T1: 1. Introduction and SR Flashcards
State the principle of equivalence
The effects of a gravitational field are locally indistinguishable from being in an accelerating reference frame.
State the Lorentz transformation x’
x’ = γ(x - vt)
State the Lorentz transformation t’
t’ = γ(t - v/c^2 x)
State the spacetime interval
ds^2 = -c^2 dt^2 + dx^2
Give the spacetime interval in index form (with Minkowski metric)
ds^2 = η_µν dx^µ dx^ν
Define inertial frame
A frame of reference which is not undergoing any acceleration.
How does special relativity imply space and time are intertwined?
The Lorentz space transformation involving time, and likewise time transformation involving a space.
An object with a single upper (lower) index indicates…
A column (row) vector.
Define inertial coordinates
The coordinate systems related by Lorentz transformation.
State the principle of general covariance
The notion that coordinates are arbitrary; what matters is the relation between events in spacetime.
Give the types of paths characterising the line interval
Timelike (ds^2<0), spacelike (ds^2>0) and lightlike/null (ds^2=0).
How are paths/curves characterised as time/light/null-like?
Depending on their tangent vector.
Define a path
A continuous one-dimensional subset of spacetime.
Define a curve
A parameterised path: giving the coordinates of the path as functions of some parameter.
Define a straight line
A curve such that, for a suitable choice of lambda, x(λ)^μ are linear functions.
