The commonly held explanation is that the electromagnetic force is transferred by virtual photons. Are the static electric and magnetic fields produced by an electron also the result of virtual photon emission? The electric field that surrounds an electron has energy density of Ue = αħc/8πr4. Do the electron’s virtual photons possess momentum (p) with energy E = pc? Are energetic virtual photons being emitted by an electron and then the energy eventually returned to the electron? Why do an electron’s virtual photons produce a measurable energy density but the virtual photons created in the vacuum produce no energy density? Does accelerating an electron abandon some of the virtual photons’ energy which then becomes a real photon? Is there a difference between the virtual photons emitted by electrons compared to the virtual photons emitted by positrons?
As you might have guessed from these provocative questions, I believe that virtual photons are not responsible for electric fields. Instead, I believe that all fields and forces have a wave-based explanation. However, I really do want to hear your answers to these questions so that I can better understand the model of an electric field visualized by respondents.
I agree that the statement that "electromagnetic force is transferred by virtual photons" is only metaphorical. On a formal level, the interaction between electrons can be derived by starting from the fundamental Lagrangean of quantum electrodynamics (which couples the matter and the electromagnetic fields) and integrating out the electromagnetic ("photonic") degrees of freedom in the functional integral formalism. In a certain approximation, this procedure yields back the Coulomb interaction between electrons. A classic reference for this is Sec. 1.5 of [A. Zee, Quantum Field Theory in a Nutshell, 2nd ed., Princeton University Press, 2010].
Electrons don't produce a static electromagnetic field, only an electric field. In order to have a dynamic electromagnetic field one must have a time varying source. A single charge won't do that.
Dear John,
when one talks of virtual quantum particles, it means that we are discussing of some quantum interactions !
Without quantum interactions one cannot have virtual quantum particles. In fact such objects are built inside nonlinear quantum propagators encoding quantum reactions (by considering my quantum gravity theory). For example the reaction e++e-->\gamma+\gamma, between positron and electron produces an intermediate massive quantum particle that can be considered a virtual photon.
Therefore, in the case of an ideal noninteracting electron one cannot talk of virtual photon or virtual quantum particles.
It is important to emphasize that such virtual quantum particles can be considered obtained by some elementary bordisms in the which nonlinear quantum propagators can be split. For a more precise terminology and information one can look my papers
[1-2] http://arxiv.org/abs/1205.2894.
My best regards,
Agostino
I agree also with Dr. Gross. I should have said electric field and magnetic field rather than electromagnetic field. To avoid further criticism of this error, I have edited the question and corrected the wording so that subsequent readers can focus on the main point. The objective of this question is to see if scientists consider electric and magnetic fields are caused by virtual photons. If these fields are not a collection of virtual photons, then how do you visualize the underlying physics of the fields? Gravity is clearly a distortion of spacetime. Is an electric field also a distortion of spacetime?
Agostino: You say, “Without quantum interactions one cannot have virtual quantum particles… in the case of an ideal noninteracting electron one cannot talk of virtual photon.” This seems to imply that your concept is that a virtual photon is only generated when some other charged particle comes close. Perhaps I am not understanding this concept, but the obvious questions are: 1) How does the electron know when to generate a virtual photon? 2) Do virtual photons propagate faster than the speed of light? There are cases when a relativistic electron interacts with a magnetic field in a way that there is not enough time to send out new virtual photons at the speed of light. 3) What produces the energy density present in an electric or magnetic field?
Giulio: Your answer is mathematically based and I am sure that it gives answers that correspond to experiments. This is the standard of success normally used in physics today. However, I feel that we live in a time that has analogies to the late 1800’s. They had equations relating to electrostatic force and magnetism, but the electron was not discovered until 1897. Once the properties of an electron were understood, then a deeper understanding of physics was gained. Today we have much more advanced equations but we do not conceptually understand the underlying physics of an electric or magnetic field. I have my own model of an electric field which generates the correct force and the correct energy density, but I am trying to understand the models of others.
