Range of electromagnetism

In summary, the argument for long range EM interactions is that the virtual photon is produced with low enough frequency to cover the necessary distance.
  • #1
lilphil1989
7
0
In a particle physics formalism, electromagnetism can be described in terms of interchange of virtual photons.

The range is then c.t = hbar / E

with t the lifetime, and E the energy of the virtual particle.

What is the argument then, for long range EM interactions, in terms of E?
Is it that the photon is simply produced with low enough frequency to cover the necessary distance? To me, this implies that the virtual photon "knows" how far it must travel, before it does so.
 
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  • #2
lilphil1989 said:
In a particle physics formalism, electromagnetism can be described in terms of interchange of virtual photons.

The range is then c.t = hbar / E

with t the lifetime, and E the energy of the virtual particle.

What is the argument then, for long range EM interactions, in terms of E?
Is it that the photon is simply produced with low enough frequency to cover the necessary distance? To me, this implies that the virtual photon "knows" how far it must travel, before it does so.

The virtual photon is not a physical particle that is emitted in order to be absorbed one light year away; it is a purely mathematical concept. In terms of Feynman diagrams it is a rule how to integrate over all allowed intermediate particle states including states off-mass-shell.

In the language of Feynman diagrams a propagator of a massless particle ~1/k2 has a Fourier transform 1/rD-2 for spatial dimension D=3, 4, ...; this is the mathematical reason for the long-range Coulom potential.

If you chose a different gauge in QED (a physical gauge like the Coulomb gauge or the axial gauge) you find the Coulomb potential ~1/r directly in the interaction Hamiltonian; the virtual particles are fluctuations on top of a static potential; this shows that a "virtual particle" is by no means uniquely defined.
 
  • #3
This is a good reason to not call these elements of path-integral formulation virtual particles. The confusion which often results is so contrary to scientific endeavor.
 
  • #4
In my course in QFT we first derived very simple Feynman diagrams in QED in the Coulomb gauge. The benefit is that you see both, the Coulomb potential and the propagators close to each other. It's more difficult than the radiation gauge but it makes very clear that the propagator is only a mathematical artefact.

If you simply take Feynman rules and diagrams w/o doing the calculation you never see the difference between an internal line and an external line; both look identical, but mathematical they are totally different entities. The external lines are somehow gauge-invariant physical entities, whereas an internal line is a gauge-dependent and therefore unphysical rule how to calculate things. As soon as you do the calculation you immediately see that external lines are something like asymptotic states (= particles) whereas internal lines are just mathematical expressions, namely certain integrals over 4d p-space.

Feynman invented his diagrams just for book-keeping; afaik the integrals existed prior to the invetion of the diagrams. Today it's the other way round; people first see the diagrams w/ knowing the math behind them.
 

1. What is the range of electromagnetism?

The range of electromagnetism refers to the distance over which the electromagnetic force can act. This force is one of the four fundamental forces of nature and is responsible for the interactions between electrically charged particles.

2. How far does the electromagnetic force extend?

The electromagnetic force is considered to be a long-range force, meaning it can act over large distances. It has an infinite range, meaning it can act between particles that are even lightyears apart.

3. Can electromagnetism act through materials?

Yes, the electromagnetic force can act through materials, but the strength of the force can be affected by the type and properties of the material. For example, some materials may block or weaken the force, while others may allow it to pass through relatively unaffected.

4. What is the role of electromagnetism in everyday life?

Electromagnetism plays a crucial role in many aspects of our daily lives. It is responsible for the functioning of electronic devices such as cell phones and computers, as well as the generation and transmission of electricity. It also plays a role in natural phenomena such as lightning and the Earth's magnetic field.

5. How is the range of electromagnetism related to its strength?

The strength of the electromagnetic force decreases as the distance between two charged particles increases. This relationship is known as the inverse-square law, meaning that the force is proportional to the inverse of the square of the distance between the particles. Therefore, the range of electromagnetism is indirectly related to its strength, with a stronger force having a longer range.

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