Re: Path Integrals, Sum-over-Histories, and the Law of Non-Contradiction
General Relativity--as it currently stands--is self-contradictory all on its own, in my view. The expansion of Einstein's field equation(s) puts r (radius) below the dividing line. Thus, when r is allowed to become 0, we get the classic "divide by zero" error. In other words, unless a way is found to forbid r becoming 0, such as one might achieve by quantizing space-time itself, this equation makes me hit the "FAIL" button. GR is a classical theory, and reality just isn't all that classical.
This problem can be more easily understood if one accepts that the low-energy limit of GR must reduce to Newton's force law:
F = G((m1 * m2)/r^2
where:
F is the force between the masses,
G is the gravitational constant,
m1 is the first mass,
m2 is the second mass, and
r is the distance between the masses.
As you can see, r cannot be 0. But what is it that stops this from occurring in GR? This problem is one of the main reasons why nobody** is trying anymore to 'classicalize' quantum field theory, but instead seek to quantize GR. This misplaced 0 cannot be allowed.
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**except old-school philosophers who hate QM, and love Aristotle, that is!
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