Home >Opinion >Columns >Hurry, lift-off’s at 9. Or maybe at 9:01

The distinctive feature of the campus of BITS Pilani, my alma mater, is a handsome clock tower with four faces. Maybe more distinctive is that the four faces show slightly different times, a source of amused pride for generations of BITSians. But seriously, the tower is an arresting sight, visible from nearly anywhere on campus, useful to couples on dates needing to get back to hostels by possible curfew times.

It also triggers a thought experiment that Albert Einstein once, well, thought through, though not in Pilani. The different times on the faces are, in a sense, fitting.

Imagine a rocket that starts at the BITS clock tower at precisely 9am on 1 January 2022 and flies away in a straight line. Imagine my BITS friend Parvathy sitting in that rocket, looking back at the tower—at one of its clocks, actually. What time will she see on the clock? Silly question, you think? Parvathy will see 9am as she begins her flight, then a minute later she’ll see the minute hand tick over to 9:01, and another minute later it will tick over to 9:02 ... on and on like that.

True, but let’s add a wrinkle to this. Say the rocket flies at a high speed—at, in fact, the speed of light. (Assume that the rocket can fly that fast, and that it accelerates instantly to that speed). What then?

Yes, the clock will show 9am as Parvathy sets out. But think of what happens when the minute hand shifts to 9:01 a minute later. The image of that shift will, in a sense, set out at the speed of light, trying to reach intrepid Parvathy so she will know a minute has passed on her beloved campus. But she’s travelling at the speed of light, too, and is a minute’s travel ahead already. So, the image will never catch her; instead, it will stay forever a light-minute behind. Put another way, Parvathy will never see that change to 9:01. For her, the clock tower is frozen at 9am. (One more assumption here is that there is some magical way that she can “see" the tower as she moves.)

If she doesn’t know about Einstein and his experiment, Parvathy will be greatly baffled by this. For if she looks at the Titan wristwatch she’s wearing, she will see it ticking along just as always, showing her 9:01 and 9:02 and so on—but the clock tower is at a standstill.

So: if Parvathy doesn’t move from the clock tower, she will see the clock’s and the Titan’s hands moving just as she, and all of us, expect them to. But if she zips off at the speed of light, she’ll see the Titan’s hands move as usual, but the clock’s hands not at all. What about at speeds somewhere between stationary and the speed of light? If you think about it, you’ll realize that as she moves ever faster, time as measured by the Pilani clock seems to get steadily slower, until it stops altogether when she reaches the speed of light.

Seems like the faster you move through space, the slower you move through time.

Yet this is not quite the full story. Imagine now what my BITS friend Washique, sitting in the clock tower, makes of this situation. He looks out of one of the tower’s narrow windows and watches Parvathy soar away. In particular, he’s looking at that wristwatch she’s got. (Yes, he can see her wristwatch in the same magical way that Parvathy sees the clock tower). What does Washique notice about the two timepieces?

Well, the hands of the clock above his head will move as he expects. So when it changes to 9:01, he naturally expects that the Titan’s minute hand will have shifted to show 9:01 as well. But remember that the Titan is moving away from him at the speed of light. So what happens to its image of that shift to 9:01? It starts out from Parvathy’s wrist at 9:01 on both timepieces, travelling towards Washique at the speed of light. But at that instant, Parvathy is an entire light-minute, or 18,000,000 km, away—because the speed of light is 300,000km/second. So the image will take another minute to reach Washique. That is, Washique sees Parvathy’s wristwatch change to 9:01 when the clock above his head shows 9:02. Similarly, he will see 9:02 on her Titan at 9:04 on the tower.

In other words, Washique sees that time, as measured by Parvathy’s wristwatch, has slowed down because of her speed through space. Not to zero, as Parvathy has noticed, but to half of what he expects: one minute seems like two.

In still other words, the idea of time is not fixed, but relative to who is measuring it, and to their movements through space. “Relative": thus Albert Einstein’s theories of relativity.

And that’s not quite the full story either. We think of Washique being stationary in the Pilani tower, and Parvathy rocketing away at the speed of light. But that’s only because we are stationary in the same sense that Washique is, that the clock tower is, and this is why the story plays out like this in our minds. Consider it instead from Parvathy’s point of view, especially if all she can see is the rocket she’s on, and the receding clock tower through her own narrow window. Think of what that word “receding" means—to her, it’s exactly as if she is stationary, and the one who is rocketing away at the speed of light is Washique, in the tower.

From Einstein’s relativistic point of view, there’s no difference between these two viewpoints.

There’s actually still more to this story, and it gets a little more complex, though also more fascinating. I’ll leave it there and jump straight to the really profound insight that all this thought led Einstein to. The deep implication of relativity is that time is not absolute, in the sense that everybody and everything doesn’t experience it in the same way. Instead, time is relative. Take two clocks that show exactly the same time right now; send one of them off on a journey; when it returns, the two will show different times.

In 1971, Joseph Hafele and Richard Keating did just this. They took four highly-accurate atomic clocks onto a plane, flying eastward and then westward around the world. After the flights, they compared those clocks to ones that had not flown. Einstein could have told them: the times displayed by the two sets of clocks differed. A tiny difference, but one that was consistent with Einstein’s theories of relativity. (Had they flown faster, the difference would have been larger.)

The deeper implication of relativity is that time and space are the same. The way to really understand our surroundings is to imagine that we are all moving—not through space alone, but through what Einstein called spacetime. Seen that way, the passage of time is just one more measure of how far we’ve travelled through spacetime, no different from how many kilometres I walked this morning, or how far a rocket flies in a minute.

And when you think in terms of spacetime, you’ll realize that Parvathy’s and Washique’s different trajectories through it make them experience time differently. Just as they experience distance differently. Though that still doesn’t explain four different times on the four faces of the clock tower.

Once a computer scientist, Dilip D’Souza now lives in Mumbai and writes for his dinners. His Twitter handle is @DeathEndsFun

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