Spontaneous mass formation from Energy

[nomadreid]

At certain concentrations of energy, there is the possibility of particles with mass forming. How does one measure "concentration of energy": by the wavelength? Or energy density? At what concentration will this occur, and why?

 

[nismaratwork]

At certain concentrations of energy, there is the possibility of particles with mass forming. How does one measure "concentration of energy": by the wavelength? Or energy density? At what concentration will this occur, and why?

You seem to be ignoring mass-energy equivalence. The answer is one of the best known equations in the world: E=MC^2...

http://en.wikipedia.org/wiki/Mass–energy_equivalence

 

[nomadreid]

Thank you, nismaratwork, but this does not answer the question: perhaps I need to be more explicit. That is, the fact that mass and energy are equivalent is supposed in my question. The Wiki article talks about a few cases of mass-energy equivalence (relativistic mass, binding energy, etc.), but does not go into the cases where a large amount of energy in a small space produces a particle with mass, for example in supercollider collisions. If you take the same amount of energy which produces a new massive particle in such a collision and spread it out in space, no such particle is formed. Hence there must be some measure of how concentrated this energy must be. This is a consideration that is not contained in the famous formula. So, I repeat: what is this measure?

 

[nismaratwork]

Thank you, nismaratwork, but this does not answer the question: perhaps I need to be more explicit. That is, the fact that mass and energy are equivalent is supposed in my question. The Wiki article talks about a few cases of mass-energy equivalence (relativistic mass, binding energy, etc.), but does not go into the cases where a large amount of energy in a small space produces a particle with mass, for example in supercollider collisions. If you take the same amount of energy which produces a new massive particle in such a collision and spread it out in space, no such particle is formed. Hence there must be some measure of how concentrated this energy must be. This is a consideration that is not contained in the famous formula. So, I repeat: what is this measure?

This should be obvious: enough to form the mass of the relevant particle. When you consider how much energy that is... not a shock that it's pretty much just pair creation-annihilation going on.

 

[nomadreid]

Thanks again,nismaratwork, but apparently I am still not being clear enough. So I might now go in the opposite direction and be a bit wordy.

As you say:

This should be obvious: enough to form the mass of the relevant particle.

This tells me how much energy. This might come from the KE of the particles in a particle collision, or a concentrated energy beam concentrated on a small enough target, or simply a photon in a pair production. In the pair production, it is clear that all the energy is in a single photon, and hence the "concentration" is defined by the wavelength of the photon corresponding to this energy. However, I am concerned about the other two cases.

First: the collision: The intuitive answer is that the collision must be "point-blank", but this does not really make sense as the two particles do not end up in precisely the same point. Another intuitive answer is that one just calculates the necessary kinetic energies and then calculates the mean distance that the particles can get to each other, but I am not sure if this is necessary or sufficient, and whether there is an easier way.

Secondly, as an example one justification for the interpretation of the Planck length as a minimum length is that attempting to measure something at a distance less than a Planck length results in a creating a black hole, shielding more precise knowledge, and this can be seen as a special case of energy to matter conversion. For the more general case, another intuitive answer is that the energy has to be concentrated on a particle, as photons don't directly combine, and that the incoming n photons have to raise the energy level of the particle in n appropriate steps before the particle has a chance to jumps down energy levels, and the particle has to then jump down all n energy levels at once to combine all the energy into one photon, so that the positions that the electrons have to be at will depend on the mean size of the target particle at the different energy levels... but this answer is not very satisfactory.

In any case, there appears to be a concept not only of the amount of energy, but also in the case of more than one energy source there is apparently some concept of a volume of space and a period of time in which the individual energies must intersect in order for particle production to take place. It is assuredly some standard concept, and it is this concept or method that I am looking for.