Thursday, January 17, 2013

How a particle tells time

One of the first things you learn about quantum mechanics is that particles have a wavelength, and thus a frequency. If the particle is in rest, this frequency is the Compton frequency and proportional to the particles’ rest mass. It appears in the wavefunction of the particle at rest as a phase. This means basically the particle oscillates, even if it doesn’t move, with a frequency directly linked to its mass.

The precision of atomic clocks in use today relies on the precise measurement of transition frequencies between energy levels in atoms which serve as reference for an oscillator. But via the Compton wavelength, the mass of a (stable) particle is also a reference for an oscillator. Can one therefore use a single particle to measure the passing of time?

This is the question Holger Müller and his collaborators from the University of Berkeley have addressed in a neat experiment that was published in the recent issue of Science:
    A Clock Directly Linking Time to a Particle's Mass
    Shau-Yu Lan, Pei-Chen Kuan, Brian Estey, Damon English, Justin M. Brown, Michael A. Hohensee, Holger Müller
    Science, DOI: 10.1126/science.1230767
As you can tell from the title of the article, the answer is Yes, one can use a single particle to measure time! They have done it, with the particle in question a Cesium atom, and call it a “Compton clock.” The main difficulty is that the oscillation frequency is very high, far beyond what is measurable today. To make it indirectly measureable, they had to cleverly combine two main ingredients, an atomic interferometer and a frequency comb.

The atomic interferometer works as follows. The atom is hit by two laser pulses, one pulse with frequency a little higher than the laser’s direct output frequency, and one with a frequency a little lower. This splits the wavefunction of the atom. A couple more precisely timed laser pulses are then used to let the wavefunction converge again. It interfers with itself and the interference pattern can be measured in repeating this process.

The relevant aspect of the atom interferometry here is that the phase accumulated by each part of the wave-function depends on the output frequency of the laser, the difference in frequency between the two pulses (tiny in comparison to the output frequency), as well as on the path taken. The path-dependent phase itself depends on the mass of the atom because the two parts of the wavefunction are not in rest with each other. So then the experimentalist can turn a knob and change the difference between the frequencies of the two pulses until the interference pattern vanishes. If the interference pattern vanishes, one then has a fixed relation between the mass of the particle, the output frequency of the laser, and the difference between the pulse frequencies.

So far, so good. If one now knows the frequency of the laser, one can measure the particle’s mass by looking at the frequency split of the pulses needed to get the interference to vanish. Alas, this is not what one wants for the purpose of a clock, which should not rely on an additional, external, measurement.

This is where the frequency comb comes in. In 2005, frequency combs brought a Nobel Prize to John Hall and Theodor Hänsch. Before the invention of the frequency comb, it was not possible to accurately determine absolute frequencies in the optical range. Relative frequencies, yes, but not absolute ones. They’re just too fast to be counted by any electronic means. Frequency combs address this issue by relating very high optical frequencies to considerably lower frequencies, which then can be counted. This is done by pulsing a low frequency signal . If one takes the Fourier transformation of such a pulsed signal, one obtains (ideally) a series of peaks – the frequency comb – whose positions are exactly known (these are the higher harmonics of the low frequency signal). If one knows the pulse pattern of the laser comb one can then substitute the measurement of a very high frequency with that of a considerably lower frequency. Ingenious!

And more ingenuity. Mueller and his collaborators use a frequency comb to self-reference the (tiny) difference in the laser pulses with the output frequency of the laser. The relation between both is then known and given by the pulse pattern of the frequency comb. This way, one gets rid of one parameter and has a direct relation between a measurable frequency and the mass of the particle: It’s a clock!

For what the precision of this clock is concerned however, it is orders of magnitude below today’s state-of-the-art atomic clocks. So unless there are truly dramatic improvements to atom interferometry, nobody is going to use the Compton clock in practice any time soon.

But this clock works both ways. It doesn’t only relate a mass to time (oscillation frequency), but also the other way round. Thus, one can use the Compton clock to measure mass if one has a time reference. With the "Avogadro Project", an enourmously precisely manufactured silicon crystals containing an accurately known number of atoms, one can scale up a single atom to a large number and macroscopic masses. This way the Compton clock might one day be used to define a standard of mass.


