by

Ciro Santilli (@cirosantilli, 36)

Four-momentum

Table of contents
- Relativistic energy Four-momentum
  - Energy-momentum relation Relativistic energy
  - Mass-energy equivalence Relativistic energy
- Spacetime interval Four-momentum
  - Proper time Spacetime interval

Relativistic energy

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Energy-momentum relation

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Mass-energy equivalence ( $E = m c^{2}$ )

 1  0 

Spacetime interval

 0  0 

In the Galilean transformation, there are two separate invariants that two inertial frame of reference always agree on between two separate events:

time
length, given by the Pythagorean theorem

However, in special relativity, neither of those are invariant separately, since space and time are mixed up together.

Instead, there is a new unified invariant: the spacetime-interval, given by:

c Δ t^{2} - (Δ x^{2} + Δ y^{2} + Δ z^{2})

Note that this distance can be zero for two events separated.

Proper time

 0  0 

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