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## Summary:

- I want to know why the choice of a signature (-+++) or (+---) has no physical impact.

Hello,

I've always heard that the choice of signature for the metric was just a matter of convention, i.e. taking (+---) or (-+++) had no physical impact. The groups O(1,3) and O(3,1) being isomorphic it made sense to me.

However, I came across an article discussing the Pin(1,3) and Pin(3,1) non - isomorphic groups . It says, and I quote :

Thanks.

Edit : the article's link https://arxiv.org/abs/math-ph/0012006

I've always heard that the choice of signature for the metric was just a matter of convention, i.e. taking (+---) or (-+++) had no physical impact. The groups O(1,3) and O(3,1) being isomorphic it made sense to me.

However, I came across an article discussing the Pin(1,3) and Pin(3,1) non - isomorphic groups . It says, and I quote :

So that would mean that it would be possible experimentally to find the true signature of the metric ? And so it would be wrong to say that the choice of signature is just a matter of convention ?Two notable positive results show that the existence of two Pin groups is relevant to physics:

- In a neutrinoless double beta decay, the neutrino emitted and reabsorbed in the course of the interaction can only be described in terms of Pin(3,1).
- If a space is topologically nontrivial, the vacuum expectation values of Fermi currents defined on this space can be totally different when described in terms of Pin(1,3) and Pin(3,1).

Thanks.

Edit : the article's link https://arxiv.org/abs/math-ph/0012006