*illusion*and our conception of it is merely a

*measure*. The only way we have to perceive time is in the relative order of events that take place, regardless whether time somehow exists independently of these events or not. All timekeeping ultimately depends on a

*frequency source*- or

*oscillator*- which is nothing but a generator of evenly spaced events. The number of events generated per second is the

*frequency*of the oscillator, and is measured in

*Hertz*.

*(Clock with a 4Hz oscillator using a pendulum resonator and a deadbeat escapement.)*

Every oscillator makes use of a

*resonator,*some source of periodicity that we take from nature: the motion of the sun, the fall of a drop of water, the swing of a pendulum, the rotation of a balance wheel, the vibration of a quartz crystal, the hyperfine transition of a cesium atom. If something happens

*faster*than the interval between the beats of that oscillator, the only way to measure that interval is to use an oscillator with a higher frequency, which may mean a different resonator: the transition of an aluminum atom or of a ytterbium atom. How do we use these oscillators? By treating each beat of the oscillator as an event, and counting the number of events that occur during the time interval we want to measure.

*(Watch with a 6Hz oscillator using a balance wheel resonator and a lever escapement.)*

Is there a maximum possible frequency? Physicists think so: the reciprocal of one

*Planck time*, which is about 5.39 x 10

^{-44}seconds. It's the amount of time it takes a photon to cross a

*Planck length.*One Planck time is the shortest time interval physicists believe can meaningfully occur, the duration it takes for the fastest possible object to cover the shortest possible distance found in nature. My calculator tells me that such a hypothetical Planck-frequency oscillator beats at a frequency of about 1.85 x 10

^{43}Hertz. That's a lot of Hertz.

*(Slow motion deadbeat escapement creating the tick tock.)*

What happens between the beats of this hypothetical Planck-frequency oscillator? The question has no meaning; we believe one Planck time is the smallest possible interval that can occur. Time might as well not exist between the beats of a Planck-frequency oscillator. If we want to talk about the time between any two events, we have to find a frequency source that generates events more frequently than the interval we want to measure - any other notion of time is purely an abstract concept - and there is nothing faster than a Planck-frequency oscillator. (I'm told there may actually be even shorter time intervals in the field of

*quantum gravity*, but they are apparently impossible to measure; what this might mean is left as an exercise to the reader.)

*(Snapshot of an oscilloscope on a 10MHz oscillator with a cesium atomic resonator.)*

I didn't come to this notion by reading about the more esoteric aspects of physics (as much as I enjoy doing that). I did it by developing and debugging real-time firmware that shaped the emission rate of ATM cells on a SONET channel carried over an OC-3 optical fiber. By building a stratum-0 NTP server with a cesium reference oscillator. By assembling an educational model of a mechanical clock.

*(Ytterbium lattice optical atomic clock at the NIST Boulder Labs.)*