Answer to Question #101064 in Mechanics | Relativity for Kishwer

Question

What are properties of interval by Donald Marolf notes ?

Answer 1

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:

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

where

$\Delta x$ - spatial separation,

$\Delta t$ - 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.