by David Shane

Created on: October 25, 2009   Last Updated: October 26, 2009

Einstein's "Theory of Relativity" is commonly divided into two parts: "special relativity" and "general relativity," and each part results in different effects on your airplane ride. Broadly speaking, special relativity tells us that the laws of physics are the same in all reference frames in uniform motion. General relativity is the modern formulation of the law of gravity.

I. SPECIAL RELATIVITY

A. TIME DILATION

Special relativity predicts two effects that relate to your airplane flight. (I'm not going to derive why they are true here, but take my word that they are true.) The first is that moving clocks run slow. This being relativity, a good question to ask is "relative to whom and the answer is, "relative to a stationary observer." So, for example, if you are standing on the ground, and I fly past you, you will observe my clock to be running slowly. That is to say, if an hour passes on your watch, you will perceive that less than one hour passes on my watch.

To me on the plane, however, time will appear to be passing normally. My hand doesn't seem to move slowly as I reach for the soda in front of me, or anything like that. And this is true no matter how quickly the plane is moving, even if it is going far faster than any plane we could ever hope to make.

Furthermore, it would be perfectly appropriate for me to regard myself as not moving, and you on the ground as moving quickly away from me. And indeed, while I believe my watch is functioning normally, I will perceive YOUR watch as running slow. This may seem like a contradiction, but it is not. It is true that if we synced our watches when we passed each other, if we came together again we really would have to agree on whose watch was ahead, and whose was behind. But in order to do this I would have to turn around, and undergo acceleration - and so the symmetry of the situation would be broken. (Read up on the "twin paradox" for more on this.)

Observations have confirmed that this effect does really occur. In the upper atmosphere, a particle known as the "muon" is produced that lives, on average, for around 2ms (2 thousandths of a second) before decaying into other particles. Thus, even if these muons were moving at the speed of light (the maximum allowable speed); we would expect almost none of them to reach the surface of the Earth. But, in reality we see that many of them do, and the reason is that time is passing more slowly for the muons. While they "think" they only live for 2ms, we see them living

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