Warped Passages - Lisa Randall [45]
Einstein’s critical insight, the one that led him to special relativity, was that ideas about time had to be reformulated. According to Einstein, space and time could no longer be considered independently. Although they are not the same thing—time and space are clearly different—the quantities you measure depend on the speed at which you are traveling. Special relativity was the result of this insight.
Bizarre as they are, one can derive all of Einstein’s novel consequences of special relativity from two postulates. To state them, we need to understand the meaning of inertial frames—a particular category of reference frames. Let’s first choose any frame of reference that moves at constant velocity (speed and direction); the one that’s at rest is often a good one. The inertial frames would then be those that are moving at fixed velocity with respect to that first one—someone running or driving by at constant speed, for example.
Einstein’s postulates then state that:
The laws of physics are the same in all inertial frames.
The speed of light, c, is the same in any inertial frame.
The two postulates tell us that Newton’s laws are incomplete. Once we accept Einstein’s postulates, we have no choice but to replace Newton’s laws with new physical laws that are consistent with these rules.8 The laws of special relativity that follow lead to all the surprising consequences you might have heard of, such as time dilation, the observer dependence of simultaneity, and Lorentz contraction of a moving object. The new laws should look very much like the old classical physics laws when applied to objects moving at speeds that are small compared with the speed of light. But when applied to something moving very fast, at or near the speed of light, the difference between the Newtonian and special relativity formulations should become apparent.
For example, in Newtonian mechanics speeds are simply added together. A car driving towards yours on the freeway approaches you at a speed that’s the sum of its speed and yours. Similarly, if someone throws a ball at you from the platform while you are on a moving train, the ball’s speed appears to be the sum of the speed of the ball itself plus the speed of the moving train. (A former student of mine, Witek Skiba, can attest to this fact. Witek was nearly knocked out when he was hit by a ball that someone threw at the approaching train he was riding.)
According to Newtonian physics, the speed of a beam of light directed at a moving train should be the sum of the speed of light and the speed of the moving train. But this can’t be true if the speed of light is constant, as Einstein’s second postulate asserts. If the speed of light is always the same, then the speed of the beam aimed at the moving train will be identical to the speed of a light beam that approaches you when you’re standing still on the ground. Even though it runs counter to the intuition gained from your experience of the slow speeds you encounter in daily life, light speed is constant, and in special relativity speeds don’t simply add up as they do in Newtonian physics. Instead, you add speeds according to a relativistic formula that follows from Einstein’s postulates.
Many of special relativity’s implications don’t jibe with our familiar notions of time and space. Special relativity treats time and space differently than they had been treated before in Newtonian mechanics, and