- #1
johne1618
- 371
- 0
Consider the uncertainty principle:
dp * dx = hbar
For photons we have the relation:
E = p c
Substituting into the above uncertainty principle:
dE = hbar c / dx (1)
As we look at a smaller and smaller piece of the zero-point field the (positive) energy diverges.
But that energy has a mass equivalent which therefore has a negative gravitational potential self-energy, dP.
dP = - G dM^2 / dx (2)
As dx -> 0 then dP -> -infinity as fast as dE -> infinity so they cancel each other out.
If we have:
dE = -dP = dM c^2
and substitute this relation into (1) and (2) we get a relation for the length scale dx:
dx = sqrt(G hbar / c^3)
This is the Planck length.
I would guess that space-time quantisation is equivalent to the zero-point energy at each point being canceled out by its negative gravitational potential energy.
dp * dx = hbar
For photons we have the relation:
E = p c
Substituting into the above uncertainty principle:
dE = hbar c / dx (1)
As we look at a smaller and smaller piece of the zero-point field the (positive) energy diverges.
But that energy has a mass equivalent which therefore has a negative gravitational potential self-energy, dP.
dP = - G dM^2 / dx (2)
As dx -> 0 then dP -> -infinity as fast as dE -> infinity so they cancel each other out.
If we have:
dE = -dP = dM c^2
and substitute this relation into (1) and (2) we get a relation for the length scale dx:
dx = sqrt(G hbar / c^3)
This is the Planck length.
I would guess that space-time quantisation is equivalent to the zero-point energy at each point being canceled out by its negative gravitational potential energy.