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I think the point is that the particle WAS somewhere when it interacted with some system. Until then, it was a wave.
You'd end up with a problem in trying to map the exact center of the field, since you can only measure the field's focus to the accuracy of uncertainty relations.
Why do you want to separate the particle from the field idea?
Why does your thought model seem so 'conventional'?You are back on the old 'what's really happening' theme. The 'particle' does or doesn't exist. What does exist is what happens when the thing we call a particle interacts with some other system. You are not allowing duality to have full reign by, somehow, insisting that, despite all the sophisticated ideas of the last 100 years, there must be a particle with other things going on around it.
There is an analogous biological situation in the question "Where are You?" Your brain is up in your head, your heart is lower down; both are 'you' and go together, with other bits to make up 'you' but in different places.
Finally, there is the 'where is the photon?' question. The answer to that is, probably 'anywhere' until it's decided to interact with an electric system. Then, the transfer of its momentum may well affect the target system in a different 'place' from where it affects the charge distribution.
So, are you suggesting that the centre of momentum of a photon may not be co-located with the centre of charge distribution of a photon? That is a valid answer to my question.
What I am really saying is that the 'location' is not relevant - You can specify location more exactly or less exactly, depending upon the experiment you do but, at best, you are only considering a 'region' rather than a particular point. Here's another thought, with just a classical scenario. The CM of a torus is at a place where there is, in fact, no mass at all; you could fire a bullet at it and have no effect at all. That's the way I see the answer to your original question.
So, are you saying that because there is no actual mass at the CM or a torus so the measure of its CM is meaningless?
Of course not - it's just a distributed object which, in many instances, could not behave 'as if' it were a point mass. If you were to hit it with a billiard ball, for instance, you couldn't predict its resulting velocity by assuming that it was a point. There is, of course, one direction of impact where you could.So why should there be concern if the precise location of a particle can't be specified?
Now, I certainly don't know the details of quantum field theory well enough to answer this question.
If I had to guess, on the basis of entanglement, I'd say that the electron acts as "entangled" and chooses a state that's compatible with the field measurement (and therefore all other fields choose states compatible with the new electron state). This would mean that the centers-of-mass/charge/color or whatever else is associated with the electron would always be at the same point.
Finally, I bet someone already has checked the answer to this. In nuclear decay (say an atom spits out a proton), there must be come point at which the proton's center-of-interaction with the strong force chooses to exist outside of the nucleus (and therefore it gets spit out). Since the electromagnetic force would also become relevant at this point, and since QCD and QED are incredibly accurate, there's probably experimental evidence as to whether the center-of-QCD-interaction and center-of-QED interaction automatically co-locate.
a gravitational field acts as a point source outside the mass causing the field
But ,just batting along in a straight line, it seems reasonable that they should be in the same place.
That's,surely, what duality is about. If it behaves, in our experiment, as if it is a particle then it is a particle. You surely don't want it to 'wiggle' just because it can also behave as a wave. The probability field could / would be more or less uniform with no 'constraining' fields.btw, is the wave transverse or longitudinal?
we all know about photons; I was talking of De Broglie waves.
But in any case, where is this photon wiggling? Is it wiggling all over the Universe?
Quotea gravitational field acts as a point source outside the mass causing the fieldOnly at infinity. The gravitational potential for a dumbell shape, for instance is not spherical. If you happen to be on the Moon, you are attracted to the Moon, not to the centre of mass of Earth and Moon. The total system doesn't behave like a point if you are within / near it.
f you are standing on the moon, and therefore have the same velocity as the moon, you need to be attracted to the common center of mass of the Earth-Moon system to follow the same path as the Moon in that system, do you not?
You have to avoid falling into common conceptual traps.