Spacetime Metric: Which signature is better?

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SUMMARY

In discussions regarding the Minkowski spacetime metric, mathematicians generally favor the (-,+,+,+) signature, while physicists predominantly use the (+,-,-,-) signature. The consensus is that Nature does not exhibit a preference for either signature, as no physical laws are altered by the choice of metric. The preference for the (+,-,-,-) signature among physicists is attributed to practical reasons, such as simplifying calculations involving four-vectors and Levi-Cività tensors. Ultimately, the choice of signature is a matter of convenience rather than a reflection of any inherent property of the universe.

PREREQUISITES
  • Understanding of Minkowski spacetime metric
  • Familiarity with four-vectors in physics
  • Knowledge of Levi-Cività tensors
  • Basic principles of special relativity
NEXT STEPS
  • Research the implications of different signatures in Minkowski spacetime
  • Explore the mathematical properties of four-vectors
  • Study Levi-Cività tensor applications in various dimensions
  • Investigate the historical context of signature preferences in physics and mathematics
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Mathematicians, physicists, and students of theoretical physics who are interested in the implications of signature choices in spacetime metrics and their practical applications in calculations.

LarryS
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It seems that, in general, mathematicians prefer the (-,+,+,+) signature for the Minkowski spacetime metric while most physicists prefer the (+,-,-,-) signature. Is there any evidence that Nature actually prefers one over the other?

As usual, thanks in advance.
 
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Nature cannot have a preference since no physics is changed. The only possible answer, IMO, is the one that you will make fewer mistakes with.
 
I think physicists prefer +--- for several reasons.
Time goes forward, space can go in either direction.
The four vector (E;p,p,p) has the length^2: E ^2-p^2=m^2. -m^2 would be awkward.
 
I think pretty much anyone who works in dimensions other than 4 prefers (-+++...). There is a great benefit to not having to remember exactly how many minus signs you have to think about when working with Levi-Cività tensors, for example.
 
The question was what Nature prefers, not what physicists or mathematicians prefer. PAllen nailed it in the first sentence:
PAllen said:
Nature cannot have a preference since no physics is changed.
The thread could have been locked at that point.
 
Orodruin said:
The thread could have been locked at that point.

And now it is.
 

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