Dear John,
in your last post you have written:
'The objective of this question is to see if scientists consider electric and magnetic fields are caused by virtual photons. If these fields are not a collection of virtual photons, then how do you visualize the underlying physics of the fields? Gravity is clearly a distortion of spacetime. Is an electric field also a distortion of spacetime? '
It is clear that you are confusing macroscopic world with microscopic world and vice versa.
When you talk about (virtual) photons you necessarily refer to microscopic world. When you talk of spacetime and at the same time of photons and gravitons, then you refer to the observed quantum microscopic world. Therefore, let us consider just this last situation. Then observed quantum phenomena are encoded by means of observed nonlinear quantum propagators, solutions of the observed quantum super Yang-Mills PDEs, say (YM)[i]. These are in general 4-dimensional manifolds having non-trivial topology determined by the observed quantum structure. In other words, to be more clear I can simply say that an observed quantum process is encoded by a 'distorsion of spcetime' by using your words.
Electric and Magnetic fields are not caused by virtual photons, they are caused by real electrons. Moving electrons cause a current. The current causes an electric and magnetic field. If the current is a DC current then their is no propagation but there are fields surrounding the source with a 1/distance drop off. If the current varies with time then there is radiation. The radiation from a point source has a power fall off of 1/r^2. Thus the propagation distance is relatively short unless their are good conditions for long range propagation such as ducting.
Dear John,
after I posted my answer I have seen the following your questions addressed to me:
'Perhaps I am not understanding this concept, but the obvious questions are: 1) How does the electron know when to generate a virtual photon? 2) Do virtual photons propagate faster than the speed of light? There are cases when a relativistic electron interacts with a magnetic field in a way that there is not enough time to send out new virtual photons at the speed of light. 3) What produces the energy density present in an electric or magnetic field? '
In order to answer to your points let me first underline that quantum fields and quantum particles are two different geometric concepts. In particular (YM)[i] is built by means of quantum fields, instead quantum particles are space-like 3-dimensional transverse sections of compact observed nonlinear quantum propagators. These are compact 4-dimensional solutions of (YM)[i] with nontrivial topology.
1) This question is misleading ! A virtual photon can be generated when, for example e- interacts with e+. Their interaction produces a topological handle between the two quantum particles, hence a suitable nonlinear quantum propagator, that generates a massive photon, before to produce two photons.
2) At this level SR and GR do not work to chracterize massive photons. These are only characterized by quantum algebraic topologic conditions and quantum conservation laws, applied to the observed nonlinear quantum propagator.
3) A quantum field in (YM)[i] in general contains quantum graviton field and quantum electro-magnetic field. Its quantum energy is characterized by its quantum Hamiltonian. In other words any solution of (YM)[i] has its quantum energy, hence its energy-spectrum.
By conclusion photons are quantum particles freely propagating by means of nonlinear quantum propagators having zero mass-gap, spin 1 and zero electric charge. Virtual photons instead are encoded by nonlinear quantum propagators having a non-zero mass-gap. Therefore the nonlinear quantum propagator encoding the reaction e++e- -> \gamma+\gamma is made by two pieces having non-zero mass-gap and another with zero mass-gap. The central piece has a virtual photon.
Agostino, Remi and Frank: I appreciate your expert answers. The picture that has emerged from the explanations is that the quantum mechanical rules and mathematical relationships can accurately predict the outcome of an experiment. But I am trying to see if anyone has a physical model of an electric field or a charged particle. For example, what is physically happening to create the energy density of an electric field? If energy is defined as E2 ≡ (mc2)2 + (pc)2, then is the energy in an electric field due to the mc2 component, the pc component or none of the above? If there are plane virtual waves carrying momentum, then what is the physical description of the waves? What is the physical reason that they come into existence and go out of existence in the way required by quantum mechanics?
