Reference Frame

up:: 031 MOC Classical Mechanics

A reference frame of space-time consists of an Affine Space $A^4$ ─ that is, a triple $(A^4,{\vec{A}}^4,\alpha )$, where $A^4$ is a set¹, a vector space ${\vec{A}}^4$ which acts upon $A^4$ via a Group Action which is both free and transitive of the additive group $({\vec{A}}^4,+)$.

Points in this affine space are called events.

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References

• ARNOL’D, Vladimir Igorevich. Mathematical methods of classical mechanics. Springer Science & Business Media, 2013.

Footnotes

1. We can think of this affine space’s set as $(A{)}^4$, that is, the cartesian product of $4$ ($3+1$) copies of each dimension’s set $A$. ↩