Is particle more than the sum of its fields?

In summary, particles are localized excitations of quantum fields, which correspond to the interactions EM, weak, strong, and gravity. While these fields can be described as solitons, they are fundamentally no different from the fields associated with particles. Perturbative approximation is a useful tool, but in reality, particles interact by exchanging quanta that carry energy, momentum, and angular momentum, and their number is not conserved in nonlinear optics. Therefore, particles are not just the sum of their fields, but a more complex and dynamic entity.
  • #1
jarekd
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Electron is a charge, what means concrete configuration of electric field, growing to infinity in the center (if it would be a point particle).
It is also a magnetic dipole moment - concrete configuration of magnetic field growing to infinity.
And a mass - concrete configuration of gravitational field, again growing to infinity in the center.
...

So particle is a sophisticated localized configuration of fields - is it also something more?
If there would be such configuration identical to of some particle, would it be already this particle, or there still would be something missing?
Stable, localized configurations of fields are generally called solitons - are particles solitons? (there are quantization methods for solitons and topological solitons like fluxons undergo quantum phenomenas like interference)
 
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  • #2
A particle is an excitation of a quantum field corresponding to that particle (so an electron is an excitation of an "electron field"). This has nothing to do with the electromagnetic field (or all other fields the electron interacts with), and it cannot be understood in a classical way.
 
  • #3
So analogously positron is just an excitation of "positron field" ... and hundreds/thousands of other particles have their own fields?
Sure we can say something like this for density: of electrons, of positrons etc. ... but fundamental fields correspond rather to interactions: EM, weak, strong, gravitational.

In analogy to density, we can introduce e.g. your "electron field", but it is an effective description counting them (including quantum correlations) - what electron creation operator does, is not only just "adding single electron to electron field", but it also would drastically change electric field of the whole Universe ... and so Gauss law forbids creating a single electron - it has to be done e.g. as electron-positron pair.

Particle physicists live in the perturbative approximation, often forgetting that it is only an approximation - in fact e.g. particle is not a plane wave, what would mean that this single particle is spread over the whole Universe.
Still using this approximation, we get Feynman ensembles among possible "classical" scenarios: e.g. electron meets positron, producing two 511keV photons.
For each of such scenario there are also real fields involved, e.g. first there is strong electric field of this electron and positron, attracting them together and finally their mass/energy is released in this EM field - as its excitations (usually carrying angular momentum): photons.

So looking at such single scenario in Feynman ensemble, is particle just its own configuration of fields, or is also something more?
Sure it would be e.g. a Dirac delta in density function for this particle (in space or momentum representation), but it is only an effective description - is particle objectively something more than just "the sum of its fields"?
 
  • #4
There are just ~50 fields or so, corresponding to the various particle types.
Sure we can say something like this for density: of electrons, of positrons etc. ... but fundamental fields correspond rather to interactions: EM, weak, strong, gravitational.
What does that mean?
In analogy to density, we can introduce e.g. your "electron field", but it is an effective description counting them (including quantum correlations) - what electron creation operator does, is not only just "adding single electron to electron field", but it also would drastically change electric field of the whole Universe ... and so Gauss law forbids creating a single electron - it has to be done e.g. as electron-positron pair.
The electric charge of the electron is by far not as fundamental for the electron as you think. It has an electric charge, this means it couples to photons. So what? It has a weak charge, it couples to W and Z bosons.
Neutrinos do not have an electric charge, and you still cannot produce them without producing (or annihilating) some other particle in the process.
Particle physicists live in the perturbative approximation
They do not.
So looking at such single scenario in Feynman ensemble, is particle just its own configuration of fields, or is also something more?
Sure it would be e.g. a Dirac delta in density function for this particle (in space or momentum representation), but it is only an effective description - is particle objectively something more than just "the sum of its fields"?
Physics can be described with those fields alone, everything else is philosophy.
 
  • #5
Fundamentally there is no distinction between the electron (and other particles) fields (note the plural) and the fields associated with the interactions EM, weak, strong, and gravity (with the possible but unlike exception of gravity). All these fields are associated with quanta which are interpreted as particles. The photon is as much a particle as the electron is and the electron fields are as much a field as the photon field is (AKA the electromagnetic field).
 
