Minkowski Diagram - Constancy of The Speed of Light

Constancy of The Speed of Light

Another postulate of special relativity is the constancy of the speed of light. It says that any observer in an inertial reference frame measuring the vacuum speed of light relative to himself obtains the same value regardless of his own motion and that of the light source. This statement seems to be paradoxical, but it follows immediately from the differential equation yielding this, and the Minkowski diagram agrees. It explains also the result of the Michelson–Morley experiment which was considered to be a mystery before the theory of relativity was discovered, when photons were thought to be waves through an undetectable medium.

For world lines of photons passing the origin in different directions x=ct and x=−ct holds. That means any position on such a world line corresponds with steps on x- and ct-axis of equal absolute value. From the rule for reading off coordinates in coordinate system with tilted axes follows that the two world lines are the angle bisectors of the x- and ct-axis. The Minkowski diagram shows, that they are angle bisectors of the x'- and ct'-axis as well. That means both observers measure the same speed c for both photons.

Further coordinate systems corresponding to observers with arbitrary velocities can be added to this Minkowski diagram. For all these systems both photon world lines represent the angle bisectors of the axes. The more the relative speed approaches the speed of light the more the axes approach the corresponding angle bisector. The path axis is always more flat and the time axis more steep than the photon world lines. The scales on both axes are always identical, but usually different from those of the other coordinate systems.

Read more about this topic:  Minkowski Diagram

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

    The constancy of the wise is nothing else but the knack of concealing their passion and trouble.
    François, Duc De La Rochefoucauld (1613–1680)

    The constancy of the wise is nothing else but the knack of concealing their passion and trouble.
    François, Duc De La Rochefoucauld (1613–1680)

    Constancy in love is a perpetual inconstancy which fixes our hearts successively to all the qualities of the person loved—sometimes admiring one and sometimes another above all the rest—so that this constancy roves as far as it can, and is no better than inconstancy, confined within the compass of one person.
    François, Duc De La Rochefoucauld (1613–1680)

    The greatest felony in the news business today is to be behind, or to miss a big story. So speed and quantity substitute for thoroughness and quality, for accuracy and context. The pressure to compete, the fear somebody else will make the splash first, creates a frenzied environment in which a blizzard of information is presented and serious questions may not be raised.
    Carl Bernstein (b. 1944)

    For eighteen hundred years, though perchance I have no right to say it, the New Testament has been written; yet where is the legislator who has wisdom and practical talent enough to avail himself of the light which it sheds on the science of legislation?
    Henry David Thoreau (1817–1862)