photons and electron-positron collisions.

[happyjack27]

i noted in the centenary of superconductors thread, discussing whether singularities exist in real life or are just mathematical abstractions, that an electron and its anti-matter pair, the positron, have opposite charge and are hypothesized to have no internal structure, so since the electromagnetic force is 1/r^2 and thus singular at the origin, for real-life to be singular at the origin, given an electron-positron pair traveling at sub-orbital velocities relative to each other, the pairs should accelerate asymptotically to infinite velocity as their distance approaches zero.

now at face this appears ridiculous. "infinite velocity? c'mon." but special relativity says "wait a minute..." infinite velocity in their own respective inertial reference frames, which in any other reference frame is simply the speed of light. but what about energy? infinite velocity = infinite energy! s.r. responds: no no, infinite velocity times finite mass = infinite energy. and e=mc^2 so that mass can be converted into energy. giving you infinite velocity * infinitesimal mass = finite energy. and after all e+mc^2 _must_ be conserved, so as its proper velocity increases its mass must diminish to keep e+mc^2 constant.

so s.r. tells you that what would happen in when an electron and positron are suborbital relative to each other, assuming they have no internal structure, is that they will turn into a pair of infinitesimally separated rotating charges traveling at the speed of light and with a net zero mass. remind you of anything? reminds me of a "photon".

so that would seem to explain, geometrically, how an electron-positron pair annihilate into a photon and vice-versa.

[Stoney3K]

so that would seem to explain, geometrically, how an electron-positron pair annihilate into a photon and vice-versa.

That does make sense on some level, even with my just-beyond-basic understanding of quantum physics and calculus.

The question is, what does that amount to when you take the 'heavier' particles (hadrons) and look at them the same way?

Protons and antiprotons are composed of several (elementary, and therefore singular) quarks, which, continuing this reasoning, would amount to multiple photons with different energies being emitted in a single annihilation.

I wonder what the whole Higgs-boson story will throw into this mathematical soup.

[happyjack27]

yeah, not sure how (or if) that would extend tpo quarks ie even neutrinos, or other bosons. but it does predict correctly that a photon has spin 1 - the spin of an electron (+/- 1/2) plus the spin of a positron (+/- 1/2).

it'd be interesting to see what other predictions come out of this. i'm thinking this might explain why the fine-structure constant (probability of a photon decaying into an electron-positron pair) has the value it does.

i'm also thing this view suggests that photons and electrons and positrons are just energetic disruptions of the electromagnetic gauge field. i.e. they are "nothing", they are just ephermeral shears/what-have-you of space.

then electrons outnumber positrons because well charge is relative so you simply say net charge = 0 and then you have to have the charge from protons counterbalance, so the electrons (which are just excitations) come in and out of existance to make a net neutral electromagnetic gauge field. so then "all" one has left to do is explain quarks and their interactions. oh, and the weak field.

the existance of different generations of fermions mind find some explanation with this model.

[Stoney3K]

so then "all" one has left to do is explain quarks and their interactions. oh, and the weak field.

I'd first like to see them take a crack at explaining gravity, and ways to influence it. The big G is, at this time, still a magical black box which just somehow seems to work.

If we can find out *how* it works, we might be able to find ways to disrupt it or augment it, and that's when things get really interesting. (I mean, the bending space and time kind of interesting.)

[happyjack27]

i wonder if you could vary the magnetic field through a bubble chamber as a function of time so as, for instance, to turn spirals into circles and circles into hyperbolas, or something like that. that might give you a finite view of some of the dynamics which otherwise be infinitesimal / singular.

sort of like changing the the coordinate system to a function of 1/r to remove the singularity at r = 0 in a 1/r^2 system before integrating.

or perhaps there are better analogs, like applying an ambient _voltage_ that changes as a function of time.

hopefully this might, with a non-vanishing probability, give you a better view of what an electron-positron pair do just before annihilation. but if not that, it still might expose other interesting phenomena.

[Jccarlton]

i wonder if you could vary the magnetic field through a bubble chamber as a function of time so as, for instance, to turn spirals into circles and circles into hyperbolas, or something like that. that might give you a finite view of some of the dynamics which otherwise be infinitesimal / singular.

sort of like changing the the coordinate system to a function of 1/r to remove the singularity at r = 0 in a 1/r^2 system before integrating.

or perhaps there are better analogs, like applying an ambient _voltage_ that changes as a function of time.

hopefully this might, with a non-vanishing probability, give you a better view of what an electron-positron pair do just before annihilation. but if not that, it still might expose other interesting phenomena.

Why a bubble chamber? most accellerators use huge spectrometers to measure particle paths these days. When I was working in the accellerator worls we used beer cans for beam targets. But for something like this you need a positron source. Not sure how you would get that. The rest is just conventional stuff you can design off the shelf.

[happyjack27]

Why a bubble chamber? most accellerators use huge spectrometers to measure particle paths these days. When I was working in the accellerator worls we used beer cans for beam targets. But for something like this you need a positron source. Not sure how you would get that. The rest is just conventional stuff you can design off the shelf.

well i mean today we don't use liquid particle detectors. we use semiconductor or wire grid, but its the same basic principle. why? so you can see the ionization tracks left by the particle and then the idea is you'd vary something w/time so that tracks that would normally grow closer at a say r^2 now grow closer at say r, so you can more clearly see their asymptotic behavior right when they're about to fuse or right after they decay. cause e.g. now maybe the acceleration is linear instead of parabolic. is suppose you'd have to vary it very very quickly, though. and that might be very difficult to do.

[happyjack27]

maybe if you have a 3-d ionization track detector, and then have a net inertia when they collide, then on average the extent travelled across the z-axis (axis that they were travelling before collision) after collisions would represent the time after collision. so then you could vary say bfield or ambient voltage across the z-axis and then yo wound't have to worry about changing it quickly - the speed at which it changes would be proportional to the average net speed of the particles after collision, which could be quite near the speed of light if you want.

so then you've just got to make sure there's a net inertia difference - put a little more energy in on one side of the colliding particles. and you suffer that's its just going to be a certain rate of change "on average" and there will be a heck of a lot of variance to that "on average".

alternatively you could vary the field strength or whatever radially. this would probably come with its own set of drawbacks too.

in either case the point is its all relative so instead of changing the incident magnetic field strength with time, you can use the fact that the particles position is changing very rapidly in time and then just put different static fields at different positions to coincide with that, and that would amount to the same thing.