Answer to Question #101064 in Mechanics | Relativity for Kishwer

Question #101064

What are properties of interval by Donald Marolf notes ?


1
Expert's answer
2020-01-09T14:15:46-0500

According to Cambridge Dictionary, interval is a period between two events or times. The definition can be expanded by Special Relativity, it can be written in mathematical form:


interval2=Δx2c2Δt2,\text{interval}^2=\Delta x^2-c^2\Delta t^2,


where

Δx\Delta x - spatial separation,

Δt\Delta t - separation in times,

which implies that interval can be a distance between two events in addition to the first definition.

The Notes on Relativity and Cosmology contain the following properties of interval:

  • Timelike separation: there is an inertial frame where events occur in the same place.
  • Spacelike separation: there is an inertial frame where events occur at the same time.
  • Lightlike separation: events are separated by zero interval in all reference frames.

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