Relativity on a Human Scale

While I mostly restricted myself to watching invited talks at DAMOP last week, I did check out a few ten-minute talks, one of which ended up being just about the coolest thing I saw at the meeting. Specifically, the Friday afternoon talk on observing relativity with atomic clocks by Chin-Wen Chou of the Time and Frequency Division at NIST in Boulder.

The real technical advance is in a recent paper in Physical Review Letters (available for free via the Time and Frequency Publications Database, because government research isn’t subject to copyright): they have made improvements to their atomic clock based on the spacing of two energy levels in a single aluminum ion (described in a Science paper, also available free at the Time and Frequency Publications Database), so it is now accurate to something like one part in 1017. They now have two “clocks” (you can argue about whether they really count as official clocks in the current configuration) based on the same ion that they can compare to unprecedented precision.

This allows a couple of really cool tricks that haven’t been published anywhere (yet), but which were the subject of the DAMOP talk. These clocks are now good enough to observe relativistic effects on a human scale: they see time dilation from motion of the ion at speeds of 10m/s or less, and the gravitational redshift caused by raising one of the two clocks a foot above the other.

Einstein’s theory of relativity predicts a number of things about the behavior of clocks that strike most people as surprising. In particular, a stationary observer looking at a moving clock will see that clock “ticking” at a slower rate than an identical clock at rest (and a moving observer will see the same effect for the stationary clock). This has been demonstrated with big old jet airliners, and is included in the time corrections to make GPS work, but the shift is minuscule for motion at ordinary human speeds– a clock moving at 10 m/s would tick slower than a stationary clock by about 10-16s every second, which is way too small to see (about 10s difference over the age of the universe).

The extraordinary stability of the aluminum ion clock, though, lets them measure this directly. The ions are held in small traps using radio-frequency fields to confine them, and the motion of the ions is very precisely controlled. They normally keep the ions at the trap center, where they move as little as possible (the small residual motion is one of the frequency shifts contributing to the uncertainty in the PRL paper), but for these experiments they offset one of the ions a little bit, so it sloshed back and forth in the trap at a well-known rate. This caused that clock to “tick” at a slightly lower rate (the “ticking” in this case is the oscillation of light connecting two energy levels, with a frequency of 1.21 1015 Hz (a bit less than 250 nm in wavelength)), exactly as predicted by relativity. The shift is detectable down to speeds of less than 10 m/s, thanks to the high quality of the clocks.

The other big relativistic effect is the “gravitational redshift,” which says that a clock at higher elevation will run at a slightly faster rate than an identical clock at lower elevation (it’s a “redshift” because this manifests as a decrease in the frequency of light sent upwards in a gravitational field). This has been observed in a famous experiment at Harvard which used Mössbauer spectroscopy to measure the tiny shift caused by shooting gamma rays up or down a 20-odd meter “tower.”

In the talk at DAMOP, Chou described using their ridiculously stable ion clocks to measure the gravitational redshift over a much shorter distance– about 33 cm. They put hydraulic jacks under one of their laser tables, and ran for a while with the two clocks at the same height, to establish the difference between their operating frequencies, then jacked one table up by a bit more than a foot, and recorded some more data. Sure enough, the difference between the clocks changed by a part in 1016 or so, exactly as predicted.

These aren’t earth-shattering results, and won’t transform anybody’s understanding of how the universe works. They do, however, provide a beautiful demonstration that relativity is real even in situations where the speeds and distances involved are on a human scale– you don’t need to be moving at half the speed of light in the vicinity of a black hole, provided your clocks are good enough.

Chou, C., Hume, D., Koelemeij, J., Wineland, D., & Rosenband, T. (2010). Frequency Comparison of Two High-Accuracy Al^{+} Optical Clocks Physical Review Letters, 104 (7) DOI: 10.1103/PhysRevLett.104.070802

Schmidt, P. (2005). Spectroscopy Using Quantum Logic Science, 309 (5735), 749-752 DOI: 10.1126/science.1114375

Comments

  1. #1 Jolyon Bloomfield
    June 1, 2010

    Ok, that is incredibly awesome. Kudos to NIST for making such incredible measurements!

  2. #2 Radha
    June 1, 2010

    Great.. So tall people age faster than us shorties?

  3. #3 Chad Orzel
    June 1, 2010

    So tall people age faster than us shorties?

    The heads of tall people age faster than the heads of short people, that’s for sure. Which is why we always seem so wise…

  4. #4 Tony Jeremiah
    June 1, 2010

    So tall people age faster than us shorties?

    I have a related question concerning the twin paradox.

