## Where “now” depends on how fast you're moving

Einstein's revolutionary solution to the problems we've
just seen starts out with a very simple “thought
experiment.” If we follow through with these
thoughts faithfully, we are led to some startling
conclusions. Among them, we find that space and time
have to be brought together into a single, unified
concept.

To see why, it is easiest to start out simple. We imagine that it is only possible to move along one line, so that space is sort of one-dimensional. Suppose that we have an astronaut floating in this one-dimensional space, with a mirror off to her right. She sends out a flash of light, which bounces off the mirror, and comes back to her. If we trace out this movement on a chart, we get a graph of everything's position in time. Press “Play 1” on the animation below. Note that we have chosen to run the chart so that the light ray moves at an angle of 45 degrees. This angle indicates the speed of that pulse of light.

That was simple enough, so now let's add another astronaut who moves to the right. We can make another chart of this. (Press “Play 2” below.) The chart is almost the same as the first one, with an extra line for the second astronaut. Note that it looks like he passes the first astronaut at the same moment as the light bounces off the mirror. We can see this in the chart by noting that the point where the red and blue lines cross is at the same level as the point where the yellow line turns back.

Of course, we remember that the two astronauts just have
different viewpoints, which should be treated
equally. That means that we should make another chart
for the second astronaut. Just as the first astronaut
was floating still in one place from her point of view,
the second is floating in one place from his point of
view. Just as he was moving to the right from her
viewpoint, she (and the mirror) are moving to the left
from his viewpoint. Also, the light must be going at the
same speed, and thus should make the same angle of 45
degrees on our chart. We get one last chart. Press
“Play 3” above.

This is the correct chart, but notice something bizarre. From the second astronaut's perspective, the two astronauts don't pass at the same moment that the light bounces off the mirror! This unexpected result, called the failure of simultaneity, comes
directly from the two facts that Einstein chose as his
basic assumptions:

The failure of simultaneity is really an astounding idea, and scientists now believe that it describes how Nature actually operates. Its effect is stronger when two observers are moving relative to each other at nearly the speed of light. Since humans don't usually move that fast compared to any other humans, we don't notice this very often. It demonstrates an interesting idea, however. Two points separated only in space from one observer's viewpoint are separated in space and time from the other's viewpoint. The notion of

For the charts above, the whole gray area represents spacetime. To make sense of it, we—its observers—just take slices out of this spacetime and split it up into space and time separately. The observer that is motionless in each chart takes any horizontal line, and says that every point on that line is at the same time. For example, in the chart from the first astronaut's point of view, the line connecting the point where the two astronauts pass and the point where the light bounces off the mirror is a flat line, so every event located along that line would be simultaneous, from her point of view.

With a little thought, it's not hard to see that the second astronaut's time slices on this diagram must be along slanted lines; in the chart from his point of view, we saw that the passing came before the bouncing. In a similar way, we see that the second astronaut's time slices in the third chart are flat lines, while the slices of the first astronaut are slanted. It may seem to go against common sense, but this is how the physical world actually operates. Again, Nature won't care which slices a particular observe takes, so all laws that correctly describe Nature should take this “spacetime” viewpoint.

We can also include a second dimension of space in our spacetime. When the observers split up this spacetime into space and time, they take slices that aren't lines, but two-dimensional sheets representing space. We can go further, and include all three dimensions of space in our spacetime. Then, the observers take infinite three-dimensional blocks for their slices. In each case, the slice—whether a line, a sheet, or a block—depends on the observer, and how fast he or she is moving.

This is the essence of the Special Relativity. Though it
was a great achievement for Einstein—explaining
the curious result of the Michelson-Morley
experiment—he didn't stop there. He decided to
allow his slices to be bent and warped in funny ways. By
doing this, Einstein introduced the world to
the General
Relativity.

To see why, it is easiest to start out simple. We imagine that it is only possible to move along one line, so that space is sort of one-dimensional. Suppose that we have an astronaut floating in this one-dimensional space, with a mirror off to her right. She sends out a flash of light, which bounces off the mirror, and comes back to her. If we trace out this movement on a chart, we get a graph of everything's position in time. Press “Play 1” on the animation below. Note that we have chosen to run the chart so that the light ray moves at an angle of 45 degrees. This angle indicates the speed of that pulse of light.

