Consider the uncertainty principle:(adsbygoogle = window.adsbygoogle || []).push({});

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 cancelled out by its negative gravitational potential energy.

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# Zero-point energy cancelled by its gravitational energy?

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