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The Planck mass plasma conjecture is the hypothesis that the vacuum of space is a kind of plasma composed of positive and negative Planck mass particles interacting by the Planck force over a Planck length, repulsive for equal and attractive for unequal Planck masses. The hypothesis permits to derive quantum mechanics and Lorentz invariance as asymptotic approximations for energies small compared to the Planck energy. Besides a spectrum of elementary particles greatly resembling the particles of the standard model, the hypothesis gives a value of the fine structure constant at the energy where the strong, the weak, and electromagnetic interaction become equal.

Planck's spectral distribution law is derived in N-dimensional space. Some relevant formulas are thus obtained and analyzed. The behavior of these formulas in higher dimensions is examined and some numerical values are calculated.

The Planck aether hypothesis assumes that space is densely filled with an equal number of locally interacting positive and negative Planck masses obeying an exactly nonrelativistic law of motion. The Planck masses can be described by a quantum mechanical two-component nonrelativistic operator field equation having the form of a two-component nonlinear Schrodinger equation, with a spectrum of quasiparticles obeying Lorentz invariance as a dynamic symmetry for energies small compared to the Planck energy. We show that quantum mechanics itself can be derived from the Newtonian mechanics of the Planck aether as an approximate solution of Boltzmann's equation for the locally interacting positive and negative Planck masses, and that the validity of the nonrelativistic Schrodinger equation depends on Lorentz invariance as a dynamic symmetry. We also show how the many-body Schrodinger wave function can be factorized into a product of quasiparticles of the Planck aether with separable quantum potentials. Finally, we present a possible explanation of wave function collapse as a kind of enhanced gravitational collapse in the presence of the negative Planck masses.

It is shown that, for the case of two different particles associated with two different Planck constants, an appropriate generalized center-of-mass transformation allows one to retain the relevant constants of the motion. Therefore, some of the problems arising from the (postulated or experimentally determined) existence of several quantization constants appear to be avoidable.

A possible way of building Planck's constant into the structure of space-time is considered. This is done by assuming that the torsional defect that intrinsic spin produces in the geometry is a multiple of the Planck length.

A statistically founded derivation of the quanta of energy is presented, which yields the Planck formula for the mean energy of the blackbody radiation without making use of the quantum postulate. The derivation presupposes an ensemble of particles and leads to a statistical interpretation of the Planck constant, which is defined and discussed. By means of the proposed interpretation ofh and as an application of it, the quantum uncertainty relation is derived classically and results as a statistical inequality. On the whole this paper is compatible with the statistical ensemble interpretation of quantum mechanics.