Existential physics: what happens “now” is relative

Excerpted with permission from Existential Physics: A Scientist’s Guide to Life’s Biggest Questions, Written by Sabine Hossenfelder and published by Viking.

The fact that the passage of time is not universal is already puzzling, but there is more. Because the speed of light is very fast but limited, it takes time for light to reach us, so technically we always see things the way they were earlier. However, we usually don’t notice this in our daily life. Light travels so fast that the short distances we see from Earth don’t matter. For example, if you look up at a cloud, you actually see the cloud as it was a millionth of a second ago. It doesn’t make much difference, does it? We see the sun as it was eight minutes ago, but since the sun doesn’t usually change much for a few minutes, the travel time of the light doesn’t make a big difference. If you look at Polaris, you will see what it looked like 434 years ago. But yeah, you might say, so what?

It’s easy to attribute the time lag between the moment something happens and our observation of it to the limitations of perception, but it has profound implications. Again, the problem is that the passage of time is not universal. If you ask what’s going on “simultaneously” elsewhere—for example, what are you doing when the sun shines the light you see now—there’s no meaningful answer to that question.

This problem is called relativity of simultaneity, Einstein himself explained this very well. To understand how this happens, it helps to draw a few space-time diagrams. Four dimensions are difficult to draw, so please forgive me if I only use one dimension of space and one dimension of time. Objects that do not move relative to the selected coordinate system are depicted in this figure by vertical lines (Figure 1). These coordinates are also known as the object’s rest frame. An object moving at a constant velocity tilts a line by an angle. By convention, physicists use a 45-degree angle to express the speed of light. The speed of light is the same for all observers, and since it cannot be exceeded, the physical object must move in a straight line with an inclination of less than 45 degrees.

Einstein now argues as follows. Suppose you want to construct the concept of simultaneity by using laser beam pulses bouncing off a mirror that is stationary relative to you. You send a pulse to the right, a pulse to the left, and move your position between the mirrors until the pulses come back to you at the same time (see Figure 2a). Then you know you’re right in the middle and the laser beam hits both mirrors at the same time.

Once you do, you know at what point in your own time the laser pulse will hit the two mirrors, even if you can’t see it because the light from these events hasn’t reached you yet. You can look at your clock and say, “Now!” In this way, you construct a concept of simultaneity that can, in principle, span the entire universe. In practice, you might not have the patience to wait 10 billion years for the laser pulses to come back, but that’s theoretical physics for you.

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Now imagine your friend Sue moving relative to you and trying to do the same (Figure 2b). Suppose she moves from left to right. Sue also uses two mirrors, one to her right and one to her left, that move with her at the same speed – so the mirror is stationary relative to Sue, just as your mirror is relative to you. Like you, she sends laser pulses in both directions and positions herself so that the pulses return to her from both sides at the same time. Like you, she knows that the pulse hits both mirrors at the same time, and she can calculate which moment corresponds to her own clock.

The problem is, she doesn’t get the same results as you. According to you, Sue doesn’t think two events that happen at the same time can happen at the same time. That’s because from your perspective, the pulse is moving towards one mirror and away from the other. It seems to you that it takes less time for the pulse to reach the mirror on her left than it takes for another pulse to catch up to the mirror on her right. It’s just that Su didn’t notice, because on the pulse’s path back from the mirror, it was the other way around. The pulse from the mirror to Su’s left side took longer to catch up with her, and the pulse from the mirror to her right was faster.

You would claim that Sue made a mistake, but according to Sue, you made the mistake because to her, you were the one who was moving. She will say that in fact your laser pulses don’t hit your mirror at the same time (Figures 2c and 2d).

who is right? Neither of you are. This example shows that, in special relativity, the statement that two events happened at the same time is meaningless.

It’s worth emphasizing that this argument works because light doesn’t need a medium to travel, and the speed of light (in a vacuum) is the same for all observers. For example, this argument does not apply to sound waves (or any other signal that does not emit light in a vacuum), because the speed of the signal is not actually the same for all observers; instead, it will depend on the medium in which it travels. In this case, one of you is objectively right and the other is wrong. Your opinion of the present may differ from mine, and this is an insight we owe Albert Einstein.

We’ve just established that two relatively moving observers don’t agree on what it means for two events to happen at the same time. Not only is this strange, it completely erodes our intuitive notion of reality.

To see this, imagine you have two events that are not causally related to each other, meaning you cannot send a signal from one event to the other, not even at the speed of light. From the graph, “no causal link” just means that if you draw a straight line between two events, the angle between the straight line and the horizontal line is less than 45 degrees. But look again at Figure 2b. For two events that are not causally linked, you can always imagine an observer that everything in that line is happening at the same time. You just need to choose the speed of the observer so that the return point of the laser pulse is in-line. But if any two points that are not causally related happen to someone at the same time, then every event is “now” to someone.

To illustrate the latter step, let’s assume that one event is your birth and the other is a supernova explosion (see Figure 3). The explosion is causally related to your birth, which means that the light from it did not reach Earth when you were born. Then you can imagine your friend Sue, the space traveler, seeing these events at the same time, so according to her, they happened at the same time.

Suppose further that when you die, the light from the supernova has not yet reached Earth. Then your friend Paul can figure out a way to travel between you and the supernova so he can see your death and the supernova at the same time. According to Paul, they all happened at the same time.

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