    As I recall, an identical twin leaves earth on a spaceship travelling at close to light speed, and returns to earth to discover his/her identical twin is older. Presumably, the age difference is due to relativistic effects on the spaceship, such that time moved slower on the ship relative to earth.

    My question, is whether the aging effect is to be viewed metaphorically rather than literally. It seems that time passage (as measured by an external clock) is different from the rate at which one ages (presumably measured by a biological clock[s]).

    If so, this would suggest another interesting experiment that would seem to connect biology and relativity. For example, if you took some organisms (e.g., flies) and put them in a situation where their relative motion is faster than another group of organisms (e.g., flies rotating in a centrifuge vs. flies in a petri dish), the ones subjected to the movement condition should be observed to live longer on average.

    So is the aging effect in the twin paradox thought experiment supposed to be viewed metaphorically or literally?

  5. #5 jason
    June 2, 2010

    That’s pretty darn cool.

  6. #6 Chad Orzel
    June 2, 2010

    If so, this would suggest another interesting experiment that would seem to connect biology and relativity. For example, if you took some organisms (e.g., flies) and put them in a situation where their relative motion is faster than another group of organisms (e.g., flies rotating in a centrifuge vs. flies in a petri dish), the ones subjected to the movement condition should be observed to live longer on average.

    The Principle of Relativity is literal, and applies to all types of “clocks,” so in principle, this would work. The problem is that the shift is absurdly small– if you look at the difference you would expect between the lifespans of a person who spends their entire life at the North Pole and one who spends their entire life at the equator (thus moving at roughly 1000 mph relative to the pole), it works out to only a few milliseconds over eighty years. There’s no way you could hope to measure that in a biology lab.

    (That specific example is a little dodgy, as there’s an effect in General Relativity that exactly cancels the shift you would expect from Special Relativity, but it’s enough to give you the size of the effects you’d be looking for.)

  7. #7 Tony Jeremiah
    June 2, 2010

    The Principle of Relativity is literal, and applies to all types of “clocks,” so in principle, this would work.

    Interesting.

    The problem is that the shift is absurdly small– if you look at the difference you would expect between the lifespans of a person who spends their entire life at the North Pole and one who spends their entire life at the equator (thus moving at roughly 1000 mph relative to the pole), it works out to only a few milliseconds over eighty years. There’s no way you could hope to measure that in a biology lab.

    I thought as much. So maximizing an observable laboratory effect would require optimal conditions involving observation time, the non-relativistic lifespan of the organism, and velocity.

    I was watching the Discovery channel the other day, and it was mentioned that the decay rate of muons travelling at relativistic speeds is 5x slower. (At non-relativistic speeds, they decay in ~2.2 microseconds).

    Ok, so here’s a variation of my question. Is there any reasonable laboratory condition where it would be possible to observe the average lifespan of mayflies (non-relativistic average lifespan, 1-2 days) increased by 1 day due to relativistic speeds? For example, assessing the average lifespan of mayflies on board a jet plane travelling at 2000 mph for 4 days non-stop, relative to mayflies sitting in a lab on earth.

    (That specific example is a little dodgy, as there’s an effect in General Relativity that exactly cancels the shift you would expect from Special Relativity, but it’s enough to give you the size of the effects you’d be looking for.)

    Yeah, acceleration changes?

  8. #8 David
    June 2, 2010

    Its interesting, I was explaining this exact point to my girlfriend yesterday. There seemed to be a disconnect for her between understanding that the difference in time on the clocks relates directly to the aging process. I believe this is due to the fact that when you discuss this in terms of aging it hits home that we are talking about time in the real sense and not just about numbers on a dial. I finally explained it by stating that if tomorrow I got on a space ship that flew around the planet at 99.9% the speed of light for 30 years (earth time) when I came home I would still be my good looking self having only aged about 1 year whilst she would be a haggled old lady.

  9. #9 Jolyon Bloomfield
    June 2, 2010

    Ok, so here’s a variation of my question. Is there any reasonable laboratory condition where it would be possible to observe the average lifespan of mayflies (non-relativistic average lifespan, 1-2 days) increased by 1 day due to relativistic speeds? For example, assessing the average lifespan of mayflies on board a jet plane travelling at 2000 mph for 4 days non-stop, relative to mayflies sitting in a lab on earth.

    You’d need a gamma factor (the Lorentz boost factor) of somewhere between 1.5-2 for that to work. As gamma = 1/sqrt(1-v^2/c^2), we can solve for v/c = sqrt(1-1/gamma^2). Putting in 1.5, which would need the slowest velocity, that gives v = 0.75 c, or 3/4 of the speed of light, which is an absurd velocity for any macroscopic object. So no, relativistic effects on any biological clocks will remain unobserved well into the foreseeable future.