Re: Heisenberg vs. Einstein

Am Tue, 16 Sep 2008 20:04:19 -0700 schrieb RichD <r_delaney2001@xxxxxxxxx>
in 5a32f3de-01ef-490a-870c-d6b578e7d732@xxxxxxxxxxxxxxxxxxxxxxxxxxx:

At the center of a black hole, we supposedly find a singularity, a point
of infinite density. Does that not violate the position-momentum
uncertainty principle, shouldn't we expect some 'fuzzyness' in the
location?

Let's take a careful look at that. The Heisenberg Uncertainty Principle
is

del(E)*del(t) >= hbar/2 = h/(2*pi)/2

Since the black hole itself is not moving with respect to the galaxy, we
can say

del(E) = del(m) * c^2

Since the black hole must be contained within itself, we can say that

del(t) * c <= del(Rs) = 2*G/c^2 * del(m)

Putting this together we get

(del(m) * c^2) * (2*G/c^2 * del(m)) >= hbar/2

or

del(m) >= sqrt(hbar/(4*G*c))

Plugging in values we get

del(m) >= 3.63*10^-17 kg

or roughly 22 billion nuclear particles (of about a proton mass).

Since the lightest black holes that we know of are on the order of a solar
mass, the uncertainty in the mass of a black hole from the HUP is 1 part
in 10^47. So even though there is some fuzziness to a black hole,
practically speaking, it's of no concern.

Side note: This also shows why all those concerns about LHC are crap and
black holes can not result in the LHC.

--
// The TimeLord says:
// Pogo 2.0 = We have met the aliens, and they are us!
.

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