Previously I asked the following question on ResearchGate: Are there any of the mysteries of physics that are beyond our intellectual capacity to conceptually understand? Most of the answers implied that the human intellect could understand anything in physics if a good model could be developed. I am attempting to find out if there are any other physical models of an electric field which explain both its energy density and its electrostatic force.
When I developed a model of the universe using only the properties of 4 dimensional spacetime, I get zero point energy, particles, gravity and electric fields. The physical model of an electric field which emerges in this analysis has an oscillating component and a non-oscillating component. This physical model generates the correct forces, correct electric field characteristics and the correct energy density. Furthermore, this model makes correct predictions for previously unknown limitations on photons and vacuum capacitors. The model of an electric field and the limit analysis is contained on pages 13 to 16 of the attached paper.
http://onlyspacetime.com/QM-Foundation.pdf
In my model electron positron pair are born 10^(-36) sec. after big bang. This happens when the available plasma at this time freeze into electron and positron mass. During this freezing, energy of electron is wound up in one direction and the energy of positron is wound up in opposite direction. This opposite winding between the two makes up the positive and negative charge which distortes the space time around them causing the electrostatic and magnetic fields. So there are no virtual photons involved. When electron and positron annihilate each other the energies of both particles unwind and so their masses are annihilated and we get massless chargeless photon which retains the electromagnetic properties of the original particles. When an isolated electron is accelerated, it emits a real photon. The energy of this photon must come from the kinetic energy of the electron so the mass and charge of the electron remains constant.
Is it right to say that something that is virtual, is a visualisation by definition, in which case you might want to reword your question...?
Dear John,
you have written:
'... But I am trying to see if anyone has a physical model of an electric field or a charged particle.'
With this respect you can reproduce the calculations reported for quantum electron in
http://www.sciencedirect.com/science/article/pii/S0362546X08006068
to the more general situation of quantum gravity given in
http://www.sciencedirect.com/science/article/pii/S1468121812000491.
In such a way you get the physical model for the quantum electron that you ask.
Let me also add that quantum particles in quantum gravity, are not more point-like objects as usually considered in QFT, therefore quantum electric and quantum magnetic energy cannot be resumed in the formula E2 ≡ (mc2)2 + (pc)2, to which you refer ...
Dear John,
The interaction between an electron and other charged particles in the Universe can be modeled as a stationary electromagnetic wave exchange (if the electron is at rest). In fact the energy density of the electric field of the electron (Ue = αħc / 8πr4) is the result of second-order scattering.
In a simple classic model (see a model at the studenst/undergraduateds level, for electrostatic interaction: I. Simaciu , Cornelius Ciubotariu: Classical model of electron in stochastic electrodynamics)., The electron scatter the electromagnetic background (Zero Point Field Classical -CZPF) and produce a field energy density Ue -1 / 4πr2. This field scattered near another electron produces Coulomb force.
The electron extract virtual energy of the vacuum. The particles are "detectors" of the energy (photons standing waves and virtual). And two conducting plates extract energy from the vacuum (the Casimir effect). The devices do not detect the virtual photons in vacuum (standing waves in vacuum) because they only measure energy differences. When an "obstacle" (two particles or two conducting plates) produces a difference in energy density when it is detected as a force (pressure difference) on the "obstacle". Virtual photons of an electron produce a measurable energy density because the density varies in space.
Best regards,
Ion
OK, Remi said,
"Does not EM emanate from anti-particles and the nucleus too? Are quarks not charged too? Besides, a varying electric field can generate a magnetic field and vice ca verca, so in principle, no sources. How do you visualize a virtual photon? "
No electric or magnetic field can exist anywhere in the universe without sources. All charged particles give rise to electric and/or magnetic fields. Be they quarks, electrons, etc... A varying electric field is not what gives rise to a magnetic field. A time varying source gives rise to electric and magnetic fields. That time varying source can be moving charges etc... Stationary fixed electric charges do not give rise to magnetic fields.
