We’ve come a long way since Newton famously declared “I do not define time.”  In fact, it has become increasingly clear that when we speak of time in physics, what we really mean is a measurement read from a clock.  So, what exactly constitutes a clock in physics?

The Clock: A Predictably Regular Motion

In physics, any predictable, regular motion can be used as a clock.  A great many clocks have been developed, from the common wrist watch that marks the passage of each day, to isotopic decay, which is used to measure time on a geological and archeological scale.  First, let’s look at your wristwatch.  It most likely operates using a quartz crystal resonator,  which amplifies a particular frequency of input power.  The crystal’s vibrational frequency is determined by its shape and cut, and each watch contains a piece of quartz that is tuned to vibrate at a standardized rate of 32,768 times per second. This standard rate is mechanically translated to the consistent movement of the hands across the watch face, which results in a consistent response to “do you have the time?”

Quartz is not the only possible clock oscillator. To tell time using caesium-133, physicists use it’s predictable transitions between quantum energy levels. Caesium crystals breathe through this transition some 9,192,631,770 times a second - 280,000 times faster than quartz - and can be used for highly precise atomic clocks. They have become the gold standard for quantifying Earth time, but there is a tiny catch. Do they always tell the same time?

Not exactly. When physicists say that time is affected by gravity or inertia, this should come as no violation of intuition.  While a lot of popular science articles try to play up the mystical angle of this idea, it may simply be a question of gravitational pressure.  

Consider that water pressure at the bottom of the ocean is far greater than the pressure near the surface, entirely due to gravity. Each water in a vertical column is pulled upon the entire earth below and pushed upon by the water column above, yielding tremendous forces at the sea floor.  Clocks based on atomic vibration are no different. At the surface of the Earth, in 1G conditions, they vibrate slower than higher up in orbit where there is less gravitational pressure to dampen vibration.

We know that there is less gravity on Mt. Everest than at Death Valley in Nevada, and so we would expect clocks to run at different speeds in those two places. In fact, this is borne out through experimentation, as researchers at the National Institute for Standards and Technology have shown that an elevation change of as little as one meter causes a clock to speed up. No mysticism necessary - there is simply less gravity to impede atomic vibration.

The funny thing about clocks, though, is that they don’t all behave consistently as gravity changes. Atomic clocks speed up with elevation due to a decrease in gravitational pressure, but a clock based on a different physical mechanism - like the hourglass - will stop altogether by the time you get into near Earth orbit! This underscores the idea that gravity affects motion, and so it affects the function of a clock. Since in physics time is what clocks say, one must choose their clock very carefully, since aspects of clock design affect their utility.

How about the sundial?  The sundial is the most ancient clock known to humans.  Does the fact that this clock ceases to track time during the night mean that time stops in the dark?  If we accept that time is what clocks do, and the sundial is the only clock available to us, then we would have no choice but to concede that under these confines, time stops in the dark.  

This is a plainly absurd claim, and underscores the importance of recognizing that “time” is simply what clocks do. The ability of a clock to say something useful about our subjective experience of being alive is only as good as our understanding of a) the limitations of the clock we use and b) the selection of the right clock for the right question.

Time Describes Systematic Change in Location

In physics, the arrow of time is the tendency toward disorder.  In the words of physicist and author Sean Carroll, “If you take all the air in this room and put it in the corner, that's low entropy. And then you let it go and it eventually fills the room and then it stops. And then the air's not doing anything. In that time when it's changing, there's an arrow of time, but once you reach equilibrium, then the arrow ceases...”  Now that’s one cold room!

What Carroll is saying is that in his hypothetical air-room, the only clock (time) available is the rate of the progression toward entropy.  This is the predictable motion of the air particles. Once no further progression towards entropy is available, and therefore no motion to be had, the clock ceases to function. It was only as useful for as long as there were motions of objects relative to one another, and the “end of time” makes sense in this condition, since inability to increase entropy means everything has been dead for a long, long time.

In Layman’s Terms, Time is Motion With Memory  

We’ve established that time is what clocks do, that the ability of clocks to tell time depends on choosing the right clock for the application, and that time requires motion. One last aspect to fold into our definition is motion.

To explain this, let’s look at a common sense form of time keeping - say, clocking a runner in the Olympics.  Establishing who has the fastest time in the race requires remembering where all the runners started in the first place. Because all of the runners start at the same place, the first one to appear at the finish-line wins and has clocked the fastest time. This test of time only works because we remember the start. If we didn’t recall the starting place for each runner, there would be no way to say who actually ran the fastest.

You probably have all sorts of clocks, and hence time-makers, which are unique to your own life.  Often, I’ll listen to music when I’m out and about running errands.  I will sometimes say to myself, '“that trip to the grocery took about an album’s worth of time.”  Without remembering the beginning of my playlist, I’ve got no sense of time.  In this way, time is the motion of the airwaves during my listening experience with respect to my memory of pushing play.  

Key Points

• In physics, time is what clocks do

• In physics, a clock is a predictably periodic motion

• In physics, time describes change:  the arrow of time is defined by the thermodynamic concept of entropy

• In laymen’s terms, time is motion and memory