Galilean and Lorentz transformation

Suppose two inertial reference frames S and S’ are moving with velocity v with respect to each other. Also suppose that an observer at reference frame S measures an event as (x, y, z, t) and another observer at frame S’ measures the same event as (x', y', z', t'). Now if we want to relate the measurements of S frame with S’ frame we have to use transformation equations.

If we take Newtonian mechanics granted then we use the Galilean transformation. Galilean or Classical transformation equations are:

x'=x-vt

y'=y

z'=z

t'=t

Notice that the time co-ordinates are measured the same by both observer—that is t'=t.

But if we take Special Relativity instead of Newtonian Mechanics than we use Lorentz transformation. Lorentz transformation equations are:

x'=\frac {x-vt} {\sqrt{1-v^2/c^2}}

y'=y

z'=z

t'=\frac {t-vx/c^2}{\sqrt {1-v^2/c^2}}

The fraction \frac {1}{\sqrt {1-v^2/c^2}} is also called relativistic gamma (\gamma).

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About f.nasim

A CS undergrad from Bangladesh.
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