Introduction To Special Relativity - Einstein's Postulate: The Constancy of The Speed of Light

Einstein's Postulate: The Constancy of The Speed of Light

Einstein's postulate that the speed of light is a constant comes out as a natural consequence of the Minkowski formulation.

Proposition 1:

When an object is travelling at c in a certain reference frame, the spacetime interval is zero.

Proof:

The spacetime interval between the origin-event (0,0,0,0) and an event (x,y,z,t) is
The distance travelled by an object moving at velocity v for t seconds is:
giving
Since the velocity v equals c we have
Hence the spacetime interval between the events of departure and arrival is given by

Proposition 2:

An object travelling at c in one reference frame is travelling at c in all reference frames.

Proof:

Let the object move with velocity v when observed from a different reference frame. A change in reference frame corresponds to a rotation in M. Since the spacetime interval must be conserved under rotation, the spacetime interval must be the same in all reference frames. In proposition 1 we showed it to be zero in one reference frame, hence it must be zero in all other reference frames. We get that
which implies

The paths of light rays have a zero spacetime interval, and hence all observers will obtain the same value for the speed of light. Therefore, when assuming that the universe has four dimensions that are related by Minkowski's formula, the speed of light appears as a constant, and does not need to be assumed (postulated) to be constant as in Einstein's original approach to special relativity.

Read more about this topic:  Introduction To Special Relativity

Famous quotes containing the words einstein, constancy, speed and/or light:

    God is subtle, but he is not malicious.
    [Raffiniert ist der Herr Gott, aber boshaft ist er nicht.]
    —Albert Einstein (1879–1955)

    Obstinacy in a bad cause is but constancy in a good.
    Thomas Browne (1605–1682)

    Among the laws controlling human societies there is one more precise and clearer, it seems to me, than all the others. If men are to remain civilized or to become civilized, the art of association must develop and improve among them at the same speed as equality of conditions spreads.
    Alexis de Tocqueville (1805–1859)

    Spades take up leaves
    No better than spoons,
    And bags full of leaves
    Are light as balloons.
    Robert Frost (1874–1963)