This Week in Phys 203/204 -- January 13 1997 --

Let's begin with a few hints on doing well in this course.

Albert Einstein, one of the most brilliant and famous physicists of the 20th century, was born in 1879 in Germany. While working at the patent office in Bern Germany in 1905, he published three classic physics papers. One describing special relativity, one explaining the photoelectric effect by proposing that light is quantized, and one on statistical physics. Later in the same year he extended the special theory of relativity to include the equivalence of mass and energy, E=mc^2. Einstein won the Nobel Prize in 1921 for his work on the photoelectric effect. He died in 1955 in the United States while working unsuccessfully on a grand unification theory.

For a detailed biography with references, see the History of Mathematics Archive. Every scientist has the benefit of the work of his or her predecessors and contemporaries. The same site describes the contributions of other mathematicians and physicists to the special theory of relativity and to the general theory of relativity

A spear 10 meters long is thrown at a relativistic speed through a pipe that is 10 meters long. Both these dimensions are measured when each is at rest. When the spear passes through the pipe, which of the following statements best describes what is observed? (and why?)

1. The spear shrinks so that the pipe completely covers it at some point.
   
2. The pipe shrinks so that the spear extends from both ends at some point.
   
3. Both shrink equally so that the pipe just covers the spear at some point.
   
4. Any of these, depending on the motion of the observer.
   

Sort of makes you want to say "Hmmmm.......", doesn't it?

Well, the warmup question is relatively straightforward, but there are several famous relativistic 'paradoxes' to really make you scratch your head! A discussion can be found here.

One interesting way to study Einstein's general theory of relativity is to watch Star Trek, though you must watch carefully because fact, speculations, and error often occur in the same episode!

This discussion is largely based on a superb book, The Physics of Star Trek, by Lawrence M. Krauss published by HarperCollins Publishers in 1995. (ISBN 0-465-00559-4) Readable and highly recommended!

Let's begin with the propulsion system. Speed is given in terms of a warp factor and the engines are refered to as the warp drive. What is meant by 'warp factor'?
This is a speed relative to the speed of light where warp factor 1 is the speed of light. In the original series, warp n was n times the speed of light. However, in later series, such as Star Trek: The Next Generation, the warp factor scale became uneven. (The decibel scale for sound levels and the Richter scale for earthquakes magnitudes are both uneven, specifically logarithmic. The warp factor scale is more unusual and has changed as the series evolved.)

But why the term 'warp'?
Well, in the theory of general relativity created by Einstein in 1915, massive objects bend or warp the fabric of space. Imagine space as a soft thin tabletop and light as a marble rolling across the tabletop. Planets are heavy spheres placed on the tabletop. The planets bend or dimple the tabletop in their vacinity. Away from planets, the table is flat and a marble rolls in a straight line. However, near a planet the table is bent so that marbles roll in a curve. The marble represents the path taken by light which is bent by strong gravitational fields. This bending effect was observed experimentally in 1919, by a British eclipse expedition led by Sir Arthur Eddington, in light from the planet Mercury traveling in a curved rather than straight path around our sun. (But I digress...)

In warped or curved space, the shortest path between two points may differ from the shortest path in flat space. For example, in flat space the shortest path between A and B is along the diameter rather than around the circle. But, if space is warped into a funnel then the shortest path is around the circle.

There are several practical problems to warp speed travel.

First, there seems to be no way for a ship to exceed the speed of light.

Second, clocks would become unsynchronized. If you zip across the galaxy to see someone, you'd be disappointed if they aged and died while you aged only a few days while in transit. (See the twin paradox.)

Both of these can be solved using a creative new solution to the equations of general relativity by Miguel Alcubierre, a physicist at the University of Wales. He was able to show that it is possible to design a solution which allows travel between any two points in space in as short a time as you like while the ship itself travels at speeds much less than the speed of light so that the occupants are not significantly effected by time dilation and clocks stay synchronized. Alcubierre's solution is simple to imagine: space compresses in front of the ship and stretches behind the ship while doing neither beneath the ship. If the compression is big enough, then a far away galaxy will be brought close so the ship thinks it travels only a short distance. The ship 'surfs' on the warped space. (This picture, due to Alcubierre, conveys the idea; however, we cannot really draw the actual situation since spacetime is four dimensional.) Note that we never address what would happen to a planet that was located within the warped space; you probably wouldn't want to live there!

So, why don't we build a warp drive?
Good question! But knowing that a solution to the equations of general relativity exists does not tell us how to build a device that makes this happen. Currently, only large gravitational fields produce warped space and in those cases space is warped like the funnel figure rather than the wave in the warp solution figure. For speculations on what would be required, see The Physics of Star Trek. For the present, warp drive exists only in the mind of the science fiction writer and theoretical physicist - and of course on TV.

                There once was a lady named Bright,
                Who traveled much faster than light.
                She departed one day, in a relative way, 
                And returned on the previous night!

                        -Anonymous

Wow, if time dilation is extended to speeds beyond the speed of light, wouldn't that mean that time would have to run backwards?
Well, there are no known examples of particles that travel faster than the speed of light. Indeed, your textbook states that nothing can travel faster than light because it would require an infinite amount of energy for a particle with mass to reach the speed of light.

Never the less, theoreticians have speculated about the existence of particles called tachyons which might travel faster than the speed of light. (See for example Bilaniuk and Sudarshan, Physics Today 22,43 (1969)) Such particles would have very unusual properties; for example, they would speed up as they lost energy. Needless to say, no such particles have ever been found and they currently exist only in the imagination of theoretical physicists and science fiction writers.

Physics Limerick Contest (Deadline Jan 15)

The American Physical Society is looking for original physics limericks. Please keep them clean...

Limericks selected will be printed in APS News and authors awarded a dunking bird, arguably the best physics toy ever invented. Author of the best limerick will win a flock. Submit entries to: "letters@aps.org", or mail to: Limerick Contest, APS News, The American Physical Society, College Park, MD 20740.

Mail suggestions and complaints regarding subject material to "gwb@shahrazad.bd.psu.edu".

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