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## Experimental Verification of Special Relativity

Experimental Evidence of Universality of Velocity of Light:The main ingredient of special relativity is, undoubtedly, the one that has to do with speed of light. It states that velocity of light in free space has same value in all inertial frames of reference and is independent of motion of the source. This statement calls for two kinds of investigation namely:

(1) is velocity of light isotropic or does it change with direction of motion?

(2) Does the velocity of light change with relative motion of source and the observer?

Michelson - Morley experiment gives answer to first question. Experiment compared upstream-downstream with cross-stream velocity of light. Within limit of experimental error, it was illustrated that velocity in both directions is same. Hence, the velocity of light is isotropic. This experiment also established the fact that there is no preferred frame of reference, the so-called the ether frame.

Despite repetition of the experiment at different times and season, the result was always the same. In 1932, Kennedy and Thorndike repeated the experiment using an interferometer with different length of arms to test the hypothesis of Lorentz contraction of the arm of the interferometer parallel to the direction of motion. This also resulted in the same conclusion that velocity in the two orthogonal directions was the same.

The velocity of light change with relative motion of the source and the observer can be examined by estimating velocity of light emitted in same direction as that of moving source. If the observer at rest in frame of moving source assigns as the velocity of light, then the observer relative to whom source is moving with velocity measures velocity of light as c' = v + c. If v is close to speed of light, then c' is definitely greater than. This is an clear violation of special relativity. So, what special relativity is telling us here is that c' = c i.e. v = 0. We know that v ≠ 0. So, value achieved for c' is result of relativistic velocity transformation. Assertion c' = c has been examined and found to agree with experiment. For instance, velocity of gamma radiation (another electromagnetic radiation propagating at speed of light ) emitted in decay of -meson moving at the velocity in excess of 0.99975c was estimated in 1964 by Farley et al to be (2.9979 ± 0.0003) x 108m/s.

Experimental Evidence of Time Dilation and Length Contraction:Time dilation and length contraction is real and can be confirmed experimentally. For emphasis, we recapitulate conclusion of discussion here. Muons are unstable elementary particles with very short life span (approx 2 x 10

^{6}s on average). So, they decay shortly after they come in existence. With typical speeds of approx 2.994 x 10^{8}ms^{-1}, muons that are created in upper atmosphere at altitude of approx 6000km by incoming cosmic rays reach earth at sea level in such profuse supply that one wonders how they handle to get this feat. In a time of 2 x 10^{6}s a muon travelling at the speed of 2.994 x 10^{8}ms^{-1}can only cover 600m of altitude.Production of muons in laboratory can be attained through in high-energy accelerators. Their decay is seen by tracking reaction products that are electrons. Muons can then be trapped and their decay is studied at rest or placed in beam and their decay studied in motion. When muons are studied at rest their lifetime is 2.198 x 10

^{-6}s. This is proper time. In a particular experiment published by J. Bailey et al in 1977, muons were trapped in the ring and circulated at very speed and momentum of about p = 3094MeV/c and lifetime came to about 6.438 x 10^{-5}s. This confirms that time is dilated while muons were in flight.Another outstanding experimental proof of time dilation is supplied by electrostatic focusing. In high energy particle accelerators, it is seen that stationary cluster of electrons or protons expanding under electrostatic repulsion do so at definite characteristic rate. When they are in fast moving beams, they expand at much slower rate.

Experimental proof of Twin Paradox:Direct experiment to test this phenomenon can't be performed but corresponding experiment can be done. Two atomic clocks are cautiously synchronized. Then one of them is flown around earth in the airplane. On return and comparison with earth clock, it is found clock which was in flight is a few seconds behind. Though due the rotation of earth, the earth clock can't be said to be in the inertial frame of reference, observation is in agreement with prediction of special relativity.

Experimental Evidence of Relativistic Doppler Effect:The experiment of Ives and Stilwel performed in 1938 gives proof of agreement with theoretical prediction. The beam of hydrogen atom, produced in gas discharge was made to travel down the tube at relativistic speed. Light emitted by two atoms and in direction parallel and opposite to relativistic velocity was simultaneously observed. The spectrograph was utilized to photograph characteristic spectral lines from two atoms and also on same photographic plate, from atoms at rest. If classical Doppler formula were valid, wavelengths of lines from two atoms 1 and 2would be place at symmetric intervals Δλ

_{1}= ±λ_{0}(u/c)^{2}on either side of line from atoms at rest (wavelength λ_{0}). Relativistic formula provides small additional symmetric shift Δλ_{2}= +1/2λ_{0}(u/c)^{2}Experimental Evidence of Relativistic momentum and Energy:Direct proof of relativistic momentum and energy comes in handy from experiments involving high-energy accelerators in study of high-energy and particle physics. Results are in excellent agreement with theoretical predictions. The atomic bomb dropped in Japan in 1945 during World War II. This came as a result of realization of mass-energy equivalence.

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