Feynman diagrams are used by physicists to represent the possible interactions between elementary particles.
Wikipedia: The lines in Feynman diagrams represent particles interacting with each other in some fashion. Mathematical expressions correspond to every line and node. The probability of certain interactions occurring can be calculated by drawing the corresponding diagrams and using them to find the correct mathematical expression. The diagrams are basically accounting tools with a simple visual representation of an interaction of particles.
So it is not the case that physicists assume that those particles exist physically during their lifetime and that they follow trajectories. That contradicts the wave aspect that quantum physics assigns to them. They prefer to assume that the particles in some virtual way do ‘try out’ all possible paths, where one is always chosen and becoming physical on measurement. Each Feynman diagram is just a way of visualizing one the possible interactions. But the temptation to view these interactions as objective physical events is strong.
The above figure is one of the simplest Feynman diagrams you can find on the internet. Shown vertically is the time (t), horizontally the position (x). This diagram shows the simplest way two electrons can affect each other. Two electrons fly towards each other, repel each other at time t0 and fly apart again at the same speeds. At the moment t0, when they are at positions x1 and x2, they exchange a photon. A photon carries a certain momentum, transfers it and thus exchanges the momentum of both electrons. After the exchange, the electrons fly apart at the same speeds at which they first approached each other. The question is, of course, how electrons ‘feel’ that there are other electrons nearby so that they have to exchange photons. The exchange, as shown here, is an instantaneous process, the path of the photon is horizontal at t0.
The photon exchanges the electron momenta
Hey, that’s curious, that makes the speed of the photon infinite. That will certainly not be the intent of the diagram. However, there is more that raises questions. The direction of the photon is not indicated. The photon could move from right to left as well as from left to right. The electrons both undergo an momentum change due to the exchange of the photon. Momentum is the amount of movement expressed in mass m times velocity v: p = mv. The left electron undergoes a velocity change Δv1. From this follows a momentum change Δp1= mΔv1, ditto for the right electron: Δp2= mΔv2. The velocity changes Δv1 and Δv2 are of equal magnitude and of opposite direction: Δv1 = -Δv2. This means that the total momentum does not change: Δv1 + Δv2 = 0 so Δp1 + Δp2 = 0. That is 100% according to an important law in physics: The total momentum of a closed system does not change.
The accounting is correct for the momenta
The photon does the transfer of the momentum, because a photon carries a momentum according to De Broglie: p=h/λ. Both electrons undergo an equal and opposite momentum change which is transferred through the photon, whether the photon moves to the left or the right. For example, suppose the photon moves to the right. The left electron undergoes an impulse change Δp1= mΔv1 = h/λ, the right-hand electron Δp2= mΔv2 = – h/λ. This last minus sign is because the photon loses its momentum when interacting with the electron on the right. Since v1 = – Δv2 holds, the total impulse Δp1 +Δp2 is preserved. If the photon travels in the opposite direction, the result is the same. So it doesn’t matter in which direction the photon moves. If the photon has the speed of light, then the impulse changes will be slightly consecutive in time. The emitting electron changes its momentum first in time, the receiving electron a little later. But that’s not a real problem. The accounting of the momenta is correct.
At least two photons are needed.
But what about the energy? A photon also carries an amount energy that is proportional to its frequency f: E=hf. That’s Planck’s law. If the photon moves to the right, the left electron must have lost some amount of kinetic energy because it has transferred it to the flying away photon: ΔE= – hf. As a result the electron on the left has lost some kinetic energy. The receiving right electron then receives this energy as gained kinetic energy. So it has a higher speed. And if the photon were to move to the left, the right electron loses the kinetic energy that the left electron gains. That can’t be right. Both scenarios conflict with the elastic collision of two objects and cause an asymmetry in the course of the interaction. If we want to achieve the same as in an elastic collision we must assume two simultaneous photons, one going from left to right and one from right to left. Both transfer energy and impulse. This way the accounting is correct again. The sum of the transmitted impulses is zero and there is no transmitted kinetic energy. We need two photons for that. In itself, a Feynman diagram can be supplemented in this way. There is no objection to that.
