again, you seem to have some basic misunderstandings about QFT, and they aren't going to be correctible in a "B" level thread. I suggest taking the time to work through a textbook.