Spacetime Metric: Which signature is better?

In summary, mathematicians generally prefer the (-,+,+,+) signature for Minkowski spacetime metric, while most physicists prefer the (+,-,-,-) signature. However, there is no evidence that Nature has a preference for either signature. The preference seems to be based on convenience and ease of use for mathematicians and physicists, rather than any fundamental difference in the physics involved.
  • #1
LarryS
Gold Member
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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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  • #2
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.
 
  • #3
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.
 
  • #4
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.
 
  • #5
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.
 
  • #6
Orodruin said:
The thread could have been locked at that point.

And now it is.
 

FAQ: Spacetime Metric: Which signature is better?

1. What is a spacetime metric?

A spacetime metric is a mathematical representation of the structure of spacetime, which combines the concepts of space and time into a single entity. It describes the way in which distances and durations are measured in a given spacetime.

2. What is the signature of a spacetime metric?

The signature of a spacetime metric refers to the combination of positive and negative signs in the metric tensor, which is a mathematical object used to calculate distances and durations in spacetime. The signature is usually written as a sequence of numbers, such as (+ + + -) or (- + + +), which represent the number of positive and negative signs along different dimensions of spacetime.

3. Which signature is better for describing spacetime?

There is no "better" signature for describing spacetime, as different signatures are useful for different applications. The most commonly used signature is (+ + + -), known as the Minkowski signature, which is used in special relativity. However, other signatures such as (- + + +) are used in other theories, such as general relativity.

4. How does the signature affect the properties of spacetime?

The signature affects the properties of spacetime in a fundamental way. For example, the signature determines the type of geometry that is present in a given spacetime, and also affects the behavior of particles and light in that spacetime. Different signatures can lead to different predictions and interpretations of physical phenomena.

5. Can the signature of spacetime change?

The signature of a given spacetime is usually fixed, but in some cases it can change. For example, in theories involving extra dimensions, the signature of the extra dimensions may differ from the signature of the four dimensions we experience in our everyday lives. Additionally, some theories suggest that the signature of spacetime may have changed in the early universe during the process of cosmic inflation.

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