I was talking to a friend, and found out, that he doesn't know about this. I assume he is not alone among physicists. Among non-scientists, this may sound like magic. The reason I turned to physics and not "other" ways of knowing, is that with this method, one can know things, that seem unknowable.
It started in Mexico City, I was at Cinvestav , and after talking with Richard Blankenbecler, I had made my mind to study at the Physics Department of UCSB. I had already studied the experimental work carried out there, for a Summer project with my dear professor Jean Pestieau. The title was something like Vector Dominance Model. J.J. Sakurai had discovered, that one could fit experimental data, by just adjusting one parameter, to find out for instance, that photons and protons behave the same way at high energies. The experimental work done at Santa Barbara was crucial to get these data. Thus, I was game, I showed up at UCSB with my suitcase full of books in September of 1973.
Robert L. Sugar accepted to direct my work there, and asked me to look at the work of T.T. Wu, and Hung Cheng. They had predicted, that proton cross sections, i.e. probability of collision, were going to increase, instead of decrease, as one increases the energy. This paper came out in 1970, in PRL. Sure enough when the data came in, they were right.
This probability keeps growing, experiment after experiment, since then.
Once talking to Arturo Cisneros Stoianowski, he mentioned the reaction of one of his Caltech professors, I think it was Murray Gell-Mann, "I guess at this rate, one day protons will be the size of trucks."
When Wu and Cheng predicted that, another Caltech Professor, Richard Feynman, was very impressed at the tour de force, of these, by then young men.
I was not intimated by these giants of theoretical physics, maybe I should've been, and started working in Professor's Sugar Ph. D. thesis problem.
I am convinced that, not only proton cross sections will keep increasing, but that I have an idea of how it happens.
It has to do with space-time dimension, but I believe, in a different way that the friend I mentioned earlier thinks.
One can think of a proton, as a neat sphere at rest. As two protons approach each other, they are not spheres, but disks, due to Lorentz-FitzGerald contraction. Special Relativity mathematics, without Quantum Mechanics, indicate that the spheres do not change size in the perpendicular direction, of their head-on collision direction.
I believe that Quantum Mechanics, allows the charged cloud around them, to diffuse in the perpendicular direction through a Brownian Motion of energy.
Voilà, there you have your expanding proton.
How is this related to 3D space?
At very high energies, particles move more, and more, how Feynman envisioned them, in real path trajectories, not clouds. The Quantum Behavior jumps, so to say, to the transversal cloud. The hard three dimensional problem of particle motions, breaks up into two simpler motions, one one-dimensional, and the other two-dimensional.