Sunday, August 26, 2012

Why our present theories collapse at Planck scale

Suppose we want to probe the Planck scale. To do that we would need a particle of a certain mass m.

According to quantum physics, for every particle, there is a wavelenth associated with it.

(1) λ = ℏ/mc

According to General Relativity, at Schwarzschild radius, when the mass collapses to a black hole:

(2) r = 2mG/c2

Equating (1) and (2), and solving for m, we get,

mBlack Hole = (ℏ c/2G)½

But the Planck mass is mpl = (ℏ c/G)½

We can see that mBlack Hole < mpl. In probing the Planck scale, the probing particle will have a mass that will precipitate its collapse into a black hole before it even attempts to probe the Planck scale.

The implication is that unless there is a theory that can circumvent QM + GR, we can know absolutely nothing of what is taking place at Planck scale, as if Nature has shut its doors to our inquisitive curiosity.
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