“What is time? If no one asks me, I know what it is. If I wish to explain it… I do not know”, famously quipped Saint Augustine. Our modern understanding of time is more scientific than ever, and many of us likely do now think we know how to explain time. While impressively the Swiss atomic clock has a range of uncertainty of 1 second in 30 million years. But the time of physics is not real time. Time is not a mathematical abstraction, there is no line of time, and the present is not some indivisible zero-point on it. 

Time is mathematical abstraction

From sundials and water clocks to hour glasses and weight-driven mechanical clocks, timekeeping devices have a long and fascinating history, driven mostly by an unrelenting quest for better precision. Nevertheless, we should remember that the usefulness of any timekeeping device depends on our gathering information through our senses, usually by looking—the location of the shadow projected on a sundial, the position of the hands of a clock, the readings of the vibrational frequency of a quartz crystal—and thus relates directly to our lived experience. A timekeeping device translates the ineffable experience of passage into the language of numbers. In doing so, it appears to reify time, giving it a mathematical precision comparable to that of physical measurements, such as distance, weight, speed, or pressure. The more precise the clock, the more distant clock time seems to be from becoming, passage, and duration.

Today’s timekeeping standard uses the frequency of specific electronic atomic transitions. Atoms have the advantage of bypassing irregularities in astronomical motions that require constant recalibration of clocks. The Swiss atomic clock FOCS-1, for example, relies on the frequency of electron jumps between energy levels in a cold cesium-133 atom, which is constant to very high accuracy so long as the clock remains in the same geographic location and at rest with respect to the ground. Under these conditions, the time interval of 1 second is currently defined as equal to 9,192,631,770 periods of orbital oscillations with this frequency. The FOCS-1 clock has the impressive uncertainty of 1 second in 30 million years.[1] The precision depends on the details of the experimental setup, consisting of a microwave cavity tuned to resonate with the electron jump frequency, like a parent pushing a child on a swing keeping the same period.

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Infinitely divisible, physical time is a mathematical abstraction.

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Still, no physical measurement can be absolutely precise. Every tool or device has an accuracy determined by its design. If a clock has a precision of a nanosecond (one-billionth of a second), it cannot be trusted to capture details of phenomena happening at scales of a picosecond (one-trillionth of a second). Thus, to every layer of reality based on measurements at a given scale, there is an underlying stratum that remains elusive. Even if, mathematically, we can divide time into smaller and smaller chunks, we could not expect to measure such shrinking time intervals ad infinitum. Infinitely divisible, physical time is a mathematical abstraction. The time line, a straight line covering the real numbers, is a useful tool for modeling time-varying phenomena with roots in the late Middle Ages (see chapter 2). It should not, however, be taken as representing the reality of time any more than a clock dial does.

Clocks don’t reveal the true nature of time; they are tools invented to abstract certain aspects of the experiential flow of time and to measure them in a systematic way. Modern clocks are products of the scientific workshop, the collective effort of scientists and engineers to isolate aspects of experience and construct measurable invariants from them. But regardless of the precision of the clocks emerging from the workshop, our understanding of time remains rooted in duration, the irreducible experience of becoming.

SUGGESTED READING Solving the mystery of time By Bernardo Kastrup

Time in the Blind Spot

To consider the time of physics—what a clock measures—as the only real time is a clear example of the chain of thinking leading to the Blind Spot. First, we surreptitiously substitute mathematical time for lived time. Next, we commit the fallacy of misplaced concreteness by declaring that abstract, mathematical time is real time. Finally, we forget that the concrete being of passage as given in duration is the primal source and condition for the meaningfulness of the notion of time. This forgetting is the amnesia of experience.

The blind spot view of time leads to quandaries. Mathematically, as we consider ever shorter time intervals, what we call the experience of nowness evaporates into no-duration. No-duration not only clashes with our immediate experience of time’s passage, its ever-flowing nature, but also elevates mathematical singularities into puzzles and inconsistencies. How could something that lasts be constructed out of point-like moments, defined as instants with no duration? How seriously should we take scientific statements about the nature of physical reality that are based on a time interval that approaches zero? As we will see when we discuss cosmology (see chapter 5), these questions become acute when we try to make sense of the origin of the universe, when we try to answer, within the framework of physics and cosmology, Leibniz’s famous question, “Why is there something rather than nothing?”

We need to distinguish the purpose of a specific notion of time from the impulse to attribute ontological primacy to it as a result of the amnesia of experience. To describe natural phenomena, the scientific narrative needs to abstract, to the largest extent possible, the passage of time from the human experience of duration. In science, the passage of time must be orderly and precise, the same for all observers with identical clocks, at least for those in the same reference frame (clock times differ for frames of reference that move relative to one another, according to the theory of relativity, but the theory also teaches us how to patch these differences). Physical time must have a universal standard, a demand that led to the “God-like” perspective of Newton’s absolute time (see below). Nevertheless, the scientific need to use a mathematically accurate definition of time should not be confused with that definition’s having any kind of ontological primacy. Insisting that it does was a major contributing factor to the Blind Spot of classical physics.

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You cannot be a mapmaker if you cannot see what you are mapping.

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Human time includes lived time and abstracted mathematical time lines. The latter emerge from the former. We could not have built an abstract notion of physical time without first having the experience of time’s passage. The mathematization of time through its representation on a continuous line composed of instants with no duration is a map, the passage of nature is the landscape, and our ineffable experience of time’s flow—Bergson’s duration—is the vehicle of our journey through the landscape. The map serves a clear purpose: the mathematical description of natural phenomena to the highest degree of precision possible. But you cannot be a mapmaker if you cannot see what you are mapping. The mapmaker should not forget what cannot be included in the map—the experience of walking the terrain, the biting chill of the mountaintop, the dappled light through the trees of the forest. Which details are important for which purpose? The map will get its users lost if the mapmaker does not understand its purpose.