Why Nobody Really Knows What Time It Is

A couple of months ago, when I gave a talk about my forthcoming book A Brief History of Timekeeping, for the Physics and Astronomy colloquium at Union, I titled it “Does Anybody Really Know What Time It Is?” This was done largely as a nod to the title of a Chicago song that I’m just old enough to remember (a reference that went over the heads of some younger faculty…), but also in full awareness of Betteridge’s Law of Headlines.

If you’re not familiar with it, and are too lazy to click on the link, this is the joke “Law” that any time an article has a headline in the form of a question, the expected answer to the question is “No.” So I used that title specifically to set up an answer in the negative— that, in fact, nobody really knows what time it is.

That might seem like a strange thing to do, especially as I’ve written an entire book exploring several thousand years of the human obsession with timekeeping, and have been banging on about it on this blog for the last couple of months as well. As a matter of fundamental physics, though, it’s absolutely true— not because we’re not good at building clocks (this is, in fact, something we’re exceptionally good at), but because “What time is it?” is not, in fact, a well-formed question with a single definitive answer.

The simplest illustration of the key problem is a phenomenon that we’ve all become more familiar with in the age of work-from-home via Zoom, namely coordinating events across long distances. If we think of time in the very oldest, most basic sense of “where are we in the course of the day?” the answer to that question depends on where you are on the surface of the Earth. When the Sun was at its highest point in the sky today for an observer on the prime meridian in Greenwich, UK, it still had close to 20 minutes to go before peeking over the horizon here in Schenectady, NY. Time as measured by the Sun, or people’s willingness to be up and about, depends very much on location.

This kind of variation in “what time it is” is merely a technical issue of coordination, though, not anything to do with fundamental physics. We can solve this problem by establishing a set of global time zones, and conventions to connect them, and enable people to know with confidence what time it is for someone at a very different longitude. As long as everyone synchronizes their clocks appropriately at the start, time zones make it easy to say what time it is somewhere else on the globe.

That “as long as everyone synchronizes their clocks” is an important caveat, though, and turns out to be a key step in the path to the “No” answer I was setting up in my talk. The basic concept is straightforward, but what seems at first like an annoying technical issue in fact is an intractable issue of fundamental physics.

We can find our way into the problem by considering one of the oldest and best ways of synchronizing clocks, namely looking at an event visible to both parties simultaneously. Dating all the way back to the late 1600’s, this was done by observing eclipses of the Galileian moons of Jupiter: once an orbit, they pass into the shadow of the giant planet, and blink out of view. These eclipses are highly predictable, and since Jupiter is incredibly far away, they can be seen by observers literally half a world apart. If you want to synchronize your clock in North America with one in Europe, you can each look up the predicted date and time for a particular eclipse of a particular moon, and when you see it, boom, you know the correct time.

Except, we’ve also known for centuries that this isn’t quite as simple as that. The eclipses are highly predictable, but the time between eclipses varies a little over the course of the year, a fact noted by the Danish astronomer Ole Rømer way back in the 1670’s. Rømer made careful observations of the variation in the time of the eclipses of Io, and deduced the correct conceptual explanation: that light has a finite speed. For one part of the year, the eclipses show up a few minutes earlier than expected, because the Earth’s orbital motion is bringing it closer to Jupiter between eclipses, and the light of the event needs slightly less time to get here. In another chunk of the year, Earth is moving farther from Jupiter, and the next eclipse shows up a little later than expected, because the light has farther to go.

So if we’re going to properly synchronize clocks, we need to account for the travel time as well. This can be done for the eclipses of moons, though it gets a little messy, so it’s easier to illustrate by imagining a slightly different scenario, where observers in two different locations exchange messages. We imagine an observer on the right in the diagram whose time we want to share with an observer to the left, but there’s a ten-minute delay in sending signals from one to the other.

To achieve proper synchronization in this scenario, the right observer sends out a time signal— “It’s noon!”, say— and when the left observer receives it, they set their clock to match. They also send an immediate return signal, letting the right observer know they got the original message. When the right observer gets the return message, they check the time— 12:20, in this case— which gives them the round-trip time for signals going back and forth.

This system works great, and with some refinements to account for the many technical issues that crop up when you try to do this for real, is more or less how we synchronize clocks over telecommunications networks. Except, there’s one important caveat: this system only works when everybody involved is standing still. When you look at this process from the point of view of someone moving relative to the people synchronizing their clocks, things go subtly wrong.

Any observer watching the process take place is perfectly entitled to imagine themselves at rest while the two observers doing the synchronization move past them, in this case traveling left-to-right. From the standpoint of the third observer, then, this means that the left observer is moving toward the initial time signal as it’s in flight. As a result, that signal doesn’t have as far to travel and thus arrives slightly earlier than expected (a bit like Rømer’s eclipses). On the return trip, the right observer is moving away from the signal, so it takes longer to get there.

You might think these different delays would cancel each other out, but they don’t— when you work through the math for the particular choice of velocities I used to make the figure above, it takes 22 minutes for the synchronization cycle to complete according to the third observer, but only 20 according to the two doing the synchronization. Even after they apply the travel-time correction, then, the two clocks will not be showing the correct time, according to the third observer. The discrepancy gets worse when the two observers synchronizing clocks are farther apart, and gets worse even faster when the relative speed increases.

This might seem like just another technical issue, but in fact, it’s a fundamental obstacle to universal time. The source of the problem is the fact that every observer is entitled to consider themselves perfectly at rest, and that’s a very deep principle of physics, the principle of relativity, which dates back to Galileo. This synchronization problem is foundational to the modern theory of relativity, as was famously pointed out by Albert Einstein in 1905, but the key idea was understood by Henri Poincaré and Hendrik Lorentz a bit earlier (though Einstein more fully embraced the implications). There is, fundamentally, absolutely no measurement you can do that will show anything other than that the clocks carried by moving observers “tick” at a different rate than otherwise identical clocks at rest.

This situation has been confirmed experimentally for speeds from a brisk walk all the way up to a high fraction of the speed of light— moving clocks really do tick slow. Things get even worse when you incorporate gravity into the mix (though that’s too complicated to explain in this already long post)— clocks near a massive object really do tick slower than clocks at higher altitude, and again, this is confirmed in experiments with atomic clocks.

And that’s why my talk title, “Does Anybody Really Know What Time It Is?” can be answered “No,” as demanded by Betteridge’s Law. It’s not that we don’t have clocks of sufficient accuracy, it’s that “what time it is” is fundamentally not a universal quantity. Every individual observer, everywhere in the universe, has their own internal clock with its own unique history of ticking at a rate that depends on how it’s moved and where it is. Thus, even if we could all agree on a single starting event to define the time “00:00:00”, there is no one single answer to how much time has elapsed since then. Nobody can really know “what time it is” because there is no right time for it to be.