Scalar Product of displacement four vector

[Tony Stark]

Homework Statement

How does the scalar product of displacement four vector with itself give the square of the distance between them?

Homework Equations

(Δs)²= Δx.Δx ( s∈ distance, x∈ displacement four vector)
or how
ds²=η_αβdx^αdx^β

The Attempt at a Solution

Clearly I am completely new to the subject, thus I have no idea about it.

 

[Noctisdark]

The flat space-time metric tensor (I love this sentence) η_αβ is a bunch of zero except when α = β so clearly we can reduce ds² to some simpler formula, Cheers !

 

[Tony Stark]

What actually do want to say? My question is how does the scalar product of 2 displacement four vectors gives the distance between them. I can not figure out the answer from your reply..

 

[Noctisdark]

I mean that η_αβdx^αdx^β = η_ααdx^αdx^α summation over α,
[EDIT: In case I'm not clear enough η₁₁ = 1, η₂₂ = η₃₃ = η₄₄ = -1]

 

[Tony Stark]

I get the whole point. Thanks for all replies.