Somewhat continued from last posts
I was thinking . . .
More and more of what I wrote in my last post seems to be to be clearer in terms of the revolution that is required in modern physics. I guess I had a "theory" [not saying it is original - ed.] occur to me this afternoon. But, as usual, I will need to start with some background information. A lot of this will come as "highlights" of my last two posts.
First, it is essential to note two of the consequences of general relativity: time and space dilation. It is certainly evident from the mathematics that the space time continuum is subject to flexing based on the motions of the objects in question. The faster one goes (relative to a certain frame of reference) the "slower" time goes, and the "longer" distance gets. This is of course proportionally opposite in the other case. Also, remembering our general relativity, mass also has the effect of bending the space time continuum.
Relativity, historically, never really had too strong of an objection from theoretical physics. But as time has gone on, various experiments have shown that the theory of relativity, though certainly not a complete mathematical description of nature, at least capture part of that description. I spoke of pulsars in my last post as a means of furnishing empirical evidence for relativity. Another is the decay rate of muons. The scientists say that muons are a dense sub-atomic particle. They "rain down" from outer space and can be detected by a simple Geiger counter. But muons that are made in laboratories decay so rapidly, that there is hardly and time for them to move. So physicists wondered how "natural" muons could travel from wherever they came from, go all the way through the atmosphere, and be detected by a Geiger counter. The trick was considering relativity. In relation to our frame of reference, the "natural" muon lived for a long period of time compared to the lab muon. But then the "natural" muon is also moving at a high fraction of the speed of light. So physicists corrected for the speed differential and compared the time that the "natural" muon "lived" before decay, and found it to be the same as a lab muon, corrected of course for the relativistic motion. The muon, in either case, looked at "from itself" as being at rest has always and everywhere the say rate of decay. It is only when we try to measure it whizzing by that the difficult arose.
Secondly, in the 1910's a mathematician, Karl Schwarzchild, was analyzing Einstein's field equations, and in doing so he discovered something odd. The field equations show that the amount of time dilation depends on the gravity of the object being studied. If we use the example of a sphere, the warpage in time directly relates to the contraction of the radius. He found that for a sphere with close to the same gravity as the sun would have a critical dimension when the time warpage would be "infinite" - aptly named the "Schwarzchild Radius". For the sun, this distance is a little less than two miles. This is what mathematically gave rise - decades later - to the theory of black holes and so forth. We could get into the observational evidence and so forth for black holes, but then we would start looking like Hawking, and drawing "light cones" and "event horizons" and I find the whole thing rather tedious. Top-down is the way to proceed here. But it is enough for my eventual point to remember the idea of a critical point where time warps greatly.
From these two observations on relativity I think it is possible to lay the groundwork for a new theory uniting quantum physics and relativity. (Of course, someone would have to look at the mathematical details - I am kind of talking out my ass here - just had some sort of "traffic jam inspiration") First, sub-atomic particles are subject to the rules of relativity, otherwise we would not have observable time dilation in muons. If muons have time dilation and can only be compared as decay rates when looked at "from themselves" then is it safe to apply this to all other sub-atomic particles (or at least the ones that have mass)? If it is the case that we can apply this to sub-atomic particles, can we also apply the bending of the space time continuum based on the mass of the particle in question? Of course, it seems clear that for the relativistic quantum mechanics to be possible we should have to apply these laws to them as well. Then we would necessarily have to apply these to the massive sub-atomic particles of the proton and neutron. Here's the difficulty for me, because I haven't worked out the math yet, what, then, is the Schwarzchild radius for a very small mass? I know we are talking of a factor of millions upon millions in mass, but we are also talking of a factor of millions and millions in terms of distance. Could it be that quantum uncertainty in the "kangaroo hops" of the orbit of an electron is caused by a severe bending of space time locally around the nucleus of an atom accordingly as it approaches its own Schwarzchild radius? especially when we consider that most of the experiments involving quantum mechanics are taken at a high rate of speed, or the bombardment of atoms with photons or other radiation that does in fact travel at the speed of light.
What is the upshot? Perhaps the method of working with statistical mechanics (or Dirac's insistence on proceeding from the Hamiltonian) are efforts in the wrong direction to unite quantum mechanics and relativity. (Again, not saying that the statistical mechanized method of understanding quantum mechanics is wrong) Perhaps we should cast aside the thought that gravitational fields do not matter on the nuclear scale and examine what would happen if we considered the time and space dilation as primary in understanding the jumpy motions of things. I wrote earlier about the geodesic, and how "straight" becomes very difficult to analyze in four dimensional space time. Perhaps the electron travels in a geodesic of its own around the nucleus of the atom, it just remain to figure how the warpage of space and time could create that path. The attractiveness of understanding quantum physics - at least in principle - from this angle is that it would make it subordinate to relativity, which, as I spent much of the last post arguing, is the more known and more noble pillar of physics.
Sadly, I fear, the more elegant, the less the likelihood of veracity.
