In 1922, Albert Einstein and the philosopher Henri Bergson publicly debated the nature of time. They were polar opposites in their approaches. I won’t go into the details, you can look it up, but towards the end of their lives they each are reported to have softened a bit towards the other’s viewpoint. As I understand it, Einstein admitted that there was at least one serious problem with the physical description of time: it couldn’t explain duration. This seems to be a purely experiential aspect of time.

            Duration is simple on the surface. It’s just how long something lasts. When we go to work and come home, we know how long our workday was. When we watch a football game, we know how long each playing quarter is and the overall length of the game from start to finish once it’s over.

            So, what’s the problem?

            The problem comes when we try to explain how those elapsed time periods are built out of fundamental time. When we assign a measure of time to an event, we know that if it’s two hours long, each hour is made up of 60 minutes and each minute is made up of 60 seconds. Obviously, some things last less than a second, so we have fractions of seconds. For particle physicists these can be very tiny fractions. So, what is the smallest fraction of time?

            There isn’t such a thing!* That’s a problem.

            In physics, time proceeds in instants that have no duration. This leads to paradoxes. In an earlier essay (The Riemann Hypothesis, Part 2 – Heisenberg and Zeno) I referenced the Greek philosopher Zeno. Here’s a passage from that essay:

            Zeno’s paradox of an arrow in flight observes that in every timeless instant of the flight the arrow exists in some position in space. Since it is definitely there, it can’t be somewhere else. Since in that instant there is no time, it can’t be moving. Since at every instant of its flight the situation is the same, the arrow can’t ever be moving. 

           Aristotle, and many others since, found counters to Zeno’s argument, which, of course, originate from the observation that yes, Zeno, the arrow is moving, which, of course, Zeno knew. 

           However, the counter arguments depend on certain definitions about infinity and the infinitely small that produce answers in line with what we observe. There is no other reason why Zeno’s definitions aren’t just as valid, and his conclusion is correct. That was his point. He was showing that either logic or observation or both have limitations.

            The problem is how to build up duration out of units that have zero duration. Anything times zero is still zero. This is the realm of calculus in our practical world, which does exactly that. Once again, though it works, the philosophical basis is shaky (See previous essay, “Calculus is Your Friend”).

            Approaching from another direction, think about the advice often given to “stay in the moment”. Don’t let the future or the past control you. Make sure you are always aware of the present because that’s all we have. But what is that moment, the present? Scientifically, it’s the line between the past and the future, both of which are measurable (by estimation for the future). We know when we were born and how long we have lived until now. We know that we are likely to live another ?? years and can conceive of measuring from now to then (approximately). But the present itself, what is it? How long does it last? What’s its duration? Mathematically, it’s zero. Something that has zero for its measure doesn’t exist in the real world!

            That’s less than satisfying. How can we live in the moment if it doesn’t exist? 

            The time we experience is sometimes called philosophical time as opposed to scientific time. This was the crux of the initial disagreement between Einstein and Bergson. Each thought the other’s time was irrelevant. So where is the connection between the two? 

            We don’t know.

            Maybe it has to do with the idea I began to develop in my essay “’a’ Divided by Zero is Real” from Pencils 2019. Maybe the time of the world is created by a real-world limit on infinite processes. My example was dividing a real number by zero. At some point, the world decides “enough already”, and stops the process. Since dividing by zero is infinite, it’s a process. It takes time. That point where the world stops the process marks the duration of something, perhaps the present moment. 

            In Zeno’s paradox, it’s dividing a distance (the flight path of the arrow) and a time period (its time of flight) into ever smaller pieces. This also defines infinity and is a process. If the world just throws up its hands and moves on, that stopping point defines a real time and so a real distance, albeit small. 

            In this model, every present moment has a duration caused by the world stopping an infinite progression. So, who or what is the “world” that makes this decision? Maybe we, the whole human race (or all of life), make this decision unconsciously as a collective solipsist per my essays on Reality. 

            Some part of us collectively says “enough is enough” constantly and creates a duration for every present moment we all experience. These would be moments in which we could live.

            Hugh Moffatt
            Nashville, Tennessee
            October 31, 2023

1) There’s a minimum quantifiable time from quantum mechanics called the Planck time. It’s tempting to think of this as the unit from which duration is built, but there is no clear connection between this and actual building blocks of duration if for no other reason than that we can choose any point in time as a starting point. There are no pre-existing blocks of time that can’t be cut, just minimum lengths that can be measured from any arbitrary starting point. Also, there’s no physical theory independently predicting this minimum time length, which still leaves open the question of where it came from.

2) There’s also a built-in delay in our sense mechanisms—sight, touch, hearing, etc.—that might seem like a candidate for a fundamental duration. The electrical impulses in our nerves and brain take quite a long time by physics standards to transmit and process the signals from the world, which, of course, also take time to reach our senses. Our experience is always several beats behind the “present” of the outer world, but if we define our “present” to moments of internal awareness, we’re left with the original problem. Also, this is a processing issue. It doesn’t address the theoretical physical problem.