Einstein, the exterminator of relativity
Truth is not relative
Einstein’s theory of relativity contains two parts, special relativity and general relativity, the former completed in 1905, the latter in 1915. After 1905, Einstein was obliged to make gravity compatible with special relativity. He had to struggle for 10 long years before he figured out how: the result was general relativity, more properly called Einstein gravity. Let us first focus on the theory of special relativity.
I must now give vent to my pet peeve. Physics contains a number of unfortunate names, some due to historical confusion long since cleared up. Probably the worst name ever is relativity, as it has spawned a swarm of nonsensical statements, such as “physicists have proved that truth is relative” and “there is no absolute truth; Einstein told us so,” uttered with smug authority by numerous ignorant fools. In fact, physicists, as exemplified by Einstein, say the opposite. I like to call Einstein the exterminator of “the relativity of truth.”
Just to set the record straight, Einstein did not use the term “theory of relativity” in his famous paper. The German physicist Alfred Bucherer, while criticizing Einstein’s theory, was the first to use, in 1906, the name1 “Einsteinian relativity theory.”
The speed of light as seen by two observers: c = c
In 1905, Einstein insisted that the laws of physics must not depend on observers in uniform motion relative to each other.
Consider two observers: a passenger sitting on a train smoothly rolling through a station at 10 meters per second without stopping, and a stationmaster standing on the ground. Suppose the passenger tosses a ball forward at 5 meters per second. To the stationmaster, the ball is evidently moving forward at 10 + 5 = 15 meters per second. That velocities add in this obvious everyday way has been known since time immemorial and is called Galilean relativity by physicists. Certainly Galileo understood it.
Incidentally, Galileo talked about sailing ships, not trains, of course. In Einstein’s days, train travel was just becoming commonplace in Europe, and so it was natural for him to use trains in his discussions.2 Later, Einstein’s trains were upgraded to spaceships. In our day, perhaps one experience most readers of this book have had is walking on a moving sidewalk in a modern airport or a large subway station.3 If the sidewalk is moving ahead at 5 meters per second, and you are walking on it at 10 meters per second, then clearly relative to the terminal building, you are moving along at 10 + 5 = 15 meters per second.
All this seemed beyond doubt until the end of the 19th century. Physicists were justifiably proud of their understanding of light being a particular form of electromagnetic wave. But now suppose that the passenger, instead of tossing a ball forward, shoots a beam of light forward. As always, denote the speed of light, as seen by the passenger, by c. All those photons in the laser beam are surging forward with speed c. Then the preceding discussion tells us that the speed of light, measured by the stationmaster, ought to be c + 10 meters per second.
But wait! Recall that Maxwell was able to calculate the speed of light using his equations. For instance, one of these might give the strength of the magnetic field generated by an electric field, varying at such and such a rate. But a physicist performing an experiment on the train to study the magnetic field generated by an electric field varying in time should arrive at precisely the same result as a physicist performing it on the ground, since otherwise, the two physicists would perceive two different structures of physical reality.
These two experimentalists can now appeal to their respective theoretical colleagues to perform Maxwell’s calculation of the speed of light. If the two theorists are both competent, they should arrive at the same answer. Thus, if Maxwell’s equations are correct, the speed of light, as measured by the passenger and by the stationmaster, should be exactly the same! In other words, c = c. There is only one speed of light, independent of observers.4
An intrinsic property of Nature
This strange behavior of light indicates that the addition of velocities cannot be simply Galilean. Maxwell’s reasoning forces us to a conclusion in violent discord with our everyday intuition: the observed speed of light is independent of how fast the observer is moving. Suppose we see a photon whizzing by and decide to give chase. We get into our starship and gun the engine until our speedometer registers 0.99 c; we are almost, but not quite, moving at the speed of light. But when we look out the window, to our astonishment we still see the photon whizzing by at the speed of light.
The key point is that the speed of light is an intrinsic property of Nature, determined by the way an electric field varying in time generates a magnetic field and vice versa. In contrast, the speed of the tossed ball in our example depended on the muscular prowess and inclination of the tosser.
The nature of time
To see why this caused such a crisis in the history of physics, we have to appreciate that the Galilean addition of velocities is based solidly on our fundamental understanding of the nature of time. To say that the train is traveling at 10 meters per second, we mean that when 1 second has elapsed for the stationmaster, the train has moved forward by 10 meters. To say that the ball is tossed forward at 5 meters per second, we mean that when 1 second has elapsed for the passenger, the ball has moved forward by 5 meters as measured by the passenger.
Newton, and everybody else, made the unspoken but eminently reasonable assumption that when 1 second has elapsed for the passenger, precisely 1 second has also elapsed for the stationmaster. Time thus conceived is referred to as absolute Newtonian time. Given absolute Newtonian time, the stationmaster would then conclude that during the passage of 1 second, since the train has moved forward by 10 meters, the tossed ball has hurtled forward through space by 10 + 5 = 15 meters and hence is traveling at 15 meters per second.
But somehow this seemingly incontrovertible logic does not work for the photon. A huge paradox!
If you think hard about it, you would conclude, just like Einstein, that the only way out is to say that the passage of time is different for the passenger and for the stationmaster. More precisely, we have to reject the “eminently reasonable assumption that when 1 second has elapsed for the passenger, precisely 1 second has also elapsed for the stationmaster.” Common sense fails!
For the stationmaster, the passenger is also passing through space. In other words, the stationmaster, while he feels that he is staying still, sees the passenger moving. If the train is sufficiently smooth, the passenger could also say that she is staying still but that the stationmaster is moving. Indeed, surely many readers have had this disorienting experience sitting in a vehicle moving sufficiently smoothly.
By this reasoning, we conclude that the passage of time experienced by the passenger is intrinsically linked to the passage of space experienced by her. Similarly for the stationmaster. For each observer, the passage of time and the passage of space are inextricably tied. Exactly how they are linked was worked* out by Einstein in his theory of special relativity in 1905.
In summary, Einstein banished space and time as separate concepts in physics. Henceforth, a new word, “spacetime,” is required to describe the world at the fundamental level.
Varying not in space, but in spacetime
We will now see that the banishing of space and time as separate concepts in physics immediately resolves Newton’s vexation with action at a distance.
Newton’s statement that the gravitational force exerted by a mass falls off as the square of the distance from the mass tells us how the gravitational field varies in space. Einstein now says that it is not quite kosher to say this; rather, it should be generalized to a statement about how the gravitational field varies in spacetime. In other words, knowing how the gravitational field varies in space, we immediately know how the gravitational field varies in time. In other words, we know immediately how much time it takes a gravitational disturbance to get from there to here. Gravitational effects do not propagate instantaneously: no more action at a distance. That weird concept, which should bother anybody with a “competent faculty of thinking,” is now banished from physics.
I have not (and could not have in the scope of this book) showed you the mathematical details of Einstein’s special relativity, but I hope that this heuristic discussion gave you a sense or flavor of how it works. In short, the insistence that the speed of light does not depend on the observer, as Maxwell told us, leads to the bizarre notion that the passage of time and the passage of space are inextricably linked. That space and time are replaced by spacetime immediately tells us how a field, be it electromagnetic or gravitational, varies in time once we know how it varies in space.
Incidentally, it follows that a gravity wave propagates with precisely the same speed5 as an electromagnetic wave propagates, namely, c.6 And thus we know that the gravity wave detected in 2016 originated 1.3 billion years ago.
* Remarkably, deriving this link requires only simple high school algebra.