Racorean, Ovidiu
(2026)
Unitary time-reversal on non-orientable spacetimes.
[Preprint]
Abstract
Time reversal symmetry occupies a distinctive role in quantum mechanics,
fundamentally requiring an anti-unitary operator to ensure a physically consistent
representation. As such, the time reversal operator combines a unitary transformation
with complex conjugation, enabling the necessary inversion of the imaginary unit
that appears in quantum commutation relations and dynamical equations. Attempts
to represent time reversal as a purely unitary operation encounter fundamental
contradictions, including violations of canonical commutation relations and issues with
the positivity of energy spectra. However, recent advances in quantum gravity and
black hole physics reveal that in spacetimes with non-orientable topology—where a
global temporal orientation is not well defined—time reversal may be realized by a
purely unitary operator. Such non-orientable geometries connect two asymptotically
spacetimes with opposite time directions, thereby encoding time reversal topologically
and removing the need for complex conjugation. In this work, we explore the
deep connection between spacetime orientability and the nature of the time reversal
operator, demonstrating that orientable spacetimes require anti-unitary time reversal
consistent with conventional quantum theory, while non-orientable spacetimes allow
unitary time reversal operators consistent with negative energy states.
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