Dear Remi,
In the stochastic electrodynamics the zero background (Classical Zero Point Field -CZPF) is considered real. In quantum electrodynamics, in the stationary states, electrons and protons changing virtual photons. In the stochastic electrodynamics, electrons and protons interact via electromagnetic waves with stochastic properties (see references and comments in the Phd thesis Stochastic Methods in Quantum and Relativistic Physics and article New Results in Stochastic Physics – Ion S., ResearchGate).
Regars
Ion
Ion and Remi: Remi asks good questions about the zero point field (ZPF) and whether it is "real". I have written papers on this subject. The short answer is that the vacuum is not an empty void. It has physical properties such as the constants c, G, ħ, εo, etc. However, the most amazing property is detected by gravitational waves as they propagate in the medium of spacetime. To gravitational waves, spacetime appears to be a very stiff elastic medium with impedance of Zs = c3/G = 4 x 1035 kg/s. (References in gravitational wave texts can be given to support this last statement.) This large impedance implies that spacetime has a tremendously large energy density which only becomes detectable when quantized angular momentum (spin) is added. Gravitational waves introduce quantized angular momentum, so they make the “fabric of spacetime” detectable. For example, the gravitational wave announced recently had a maximum frequency of about 250 Hz. When this wave propagates in the medium of spacetime, the spacetime at that frequency seemes to have energy density of about 1032 J/m3. This “interactive energy density Ui” is frequency dependent according to the equation Ui = (1/16π)(ω2c2/G) where ω is the angular frequency of the gravitational wave.
This all fits with the model of spacetime which has zero point energy being small amplitude waves in spacetime which lack quantized angular momentum. They modulate the distance between points by Planck length at Planck frequency. These waves act like harmonic oscillators with energy E = ½ ħω. They explain the uncertainty principle and the probabilistic characteristics of quantum mechanics. They are normally undetectable because of their small amplitude and the fact that we can only interact with fermions and bosons which are entities with quantized angular momentum. Ultimately this all relates to the physical explanation of an electric field. An electric field is a quantifiable polarization of the ZPF that fills spacetime.
John: I apologize for the discussion about stochastic electrodynamics!
Remi: Your knowledge about stochastic electrodynamics is superficial. Perhaps, your knowledge is guided by the views of physicists who support only quantum model and not on a comprehensive study. Quantum model allows quantitative assessments very good, but does not provide a physical understanding (causal) quantum properties. The situation is similar with general relativity. It is a mathematical model of the gravitational interaction that says little about the interaction phenomenology (causative physical model). The failure of quantification of gravitational interaction
is the result of these models which are more mathematical than physical.
Ion
Four momentum of an elementary particle transforms as a vector. So, taking the dot product of four momentum with itself gives a Lorentz scalar, which is frame independent. Simply by computing pμpμ and equating that to (m0c)2 we get relativistic energy momentum relation valid for any particle (also macroscopic objects). This is a classical relation.
Next in a quantum field theory a diagram can have two different types of lines. 1) External lines, which are observed and 2) Internal lines, which are not observed. External particles are always real. Internal lines can be either real or virtual. An internal line is real if energy momentum relation (note that it is a classical relation) is obeyed, and virtual if this relation is violated for a short duration of time.
In the case of photon, m0=0, so mass shell is pμpμ = 0, or E2 - p2 = 0. This is a classical relation between the momentum of a photon and it's energy. In a quantum world, both E and p have inherent quantum mechanical uncertainty. Therefore it is most natural to expect that for a short time the relation E2 - p2 = 0 for a photon will be violated, and in that short duration of time the photon is defined as a virtual photon.
Vacuum space can be thought of as a swarm of microstates filled with energy or unfilled. The ZPE has an average wavelength and frequency in which the virtual particles are energy potentials that are not large enough to make real particles pairs and separate them by more than one wavelength.
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