  • #6
mfb said:
Physics can be described with those fields alone, everything else is philosophy.
While I would distinguish fundamental fields (of interactions) from the effective ones (counting different types of particles), I agree here - particles are just localized excitations of some fields (so formally they are solitons).
I know that in quantum description you don't like the "localized" word as you usually work in the momentum space approximation, but in reality e.g. protons are usually localized for example in the centers of concrete atoms.
dauto said:
The photon is as much a particle as the electron is and the electron fields are as much a field as the photon field is (AKA the electromagnetic field).
You are talking about perturbative approximation, in which you imagine interaction between two charged objects as neverending stream of photons.
It is a useful picture for this approximation, but the reality is very different - photon has e.g. spin 1, so both interacting particles would have to change spin every time ... this spin corresponds to http://users.df.uba.ar/schmiegelow/materias/FT2_2010_1C/extra/PhysRev.50.115.pdf [Broken] - so both interacting particles would have to change angular momentum every time (and also energy and momentum) ...
Photons are sophisticated EM waves - e.g. electron changes angular momentum, so like behind marine propeller, Noether theorem says there have to be produced a wave carrying this angular momentum - where, beside description, you need some additional fields here?
... and their number is not conserved in nonlinear optics ... and you can have much more complex EM configurations, like topologically knotted ones: http://physicsworld.com/cws/article/news/2013/oct/16/physicists-tie-light-into-knots - how do they look in your "photon field"?

From the other side, electron is just the lightest charge ... knowing electric field around, if Gauss law says that there is negative charge inside, you can be almost certain that there is electron inside (or anti-proton).
 
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  • #7
jarekd said:
You are talking about perturbative approximation, in which you imagine interaction between two charged objects as neverending stream of photons.
It is a useful picture for this approximation, but the reality is very different - photon has e.g. spin 1, so both interacting particles would have to change spin every time ... this spin corresponds to very real "mechanical" angular momentum - so both interacting particles would have to change angular momentum every time (and also energy and momentum) ...
Photons are sophisticated EM waves - e.g. electron changes angular momentum, so like behind marine propeller, Noether theorem says there have to be produced a wave carrying this angular momentum - where, beside description, you need some additional fields here?
... and their number is not conserved in nonlinear optics ... and you can have much more complex EM configurations, like topologically knotted ones: http://physicsworld.com/cws/article/news/2013/oct/16/physicists-tie-light-into-knots - how do they look in your "photon field"?

From the other side, electron is just the lightest charge ... knowing electric field around, if Gauss law says that there is negative charge inside, you can be almost certain that there is electron inside (or anti-proton).

You're not listening because you think you know something that you really don't. A photon is a quanta of electromagnetic field and an electron is a quanta of the electron field. The number of electrons is not a conserved quantity. Se for instance the beta-decay where an electron is produced while a neutron converts into a proton. Electric charge is conserved, that's true but the number of electrons isn't.
 
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  • #8
jarekd said:
particles are just localized excitations of some fields (so formally they are solitons).
I know that in quantum description you don't like the "localized" word as you usually work in the momentum space approximation, but in reality e.g. protons are usually localized for example in the centers of concrete atoms..
One of your confusions - localized or not, elementary particles are not solitons. Solitons are solutions to certain nonlinear wave equations. Localized elementary particles are linear superpositions of plane waves.
 
  • #9
dauto said:
You're not listening because you think you know something that you really don't. A photon is a quanta of electromagnetic field and an electron is a quanta of the electron field. The number of electrons is not a conserved quantity. Se for instance the beta-decay where an electron is produced while a neutron converts into a proton. Electric charge is conserved, that's true but the number of electrons isn't.
Indeed, the number of electrons is not conserved ... what is ultimately conserved is charge: guarded by electric field around due to Gauss law - and so often more appropriate than "electron field" is just "charge density rho" - something basic while considering electromagnetic field and definitely not fundamental.
Sure you can introduce additional fields, like density of electrons or similarly your "electron fields", but it is only for an effective description.
The difference between density scalar field and quantum fields of particles is that the latter additionally contains information about their correlations/superpositions.

Like with photons - electron changes e.g. orbital angular momentum, so Noether law says there have to be produced wave carrying angular momentum ... where do you need some additional fundamental fields here?

