0.13 Chapter 4.light and matter – dielectric behaviour of matter  (Page 4/4)

“Our aether – does it really exist ? I donot believe that more precise observations could ever reveal more than relative displacement.”

In 1905, Albert Einstein introduced his special theory of Relativity in which he showed that,

“the introduction of ‘Luminiferous Aether’ will prove superfluous in as much as the view here to be developed will not require an absolutely stationary space.” E-M wave was now envisaged as a self supporting and self-sustaining process without the need of a sub-stratum.

4.1.3.1. Special Theory of Relativity.

Newtonian Mechanics fails the test of invariance of the speed of light from frame to frame. Einstein resolved this failure of Newtonian Mechanics.

Time measured by a clock in a given frame of reference is called PROPER TIME.

In moving frame, time measured by a clock placed in the same frame of reference is:

Therefore

Equation (6) implies that time slows down in moving frame as observed from rest frame. That is a person in a moving frame will be seen to age slowly when observed from the rest frame

Some examples of Time Dilation:

Example 1. This experiment was carried out in CERN.

Positive Kaons have a rest lifetime of τ _K = 0.1273μs.

In the lab, it is generated at a velocity of 0.927c.

At this Relativistic Speed its observed life-time = 0.879357μs.

This is the result of Time Dilation.

Distance travelled in the Lab before it decays is = 0.927c×0.879357μs = 244m

Example 2 .

Cosmic Rays are continuously bombarding our atmosphere. Cosmic Rays consist of PROTONS.

Protons collide with Nitrogen Molecule to form to form Pions. Pions decay to Muons. This occurs at a height of 45Km. Muons belong to Leptons. Electron and Tau-lepton belong to the same group of the particles.

Velocity of Muons = 99.9943% of c.

Its rest lifetime = τ _μ0 = 2.2μs. That is in rest frame the lifetime is 2.2μs.

If it was travel at 99.9943% of c for its rest lifetime of 2.2μs it would travel only 659.5m and it could never be detected on the ground detectors.

But it is detected.

This is because its observed lifetime from Ground is 0.0192988s and it is travelling at 99.9943% of c. Hence distance travelled as observed from the ground = 5785.3Km. Muon has been generated 45Km above the Ground. Hence it easily reaches our Ground and is readily detected.

In a moving frame transverse dimensions remain unchanged.

Let v _x , v _y , v _z be the velocities of a body in rest frame.

Let v _x ^’ , v _y ^’ , v _z ^’ be the velocities of a body in a moving frame. The moving Frame is moving with velocity V in (+)ve x-direction.

Transformation of Velocities from Moving Frame to Rest Frame is given as follows:

If the observation is instantaneous then velocity of light ‘c’→ infinity and (8) reduces to:

While sitting in a moving train, moving in (+)ve X direction with velocity V, if we measure the velocity of Wind which in rest frame is moving in (+)ve X direction at a velocity v _x then in moving frame the observed or measured value of the velocity of Wind is:

But velocity of light is not infinity hence measured value of the velocity of Wind from the moving frame is given by equation (8).

4.3.1.2.Michelson-Morley Experiment and the invariance of the velocity of light.

Velocity of PHOTON from a moving train is given by Equation (8).

Rearranging the terms we get:

Open the bracket in (12);

Put dashed terms on LHS and undashed terms on RHS:

But in Rest Frame v _x = c for a photon therefore measured in a moving frame:

The set of transformations achieved by Equation (8) has to be postulated in order to arrive at the invariance of velocity of light as demonstrated by Michelson-Morley.