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We then have a better estimation for the total probability amplitude by adding the probability amplitudes of these two possibilities to our original simple estimate. Based on the properties of the cross product, this produces a vector that is perpendicular to both the velocity and magnetic field vectors.

They are related to our everyday ideas of probability by the simple rule that the probability of an event is the square of the length of the corresponding amplitude arrow. Each diagram involves some calculation involving definite rules to find the associated probability amplitude.

An electron moving backwards

The amplitude arrows are fundamental to the description of the world given by quantum theory. An electron moving backwards in time can be viewed as a positron moving forward in time.

Feynman avoids exposing the reader to the mathematics of complex numbers by using a simple but accurate representation of them as arrows on a piece of paper or screen. The simplest process to achieve this end is for the electron to move from A to C an elementary action and for the photon to move from B to D another elementary action.

Compton scattering But there are other ways in which the end result could come about. That basic scaffolding remains when one moves to a quantum description, but some conceptual changes are needed.

The amplitude arrows are

The sum of these two vectors is the Lorentz force. In the absence of an electric field, the force is perpendicular to the velocity of the particle and the direction of the magnetic field. Quantum mechanics introduces an important change in the way probabilities are computed. If both electric and magnetic fields are present, the Lorentz force is the sum of both of these vectors. The sum of all resulting arrows represents the total probability of the event.