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Special Relativity

When Einstein formulated the theory of Special Relativity, he was also going against a prevailing point of view. In fact he was destroying the Galilean theory, which required an absolute system of coordinates. Fortunately physicists were open-minded and the powers of Church and State had no interest in defending the memory of Galileo, so Einstein's theory was quickly accepted. Yet still, after all these years, few people fully appreciate the consequences of taking Einstein's theory at face value. If you believe Special Relativity, you have to abandon one of the most important ideas, which is the basis of our understanding of the world—the idea of time as we know it.

What is time? It is the flow from one event to another. Things "happen" in time. The present is the only thing that really exists. The past is gone and the future hasn't happened yet. Not so in Special Relativity!

Let's start by exploring our notion of the Present. If one were to define it, the present would consist of all the events that happen simultaneously with our observation. Events are things that happen at a certain time and in a certain place. And here's the rub—in Special Relativity, simultaneity is subjective (see sidebar). Events that are simultaneous for one inertial (roughly—moving with constant speed) observer might not be simultaneous for another inertial observer. Their "presents" consist of different sets of events. The two may be very near each other at the moment of the observation, but their presents will be different.

Simultaneity in Special Relativity

Einstein is famous for his gedanken experiments that explain some of the difficult aspects of his theory. In this example, we have two relativistic (meaning: moving almost with the speed of light) trains running in opposite directions with the same speed, and passing each other in front of a stationary (with respect to Earth) observer. The basic axiom of Special Relativity is that physics is the same in every inertial frame, so it should be the same for the observer riding on the train as it is for the stationary one. Imagine that the two trains are of equal length and they both have electrically charged balls at each end. When the back end of the first train is at the closest distance to the front end of the second train, a spark is triggered between the balls and is seen by both observers. Another spark is triggered when the front end of the first train aligns with the back end of the second train.

First let's see what the situation looks like from the point of view of the stationary observer. She is positioned in such a way that, when the trains pass each other, she is right in the middle between the ends of the trains. At that point the sparks fly between the balls at each end of the first train and the second train. The sparks produce light, which travels toward the stationary observer and arrives to her simultaneously from both sides (see Fig 2.). She thus considers the two sparking events to be simultaneous.

But let's now look at the same situation from the point of view of the observer on one of the trains. In his frame of reference, his train is at rest and the other train moves very quickly towards it. Since the other train moves so quickly, it undergoes a Lorenz contraction—it becomes shorter than the observer's train. The sparks will now fly between the back end of the oncoming train and the front end of his train earlier than the sparks between the front end of the moving train and the back end of his train (see Fig 3.). Since he is positioned right in the middle of his train, the light from the first spark will arrive earlier than the light from the second spark. He will conclude that the two events were not simultaneous. The reports of the two observers will be different.

By the way, in the stationary observer's frame, the two trains are also shortened, but since they move with the same speed with respect to her, their lengths are still equal.

 Fig 2. Three snapshots of the events as seen from the point of view of the stationary observer (black ellipse). (a) The trains are approaching from opposite directions. (b) The sparks are triggered when the ends of the trains align. (c) The light waves from both sparks reach the observer at the same time. Fig 3. Four snapshots of the events as seen by the observer on the first train. (a) The second train is approaching—it is shortened because of the Lorenz contraction. (b) The first spark is triggered when two ends align. (c) The second spark is triggered when the other two ends align. (d) The light wave from the first spark arrives at the observer on the train. The second light wave will arrive later.

This picture cannot be reconciled with the notion of the Present as the only thing in existence at a given moment of time. Events that one observer considers happening in his present might already be in the past or still in the future with respect to another. Do these events "exist" at that moment? If they exist from the point of view of one observer, how can they be part of a future that has not happened yet for another? No matter how much we try to weasel our way out of this conundrum, we'll have to accept that all these events, future and past, "exist" in some sense. Mathematically, they are just points in the four-dimensional space-time continuum. But now, unless we want to stick to the modern equivalent of epicycles, we have to admit that the existence of all these events is physical.

Let me reformulate this statement as one of the postulates of our minimalist interpretation of modern physics: All events, past, present and future, exist. This is not such a stretch if you consider that relativistic mechanics is fully deterministic. In a deterministic theory there is no evolution, only some structure imposed upon space-time. Trajectories of all particles are fixed once and for all by their equations of motion and some initial conditions in the far away past. It would be tempting to imagine some kind of a spark that marks the present, moving along the 4-dimensional lifeline of an observer. But such movement within space-time would itself have to happen in time—a time different from the time coordinate along the lifeline of the observer. Nowhere in the theory of relativity is there any mention of an external time that would let the whole space-time evolve.

I know this is a little disturbing and at odds with our experience. I will try to reconcile these ideas with our perceptions later on. But first we have to see if our postulate is still valid when we plug quantum mechanics into the picture.

Next: Quantum Mechanics.