Basic questions on collisions, particles

[Helicobacter]

Since particles are really better described as exponentially decreasing energy amplitudes fields in a configuration space (space-time)...how close do the max energy point of a particle and the max energy point of a antiparticle have to be before they annihilate? This critical distance between the energy peaks is determined by what?

Furthermore why does a electron and positron annihilating produce two photns and not three "gummybear particles" (invented by me) with each having [MEV of postron+MEV of electron]/3 mass?

Claim: the graph on y axis: number of such atoms in the universe, on the x axis: atoms of a certain proton count (increasing)...is distributed with a shape that reminds of the distribution of the exponential family.
Is my claim true? If so, why?im not a physics person so please keep it light.

 

[mathfeel]

Since particles are really better described as exponentially decreasing energy amplitudes fields in a configuration space (space-time)...how close do the max energy point of a particle and the max energy point of a antiparticle have to be before they annihilate? This critical distance between the energy peaks is determined by what?

There is no such thing as a critical distance. The size of the wavefunction packets is not an intrinsic properties of eletrons/positrons, but what state they are in. And in any states, there is a finite probability that they would annihilate and turn into some other pairs (photon is not the only process, just one with relative high probability). The probability is intuitive related to how much the two packets overlap.

Furthermore why does a electron and positron annihilating produce two photns and not three "gummybear particles" (invented by me) with each having [MEV of postron+MEV of electron]/3 mass?

The basic equations of nature (known as the Lagrangian) has a term that couples a charged particle, its charged anti-particle, and two photons. At the beginning, theoretical physicists put such terms in there there because we observe particle/anit-particle annihilation into two photons. Now if someone discover (as in make an observation of) a process of annihilation into three gummybearon, then we'll be forced to put something that describe gummybearon and its interaction with electrons/positions in there.

Well, that's not the entire story. Modern physics have developed symmetry arguments why certain term describing certain field must be in the basic equations and in what form (e.g., annihilating to three photons are not allowed). So you can say that the existence of photon and how it couples to charged particle--that is, electromagnetism itself--is a consequences of the symmetries of nature.

 

[Helicobacter]

Thanks for your answer!

There is no such thing as a critical distance. The size of the wavefunction packets is not an intrinsic properties of eletrons/positrons, but what state they are in. And in any states, there is a finite probability that they would annihilate and turn into some other pairs (photon is not the only process, just one with relative high probability). The probability is intuitive related to how much the two packets overlap.

Does this mean if you have a test tube filled with a certain particle and another test tube filled with its antiparticle then you have to be afraid of the thing exploding in your face if you even bring the test tubes close together (because the fields permeate thought the glass as if it weren't there)? From which point will the explosion have its "epicenter"...can it be in a midpoint (or something within that neighborhood) of the peak energy level points of two hating particles?
Approximately how close do you have to being the test tubes so that there is a 50% of explosion within one second?
What determines what state a particle is in? Its energy? How do you give more energy to a particle? Do you bombard it with other particles to do so? So, when you bombard it with less than the critical amount to promote it to the next state will it not gain any energy and through the conversion of energy the other particle gets repelled with the same amount of energy that it took to shoot it in?

Well, that's not the entire story. Modern physics have developed symmetry arguments why certain term describing certain field must be in the basic equations and in what form (e.g., annihilating to three photons are not allowed). So you can say that the existence of photon and how it couples to charged particle--that is, electromagnetism itself--is a consequences of the symmetries of nature.

I don't understand this part. Does this mean that given our "modern physics interpretation" can predict that two photons realize from this collision without explicitly stating the definition of the photon in the physics model ?