For this effect to become perceptible, one must move very quickly. It was first measured in the 1970s, using precision watches on airplanes.23 The watch onboard a plane displays a time behind that displayed by the one on the ground. Today, the slowing down of time can be observed in many physics experiments.
In this case, too, Einstein had understood that time slows down before the phenomenon was actually measured—when he was just twenty-five years old and studying electromagnetism.
It turned out to be a not particularly complex deduction. Electricity and magnetism are well described by Maxwell’s equations. These contain the usual time variable t but have a curious property: if you travel at a certain velocity, then for you the equations of Maxwell are no longer true (that is, they don’t describe what you measure) unless you call “time” a different variable: t´.24 Mathematicians had become aware of this curious feature of Maxwell’s equations,25 but no one had been able to understand what it meant. Einstein grasped its significance: t is the time that passes if I stay still, the rhythm at which things occur that are stationary, like myself; t´ is “your time”: the rhythm at which things happen that move with you. Thus, t is the time that my watch measures when it is stationary, and t´ is the time that your watch measures when it is moving. Nobody had imagined previously that time could be different for a stationary watch and one that was being moved. Einstein had read this within the equations of electromagnetism, by taking them seriously.26
A moving object therefore experiences a shorter duration than a stationary one: a watch marks fewer seconds, a plant grows more slowly, a young man dreams less. For a moving object, time contracts.* Not only is there no single time for different places—there is not even a single time for any particular place. A duration can be associated only with the movement of something, with a given trajectory.
“Proper time” depends not only on where you are and your degree of proximity to masses; it depends also on the speed at which you move.
It’s a strange enough fact in itself, but its consequences are extraordinary. Hold on tight, because we are about to take off.
“NOW” MEANS NOTHING
What is happening “now” in a distant place? Imagine, for example, that your sister has gone to Proxima b, the recently discovered planet that orbits a star at approximately four light-years’ distance from us. What is your sister doing now on Proxima b?
The only correct answer is that the question makes no sense. It is like asking “What is here, in Beijing?” when we are in Venice. It makes no sense because if I use the word “here” in Venice, I am referring to a place in Venice, not in Beijing.
If you ask what your sister, who is in the room with you, is doing now, the answer is usually an easy one: you look at her and you can tell. If she’s far away, you phone her and ask what she’s doing. But take care: if you look at your sister, you are receiving light that travels from her to your eyes. The light takes time to reach you, let’s say a few nanoseconds—a tiny fraction of a second—therefore, you are not quite seeing what she is doing now but what she was doing a few nanoseconds ago. If she is in New York and you phone her from Liverpool, her voice takes a few milliseconds to reach you, so the most you can claim to know is what your sister was up to a few milliseconds ago. Not a significant difference, perhaps.
If your sister is on Proxima b, however, light takes four years to reach you from there. Hence, if you look at her through a telescope, or receive a radio communication from her, you know what she was doing four years ago rather than what she is doing now. “Now” on Proxima b is definitely not what you see through the telescope, or what you can hear from her voice over the radio.
So perhaps you can say that what your sister is doing now is what she will be doing four years after the moment that you see her through the telescope? But no, this does not work: four years after you have seen her through the telescope, in her time, she might already have returned to Earth and could be (yes! this is really possible!) ten terrestrial years in the future. But “now” cannot be in the future . . .
Perhaps we can do this: if, ten years ago, your sister had left for Proxima b, taking with her a calendar to keep track of the passage of time, can we think that now for her is when she has recorded that ten years have passed? No, this does not work either: she might have returned here ten of her years after leaving, arriving back where, in the meantime, twenty years have elapsed. So when the hell is “now” on Proxima b?
The truth of the matter is that we need to give up asking the question.27
There is no special moment on Proxima b that corresponds to what constitutes the present here and now.
Dear reader, pause for a moment to let this conclusion sink in. In my opinion, it is the most astounding conclusion arrived at in the whole of contemporary physics.
It simply makes no sense to ask which moment in the life of your sister on Proxima b corresponds to now. It is like asking which football team has won a basketball championship, how much money a swallow has earned, or how much a musical note weighs. They are nonsensical questions because football teams play football, not basketball; swallows do not busy themselves earning money; sounds cannot be weighed. “Basketball champions” refers to a team of basketball players, not to footballers. Monetary profit refers to human society, not to swallows. The notion of “the present” refers to things that are close to us, not to anything that is far away.
Our “present” does not extend throughout the universe. It is like a bubble around us.
How far does this bubble extend? It depends on the precision with which we determine time. If by nanoseconds, the present is defined only over a few meters; if by milliseconds, it is defined over thousands of kilometers. As humans, we distinguish tenths of a second only with great difficulty; we can easily consider our entire planet to be like a single bubble where we can speak of the present as if it were an instant shared by us all. This is as far as we can go.
There is our past: all the events that happened before what we can witness now. There is our future: the events that will happen after the moment from which we can see the here and now. Between this past and this future there is an interval that is neither past nor future and still has a duration: fifteen minutes on Mars; eight years on Proxima b; millions of years in the Andromeda galaxy. It is the expanded present.28 It is perhaps the greatest and strangest of Einstein’s discoveries.
The idea that a well-defined now exists throughout the universe is an illusion, an illegitimate extrapolation of our own experience.29
It is like the point where the rainbow touches the forest. We think that we can see it—but if we go to look for it, it isn’t there.
If I were to ask, “Are these two stones at the same height?” in interplanetary space, the correct answer would be: “It’s a question that doesn’t make sense, because there isn’t a single notion of ‘same height’ throughout the universe.” If I ask whether two events—one on Earth and the other on Proxima b—are happening “at the same moment,” the correct answer would be: “It’s a question that doesn’t make sense, because there is no such thing as ‘the same moment’ definable in the universe.”