Bill_K said:
One of your confusions - localized or not, elementary particles are not solitons. Solitons are solutions to certain nonlinear wave equations. Localized elementary particles are linear superpositions of plane waves.
So you are saying that e.g. proton is just "a linear superposition of plane waves"?
Superposition of plane waves can have practically any shape, which can further evolve, disperse due to velocity differences ... while proton always looks nearly the same and is well localized - there are required nonlinearities holding it together.
Even in perturbative approximation you will get nowhere without nonlinearities (interactions) - usually approximated by the lowest term there.
 
  • #10
jarekd said:
Sure you can introduce additional fields, like density of electrons or similarly your "electron fields", but it is only for an effective description.

That's where you going wrong. The electron fields are the fundamental description while the particle is obtained as a localized quanta of the field. The same thing is true about the electromagnetic fields. The fields are the fundamental description. There is no meaningful way in which one field is more or less fundamental than the other.
 
  • #11
jarekd said:
You are talking about perturbative approximation, in which you imagine interaction between two charged objects as neverending stream of photons.
It is a useful picture for this approximation, but the reality is very different - photon has e.g. spin 1, so both interacting particles would have to change spin every time ...
The photon is described by a field Aμ which is a 4-vector. It gives the photon's polarization. For light waves the polarization is transverse, and the photon's angular momentum is ±1 along the direction of propagation.

The photons associated with the Coulomb interaction have a timelike polarization. That is, they are described by the fourth component A0. The angular momentum for this polarization is zero.
 
  • #12
dauto said:
The fields are the fundamental description. There is no meaningful way in which one field is more or less fundamental than the other.
Indeed we need a definition of "more fundamental" for this discussion - let us think about it.
Generally thermodynamical description is seen effective (effect) instead of fundamental (reason) - so having a classical particle in a box, you could give its trajectory or average it over time and give just density as averaged trajectory.
Clearly the trajectory is more fundamental here than the density - as you can infer density from trajectory, but cannot do the other way.

So I think the definition of "A is more fundamental than B" can be: you can infer B from A in unique way, but you cannot do it the opposite way (?) - it is a partial order.

So let us now look at electromagnetic field and electron field.
Assume there is only a single electron in the Universe - EM field says not only where this electron is, but can also tell a lot about its history ... what electron field can tell here?
 
  • #13
jarekd said:
So you are saying that e.g. proton is just "a linear superposition of plane waves"?
Superposition of plane waves can have practically any shape, which can further evolve, disperse due to velocity differences ... while proton always looks nearly the same and is well localized - there are required nonlinearities holding it together.
Even in perturbative approximation you will get nowhere without nonlinearities (interactions) - usually approximated by the lowest term there.

No. no non-"linearities" are required to keep a photon together. If the photon is in a vacuum there will be no dispersion and if it is in a medium it will be the non-linearity of the medium response to the photon that creates the dispersion to begin with, so it is kind of nonsensical to say the non-linearity keep it together. They actually pull the wave packet apart. Note also that doesn't mean the photon is torn apart. It only means that its location becomes more uncertain.
 
  • #14
jarekd said:
Indeed we need a definition of "more fundamental" for this discussion - let us think about it.
Generally thermodynamical description is seen effective (effect) instead of fundamental (reason) - so having a classical particle in a box, you could give its trajectory or average it over time and give just density as averaged trajectory.
Clearly the trajectory is more fundamental here than the density - as you can infer density from trajectory, but cannot do the other way.

So I think the definition of "A is more fundamental than B" can be: you can infer B from A in unique way, but you cannot do it the opposite way (?) - it is a partial order.

So let us now look at electromagnetic field and electron field.
Assume there is only a single electron in the Universe - EM field says not only where this electron is, but can also tell a lot about its history ... what electron field can tell here?

The electron field can tell you that electrons can be created or destroyed so your assumption of a universe with just a single electron in it is physically inconsistent. That's been known to be the case for about 80 years now since the advent of Quantum Field Theory.
 
