[another_someone]

Quantum physics, or to give it its more formal name, quantum electrodynamics, tells us that particles are waves, and that the waves describe a probability of a particle being in a given place.

The question is, how do you define a particle as being in one place or another?

The classical way of determining the location of a particle (traditionally an electron, or a photon) is to judge where the electric field of the particle is - but is this an accurate description of the location of the particle, or just a description of the field surrounding the particle.

The other field that is commonly associated with matter, and that can be measured at a distance, is the gravitational field, but there are problems integrating QED with gravity.  Does this mean that the centre of the gravitational field does not posses the same probabilistic nature as the centre of the electric field, and is the foci of the electric and gravitational forces generated by a particle always co-located?

More broadly, is there any way of asserting that the foci of an electric field of a particle defines the location of the particle, and that any uncertainty in the foci of that electric field should be translated into a genuine uncertainty about the actual location of the particle itself?

[lyner]

I think the point is that the particle WAS somewhere when it interacted with some system. Until then, it was a wave.

[another_someone]

I think the point is that the particle WAS somewhere when it interacted with some system. Until then, it was a wave.

But was the particle at the central focal point of the electric charge of the particle?  The particle interacted through the forces (most commonly, the electric force), so we can say by virtual of the interaction, where the force is - but just as you could not say where the centre of the Earth is just by mapping its magnetic field, so you cannot determine where the centre of an electron is just by mapping its electric field (as with the Earth, you can expect the two to be close, but can we say they are actually in the same place?).

[JP]

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.  My educated guess is that the electron could be anywhere in the inherent uncertainty "fuzz" you see when you try to determine the center of the field. 

[another_someone]

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.   

Is this actually a problem?

Is not the problem that you cannot map where and when a particle is, but the where can be mapped with arbitrary precision (at least down to a plank length) so long is don't care too much about when - and similarly, you can map the track of an electron with arbitrary precision, so long as you don't care too much about its velocity.

[another_someone]

I think the point is that the particle WAS somewhere when it interacted with some system. Until then, it was a wave.

But the particle did not interact with the system - it was the fields of the particle that interacted with the system - so is the wave representative of the particle, or only of the fields emanating from that particle?

[JP]

I'm not an expert on quantum field measurements, but I think what's going to happen is that the electric field generated by a particle is tied to that particle (the particle couples to the field, in the language of field theory).  If you measure the field you have to suck up some of its energy (probably in the form of everyone's favorite particle: photons), which in turn perturbs the electron a bit.  In a more classical sense, to measure the field you need some sort of charge on your detector (or else it won't interact with the field), and this charge will nudge the electron so that the uncertainty principle is preserved no matter how well you try to measure the field. 

[lyner]

Why do you want to separate the particle from the field idea? The two are just manifestations of the same thing. You call it a particle (when you choose to) when it can be identified as interacting with some system (e.g. when it apparently bashes something out of the way). As to 'where it is', that's to do with  looking at the wave function as a probability density function; the 'particle interaction' is more likely to happen at maxima in the probability function. It's  position is one of those 'known unknowns', perhaps.

[another_someone]

Why do you want to separate the particle from the field idea?

A particle has a number of properties - most significantly, many have electric fields and have mass/inertia.  Some are also subject to other fields. Can we be certain that these properties are precisely co-located?

The problem is that we cannot presently really measure the gravitational field of a single particle, but if we could, would we find the centre of the electrical and gravitational fields to be co-located?  I realise that this is speculation on what we do not yet know, but it does indicate that there is substance to the notion that the location of the centre of the electric field of a particle is not the only centre it may have.

In particular, we are having problems integrating relativity and quantum descriptions of particles, but the quantum description of the particle is based on our understanding of the electric field, while the relativistic description of the particle is based on our understanding of mass and gravity.

If the fields are not co-located, could there be a rotational momentum generated by different forces being centred differently and interacting with the external environment from those different centres?

[lyner]

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.
Duality doesn't have such restrictions. It allows a particle to be a particle when you look at it that way and a wave or other fields when you look at it in another way. If you want the 'particle' to 'be' somewhere then it may well be that, depending on which property (E.G. mass or charge) you are  considering, the centre of the probability function (where the particle can be considered as being) will be in a number of different places. It doesn't seem worth losing sleep over.
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.
If you get into a car, then you become a driver and the car becomes a part of you, too; we all develop nerve endings on the outside surface of our cars.

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.

[another_someone]

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.

Although the summary phrasing of the title might imply that, but as I have suggested above, I am being more flexible than that.

The underlying question probably is not so much about where is the geist of the particle, but rather whether all of the aspects of the particle need be in the same place (when we say that we measure a particle, using one property of a particle, to be in one place, does it follow that the other properties of the particle must be co-located)?

