Is this non-Riemannian Spacetime Geometry Conceivable?

Eugene Shubert

Is it possible to define a non-Riemannian geometry to justify the existence of a “metric” of the form:

1/ds^2 = 1/dt^2 – 1/(dx^2 + dy^2 + dz^2)

I’m thinking of ds as an invariant that represents a differential increment of proper time. That would imply that the total amount of elapsed proper time t' would be equal to
t/sqrt (1-1/V^2) where V^2 = (dx/dt)^2 + (dy/dt)^2 + (dz/dt)^2.
I would interpret V^2 > 1 to be a superluminal velocity.

Bouchard · Posted: Tue Jun 10, 2003 10:57 pm Post subject:

Eugene,
The answer is Yes and No.

thanks Ken (Quantum Mechanic with a Wrench)
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