RE: First collisions at the LHC with unprecedented Energy! (Ask a particle physisicist)
June 2, 2015 at 9:52 pm
(This post was last modified: June 2, 2015 at 10:06 pm by Alex K.)
(June 2, 2015 at 9:31 pm)JuliaL Wrote: How could you show that?
The wave packets of location probability density have extent don't they?
Is it a convenience? or are they definitely zero dimensional?
Or do we just not know?
I'm gonna back away slowly now...
Too much weirdness for me.
How does something without dimensions affect other things without dimensions?
Fields?
Particle exchanges?
Magnets? How do they work?
Rock crushers?
Ok great point. The size of wave functions is not the same as the size of a particle, although that's a subtle point I admit. Despite having a wave function which gives an uncertainty in location, the particle is assumed to be pointlike - actually, the fact that we can write the wave function of one particle as f(x) in the first place, as just the function of one coordinate, tells you that we characterize it as a point particle in the theory with a coordinate x. This is e.g. opposed to string theory, where you would have a wave function which depends not just on one coordinate x but on the whole position of the entire one-dimensional string in space.
How such a zero-dimensional object interacts with others... one can write down a field theory for it and it just works - I can say though that this zero-dimensionality is probably the reason for all the infinities one encounters in quantum field theory, which one has to "renormalize" in order to get sensible finite results...
Experimentally, one should see typical deviations from point-likeyness in the energy dependence of scattering amplitudes of these particles, which should drop off once the energy reaches
E~ c*h / size (c speed of light, h Plancks constant), which is the energy where one can start to resolve this size.
(June 2, 2015 at 9:40 pm)Chuck Wrote:(June 2, 2015 at 5:43 pm)Alex K Wrote: All elementary particles have by definition no known spatial extent at all
Perhaps not by definition, but by an assumption convenient to theoretical analysis, which remains convenient because it has not yet been contradicted by results of the highest resolution measurement we have yet been able to make I think?
Yes, you're right - I was thinking of the field theory treatment of elementary as opposed to composite particles , which we already know have some spatial extent. But one could imagine having "elementary" particles with some sort of nonzero size. The theory simply doesn't involve this feature.But with good reason because it is not observed on currently accessible scales.
The fool hath said in his heart, There is a God. They are corrupt, they have done abominable works, there is none that doeth good.
Psalm 14, KJV revised edition
