35.6 Length Contraction, Time dilation and Relativistic Law of Velocity Addition

The consequences of Equation (3) can be shown to be

Length contraction

Moving rod contracts in length by factor of

Time dilation

Moving clock dilates in time interval measured by factor of

Relativistic Law of Velocity Addition

If an object is in motion with velocity (u'_x, u'_y, u'_z components) in frame S' and the velocity of the object measured in S is (u_x, u_y, u_z components) then ,

Thus, Speed of light is same in S' and S; as it should be. Also note that according to Galilean Law of Velocity Addition,

But, Michelson- Morley experiment has shown that,   u_x     =    C  only.

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Index

35.1 Frames of References
35.2 Galilean Principle of Relativity and Invariance of Newton's Laws of motion
35.3 Galilean Law of Velocity Addition
35.4 Absolute Frame of Reference
35.5 Einstein's Postulates
35.6 Length Contraction, Time dilation and Relativistic Law of Velocity Addition
35.7 Relativistic Mass and Mass - Energy Equivalence

Chapter 1