Chapter 13: Star Birth and Death

James Clerk Maxwell

Albert Einstein 1921

As a five-year-old boy in 1884, Einstein marveled at the invisible power that moved a compass needle. Keeping hold of this curiosity, he went on to study the elegant set of equations Scottish physicist James Clerk Maxwell developed for magnetic and electric phenomena in the 1860s. He learned that light and all other forms of electromagnetic radiation are caused by the oscillation of linked electric and magnetic forces. In Maxwell's formulation, the speed of the radiation emerges as a universal constant, independent of the motion of the observer. Einstein's special theory of relativity started with his whimsical teenage conjecture: what would the world look like if I rode on a beam of light?

Suppose, as Einstein did, that you are traveling in a car at 100 kilometers per hour and throw a ball forward at 50 kilometers per hour, you would expect that the ball would travel toward someone standing on the ground at 100 + 50 = 150 kilometers per hour. Similarly, if you are traveling at 80 kilometers per hour and throw a ball backward at 60 kilometers per hour, it will reach the stationary observer at 80 - 60 = 20 kilometers per hour. These are the familiar rules of motion defined by Galileo and Newton. But what if you were traveling in a spaceship at one-third the speed of light, 100,000 kilometers per second, and you shone a beam of light forward at the speed of light, 300,000 kilometers per second? Intuition tells you that a stationary observer ahead of you would measure the light arriving at 300,000 + 100,000 = 400,000 kilometers per second and an observer behind you would measure 300,000 - 100,000 = 200,000 kilometers per second. There is the paradox: either the speed of light is always constant as Maxwell said, or motions add and subtract the way Newton described. Can we ever catch up with a beam of light? The answer turns out to be no.

Edward Morley

Albert Michelson

Observations and special relativity say that the speed of light is always the same. In the 1880s, American physicist Albert Michelson and chemist Edward Morley showed that the light from a star always arrives at 300,000 kilometers per second. It never shows the annual addition and subtraction of the motion of the Earth as the Earth orbits the Sun. Einstein elevated the constancy of the speed of light to a law of physics. He also argued that laws of physics do not depend on the state of motion of the observer. Newtonian concepts of absolute space and time must be abandoned.

The universal constancy of the speed of light has some fascinating consequences. Einstein, and those who have come after him, have used Gedanken experiments, or thought experiments, to try and reason through different "What if" experiments.

The first thought experiment has to do with time and stems from a thought Einstein had while riding home in a streetcar in Bern. He saw the clock tower passing behind him and wondered how the clock would appear as the streetcar moved faster and faster. At 300,000 kilometers per second, the streetcar would be moving away as fast as the light wave that showed the time as 6 p.m., for example — time would be frozen! A perhaps more correct way to look at this is to remember all observers see light traveling past at the same rate. If you are flying along a light beam, the only way you can see it traveling at the same rate that a stationary person sees it traveling is if your watch ticks slow. (Just like a stationary person will observe a passing car going 60 miles per hour north, while a driver going 50 mph north will only see the passing car as going so fast relative to them if their watch is running really really slow.)

In everyday life, this clock slowing doesn't add up to much. A frequent flier who spends 100 hours a month on airplanes might gain 1/1000,000 of a second by the end of the year! You have to go really fast for serious time contraction to change. Astronauts traveling at 90% of the speed of light only age half as fast as people left back on Earth. From this comes the idea that objects moving at close to the speed of light, or relativistic speeds, suffer a physical contraction and actually get shortened in the direction of motion. This shrinkage occurs in such a way as to preserve the constancy of the velocity of light. A baseball moving at exceptionally high speed would be flattened to a pancake.

The third effect of relativity is the increasing mass of an object as it approaches the speed of light. We have seen that mass has an equivalent energy by the relation E = mc². As an object is accelerated towards the speed of light, the energy it is given goes into increasing the mass, not the velocity. Fast-moving objects acquire more inertia; they resist any change in their motion, and they can never achieve the speed of light because infinite energy would be needed! Here is a thought experiment to help you understand this. Someone watching the antics on a fast-moving spacecraft would see everything slowed down — as the ticking of the watch slows, so does the ticking of day-to-day activities, essentially putting everything into slow motion. If someone on the space shift dropped a glass, it would appear to an outside observer to very very slowly drift to the space craft's artificial gravity floor. Meanwhile, the astronauts would perceive the same glass as falling just as it would in your kitchen on Earth. Since in your kitchen, the glass would likely shatter, both the stationary observer and astronauts also see it break. But, if it only, ever so slowly, drifted to the ground from the perspective of the stationary observer, why did it break? Well, if the acceleration toward the ground is lessened, the mass has to increase for the same effect to occur on impact. From the stationary person's perspective, a very very heavy glass (that was contracted in the direction of motion) slowly fell and then shattered.

Schematic view of Einstein's train thought experiment, with two lightnings striking both ends of the moving train simultaneously (as perceived in the stationary observer's inertial frame). Event simultaneity differences are shown for both inertial frames, supported by Minkowski diagrams (not in scale).

None of the weird effects of relativity are tricks or illusions; they are real physical phenomena. Physicists have shown that particles moving at relativistic speeds "bunch up" in the direction of motion and have larger mass-energy. They have confirmed that accurate atomic clocks traveling on a jet plane keep slightly slower time than an identical clock on the Earth. The predictions of special relativity are confirmed in physics laboratories thousands of times a day. Although special relativity supersedes Newton's laws of motion, the unusual effects are significant only close to the speed of light. Thus relativity is barely detectable when the velocity v is much less than c, and v/c « 1. This is the case for spacecraft and fast cars and well-struck baseballs. At everyday low speeds, Newtonian equations work extremely well.