Relativity

Relativity. The Michelson-Morley Experiment. Einstein's Principle of Relativity. Consequences of the Special Theory of Relativity.

special theory of relativity.
Regarding the theory, Einstein wrote:
“The relativity theory arose from necessity, from serious and deep contradictions in the old theory from which there seemed no escape. The strength of the new theory lies in the consistency and simplicity with which it solves all these difficulties . . .”

must be the same in all inertial frames of reference.

transformation equation

in the speed of light was first performed in 1881 by Albert A. Michelson and later repeated under various conditions by Michelson and Edward W. Morley (1838–1923).

No fringe shift of the magnitude required was ever observed.

Light is now understood to be an electromagnetic wave, which requires no medium for its propagation.

in the fringe pattern.

two postulates:

1. The principle of relativity: The laws of physics must be the same in all inertial reference frames.
2. The constancy of the speed of light: The speed of light in vacuum has the same value, c = 3.00 · 108 m/s, in all inertial frames, regardless of the velocity of the observer or the velocity of the source emitting the light.

such thing as an absolute length or absolute time interval. Furthermore, events at different locations that are observed to occur simultaneously in one frame are not necessarily observed to be simultaneous in another frame moving uniformly with respect to the first.

other words,
two events that are simultaneous in one reference frame are in general not simultaneous in a second frame moving relative to the first. That is, simultaneity is not an absolute concept but rather one that depends on the state of motion of the observer.

Einstein’s thought experiment demonstrates that two observers can disagree on the simultaneity of two events. This disagreement, however, depends on the transit time of light to the observers and, therefore, does not demonstrate the deeper meaning of relativity. In relativistic analyses of high-speed situations, relativity shows that simultaneity is relative even when the transit time is subtracted out.

than unity, this result says that the time interval Δt measured by an observer moving with respect to a clock is longer than the time interval Δtp measured by an observer at rest with respect to the clock. This effect is known as time dilation.

interval.

The proper time interval is the time interval between two events measured by an observer who sees the events occur at the same point in space.

rest and for muons traveling at a speed of 0.999 4c.

an object is the length measured by someone at rest relative to the object. The length of an object measured by someone in a reference frame that is moving with respect to the object is always less than the proper length. This effect is known as length contraction.

If an object has a proper length Lp when it is measured by an observer at rest with respect to the object, then when it moves with speed v in a direction parallel to its length, its length L is measured to be shorter according to

place only along the direction of motion.

make a space–time graph, in which ct is the ordinate and position x is the abscissa.

A path through space–time is called a world-line. At the origin, the world-lines of Speedo and Goslo coincide because the twins are in the same location at the same time. After Speedo leaves on his trip, his world-line diverges from that of his brother. Goslo’s world-line is vertical because he remains fixed in location. At their reunion, the two world-lines again come together.

of time dilation is the shift in frequency found for light emitted by atoms in motion as opposed to light emitted by atoms at rest. This phenomenon, known as the Doppler effect. In the case of sound, the motion of the source with respect to the medium of propagation can be distinguished from the motion of the observer with respect to the medium. Light waves must be analyzed differently, however, because they require no medium of propagation, and no method exists for distinguishing the motion of a light source from the motion of the observer.

source and an observer approach each other with a relative speed v, the frequency fobs measured by the observer is

The most spectacular and dramatic use of the relativistic Doppler effect is the measurement of shifts in the frequency of light emitted by a moving astronomical object such as a galaxy. Light emitted by atoms and normally found in the extreme violet region of the spectrum is shifted toward the red end of the spectrum for atoms in other galaxies—indicating that these galaxies are receding from us. The American astronomer Edwin Hubble (1889–1953) performed extensive measurements of this red shift to confirm that most galaxies are moving away from us, indicating that the Universe is expanding.

ball while standing on a railroad flatcar moving at 110 mi/h. The ball is thrown in the same direction as that of the velocity of the train. Applying the Galilean velocity transformation equation, the speed of the ball relative to the Earth is (a) 90 mi/h
(b) 110 mi/h (c) 20 mi/h (d) 200 mi/h (e) impossible to determine.

long in a spacecraft that is moving at high speed through space. Will an Earthbound observer, who is watching the movie through a powerful telescope, measure the duration of the movie to be (a) longer than, (b) shorter than, or (c) equal to two hours?

time they spend traveling in space. After a long voyage traveling at a speed approaching c, would a crew rather be paid according to (a) an Earth-based clock, (b) their spacecraft’s clock, or (c) either clock?