Special Theory of Relativity
In a nutshell SPECIAL THEORY OF RELATIVITY says that :-
1. Speed of light is constant.
2. The more fast you move in space , your length will reduce for the outside observers.
3. The more fast you move through space, time will pass slower to you.
4. Nothing can travel faster than light.
● WHAT IS THE NEED OF SPECIAL THEORY OF RELATIVITY?
Classical mechanics tends to fail while explaining the motion of objects which it is moving almost equal to speed of light. (Basically objects having speed equal to speed of light)
As if we go through the velocity of light through classical mechanics, it depends on the frame of reference (It can be assumed a set of axes to which the observer is permanently attached ) ,but Michelson-Morley experiment proves that light doesn’t depend on frame of reference even if an observer is moving with 200000 km/s (speed of light ~ 300000 km/s) From here the special theory of relativity came into action.
It explains everything about an object which is moving almost equal to speed of light.
MICHELSON-MORLEY
EXPERIMENT.
It paved the way for the theory of special relativity
• Young double slit experiment had proved that light behave like a wave . So wave need a medium to travel for which a imaginary medium was named as ‘LUMINIFEROUS AETHER’
•So to prove the existence of aether MICHELSON and MORLEY came to the scenario.
•The experiment performed compared the speed of light to notice the relative motion of earth
The result was negative, in the experiment Michelson-Morley found that their is no change of speed of light in the direction the aether is moving.
The speed of light remains the same even if the aether moves relative to light the speed remains fix.
This proves of the no existence of aether medium for light to travel.
Experiment
To understand the experiment clearly let us give some notation to all apparatus.
1. Both the mirror let us tell ‘A' and ‘D'
2. Let us tell coherent light source as ‘B'
3. Let us tell semi-silvered mirror as ‘C'
4. And the final light Detector tell us as ‘E'
(Here we have assumed that aether is traveling from right to left relatively and parallel to horizontal)
-When the light came from the source and strikes to ‘C' some of the part get reflected and goes to ‘B' and some of the part transmission to ‘D'
-After getting reflected from ‘A' and ‘D' the light rays get reflected and transmitted and went to ‘E'
-So the phase difference is only because of path as it had been emitted from the same source so the phase difference will be only because of length ‘AC' and ‘CD'
-Then let us assume that at ‘E' we see a constructive interference
Let in 1st case As the system is moving with relative to aether with an angel 0° with the horizontal (relative to aether) then their is a path difference and we have got constructive interference and in 2nd case when we made the system to travel at an angle 45°(with relative to aether) then there is no path difference and when the system is made to move at an angle 90° (with relative to aether) there is a path difference.
So due to alternate phase difference because of path difference we should have observed alternative constructive and destructive interference but when this experiment conducted for years it had been observed that their is no difference in fringe (means if it is constructive then it will do content instead for infinity time and same with destructive instead)
★This proves that there is no aether medium for light to travel.
Galilean and Lorentz Transformation.
Let’s take two frame of reference as D(black one) and D'(yellow one) and consider a point S.
Let D' frame move with a velocity ‘V' so the coordinate of ‘S' will be (X',Y',Z').
If light travel from +X to -X then D will observe speed of light to be ‘C'(speed of light ) but for frame D' who is moving with some velocity V ( let say 100000 km/s) then D' will observe the speed of light to be C+V , according to Galilean transformation but which is actually not the correct scenario here. The culprit over this scenario to keep the light speed constant is TIME by changing dilating itself.
●Then to make this correction Lorentz Transformation come into action.
LORENTZ TRANSFORMATION
It is a transformation equation that transforms one space-time coordinate frame to another frame which moves at a constant velocity relative to the other . This was the foundation of special theory of relativity. As the Galilean transformation couldn’t explain that light doesn’t depend on frame of reference.
LENGTH CONTRACTIONS
It explains that length of a body is measured to be the greatest when a body is at rest relative to the observer and when it moves with a velocity V relative to the observer, it’s measured length is contracted in the direction of its motion by a factor: root of (1- v2c2) , whereas it’s dimensions perpendicular to the direction of motion are unaffected.
L = L(not) √1-v²/c²
L- length measurement of an observer moving relative to the object being measured.
L○ – length measurement of an observer at the rest relative to the object being measured.
V - speed of object
C – speed of light
TIME DILATION
For a body moving with a very high speed , the time seems to be slower than the time referenced to rest. This slowed up time or increased up time can be calculated by a relation :-
T= T(not)/√1-v²/c²
T – Dilated time i.e time interval measured by a clock which is moving with velocity ‘V' w.r.t observer
T○ – Time interval measured by a clock which is at rest w.r.t observer.
V – speed of the object
C – speed of light.
●Energy-mass relation
Before Einstein, the mass and energy were considered as separate or independent physical quantities. Einstein by his theory of relativity proved that energy and mass are related to each other , and every substance has energy due to it’s mass also. Then he formulated a formula for energy – mass equivalence :-
E= MC²
E – energy
M – mass
C – speed of light
Article by- Chinmaya Chirantan
For more- futuristicphotons.blogspot.com
Comments
Post a Comment