Tejinder,
Thank you for the information. Also, I like the term m-mass, you have given a name to a area that physicists have looked at and noted as peculiar, but have not pursued. This is a good area for a FQxi grant!
The reason I like the term m-mass is because it could stand for "missing" mass. This is missing mass on a QM level. And with a certain amount of "that is impossible" it may be the source of dark matter and energy on the cosmic scale.
How I got interested in this stuff:
1. I made a simple theory starting from Zeno's paradox. It struck me that the agreed upon math solution to the paradox was at best "ugly". How can anyone say that getting a finite time from an infinite series means that Achilles will pass the turtle! The math is correct it but it has no meaning in the physical world. The simple theory that overcomes the paradox is that particles move by "hopping" over space-time.
2. I combine "hopping" with the deBroglie wave equation and get three equations. I chose one of the equations (that I could partially solve) and wrote my essay based on my analysis. The equation I plotted is given in the section before the graph (figure 1). This equation gives hopping velocity that ends at the Planck mass.
3. The graph of figure 1 is way beyond coincidence, and I tend to trust it and its indication that quantum physics ends at the Planck mass.
My encounter with m-mass:
1. I wanted to make plots of a hierarchy of masses from the electron to the Planck mass. I wanted particles for this plot and not things like "fleas" (which are about a Planck mass). Particles hop as one thing, whereas everything else hops as distributed mass and is a statistical complex that looses the quantum mechanical nature of "pure" particles.
2. Here is the progression of particle mass: (electron)-(proton)-(atoms)-(simple molecules)-(Buckyballs)-(m-mass)-(Planck m)
3. From the electron to the Buckyball C60 the mass goes to 10^-24 kg
There is nothing from 10^-24 to 2.2x10^-8 kg particle wise.
That is an enormous gap preceding the entry to ordinary distributed mass
and classical physics. You noted this in your essay.
4. One "wild" possibility for filling some of this gap is "cosmic dust" which
I believe ranges from 10^-16 to 10^-8 kg. I do not believe anyone is
considering that this dust may have QM properties.
5. The science fiction author Philip Pullman wrote a trilogy titled "His Dark
Materials" that involves "dust" and Cambridge scholars interested in
particle physics. Could it be that Pullman has been consulting with
Penrose? PS I enjoyed the trilogy.
Thanks for your correspondence, you are on to something.
Don L.