Photons exerting forces on Charges

Question

I have read on this website that a photon can be considered made up of a virtual electron and a virtual positron. And since photons don't have a classical momentum and are not deflected by static charges, then why would they exert forces on charges? Does this mean that Newton's third law is violated all the time in CERN? Do the accelerators receive a recoil? (or maybe its just too tiny to detect?)

Answer 1

Newton's third law belongs to the framework of classical mechanics:

When one body exerts a force on a second body, the second body simultaneously exerts a force equal in magnitude and opposite in direction on the first body.

Photons are quantum mechanical objects and are studied with quantum mechanics. The classical regime emerges from the underlying quantum mechanical frame, and there is continuity, but not in the sense of carrying Newton's laws intact to the QM frame.

In quantum mechanics the concept of "force" is described as an "interaction". A particle interacts with another particle and there are precise rules prescribing how the interactions happen. Interactions can be electromagnetic, or strong or weak, corresponding to macroscopic force concepts . Virtual particles, in your question virtual electrons and positrons, are just mathematical representations carrying the quantum numbers of the corresponding name, but not the mass. Please look at this answer of mine to get a feeling on what a virtual particle is.

In quantum mechanics one has a mathematical description of a "particle" with a wavefunction, a solution of the corresponding equation, for photons it is a quantized Maxwell equation, for electrons and positrons the Dirac. These are complex functions. All measurements in physics give real numbers. Thus a mathematical wavefunction that describes a photon as a virtual electron positron pair is not something measurable in the lab. To get a measurement the photon has to interact, and in quantum mechanics, only probabilities of interactions at (x,y,z,t) between a photon and a real electron for example, give measurable quantities like momenta and energies which are needed to check consistency with energy and momentum conservation , which macroscopically will build up Newton's laws.

In Compton scattering, for example, a photon interacts with an electron and the diagrams giving the interaction , called Feynman diagrams, are precise directions for the integrals which will calculate the real numbers for the interaction probabilities.

The electron positron loops of individual lines are higher order terms and enter with a small coefficient in the calculations due to the two electromagnetic vertices and get integrated over in order to get a real number for predicting the probability of interaction. Virtual loops can only have a meaning within an interaction.

The only laws that apply at the quantum mechanical level are conservation laws, of energy momentum, angular momentum and a plethora of quantum numbers according to the interactions.

Answer 2

You have several questions here which seem to result from misunderstanding the nature of photons. In addition, the word "classical" is doing a lot of work which it probably shouldn't be:

1. Photons do have momentum. In QM it's related to the wavelength and frequency. In macroscopic situations it's the Poynting flux. You can't use the non-relativistic particle calculation of $p = m v$ because 1) the Poynting flux dominates the mass-based component of momentum since the mass is zero, and 2) since the mass is zero, photons travel at the speed of light which requires relativistic calculations. Those equations give $p = \frac{0}{0}$, undefined. Thus trying to blindly apply non-relativistic Newtonian mechanics to massless relativistic particles is guaranteed to fail.

2. Photons are deflected by charges, but the charges don't remain "static". Each time a charge deflects a photon, it feels a recoil. You're going to run into trouble if you try to compute the details of the scattering without accounting for relativity and quantum mechanics, but conservation of momentum & energy still apply.

3. Newton's third law is not violated in particle accelerators, except in the sense that quantum mechanics is constantly borrowing energy & momentum for immeasurably brief periods of time and over immeasurably short distances. The actual observable particle-photon interactions conserve momentum, but the math hints that such might not be the case on extraordinarily tiny scales.

4. Yes, accelerators and their targets receive recoil. It's tiny because accelerators are massive and charged particles are tiny. You'd need something like 20 digits of precision in the momentum measurement to sense it.