Special relativity

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  • Created by: Monikak
  • Created on: 15-01-16 14:17

Michelson-Morley experiment - Interferometer

Michelson and Morley designed the 'interferometer' to test the ether hypothesis.

Light beam from a monochromatic light source is split into two beams at the back of the semi-silvered glass block

One of the light beams continues towards M1 (mirror), is reflected back towards the glass block inside which it is partially reflected towards the viewing telescope

The other beam is due to partial reflection at the block reflected towards M2 (mirror) where it is relfected back towards the glass block, and into the viewing telescope

The compensator glass block is present to ensure that both beams travel through the same thickness of glass otherwise the wave trains would not overlap

Light fringes are observed because of the difference of the path lenghs of the two beams. Bright fringe when beams arrive in phase, dark fringe when out of phase. 

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Experiment as means of detecting absolute motion

Suppose apparatus is alligned so that M1 travels parallel to the earth's motion, and M2 travels perp to the earth's motion. Then rotating the apparatus 90deg in a horizontal plane would swap beam directions relative to earth's motion. 

If ether hypothesis correct:

  • difference in travel times of the two beams reverse
  • shift in fringe pattern - M&M predicted that the fringes would shift by about 0.4 of fringe width and the apparatus was sensitive enough to detected shifts of 0.05 fringe width. 

However NOTHING HAPPENED. This failure to detect the shift in the fringe pattern resulted in the abolition of the ether theory and the realisation that the speed of light is invariant ie. independent of the motion of the light source and motion of any observer. 

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Einstein' theory of special relativity

To develop his thoery of special relativity, Einstein started from two postulates

1. Physics laws have the same form in all intertial frames of reference (frames of reference that move at constant velocity relative to each other)

2. Speed of light in free space is invariant - always the same and independent of the motion of the light source or the observer

An inertial frame of reference is one in which all bodies move at constant velocity unless acted upon by an external force i.e. there's no inherent acceleration

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Time dilation

A moving clock runs more slowly than a stationary clock

Time between two events is stretched out or dilated according to the moving observer, in accordance with the formula 

\Delta t' = \frac{\Delta t}{\sqrt{1-\frac{v^2}{c^2}}} 

where t is the 'proper time' and t' the 'dilated time'

Time dilation has been proven using particle accelerators.

Half life of muon particles was significantly longer (1.5 μs at rest, to 17 μs

) when in motion

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Length contraction

A rod moving in the same direction as its length appears shorter than when stationary

L=\frac{L_{0}}{\gamma(v)}=L_{0}\sqrt{1-v^{2}/c^{2}}

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Mass and energy

Relativistic mass

The mass of an object increases with speed in accordance with Einstein's relativistic mass formula. This formula also shows us that the mass of an object increases when it gains kinetic energy.

Einstein went further and proved that transferring energy in any form:

- TO an object, increases its mass

- FROM an object, decreases its mass

He showed that energy and mass are equivalent and interchangeable as given by the equation

E = m c^2

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