RELATIVITY

TIME DILATIONLENGTH CONTRACTIONTWIN PARADOX

Relativity :

Theory of relativity :

Encompasses two theories of Albert Einstein special relativity and general relativity.

Albert Einstein:

Description :

was a German born theoretical physicist who developed the theory of general relativity, effecting a revolution in physics. For this achievement, Einstein is often regarded as the father of modern physics and one of the most prolific intellects in human history. He also contribute the paper “On the Electrodynamics of Moving Bodies” (Annus Mirabilis) that is publish in the scientific journal in 1905.

Relativity:

Special Relativity :

Is a theory of the structure of space time. It was introduce by Albert Einstein’s 1905 paper “On the Electrodynamics of Moving Bodies”

General Relativity:

Is a theory of gravitation develop by Einstein in the year 1907-1915. the development of general relativity began with equivalence principle under which states of accelerated motion being at rest in gravitational field are physically identical

Special Relativity is based on two postulate;

The laws of physics are the same for all observers in uniform motion relative to one another. (Principle of relativity)

The speed of light in a vacuum is the same for all observation, regardless of their relative motion or of the motion of the source of light.

The resulting theory agrees with the experiment. Better than classical mechanics, e.g. in the Michelson-Morley experiment that supports postulate 2, but also has many surprising consequences. Some are :

Relativity of Simultaneity: two events, simultaneous for one observer, may not be simultaneous for another observers on relative motion.

Time Dilation: moving clocks are measured to tick more slowly than an observers stationary clock.

Length contraction: objects are measured to be shortened in the direction that they are moving with respect to the observer.

Mass-energy equivalence: E=mc2, energy and mass equivalent and transmutation.

Maximum speed is finite: No physical object, field line can travel faster than speed of light in a vacuum.

Time:

Is not an absolute but is relative to the motion between the observer and the event that is being observed.

Light clock:

Light clock: light will bounce up and down between parallel mirrors and tick-off equal intervals of time.

Time dilation:

“The apparent slowing down of time for an object moving at relativistic speeds.”

Time dilation:

Formula:

to = time interval of flash to bounce between two mirror.

v = velocity between the observer and the object

c = speed of light

Sample Problem

Leo and Christian are twins. At the age of 30, Leo left for a round trip to a distant star in a spaceship with a speed of 0.95 c relative to earth. The trip took 20 years according to the ship.

Find the age upon Leo’s return.

Twin paradox

Is a experiment in special relativity in which a twin makes a journey into space in a high-speed rocket and returns home to find he has aged less than his identical twin who stayed on earth. TwinParadox

Length contraction:

The apparent shrinking of an object moving at relativistic speed

Lorentz-FitzGerald contraction

FitzGerald is better known for his conjecture in his short paper "The Ether and the Earth's Atmosphere" (1889) that if all moving objects were foreshortened in the direction of their motion, it would account for the curious null-results of the Michelson-Morley experiment. FitzGerald based this idea in part on the way electromagnetic forces were known to be affected by motion. In particular, FitzGerald used some equations that had been derived a short time before by his friend the electrical engineer Oliver Heaviside. The Dutch physicist Hendrik Lorentz hit on a very similar idea in 1892 and developed it more fully into Lorentz transformations, in connection with his theory of electrons.

Lorentz-FitzGerald contraction

Hendrick Lorentz In 1895, with the attempt to explain the Michelson-Morley experiment, Lorentz proposed that moving bodies contract in the direction of motion (see length contraction; George FitzGerald had already arrived at this conclusion, see FitzGerald-Lorentz Contraction). Lorentz worked on describing electromagnetic phenomena (the propagation of light) in reference frames that moved relative to each other. He discovered that the transition from one to another reference frame could be simplified by using a new time variable which he called local time.

Length contraction

Formula:

L0  is the proper length (the length of the object in its rest frame),

L is the length observed by an observer in relative motion with respect to the object,

 v is the relative velocity between the observer and the moving object,

c is the speed of light,

Sample Problem

A spaceship travelling at 0.50 c relative to earth is 45 m long as measured by its crew. How long is the spaceship as measured by the mission control in Texas?