Introduction: The Planck Aether Hypothesis
In his "Optics," Newton makes the conjecture that the ultimate building blocks of matter are hard frictionless spheres. With a few assumptions, similar but different from those made by Newton, I derive quantum mechanics with a spectrum of elementary particles greatly resembling the known spectrum of elementary particles, and Lorentz invariance as a dynamic symmetry for energies small compared to the Planck energy. These assumptions are (G Newton's constant, h Planck's constant, c velocity of light):
From the two Planck relations:
Gmn2 = he
mprpc = h
(h= 2nh) Planck's mass, length and time are obtained:
Expressed in terms of these units the Planck force is
Fp = c4/G =~1050 dyn
range rp is equal to U — Fprp = mpc
Because the compactified assembly of positive and negative Planck mass particles defines an absolute system at rest with these particles, one may speak of an aether composed of densely packed Planck mass particles which one may simply call the Planck aether.
A repulsive force acting between two positive Planck mass particles will repel the particles, but an attractive force acting between two negative Planck mass particles will do the same because for a negative mass the direction of the acceleration is opposite to the direction of the force. Applying the same force rule, whereby a positive Planck mass particle exerts a repulsive, and a negative Planck mass particle an attractive force, a positive and negative Planck mass particle should be attracted towards each other. This force law is different from the force law which would apply if the Planck mass particles are the source of a Newtonian gravitational field, but in the proposed theory all fields and elementary particles are to be understood as quasiparticles resulting from collective excitations of the dense assembly of positive and negative Planck mass particles. As in condensed matter physics where the attractive force of phonon fields has its cause in the repulsive short range force between the molecules, long range forces, like electromagnetic and gravitational forces, are conjectured to have their cause in the short range forces between the Planck mass particles. Recognizing this possibility, to explain all long range forces by collective excitations of a medium with short range forces, frees one from the need to impose a Newtonian gravitational force law between the Planck mass particles. A vacuum composed of Planck mass particles subject to Newton's (or Einstein's) law of gravitation would be unstable even in the absence of negative masses, because an assembly of positive Planck masses alone would already be unstable against gravitational collapse. The addition of negative masses would increase the instability by selfaccelerating pairs of positive and negative masses. The proposed alternative force law between the Planck mass particles not only makes the assembly of the positive and negative Planck mass particles stable, but gives this assembly a striking similarity to condensed matter, where electric charges of equal sign repel, and those of opposite sign attract each other. Unlike other attempts to arrive at a "final theory", assuming without exception that it should be found in some kind of "world formula," the proposed alternative theory instead assumes a fundamental structure described by the already known laws of Newtonian mechanics.
There is another reason in favor of the Planck aether hypothesis assuming a discrete structure at the most fundamental level of nature. It is very plausible that nature works very much like a computer with discrete elements. But if this is true, then the Lorentz group can not be the fundamental group because it is noncompact. It is this property of the Lorentz group which leads to the requirement that elementary particles must be mathematical points. something very implausible. The condition for elementary particles to be zero dimensional points can be relaxed by assuming that they are one dimensional lines (strings), but only by paying the high price of more than the four space-time dimensions of physics. This problem can be altogether avoided by assuming that the fundamental group is the Galilei group, which (unlike the Lorentz group) is compact.
Making the smallest number of conceivable assumptions, the Planck aether hypothesis can be seen as an attempt to bring the reductionist program of science to its ultimate goal. String theories by comparison, have to make in fact many more assumptions, because they have to elect from a multitude of several thousand one particular compactification for the superfluous dimensions. The price paid for the simplicity of any conjectured fundamental law, like the Planck aether hypothesis, is the very large number of possible solutions, including those solutions which are from a human perspective not desirable. A fundamental law excluding all those undesirable solutions (creating a paradise-like world) would have to incorporate so many restrictions that it would by comparison be extremely complicated.
The complete symmetry between the positive and negative masses of the Planck aether suggests a spontaneous symmetry breaking, whereby the shadow matter assumes the role of Dirac's sea of fully occupied negative energy states. This, of course, can here only happen after the dynamic establishment of quantum mechanics and relativity, leading to Pauli's exclusion principle. Because of the complete symmetry between the positive and negative Planck masses, the spontaneous symmetry breaking can either lead to a world with the negative masses in the Dirac sea, or the other way around, but which because of the arbitrary assignment of what is positive and negative would be indistinguishable.