Scalar Product of displacement four vector

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Homework Help Overview

The discussion revolves around the scalar product of displacement four vectors and its relation to the distance between them, situated within the context of spacetime metrics in physics.

Discussion Character

  • Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Participants explore the implications of the scalar product of four vectors, questioning how it relates to distance. There is an attempt to simplify the metric tensor's role in the equation.

Discussion Status

Some participants have provided insights into the structure of the metric tensor and its simplifications, while others express confusion about the relationship between the scalar product and distance, indicating an ongoing exploration of the topic.

Contextual Notes

One participant notes their unfamiliarity with the subject, which may affect the depth of the discussion. Additionally, there are references to specific components of the metric tensor that may require further clarification.

Tony Stark
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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
ds2αβdxαdxβ

The Attempt at a Solution


Clearly I am completely new to the subject, thus I have no idea about it.
 
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The flat space-time metric tensor (I love this sentence) ηαβ is a bunch of zero except when α = β so clearly we can reduce ds2 to some simpler formula, Cheers !
 
Last edited:
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..:oldconfused::oldconfused::oldconfused:
 
I mean that ηαβdxαdxβ = ηααdxαdxα summation over α,
[EDIT: In case I'm not clear enough η11 = 1, η22 = η33 = η44 = -1]
 
Last edited:
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I get the whole point. Thanks for all replies.
 

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