  • #15
dauto said:
No. no non-"linearities" are required to keep a photon together. If the photon is in a vacuum there will be no dispersion and if it is in a medium it will be the non-linearity of the medium response to the photon that creates the dispersion to begin with, so it is kind of nonsensical to say the non-linearity keep it together. They actually pull the wave packet apart. Note also that doesn't mean the photon is torn apart. It only means that its location becomes more uncertain.
Ok, so what is happening when a single optical photon goes through a prism?
If you don't have something holding it together, shouldn't different components of its Fourier transform choose different angles - dispersing it?
The electron field can tell you that electrons can be created or destroyed so your assumption of a universe with just a single electron in it is physically inconsistent. That's been known to be the case for about 80 years now since the advent of Quantum Field Theory.
Does EM field forbids it? The Gauss law only guards total charge, does it forbid e.g. spontaneous pair creation?

Sure, there is something missing in pure EM field: that charges are quantized - and quantum description only assumes that.
EM field can be easily extended to make that Gauss law counts topological charge (still behaving accordingly to Maxwell's equations), which just have to be integer as in the nature - see e.g. Faber's model I discuss here: https://www.physicsforums.com/showthread.php?t=710042
 
  • #16
jarekd said:
Ok, so what is happening when a single optical photon goes through a prism?
If you don't have something holding it together, shouldn't different components of its Fourier transform choose different angles - dispersing it?
Yes a photon wave packet disperses when it goes through a prism even if it is a single photon wave packet - that is the position of the photon becomes more uncertain over time, and yet the photon doesn't dissolve over time and when detected it is still observed as a localized particle. But the place where that photon is found becomes more uncertain since it can be found anywhere inside of the wave packet which is becoming broader as it disperses.

Does EM field forbids it? The Gauss law only guards total charge, does it forbid e.g. spontaneous pair creation?

Sure, there is something missing in pure EM field: that charges are quantized - and quantum description only assumes that.
EM field can be easily extended to make that Gauss law counts topological charge (still behaving accordingly to Maxwell's equations), which just have to be integer as in the nature - see e.g. Faber's model I discuss here: https://www.physicsforums.com/showthread.php?t=710042

I'm not sure I understand where you're going with that. How does that link with your previous statements?
 
  • #17
dauto said:
Yes a photon wave packet disperses when it goes through a prism even if it is a single photon wave packet - that is the position of the photon becomes more uncertain over time, and yet the photon doesn't dissolve over time and when detected it is still observed as a localized particle. But the place where that photon is found becomes more uncertain since it can be found anywhere inside of the wave packet which is becoming broader as it disperses.
My point here is that, in contrary to your linear superposition, in reality optical photon does not disperse, but its energy remains localized to finally e.g. excite a single atom with the whole energy ... that you need something more than linear superposition to really understand optical photons.
I'm not sure I understand where you're going with that. How does that link with your previous statements?
You were claiming that quantum field theory is somehow better because it allows for various number of particles, so I have replied that EM field also allows for it.
Especially when we extend it to enforce charge quantization as topological charge - then you get soliton particle models in which you also naturally have various number of particles.
For example here is a nice animation of soliton-antisoliton annihilation in 1D: http://en.wikipedia.org/wiki/Topological_defect#Images . Run it backward and you get pair creation.
And to describe solitons you also can perform quantization procedure, getting Feynman ensemble among possible scenarios - exactly like in QFT, but with particles obtaining internal structure - being solitons.
 
  • #18
jarekd said:
My point here is that, in contrary to your linear superposition, in reality optical photon does not disperse, but its energy remains localized to finally e.g. excite a single atom with the whole energy ... that you need something more than linear superposition to really understand optical photons.

And my point is that you're mistaken to believe they don't disperse. They do disperse. You're correct that the photon's energy will be absorbed by a localized atom but that does not mean the photon didn't disperse. All it means is that the photon is quantized and must be absorbed all at once. The atom is much smaller then the wavelength of the light absorbed. Try creating a soliton with a length much more localized than its own wavelength. let me know if you're successful. Clearly the photon was NOT localized prior to being absorbed. You're trying to understand a quantum phenomenon using a classical model. No surprise you're getting all tangled up with misconceptions and non-sense.
 
