Is a (-,-,-,-) metric signature meaningful?

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SUMMARY

A metric signature of (-,-,-,-) is physically identical to (+,+,+,+), representing Euclidean four-space, which lacks a time dimension and consists solely of spatial dimensions. The ability to flip all four signs in the metric signature does not alter its physical implications or connection to observable phenomena. This discussion highlights that different signatures, such as +--- and -+++, do not convey distinct physical realities.

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jfy4
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Hi,

Is a metric signature of (-,-,-,-) unphysical?

Thanks,
 
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You can flip all four signs in the signature, and it doesn't mean anything in terms of connection with observation. For example, my favorite signature is +---, but much of the literature uses -+++. They don't mean anything physically different.

So ---- would be physically identical to ++++, describing Euclidean four-space. Such a space has no time dimension, just space.
 
bcrowell said:
You can flip all four signs in the signature, and it doesn't mean anything in terms of connection with observation. For example, my favorite signature is +---, but much of the literature uses -+++. They don't mean anything physically different.

So ---- would be physically identical to ++++, describing Euclidean four-space. Such a space has no time dimension, just space.

Thank you very much.
 

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