## Mathematical and Computing Sciences Question #91

Ian Rosner, a 15 year old male from the Internet asks on November 20, 1999,

Can you explain the fourth dimension and state simply Einstein's Theory of Relativity?

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### Barry Shell answered on November 20, 1999

You can read about the greatest living geometer, HMS Coxeter. For an explanation of the fourth dimension, look on that page under "The Science". You may also wish to look up "hypercube" and "tesseract" elsewhere on the web. An excellent explanation can be found at the website of the University of Minnesota Geometry Centre.

If this still does not help, try looking up "dimensional analogy."

Click here for a tutorial on relativity by John Baez, from the math department at UCR.

### Carl HInton, Amateur Astronomer, Northampton, U.K. answered on June 21, 2003

[Editor: Although relativity is much more complicated than this, especially at cosmic distances and speeds, here is one simplified explanation.]

I drive down a motorway at 70 Km/h a car coming the other way is driving at 80 Km/h. We are travelling at 150 Km/h relative to each other. If we were both travelling in the same direction we would be travelling at 10 Km/h relative to each other. Speed depends on direction, and what we are measuring against.

For more on Space-Time you might like to borrow "Black Holes - A Travellers Guide" ISBN 0-471-19704-151495 from your school or local library. It has some great explanations, and a good story-line too.

### John Russo, undergrad student at Gwynedd-Mercy College, PA answered on November 29, 2003

Carl Hinton's answer is correct in terms of Newtonian physics; however, relativity is based on the fact that light does not behave like the cars in Carl's example. The Michelson-Morley experiment showed that the speed of light (c) is NOT affected by the relative motion of the observer. This would be like having the eighty mile an hour car approach you at 80 mph even when you are going 70. (You would thus think that the car was only moving at 10mph). Yet if the same car approached you from the rear its speed relative to you would still be 80mph (thus making you think that it was moving at 150mph). Even more confusing is the fact that three separate observers observing our 80mph car "simultaneously" and having various speeds relative to one another would all measure the speed of the other car at 80mph. In this regard, the theory of relativity is based on the finding of an absolute in the universe; namely "c" the speed of light in a vacuum.

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