Electron + Positron Annihilation Process

[Rade]

I have a question about the dynamics of the electron (-) plus positron (+) annihilation process.

 

As I understand the situation, when the two first come close together (how close I do not know, but as I understand the situation it really is not close at all given the small scale involved), before they annihilate, they form a system called the positronium, where the (-) and (+) orbit around each other and then they emit photons that contain 100% of the positive energy that was present in both the (-) and (+), and then, these two entities that once had mass and charge and spin just vanish (i.e., they annihilate).

 

But wait--why must this be true ? Why not just have the (-) and (+) entities, after they emit the photons, both take a quantum energy movement such they both reach a lower 'negative energy' system state with negative mass--that is, they not vanish at all--they still present but of course cannot be measured--a type of veiled reality--vanished from human measurement (what we think we know is real) yet still present in reality (what really is real).

 

Is this not exactly what is predicted by the Dirac Equation ?--that there is no effective mass or energy annihilation when the electron (-) meets the positron (+), just a quantum change from positive mass and energy to negative mass and energy. Such a wonderful and symmetric solution to the process of annihilation appears to come from the Dirac Equation--but perhaps I have no idea what I am saying. So please show where my thoughts are in error (oh, and yes, where Dirac was in error too).

[lawcat]

I thought that this was simply explained by the convergence of two spinors; as the two spinors converge, having opposite moments, they come to rest (the moment vectors cancel out); that being the case, and according to the Dirac equation, momentum disappears, and all you have left is mc2--photon traveling away. To me this makes sense, but if you claim that it does not have to be, then you should provide a more detailed analysis--especially considering that the two are mirror images of each other.

[Qfwfq]

But wait--why must this be true ?

This is what is observed quite frequently and

Is this not exactly what is predicted by the Dirac Equation ?

the Dirac equation accounts for the anihilation as observed.

 

The negative energy states have a rather fanciful interpretation which is not experimentally distinguishable from the more realistic (and observed) phenomena of pair production and anihilation; this implies that we either cannot observe the negative energy states or that they don't actually exist. The mathematical construct is compatible with observed reality but describes it "in its own little way", so to speak. A very neat way, actually, but which should be regarded as a just mathematical trick.

 

The fanciful picture, suggested by Dirac himself, is that of there being a uniform sea of electrons in all the possible negative energy states except for the occasional lacking one, which we observe as the antiparticle in the corresponding positive energy state. This is clearly not something we can test, though as a model it works quite like the charge carriers in a semiconductor.

 

P. S. When anihilation occurs, we might say that either of the two (but not both) leaps into the unoccupied negative energy state and that the observable effect is of both disappearing.