The twist ring seems like such a good solution, so why am I not jumping all over the sofa? Because I’d be jumping the shark, that’s why. The number one reason reason why physicists ignore those who claim any solution that gives a finite electron radius, and especially the Compton radius, is experimental evidence. This evidence has many forms but probably most significantly comes from scattering experiments, the experiments done in accelerators.

Why are experimental physicists smashing particles into each other? Can’t we just use a ruler, or look through the Hubble telescope in the wrong end? The problem is that even the Compton radius is too small, never mind the apparent zero radius of the electron, to look at with high energy photons in a microscope. This radius, 2^10^-11 cm, is about 100 times smaller than the approximate size of a simple atom. Obviously, an electron microscope, which bombards its observed target with electrons, isn’t going to help when looking at electrons–you need particles, whether photons or other particles, significantly smaller than the object you are looking at to be able to form an image of the target. The electron frequency is around 20 EHz, 100000 times higher frequency than visible light, where Gamma rays exist. We don’t have Gamma ray microscopes that are within range of imaging an electron–we’d need Ultra Gamma ray microscopes, and even if it was possible to make such a thing, the inability of holding an electron still for a radius measurement, and the destructive energy of such rays, would completely destroy any hope of getting useful information.

So–what DO physicists do? They smash particles against each other. We can’t control exactly where a beam comes in relative to a cross-section of the target particle at this scale, so a direct measurement of particle sizes is still impossible–but just like those amazing experiments that have found extra-solar planets around far-too-distant stars, there are ways to get what we need indirectly. Those experiments, whether looking for distant planets or tiny particles, measure indirectly tiny variations of observable parameters caused by the target, and then analyze the results to show that the only explanation can be planets or particles of some size.

It turns out there is an amazing amount of information and good conclusions we can draw from particle collisions. There are a variety of ways to do collisions, but let’s think about an experiment that shoots the smallest possible particles or photons from a source and tries to hit a stationary target particle that we want to learn about. We can very easily determine whether a particle is a point or a homogenious region (mass of the particle is dispersed from the center) by detecting the bounce-off angle of a fixed target. If no particles ever bounce back toward the shooting source, but there is a probability distribution of deflection angles away from the source, that’s a very good signature for a homogenious region. If we get a probability distribution where the angle of deflection is uniformly random, we are hitting a knife edge–a point, a rail, a ring of something that has practically a zero diameter.

We can easily measure the mass of the target by observing conservation of momentum of both the shooting and target particles. We can measure the charge of a particle by seeing how it curls in a magnetic field (you wonder how tiny quarks were found, and how they determined there were two or three of them–it was the result of complex smashed particle sprays that showed there had to be short-lived point-like particles with charges 1/3 that of an electron). And so on. Experimental physicists have earned their PhDs and livelihood based on ever more clever ways of extracting information out of experiments they devise.

Now, the one result we care about that is unequivocal–when such accelerator experiments are done on electrons, regardless of the increasing energy and finer resolution of the shooting particles, there have never been any results that show any other than a knife edge result–the uniform distribution of bounce-back shooting particles. (Note, it’s actually somewhat more complicated that a uniform distribution, because we can’t control where within a particle cross-section or it’s immediate neighborhood we can hit–it’s a bit of mathematical work to get the actual distribution cones–but the principle is still valid, we can get the cross-section of interaction by the experimental distribution of deflection angles).

The crucial question is this. Can scattering experiments distinguish between different knife edges such as points, lines, or rings, given that a collision at the point of impact will look the same in each case (remember that the distance scale is too small to have any control over where we hit in the target particle cross-section, or even to assure that we hit the cross-section at all). I think a pretty good argument can be made, assuming a true knife-edge, that the ability to discern the shape and dimension of the knife-edge is not possible. Let’s go more into this next time, to try to guess how we *could* come up with a shape determination.


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