  1. I must admit that "smaller"/"larger" frequency is really confusing me. Granted you do state frequency is proportional to mass, which can be "larger". But it's the inverse which is traditionally a size.

  2. Frequency is the number of oscillations in some period of time. A large frequency is a large number of oscillations. A small frequency is a small number of oscillations. A large frequency is a small wavelength and a small frequency is a large wavelength.

  3. True, but in English (and in German (in translation, of course), for that matter), one normally uses "high" and "low" rather than "large" and "small" when talking about frequency.

  4. Well, if it improves the clarity, I'll be happy to change this. So I've replaced all instances of large frequencies with high frequencies and small frequencies with low frequencies.

  5. The Compton wavelength does depend not only on the particle mass, but its relative speed, which makes the clocks based on this principle more vulnerable to experimental errors - or not? In addition, the clock based on extrinsic frequency of vacuum fluctuations will be probably even more sensitive to changes of vacuum density, than the clock based on intrinsic frequency, so it cannot serve as a mass standard better, than existing prototypes. If the Earth will pass trough dense cloud of dark matter, it will decrease both mass of particle, both Compton wavelength accordingly.

  6. Zephir:

    That the wavelength depends on the relative velocity is the reason for the phase shift. Best,


  7. Only for uncharged particles. For charged particles the Compton frequency shift is equal to the de Broglie frequency associated with the moving charged particle, which is momentum dependent.

  8. Zephir: Yes, the phase depends on the momentum, which depends on the restframe, is what I'm saying. I don't know what problem you have with charged particles (and which charge anyway?).

  9. Interesting! I have read in Roger Penrose's book "Cycles of Time" that one cannot build a clock from photons alone, since they don't have mass. Sounds good. But they have a frequency? Why can't we use that for building a clock? Is it because a frequency alone wouldn't help, since we also would have to measure something else?

  10. Frank:

    The frequency of a photon is not an invariant, unlike the mass of a particle. It depends on the reference frame. You can't use it as a "tick" unless you have some other means to fix the frequency. (Eg if you know it comes from some atomic transition.) Best,


  11. Given a known mass, this experiment measures the Planck constant. The Avogadro sphere is a method to accurately reference the mass of a 28Si atom to the kg prototype.

    IIUC, this is essentially equivalent to the Watt balance experiment. This would make it another realization of the same proposed definition of the kg rather than an alternative definition.

  12. Wow! I wonder if David Hestenes knows about this article? This could help validate his "Zitterbewegung Interpretation of Quantum Mechanics". I sure would like to read this paper without having to pay for it. I'm a taxpayer in good standing. :-) If someone could email to I would apreciated it.

  13. Hi Bee,
    Is it known whether the phase of a given Cesium atom is unique or whether it correlates to those in its vicinity?

  14. This is interesting, as more about how we can *use* a particle to tell time than it telling time within itself. A structureless particle like a muon doesn't have any known process to "mark" time (like with internal clockwork.) Hence both of these are truly mysterious:
    1. Muons are unstable - decay even though no known "internal process" - pure "law" involved.
    2. They are identical as best we can tell, but probabilism means some live longer than others.
    Not a clockwork universe!

  15. Good discussion but like Neil Bates, I think it opens the door to a bigger discussion which is:Do all of the fundamental behaviors of particles, forces and fields exist "in" time or do those very behaviors define what time actually is? If we were able to examine those precious two microseconds of muon decay closely, what would we find? Is there a fundamental behavior, taking place once or repeating itself many times over during the two microseconds before, during and after the W particle intermediate? And how does this fundamental behavior in the muon speed up or slow down if the muon experiences a velocity change and/or position change in a gravitational field? Could a moun, moving at extremely high velocity, take longer to produce a W particle, or have a longer-lived W particle, or some other behavior, simply because it has a higher velocity relative to some background field or is placing a strain on a field of its own that is being dragged along?

    During high velocity, a disturbance could be created between the muon and one of its own fields, or a field it is moving through. Gravity could be creating the same net effect by having an influence on a background field, or one of the muon’s own fields as the muon remains stationary. In either event, this disturbance could slow the rate that the fundamental behaviors can occurr which we would emergently see as slower time.


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