Erlangen 2026 – scientific programme

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MP: Fachverband Theoretische und Mathematische Grundlagen der Physik

MP 11: Various Topics in Relativity

MP 11.4: Talk

Thursday, March 19, 2026, 17:00–17:15, KH 00.015

Negative square roots: Wishful thinking in spacetime physics — •René Friedrich — Strasbourg

The current approaches to quantum gravity are all based on the fundamental assumption of a Lorentzian spacetime manifold as it was understood by Minkowski in his famous lecture "Space and Time" in 1908. However, this assumption is far from being free of inconsistencies:

a) The squared metric "F" used by Minkowski does not apply to spacelike spacetime intervals (problem of negative squares), revealing that spacetime is not continuous in spacelike direction.

b) To remedy this, Minkowski introduced a sort of twofold patchwork metric ("F" and "-F").

c) This handling of the problem was not acceptable for many physicists and led to the proliferation of a multitude of different "conventions" for the spacetime interval which have become a veritable "elephant in the room" of spacetime physics.

d) Misner-Thorne-Wheeler took the problem to extremes, by setting two opposite metrics equal, a positive square with a negative square, implying a real number equal to an imaginary number. Real equals imaginary: That is just the definition of wishful thinking (!).

e) The current approaches to quantum gravity should check the basic assumptions they are relying on, because every theory is only as good as its underlying assumptions.

Keywords: Quantum gravity; General relativity; Spacetime interval; Black holes; Lorentzian metric