## Why Is Relativity Useful? Because Elementary Particles Tend To Be Relativistic

When one learns Relativity, one discovers that the physics of fast moving frames is different (slower). But then turns out that the speeds involved are enormous. How practical is this? Very. It turns out elementary particles move very fast. The speed of the electron in the fundamental atom, the hydrogen atom, can be readily evaluated, using conventional kinetic energy, equating it to potential energy from the Coulomb force and then estimating the size of the electron “orbital” from the Uncertainty Principle. One gets 2,200 kilometers per second, c/137. The speed of light divided by the “Fine Structure Constant”…

Nice little mix between Kinetic Energy a la Emilie du Chatelet plus Uncertainty principle, gives 2,200 km/s in hydrogen… Now, of course, in my own SQPR, the electron gets somewhat delocalized, so it all has to be taken with a grain of salt…

Now a “wild” electron will move much faster. How do we know that? Dirac contrived the simplest relativistic wave equation he could imagine an electron to satisfy. That Dirac equation predicted several (then) weird phenomena, soon observed. Even more strangely, that fit the work of the geometer Elie Cartan (15 years earlier). Now we sort of understand or more generally guess, that it has to do with taking the square root of space (don’t ask).

In any case, the success of the relativistic equation shows that, around another electron (say) electrons will zoom in and out close to the speed of light. It’s sort of proof by theory: build a theory predicting unexpected results, find those experimentally, then go back… to prove the “axioms” that way. Inducto-deducto-experimental-logical approach?

Inside nuclei, quarks move at relativistic speeds (that is, close to the speed of light…) CERN can actually measure those.

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Modern Relativity theory caused an initial stir because it revealed that time was local. There was no universal time: clocks ran slow in a fast frame.

A statement like this has plenty of hidden theory behind it, so it could cause perplexity to some… “Fast” could cause a problem: does not Relativity say that all reference frames in uniform motion relative to each other have the same physics? So many expositions of Relativity simply say there is no problem, they sweep that “problem” under the rug.

I love intellectual combat, so I will not.

A little bit of history for motivation here. Albert Einstein was impressed by Mach, and his Principle. That’s why he said he tried to develop General Relativity. Mach’s Conjecture is that “local physical laws are determined by the large-scale structure of the universe“. That remains a Graal, but I see the EPR, taken the way Einstein hated it, as a ray of hope.

Einstein described the Mach conjecture in 1913, in a letter to Mach: …”inertia originates in a kind of interaction between bodies”…

Einstein may have realized that all he was trying to do was to integrate, in the mathematical sense, the extremely local Poincare Relativity. So the theoretical effort of General Relativity was going from infinitesimally local to less local… But that said nothing global. So the quest should have looked hopeless, but that was all what anybody could think of. (In my opinion Quantum Physics and the Popper-Einstein EPR provides us with completely new conceptology… enabling us to start to hope globally)

Patrice Ayme

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