Photon-particle interaction, uncertainty

The uncertainty for the momentum of the particle M, after interaction with the photon, can be predicted in many different ways, as can bee seen in a variety of textbooks on quantum mechanics. Each author tries a slightly different approach, taking into account more or fewer factors, but at the end, of course, all of them unavoidably find the same formula. The main reason why all of these authors find the same final formula, even when they follow different approaches, results from the known fact that the uncertainty for the position is fixed and given by the microscope theoretical resolution. Therefore, since the uncertainty for the position is fixed, there is no liberty for the expression of the uncertainty in momentum if one whishes, as is always the case, to stay in agreement with Heisenberg s uncertainty relations. 

This value, as expected, relates to the maximum possible momentum transferred from the photon to the microparticle, even if some values of the diffusion angle obviously have a very low or even zero probability. As stated before, this formula for the uncertainty in the momentum of the small particle M after the measurement is precisely the same for both microscopes. In either case, it is necessary to keep in mind that, in this step of the measuring process of the error of the two conjugated observables, the interacting photon behaves like a corpuscle. 

How is this possible Consider the familial- electromagnetic interaction. Two charged particles can be imagined to interact electromagnetically by the emission of virtual photons that are continuously emitted and absorbed by the particles (i.e., exchanged). The Heisenberg uncertainty principle tells us that... 

Figure 5.14 When a photon interacts with an electron at rest, both the velocity and the position of the electron are modified. This illustrates the Heisenberg uncertainty principle. It is impossible to know at the same time the position and the velocity of a particle. Explain Why has the photon s energy changed ... 

Heisenberg s idea involved the detection of electrons. Electrons are detected by their interaction with photons. Because photons have about the same energy as electrons, any attempt to locate a specific electron with a photon knocks the electron off its course. As a result, there is always a basic uncertainty in trying to locate an electron (or any other particle). The Heisenberg uncertainty principle states that it is impossible to determine simuitaneousiy both the position and velocity of an electron or any other particle. This was a difficult idea for scientists to accept at the time, but it is now fundamental to our understanding of hght and matter. 

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