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.

I agree - but the one thing one can say about my heart and my head is that they are not co-located.

This can become even more complex when one looks at 'virtual' existence (by that, I don't mean virtual life, but I mean to be able to project one's existence through means of telecommunications, and so to be able to interact with things at a great distance as if one is locally there with the thing one interacts with).

Issues of where is a thing get even more complex when one looks as vegetative reproduction - is a cutting of a plant a new plant, or an extension of the original plant.

All of these are valid questions, but they do not invalidate my own question.

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.

[lyner]

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.

[another_someone]

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?  I would have thought that to be far from true.  The CM is still the nominal point by which one must measure kinetic forces acting upon the whole torus.  How that mass is distributed may reflect the local structure of the torus, and so how forces acting upon one part of that structure may effect the structure - but in terms of elementary particles, we know nothing of any internal structure, but knowing where gross forces act upon the particle is still meaningful.

Another comparison that might be more meaningful is the Decca radio navigation system.  From a distance you can follow a track right through the middle of the transmitters.  Ofcourse, there is no actual beacon transmitting at the  centre point of the signal, and as you get real close to the transmitters, the apparent straight line vectors of the transmitter actual turn into hyperbole, but at a distance, it just looks like straight lines emanating from the virtual centre.  The virtual centre is still meaningful, even if the close up structure may be more complex.

[lyner]

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?
With a time-based navigation system you can hardly say that the locus of a particular phase relationship 'emanates' from anywhere; each point on the locus (hyperbola) has equal weight.

[another_someone]

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?

But this is where the analogy breaks down - you can never hot an electron, and you can only interact with its fields (OK, being pedantic, you could say that the same is true for the torus, but the fields are so small that the conform to the apparent torus shape of the object).  As far as I am aware, an electrons electrical field (in free space - i.e. when not distorted by its environment) is spherically symmetric, and thus for all practical purposes you are hitting a spherical object (albeit, only the spherical fields of the object).

Granted, that when you hit the electric field of the electron, and if the electric field of the electron is not co-located with the centre of mass of the electron, then the rebound becomes unpredictable - but then, the whole point about quantum physics is that the track of an electron is unpredictable, and may only be given probabilities rather than certainties.

[shmengie]

I could be wrong, but it seems the crux of the issue is that which bugged Einstein.

The Atomic world is so small we can't know it's state w/out changing it.  Since the goal of observation is not to change the state but to know it, this causes a Pandora state of dilemma.   "I want to know"  but "You can't know" but "I want to know" but...

I don't think god is plays dice w/the universe, but w/out being able to examine the quantum world without an external 5th dimensional point of view, it is going to be like playing dice, hence the quantum theory.

Since the quantum theory provides statics which map out probabilities well enough, the "who", "what", "when" and "where" any one particle is not as relevant as what will likely happen.

Otherwise, the transistor may never have been invented and we couldn't converse in this fashion, now.  We might still be restricted to using vacuum tubes if it were not for the quantum wave theory...

Perhaps we should consider the quantum theory a 5th dimensional point of view.

[JP]

This is a really interesting question, and it's been bugging me since you posted it.  After a bit of thinking and a little research, I think I can pose the question a bit more formally in terms of quantum field theory.

You basically need to work in a full quantum field theoretical approach to answer this.  That's because you have to deal with the electron generating more than one field at a time and measuring both those fields to determine their "center."  Now the electron itself is some underlying field--it's a particle with some probability distribution in both position and momentum.  The electron generates other fields by "coupling" to them--the coupling strength would have to do with charge for electromagnetism energy for gravity, etc.

So the question boils down to something like this: Does the coupling between a field and the electron force the electron to "choose" to live in only states compatible with that particular field measurement?  This seems very similar to entanglement. 

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.

[another_someone]

Now, I certainly don't know the details of quantum field theory well enough to answer this question.

But still probably considerably better than I.

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.

That is approximately the kind of guess I would think most people make; but the question is whether we can do better than guess. 

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.

It would indeed be interesting if someone can find such an experiment.

But, as I said, even beyond QCD and QED, what about gravity/mass, which seem not to fit well into the quantum model?

[LeeE]

Just another vote for this being a very interesting question:)

The only observation I'd offer is that a gravitational field acts as a point source outside the mass causing the field.  Curiously, but not relevent, at the center of a spherical mass, the gravitational field is zero.

[lyner]

I have a feeling that an electron, in a bound state (wierd shaped probability function), could well have its effective charge / electric field centre not in the same place as its effective mass centre.
But ,just batting along in a straight line, it seems reasonable that they should be in the same place.