T1: 1. Introduction and SR Flashcards

1
Q

State the principle of equivalence

A

The effects of a gravitational field are locally indistinguishable from being in an accelerating reference frame.

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2
Q

State the Lorentz transformation x’

A

x’ = γ(x - vt)

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3
Q

State the Lorentz transformation t’

A

t’ = γ(t - v/c^2 x)

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4
Q

State the spacetime interval

A

ds^2 = -c^2 dt^2 + dx^2

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5
Q

Give the spacetime interval in index form (with Minkowski metric)

A

ds^2 = η_µν dx^µ dx^ν

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6
Q

Define inertial frame

A

A frame of reference which is not undergoing any acceleration.

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7
Q

How does special relativity imply space and time are intertwined?

A

The Lorentz space transformation involving time, and likewise time transformation involving a space.

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8
Q

An object with a single upper (lower) index indicates…

A

A column (row) vector.

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9
Q

Define inertial coordinates

A

The coordinate systems related by Lorentz transformation.

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10
Q

State the principle of general covariance

A

The notion that coordinates are arbitrary; what matters is the relation between events in spacetime.

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11
Q

Give the types of paths characterising the line interval

A

Timelike (ds^2<0), spacelike (ds^2>0) and lightlike/null (ds^2=0).

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12
Q

How are paths/curves characterised as time/light/null-like?

A

Depending on their tangent vector.

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13
Q

Define a path

A

A continuous one-dimensional subset of spacetime.

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14
Q

Define a curve

A

A parameterised path: giving the coordinates of the path as functions of some parameter.

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15
Q

Define a straight line

A

A curve such that, for a suitable choice of lambda, x(λ)^μ are linear functions.

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16
Q

How does a suitable choice of λ ensuring x(λ)^μ affect the tangent vector?

A

x(λ)^μ describes a straight line and hence the tangent vector is a constant.

17
Q

What kind of trajectory to particles follow?

A

Timelike (ds^2 < 0)

18
Q

What does the trajectory of particles imply about the choice of parameter for linear functions?

A

Particles are follow timelike trajectories. The parameter that makes x(λ)^μ is proper time up to rescaling.