How could self-energy Feynman diagram be compatible with fundamental laws of physics? Let's consider this electron self-energy Feynman diagram:

The electron radiates a virtual photon, that is absorbed again by the electron.
There are two points that look incompatible with fundamental laws of physics.

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*the photon that is radiated flight in straight line, so if it goes with any non-null angle with respect to the angle of the electron, it is stricly impossible that it comes back to the flight direction of the electron. Even if this is only a schematic, concretely, when the electron radiates a photon, the electron must change its direction in order to conserve the transver momentum, while the photon flight in straight line, so the electron could not encounter again the photon : they are not travelling in a same direction, so how could the photon be absorbed again by the electron?


*the photon flights with speed of light $c$. The electron has a non null mass, so its speed is strictly lower to $c$. So when the electron emits the photon, immediately after, the photon is already further to the electron : the electron could never catch the photon.
The feynman diagram of the self-energy looks incompatible with two fundamental laws of physics, isn't it?
So how could self energy Feynman diagram be compatible with fundamental laws of physics?
 A: Feynman diagrams aren't spacetime diagrams, or even schematics; they are pretty, physically-suggestive pictures which are associated to terms in an ugly perturbation series.  They can provide some nice physical intuition when interpreted properly, but taking them too literally (especially when it comes to internal lines, the so-called virtual particles) leads to much confusion.
A: Virtual particles are off-shell, meaning that they don't follow the usual relationship between energy and momentum that follows from the classical equations of motion. In particular, for a virtual photon, $E \neq c p$. This means that the phase velocity $v=\frac{E}{p} \neq c$. In fact it's not even really possible to define a velocity associated with this virtual photon.
As J. Murray said, it's best not to take virtual particles too seriously as particles, they are essentially a colorful analogy and calculational device to help understand a complicated perturbative expansion.
A: Read chapter 28 "Electromagnetic mass" in the Feynman lectures of physics. It is about self interaction. Of course, it is not compatible with our own logic: on one hand we consider the electron unchanging, on the other hand we put in its equations of motion a strong self force (self-induction). No wonder, this "contribution" is then subtracted by us by hand - to get rid of it.
In QED it is the same effect - one must renormalize the electron mass; otherwise the calculation gives wrong physical results. But it is not sufficient either: one has to sum up soft radiation modes whose probabilities are nearly equal to unity - in order to obtain a physically meaningful result.
