Suppose an event is measured to be at a = (0,-2, 3, 5) in one reference frame. find the components of this event in another reference frame that is moving with a speed of 0.85 relative to the original frame, in the positive x-direction

(2.3529, -3.7966, 3,5)

Explanation:

We can do this simply by taking the Lorentz transformations:

Taking the coordinates

in one reference frame, and taking the second reference frame moving at speed v in the x-direction of the original frame, the Lorentz transformations are:

For our problem

So, the transformation will give

The coordinates of the same event in this moving frame are a' = (3.226, -3.7966, 3, 5).

Explanation:

Given:

The coordinates of the event are given as (t, x, y, z)

Therefore, for the first frame, the event a has coordinates:

t = 0

x = -2

y = 3

z = 5.

The coordinates of the same event in the moving frame as given by the Lorentz transformation as

where,

In natural system of units, c = 1.

Therefore,

The coordinates of the same event in this moving frame are a' = (3.226, -3.79, 3, 5).

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