Special relativity

Speed of light

Maxwell’s equations gave the velocity of light c as m/s; and this is just what is measured. The question then arose: in what reference frame does light have precisely the value predicted by Maxwell’s theory?

Ether

Nineteenth-century physicists viewed the material world in terms of the laws of mechanics, so it was natural for them to assume that light too must travel in some medium. They called this transparent medium the ether and assumed it permeated all space. It was therefore assumed that the velocity of light given by Maxwell’s equations must be with respect to the ether.

Earth Moon1 1/3 sec

8100.3

The Michelson-Morley experiment (1880s)

Postulates of the special theory of relativity

2. Light propagates through empty space with a definite speed c independent

of the speed of the source or observe.

1. The laws of physics have the same form in all inertial reference frames.

Simultaneity

Two events which take place at different locations and are simultaneous to one observer, are actually not simultaneous to a second observer who moves relative to the first.

Time dilation

Clocks moving relative to an observer are measured to run more slowly as compared to clocks at rest relative to that observer.

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The time interval which represents the time interval between the two events occurring at the same point in space, is called the proper time.

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Muon decay

The elementary particle muon is not stable and always decays into lighter particles. Its mean lifetime at rest is 2.20 .

When a muon is traveling at v = 0.6c with respect to the laboratory, how far does the muon travel in the laboratory, on average, before decaying?

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Twin paradox

Length contraction

A spacecraft travels at speed v from Earth to Neptune. The distance between the planets, as measured by the Earth observers, is .

The time between departure of Earth and arrival of Neptune, observed from the spacecraft, is the proper time, since the two events occur at the same point in space (i.e., on the spacecraft). Therefore the time interval is less for the spacecraft observers than for the Earth observers.

Thus the distance between the planets as viewed by the spacecraft observers is

The length of an object moving relative to an observer is measured to be shorter along its direction of motion than when it is at rest.

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The time required for the trip, measured from Earth, is

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Lorentz transformations

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Galilean transformation Lorentz transformation

Mass and energy

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• Movie:

The Mechanical Universe (disk 43)