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I had a teacher, Miss Forkins in Std 1 (1922), who taught us a poem by Robert Louis Stevenson entitled "From a Railway Carriage". It ran as follows:

Puff-puff; puff-puff-puff;
Faster and faster.
Faster than fairies faster than witches,
Bridges and houses, hedges and ditches;
And charging along like troops into battle,
All through the meadows the horses and cattle;
And all of the sights of the hill and the plain,
Fly as thick as driving rain.
Here is a mill and there is a river,
Each a glimpse and gone forever.

Our teacher told its that this poem forms the basis for Albert Einstein's Theory of Relativity because, relative to the cattle in the meadow the train is dashing by, but relative to the train the cattle are rushing as if into battle.

Einstein made use of the railway carriage in motion relative to the embankment which is at rest. Einstein made the point that if a man standing in the moving carriage drops a pebble he will see it falling vertically to the floor of the carriage. But an observer, standing on the embankment will see the pebble describing a curved path, a parabola, as it falls to the floor.

Who is right?                        

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The man in the carriage is at rest relative to the carriage, his FRAME OF REFERENCE.

The man on the embankment is at rest relative to the embankment but sees the train speeding by with the man and the pebble. When the pebble is released, it seems to describe a parabolic path. Why not a sloping straight line? Because the train and contents are subject to the downward force of gravity exerted by the Earth, which accelerates the pebble as it falls, hence the curved path.

This is the Principle of Relativity in a restricted sense, called the Principle of Special Relativity, special because it refers to Galileian/Newtonian frames of reference. Einstein worded the Principle as follows:

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If the embankment is one frame of reference; the train moving uniformly in a straight line, is another frame of reference which is being translated (moved) along the x-axis, say from K to K’ with a velocity v. In the time t the frame K’ moves through the distance vt. The position of a point x' seen in frame K' will be seen from K as being x - vt. - in Classical Mechanics.

But the Earth, itself, of which the embankment forms part, is not only spinning around its axis at 1666 km per hour at the equator, but moving forward in an elliptical orbit around the Sun at 30 km/second; and the Sun, together with the Earth, is revolving around the centre of the Milky Way at a speed of 250 km/sec., and the Milky Way is revolving about a point between itself and the Andromeda Galaxy, M31, at hundreds of kilometres per second, and the Local Group of galaxies is revolving as a group around the centre of gravity between itself and the nearest cluster of galaxies, which is moving etc., etc…

Measurements are made by making use of a ray of light. The speed of light is 300 000 km/second in vacuo. ( Velocity is a vector, which indicates a speed along a straight line. In this sense we also speak of the velocity of light is 300 000 km/sec ).

The speed of light is the same for all colours, red to violet and also holds for other wavelengths, infrared and ultraviolet; microwaves and X-rays; radiowaves and gammarays.

The astronomer Willem de Sitter showed that the speed of light does not depend on the speed of the body emitting the light. Star B revolving around Star A emits light at the same speed c, whether it is approaching the Earth at B in its orbit or whether it is receding from the Earth at B' in its orbit. A galaxy which is so far away that it is receding at the speed of light will still be visible by the light which it emits, even if it is at the observable edge of the universe.

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Now let us come back to the railway carriage. Imagine that a ray of light is propagated along the length of the railway embankment with a velocity c, while the carriage moves in the same direction at velocity v. The light has to catch tip on this velocity v and thus the velocity of the light relative to the moving carriage will be given by w = c - v, i.e. somewhat less than the velocity of light in vacuo c. But the velocity of light should be the same for a moving carriage as for the stationary embankment. So w = c - v contradicts the fundamental Principle of Relativity. We must therefore find some other law besides w = c - v for the propagation of light which will comply with the Principle of Relativity.

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If lighting strikes the embankment simultaneously at two points A and B, distant from each other, we must be able to prove that this happened simultaneously.

We do this by placing an observer exactly midway between A and B at M and supply him with two mirrors mounted at right angles to each other so that he can see points A and B simultaneously.

If the observer sees the two flashes simultaneously reflected in the mirrors then the flashes can be considered to have taken place simultaneously IF the speed of light from A to M is equal to the speed of light from B to M. To measure these speeds the observer needs two clocks, placed at A and B, that register identical times and have the same rates of running.

Assuming the strokes of lightning on the embankment at A and B are simultaneous as seen by M on the embankment, will they be seen as simultaneous by observer M’, travelling at speed v with the train? Einstein says "No", because M' is hastening towards B' and away from A’. Thus he will see the flash from B’ slightly earlier than the flash from A'.

Therefore events which are simultaneous relative to the embankment are not seen as simultaneous relative to the moving train and vice versa.

Every reference frame has its own particular time which gives the times of events relative to that particular FRAME OF REFERFNCE.

Therefore the concept of time cannot he ABSOLUTE. Just think of the various time zones which prevail on the Earth.

The apparent contradiction of the Principle of Relativity whereby w = c – v therefore vanishes when we realise that time is relative.

Also, if the observer in the moving carriage walks along the length of the train, he does not cover the same DISTANCE per second relative to the embankment.

Picture a man walking up an escalator. He seems to speed along.

Therefore space itself (or distance) is relative.

We must therefore get rid of the classical Galileian/Newtonian concepts that:

the time interval (time) between two events is independent of the condition of motion of the frame of reference, and

that the space-interval (distance) between two points on a rigid body is independent of the condition of motion of the frame of reference.

Einstein's theory conceives of a relation between place and time of individual events relative to different frames of reference such that every ray of light possesses the same velocity of transmission c, relative to each of the different frames of reference K and K', having axes x, y, z and x', y' z'.

Classical Physics had presumed that since light travels in waves there had to be a medium to carry the waves, the ether. The experiment done by Michelson and Morley to find out if there was an ether wind passing the Earth proved negative and that the velocity of light in all directions is the same, c.

If we draw graphs showing distance d against time t, we have for stationary state as in A, the straight line is horizontal: time increases from 0 to T, but the distance d does not increase - it is designated by a horizontal straight line.

For uniform forward motion, as in B, we get a straight line with upward slope - both d and t increase steadily.

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When acceleration takes place, as in C, we get an upward sloping curve.

When retardation takes place, as in D, we get a curve with downward slope.

Now imagine we have a man standing in a lift, an elevator, of which the back wall consists of carbon paper and that it can move up and down against a smooth wall. Any mark made on the carbon paper will show on the wall.

The man, says he is at rest and proves it by drawing a horizontal line across the back of the lift. The straight line X - X' has no slope, either on the carbon paper or on the smooth wall. We agree that he is at rest.

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We then let the lift descend at a uniform speed. He again draws a horizontal straight line and says he is at rest. The copy made through the carbon paper shows a downward sloping straight line XY. He still says that he is at rest, but we say "No, the downward sloping straight line on the smooth wall proves that relative to the wall you were in uniform motion"

We then send one of our henchmen up the lift shaft with a pair of snips, and unknown to the man in the lift, he cuts the cable by which the lift hangs! He again draws a horizontal straight line and maintains that he is still at rest. The parabola on the smooth wall shows that he accelerated until the lift crashed on the bottom of the shaft, where we see that he is very still.