That was simple enough, so now let's add another astronaut who moves to the right. We can make another chart of this. (Press “Play 2” below.) The chart is almost the same as the first one, with an extra line for the second astronaut. Note that it looks like he passes the first astronaut at the same moment as the light bounces off the mirror. We can see this in the chart by noting that the point where the red and blue lines cross is at the same level as the point where the yellow line turns back.

This is the correct chart, but notice something bizarre. From the second astronaut's perspective, the two astronauts don't pass at the same moment that the light bounces off the mirror! This unexpected result, called the failure of simultaneity,

Simultaneous events are events in different places which happen at the same time. It turns out that this concept depends on how quickly one is moving. That is, if two observers are moving relative to each other, they will not be able to agree on the simultaneity of events. This is the Failure of Simultaneity.

- different observers moving relative to each other should be treated equally
- everyone measures the same speed of light

The failure of simultaneity is really an astounding idea, and scientists now believe that it describes how Nature actually operates. Its effect is stronger when two observers are moving relative to each other at nearly the speed of light. Since humans don't usually move that fast compared to any other humans, we don't notice this very often. It demonstrates an interesting idea, however. Two points separated only in space from one observer's viewpoint are separated in space and time from the other's viewpoint. The notion of

*here*seems to get mixed in with the notion of*now*. That is, the notion of*space*gets mixed in with the notion of*time*, in a way that depends on the observer, and how fast he or she is moving. Einstein decided that it was appropriate to make these two concepts into one: space and time would become spacetime. A concept in physics which merges our usual notion of space with our usual notion of time. Just as space as we know it has three dimensions, spacetime has four dimensions—with time as the fourth dimension.

For the charts above, the whole gray area represents spacetime. To make sense of it, we—its observers—just take slices out of this spacetime and split it up into space and time separately. The observer that is motionless in each chart takes any horizontal line, and says that every point on that line is at the same time. For example, in the chart from the first astronaut's point of view, the line connecting the point where the two astronauts pass and the point where the light bounces off the mirror is a flat line, so every event located along that line would be simultaneous, from her point of view.

With a little thought, it's not hard to see that the second astronaut's time slices on this diagram must be along slanted lines; in the chart from his point of view, we saw that the passing came before the bouncing. In a similar way, we see that the second astronaut's time slices in the third chart are flat lines, while the slices of the first astronaut are slanted. It may seem to go against common sense, but this is how the physical world actually operates. Again, Nature won't care which slices a particular observe takes, so all laws that correctly describe Nature should take this “spacetime” viewpoint.

We can also include a second dimension of space in our spacetime. When the observers split up this spacetime into space and time, they take slices that aren't lines, but two-dimensional sheets representing space. We can go further, and include all three dimensions of space in our spacetime. Then, the observers take infinite three-dimensional blocks for their slices. In each case, the slice—whether a line, a sheet, or a block—depends on the observer, and how fast he or she is moving.

This is the essence of the Special Relativity.

Einstein's version of the laws of physics, when there is no gravity. The two fundamental concepts in the foundation of this theory are equality of observers, and the constancy of the speed of light. The first of these means that the laws of physics must be the same, no matter how quickly an observer is moving. The second means that everyone measures the exact same speed of light. This theory is useful whenever the effects of gravity can be ignored, but objects are moving at nearly the speed of light. It has been successfully tested many times in particle accelerators, and orbiting spacecraft. For objects moving much more slowly than light, Special Relativity becomes very nearly the same as Newton's theory, which is much easier to use.

Einstein's version of the laws of physics, when there is gravity. Building on the Special Theory of Relativity, this theory generalizes Einstein's work so that the laws of physics must be the same for all observers, even in gravity. Einstein showed that gravity is best understood as a warping of the geometry of spacetime, rather than as a pulling of objects on each other. The crucial idea is that objects move along geodesics—which are determined by the warping of spacetime—while spacetime is warped by massive objects according to the formula

**G**= 8 π**T**.