The definition is somewhat arbitrary, but still has some real physical significance. In actual fact, a proton is a field, so it doesn't have sharp boundaries. But the amplitude of the field still dies off very rapidly with distance from the center, so you can pick some arbitrary small value and say "the point at which the amplitude becomes less than this value is the radius of the proton". What matters is not really the number that you get out of this, but the fact that the experimental results of measuring this value appeared to change in the presence of muons. This was a phenomenon that was not predicted by present theory, and if it had held up, would have been a major breakthrough. One of the biggest problems in physics right now is that there are no experiments (except possibly this one) whose results are at odds with the Standard Model. That makes it hard to improve the model!
There are some really good responses to lisper's post: what about 96% of the universe's mass, neutrino mass, what about gravity for that matter. (zing!)
The thing about those particular questions is that they only tell us that the standard model is incomplete. Gravity exists. The fact that it's not in the standard model doesn't necessarily mean that the model is broken, just that gravity needs to be added somehow.
What we need more of are instances where the standard model makes a precise numeric prediction and it's dead wrong. That puts a spotlight on every piece of the standard model that went into the prediction.
"One of the biggest problems in physics right now is that there are no experiments (except possibly this one) whose results are at odds with the Standard Model."
What about Neutrino masses? Or the Muon 'anomalous' magnetic moment?
Does the magnitude of the field wave drop at some fixed shape (like an exponential)?
Is the wavelength fixed? Is it in meters?
Is it the field of a proton made up of multiple frequencies/modes?
Is a proton’s influence on fields extend to all space or is there a point (within the hubble sphere) at which a proton does not influence fields at all?
- Yes, it's fixed. It's also a complicated function.
- A quantum mechanics wave function does not necessarily have a wave length or a frequency. It is a different concept from waves, although classical waves are a consequence of it.
- In QM all particles influence all of space. It is also too small an influence to make any difference.
> One of the biggest problems in physics right now is that there are no experiments (except possibly this one) whose results are at odds with the Standard Model.
If we say that new physics comes from inconsistencies (either between theory and experiment, or simply within a theory), then there is plenty of new physics to be done, for example the pretense that an electron is a fundamental particle results in the inconsistency with predicted infinite mass. (I claim to have a solution, but I am sitting on it because I believe with a bunch more effort it can explain the dimensionless number that relates planck charge with electron charge, essentially explaining planck's constant and QM in quasiclassical terms...)
Hah! Fermat's comment indicated a willingness but lack of space.
My comment indicates unwillingness because I think I can deduce more from the insight. (resolving the infinite mass inconsistency was not in the original scope of my attempt, it just happened to roll out while trying to deduce the dimensionless ratio)
Anyway, the main point I was making was that there is plenty of work to be done, because theres plenty of unresolved problems left.
The usual deadlock picture (that theorists can't proceed if experimentalists don't bring new data, and experimentalists can't proceed if theorists don't bring good discriminative tests) hides either laziness or ignorance.
The definition is somewhat arbitrary, but still has some real physical significance. In actual fact, a proton is a field, so it doesn't have sharp boundaries. But the amplitude of the field still dies off very rapidly with distance from the center, so you can pick some arbitrary small value and say "the point at which the amplitude becomes less than this value is the radius of the proton". What matters is not really the number that you get out of this, but the fact that the experimental results of measuring this value appeared to change in the presence of muons. This was a phenomenon that was not predicted by present theory, and if it had held up, would have been a major breakthrough. One of the biggest problems in physics right now is that there are no experiments (except possibly this one) whose results are at odds with the Standard Model. That makes it hard to improve the model!