  • #19
dauto said:
And my point is that you're mistaken to believe they don't disperse. They do disperse. You're correct that the photon's energy will be absorbed by a localized atom but that does not mean the photon didn't disperse. All it means is that the photon is quantized and must be absorbed all at once. The atom is much smaller then the wavelength of the light absorbed. Try creating a soliton with a length much more localized than its own wavelength. let me know if you're successful. Clearly the photon was NOT localized prior to being absorbed. You're trying to understand a quantum phenomenon using a classical model. No surprise you're getting all tangled up with misconceptions and non-sense.
If you also see e.g. electron or proton as just "linear superposition of waves", any dependence on momentum while a scattering, would also analogously disperse this particle ... so you are claiming that single particles can disperse ...
So how does e.g. electric field look around such dispersed elementary (indivisible!) charge?
 
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  • #20
jarekd said:
You were claiming that quantum field theory is somehow better because it allows for various number of particles, so I have replied that EM field also allows for it.
Especially when we extend it to enforce charge quantization as topological charge - then you get soliton particle models in which you also naturally have various number of particles.
For example here is a nice animation of soliton-antisoliton annihilation in 1D: http://en.wikipedia.org/wiki/Topological_defect#Images . Run it backward and you get pair creation.
And to describe solitons you also can perform quantization procedure, getting Feynman ensemble among possible scenarios - exactly like in QFT, but with particles obtaining internal structure - being solitons.

Well, classical electrodynamics don't have photons at all so I'm still have no idea what do you mean by variable number of particles here. Unless you quantize the theory - that is unless you use QFT, there are no photons, just waves. Do not confuse a localized wave such as a soliton with a quanta such as a photon. They are not remotely related to each other.
 
  • #21
jarekd said:
If you also see e.g. electron or proton as just "linear superposition of waves", any dependence on momentum while a scattering, would also analogously disperse this particle ... so you are claiming that single particles can disperse ...
So how does e.g. electric field look around such dispersed elementary (indivisible!) charge?

Yes, you're starting to get there. Single electrons just like single photons do disperse as a consequence of the unavoidable uncertainty in their momentum as per the Heisenberg Uncertainty Principle (HUP).
 
  • #22
dauto said:
Well, classical electrodynamics don't have photons at all so I'm still have no idea what do you mean by variable number of particles here. Unless you quantize the theory - that is unless you use QFT, there are no photons, just waves. Do not confuse a localized wave such as a soliton with a quanta such as a photon. They are not remotely related to each other.
I honestly don't know what are you talking about.
Look for example here for "new family of solutions to Maxwell's equations that are knots of light that do not disperse or lose their specific topological properties as they propagate.": http://physicsworld.com/cws/article/news/2013/oct/16/physicists-tie-light-into-knots
And generally Noether theorem says that a field is rotationally invariant, it conserves angular momentum - so if e.g. electron changes orbital angular momentum, there has to be created EM wave carrying this angular momentum - photon.
 
  • #23
jarekd said:
I honestly don't know what are you talking about.
Look for example here for "new family of solutions to Maxwell's equations that are knots of light that do not disperse or lose their specific topological properties as they propagate.": http://physicsworld.com/cws/article/news/2013/oct/16/physicists-tie-light-into-knots
And generally Noether theorem says that a field is rotationally invariant, it conserves angular momentum - so if e.g. electron changes orbital angular momentum, there has to be created EM wave carrying this angular momentum - photon.

That's an interesting article but it has nothing to do with photons. The article seems to be talking about a novel solution to the classic Maxwell equations. A photon is not a solution to the classic Maxwell equations. A photon is a solution to the Quantized Maxwell equations. If you don't understand what is the difference between a classical and a quantum theory than it will be very hard to understand why a photon is not just a localized wave.
 
  • #24
Thread closed pending discussion among the Mentors.
 

1. What is a particle?

A particle is a small, localized object that is considered to be a building block of matter.

2. What are fields?

Fields are physical quantities that exist in space and can exert a force on particles within that space.

3. How are particles and fields related?

Particles and fields are closely related, as particles are considered to be excitations or disturbances within their respective fields.

4. Is a particle more than the sum of its fields?

This question is a topic of debate in the scientific community. Some theories suggest that particles are made up of multiple fields, while others propose that particles are fundamental and cannot be broken down into smaller components.

5. What evidence supports the idea that a particle is more than the sum of its fields?

There is currently no definitive evidence to support either side of this debate. However, ongoing research in fields such as quantum mechanics and particle physics may provide new insights into the nature of particles and their relationship with fields.

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