There should be a simpler story
A correct story with the exchange of photons becomes considerably more difficult with particles that attract each other, such as an electron and a positron. Isn’t it actually simpler to assume a single interaction in which the charged particles exchange their momentum but no energy? In my opinion, a photon is nothing more or less than the observation of an energy exchange that must have occurred. The assumption that it should be a physical particle is the result of the image imposed on us by classical physics. A photon can therefore also be regarded as nothing more than the observation of an impulse exchange. Elsewhere on this website, and also in my book, I argue extensively that the photon does not physically exist and thus does not travel. The photon is, I think, a reified abstraction.
Quantum field theory
In quantum field theory it is assumed that a moving electron, which is a non-physical probability wave as long as it is not measured, is surrounded by a cloud of virtual (!) photons, where two of them become real photons in this case, to take care of the momentum exchange . This representation replaces Maxwell’s electromagnetic field concept. Actually Maxwell wasn’t very happy with his field concept since he had to assign properties to empty space. Quantum field theory now replaces that electromagnetic field by assuming large amounts of virtual photons popping in and out thin air. In this way you avoid the troublesome idea that electrons would have ‘feel’ each other’s proximity and decide ‘in time’ to perform an impulse exchange in order to move away from each other again. In this way the objective electromagnetic field has been replaced by something even more complex and ultimately based on the field concept, a state of empty space, this time chock-full of virtual particles. Admittedly, quantum field theory does provide very precise predictions. But that could also be said about the epicycles of Ptolemy.
Virtual dancing with quantum fields, a dream
Before 1900 we had the rather simple billiard ball model of the universe. Quantum field theory has now taken its place. To get an idea of its message let’s assume that you’ve been worrying deeply about quantum fields and those virtual photons. Exhausted you fall asleep and you start dreaming. You find yourself in a dance outfit on a huge expanse of ultra smooth dance floor where you can’t see the walls. Everywhere people are dancing, it is swarming with them in some places. In quieter places you see someone alone doing a pretty good pirouette. The floor so slippery that there’s no way you can move from your place. How do the others do that? Then you notice that billiard balls are constantly appearing and disappearing everywhere in the air. The heavier the ball, the faster it disappears again. The smaller and lighter ones last a little longer but eventually they disappear too. You understand that those balls are virtual but that they are physical for a short time. Now you understand, you want to dance and you are looking for someone to dance with.
Then you see someone repulsive sliding towards you. You don’t want to dance with this person. So, you grab a large heavy virtual billiard ball, that just appears in the air near you, and you throw it in this person’s direction. The other person catches the ball neatly after which it immediately disappears again into thin air. The result is that you two are sliding apart again. Then you see someone really attractive. You want to dance with that person, but the person is gliding along a trajectory that does not come close to your trajectory. So, you grab another billiard ball, that conveniently pops up at that moment. You throw the ball in the opposite direction and you see to your pleasure that the other person does the same. You move towards each other and begin to dance happily … and then you wake up. End of dream. Regrettable.
But you now suddenly understand the idea of the quantum fields a lot better. It’s just the old billiard balls story again. But now they are ‘virtual’. Virtual is a concept from optics and means that an object exists physically but not physically, it is not tangible. A rainbow is a virtual object. You can’t grab it but materialistic thinking tries to do just that.
When I think about this tortuous explanation with virtual photons, it inadvertently reminds me of the epicycles of Ptolemy that ‘explained’ the movements of the planets in the heavens in a very complex way and that lasted for 1400 years because the idea of the earth at the center was something people preferred rather strongly and, more important, because it was so accurate in its predictions. Take a look at the Ptolemaic animation of the movement of Mars through the heavens below to get an understanding of its utter tortuous complexity. Ptolemy’s epicycles were indeed virtual.