What might be the physical character of a hypothetical Planck mass?

v. 4 n. 30

Physics is appropriate to the small limit of the Planck scale. This scale is apparent with arrangements of natural constants as in Figure 1.

The strong force was expressed earlier as

Fs = Gs m1 m2 / r^2 .................................................... (subatomic) ................. (1)

where Gs = G [1.3(1- v^2/c^2)^-3/2] ................ (v→c only) ..................... (1a)

and v is the tangential velocity of mass m2 relative to mass m1. For a single rotating mass of finite size as in the cover image, m2=m1, where one half of the mass is rotating with respect to the other half. Equating this attractive force with the inertial effect tending to explode the single mass,

Gs m1 m1 / r^2 = m1 v^2 / r, so that

r = Gs m1 / v^2 ...................................................... (v→c) ....................................... (2)

where r is the size of mass m1.

A "relativity-quantum bridge" was derived earlier as

γ^2 = n/2 (α.G)^-1, or

(1- v^2/c^2)^-1 = (n/2) ?c / G(m1+m2)m2. ........ (v→c only) ................. (3)

Combining Equations (1a) (2) and (3) when m1=m2 equals the Planck mass and n=1, then

r = Planck length.

In addition to indicating the viability of these equations, this suggests that any physically real Planck mass rotates at near-light speed, and the integrity of this mass is based on gravitation. It would seem that a rather arbitrary definition of the Planck scale and elementary manipulation of natural constants to obtain values for length, mass and time, might give the physical function of light speed, c, in Figure 1, in addition to being the abstract representative for relativity. Similarly for G (gravity) and ? (quantum mechanics) in the equations.

Cover image: BingAI

Cover image caption: Representation of a Planck mass, rotating at near-light speed.