It’s All Relative

One of most disturbing conclusions from Einstein’s Special Theory of Relativity (the General Theory would come ten years later, in 1915) is that time appears different for different observers.  We think of time as uniform, as something that ticks away the same for everyone, the pendulum swings the same in New York as in Sydney, in Tokyo as in Buenos Aires.  But the conclusion that the speed of light is the same for each observer leads to the conclusion that time cannot be absolute.

Imagine you are on a special train, one that can move at near the speed of light.  You have an accurate clock, one that operates by pulse of light from a source vertically to a mirror six feet above the source, which reflects the light back to the source.  The time it takes for this to happen is one tick of your clock.  A little bit of high school algebra gives the time for a tick as .000000012 seconds.  You will measure this time the same whether your train is at rest or moving at near the speed of light because of Galileo’s relativity principle.

Now imagine that the train moves at 80% of the speed of light past a station where a friend can see you and your clock.  Your friend sees the light pulse go up and be reflected, but because of the speed of the train, the upper mirror has moved, relative to your friend by the time the pulse has reached it and the source has moved farther by the time it comes back. To your friend, the light pulse has to travel farther than it has to travel for you.  Since the speed of light is constant for both of you, your friend measures the time between ticks as .00000002 seconds.

English: The clock, as observed in a frame whe...
English: The clock, as observed in a frame where it is moving at some speed ‘v’. In this case, the photon traces out a triangular path which is longer than in the rest frame. But since the speed of light is the same in all frames, this necessarily leads to a lengthening of the period of the clock, as derived in the image. SVG version of the original, :Image:Time-dilation-002.jpg. (Photo credit: Wikipedia)

Your friend therefore measures the time between the same two events as being longer than you measure it to be.  This time difference is known as time dilation, the stretching of time.  One question immediately arises: Is this time dilation real or is it just an illusion?  It is absolutely real.  Ordinarily time differences in systems moving relative to each other are minute because ordinarily objects don’t move at speeds near that of light.  But the special theory of relativity has to be taken into account for Global Positioning Systems (GPS) to function properly.  This is a perfect example of how pure science, which appears to have no useful application at the time of its discovery, later proves to have real application for millions of people.

There is another effect.  In addition to time dilation, special relativity predicts space contraction.  The effect of this is that to your friend on the platform at the station you appear thinner, though just as tall, than you are on the train.  Belcause of these two conclusions, a third conclusion, perhaps the most mind-boggling of all, appears:  That, at least on some level, space and time are interchangeable.  This led to a new view of the universe.  It does not consist of space and time, where something that affects one does not affect the other.  Instead the universe consists of spacetime, four unified dimensions in which an event in one dimension has consequences in the other three.

The time was approaching for a showdown between two of the greatest heavyweight in physics, Newton and Einstein.  The match up would occur in the ring of gravity.





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