According to the SEP:

Wigners pioneering identification of the types of particles with irreducible unitary representations of the Poincare group has been exemplary until the present.

Regarding the question of whether Wigner had supplied a definition of particles, one must say that though he has contributed a valuable and fruitful classification of particles; his answer does not contribute very much to what a particle is and whether a given theory can be interpreted in terms of it.

Classically we think of an electron as a point particle which generates an electric field; one speaks of an electron and it's field - as though they are two ontologically different concepts; in a sense they are as one lacks all extension and the other does not.

The electron as a particle is generally regarded as prior, as is captured by how one speaks or writes of it.

But, in no instance do we see the bare electron without this field; so by what reasoning should we think of it as prior; other than the bias we have for atomic theories?

Let us try a little Gedanken experiment and eliminate the electron whilst leaving the field as it is.

Can we locate the classical position of the electron? Yes - by locating the position of the field with the most electric intensity.

Can we quantify the charge that this hypothetical particle has? Yes - because the relation to a field to its charge is deterministic.

Given that the particle can be determined - it's position and properties, from the field; and classically we can determine the field from the particle - so the two pictures are equivalent; then by what principle should we choose the particle picture over the field?

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    I'm voting to close this question as off-topic because it seems to be a question about physics. – James Kingsbery Mar 30 '15 at 15:20
  • I'd argue that its in the tradition of natural philosophy as in Descartes and Liebniz. – Mozibur Ullah Mar 30 '15 at 16:19
  • And that it's about the ontology of an electron – Mozibur Ullah Mar 30 '15 at 16:24
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    "...one speaks of an electron and it's field..." and its mass and its spin and its wave-function and all sorts of other ontologically different concepts associated with the electron. fact is, physicists don't know exactly what the electron is, but they don't know exactly what the Universe is either nor do they know exactly what we are (and neither do the biologists). – robert bristow-johnson Mar 30 '15 at 18:34
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    I recommend closing as well. This should be a physics question. However, more importantly, it's discussing an electron using classical mechanics and trying to ask some VERY pointed questions about its essence. In reality, answer answers to these questions run the risk of actually leading you astray. Quantum Mechanics offers an answer to all of these which is much less intuitive, but has actually survived modern testing. Exploring the classical electron in any other light is like trying to find ways to maximize the value of buggy whips after Ford's car replaced the horse drawn carriage. – Cort Ammon Mar 31 '15 at 20:43

OK, but everything with mass also exists only alongside 'its field', the gravitational field its mass creates. So it seems many particles come with fields. Is there an objection to the electric field that does not apply to the gravitational one?

Further as I understand it, the strong force is also a field, and a separate one. So a better question, then, is why this one of the three (or more) fields is absent for specific particles. Rather than considering it special, it seems to me that we should assume everything comes with all of he fields, but that a neutron happens to be an electron and a proton overlaid, canceling out this particular one of the fields. And this is the only field which we happen to be in the position of seeing both the positive and negative versions of. (Since we are not allowed to get near antimatter.)

From this perspective, (which I think is close to Maxwell's approach to electricity), then, there is a consistent model where spatial forces are prior to particles. In that model, particles are not really objects, but, instead, inflow/outflow points for the fluids that make up the lines of force for the fields, the same way lines of current make up a laminar flow between a source and a sink in a conformal field.

Particles then have mass (or not) because one of the fields they 'source' or 'drain' is gravity. The have the ability to localize because they source or drain the field for the strong nuclear force, and they have charge because they source or drain some electromagnetic 'substance'.

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  • 'That many particles come with fields' - is the view I'm arguing against; because it suggests that particles are prior and fields are after; perhaps I'm making too much of language; but the particle-field dichotomy to me is as suspect as the particle-wave one; ought we to have substance dualism in physics? – Mozibur Ullah Apr 1 '15 at 17:18
  • In 'that model particles are not objects' - its similar to what I'm arguing for. – Mozibur Ullah Apr 1 '15 at 17:20
  • From certain mathematical points of view, all logic is modal and modal logic is always circular in its 'logical priority'. Every mode has a dual, and the dual is logically prior to reality if reality is logically prior to the mode. Necessity has the dual notion of 'possibility' -- the property of not necessarily being absent. Something may have to exist in order to be necessary, but then it has to be possible in order to exist. But if possibility is just a different sort of necessity, how are any of the three logically prior to any of the others? – user9166 Apr 1 '15 at 18:04
  • So as a mathematician by training, it is hard to see where the choice of model matters at this level. You can pick one basis, and I another, and if the results end up isomorphic, both starting points are equally good, and their bases are equal in logical priority. – user9166 Apr 1 '15 at 18:05
  • physical intuition or argument, I would argue is different from the mathematical; mathematically there is no problem with 'action at a distance'; which is one reason why Newtons Gravitiobal Theory worked as well as it did; it's Faraday/Maxwell that returned the notion of locality back into Physics via the notion of the Field; probably the real history is more complex and subtle than this; the notion of the aether is similar. – Mozibur Ullah Apr 1 '15 at 18:47

An electron has mass; does that make it less "ghostly"?

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  • To keep the question simple I was neglecting mass...but in fact the same argument holds for mass. – Mozibur Ullah Mar 29 '15 at 18:07
  • @MoziburUllah, what do you mean? – nir Mar 29 '15 at 18:31
  • Suppose the Earth just disappeared but somehow leaving behind its gravitional field; by measuring it one can establish the mass of the earth (and its shape); thats the same argument that I was playing with above. – Mozibur Ullah Mar 29 '15 at 18:39
  • Its an argument to show that fields should be considered prior to particles; and is in line with descartes identification of space & matter via his res extensa. – Mozibur Ullah Mar 29 '15 at 18:44
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    if there is no common source for the EM and gravity fields we measure when we believe an electron is present, then do you propose that one of these fields creates the other? – nir Mar 29 '15 at 18:50

Nir's short answer makes the point of why an electron is not just it's associated field configuration: electrons have other properties mass, spin, lepton number, probably others, that distinguish it from other things with equivalent fields (mu and tau leptons, or anti-protons if you don't look at them too closely). There was an idea put forward in the early 20th century (something along the lines of the classical electron radius -- this was the Abraham-Lorentz model) that the mass of an electron could defined due to the energy in the fields via the mass<->energy equivalence in relativity. This idea failed -- one prediction was that the electron would have a measurable radius that hasn't been seen, and in general doesn't mesh with current QFT. All of this is to say that an electron has more features than just it's EM field configuration.

As to why the field is "associated" with the particle -- the post-hoc explaination is that there are different things (the other charged leptons) that have the same field configuation, but different intrinsic properties (like mass). The real reason is because "particle" is an idealization/extension of the everyday notion of a thing that we can pick up and move around, taken to the limit where any internal structure is irrelevant. Since most things that we deal with day-to-day don't have observable electric charge, people tend to see the electron's field as something extra attached to an otherwise uncharged particle.

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