Objections
Misner, Thorne & Wheeler (1973, “Gravitation”, p. 840)
object to the mirror interpretation
of the Schwarzschild geometry on the grounds that:
(1) it produces a sort of “conical” singularity
at the crossing point of the two horizons,
\(t_\textrm{K} = r_\textrm{K} = 0\)
(where the two red lines
cross in the Kruskal-Szekeres spacetime diagram);
and (2) it leads to causality violations in which a person can meet
themself going backward in time.
The 1st objection is true.
Spacetime at the crossing point of the two horizons
has a non-standard ‘spin 2’ kind of structure.
Just as rotating a spin 2 particle by \(180^\circ\) in space leaves it
unchanged,
so also rotating spacetime around the horizon crossing point by \(180^\circ\)
leaves the spacetime unchanged.
Is this cause to reject the mirror spacetime structure,
or is there interesting physics here?
The 2nd objection is false.
The Kruskal-Szekeres spacetime diagram shows that
the Universe and its mirror image are causally disconnected from each other.
A person who starts in the Universe on the right cannot pass through
the horizon (the red line
slanting from bottom right to top left)
to the mirror Universe on the left, and vice versa.
However, if no signal can pass between the Universe and its mirror image,
then there is no observational way to tell whether the mirror image
is really there or not
(unless there are observable consequences
from quantum mechanical tunnelling between the Universe
and its mirror image?).
And if there are no observational consequences for any observer,
then who knows and who cares.
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