Radioisotope clocks

This idea for thread was triggered by this comment, by Farsight, in a post in the Black holes thread:

Farsight said:

DeiRenDopa said:

For example, you seem to think that two clocks, separated by a foot or so in elevation are (must be?) in the same reference frame; i.e. that they can both measure 'local' time and that the 'local' is the same.

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No. They're just two clocks at different elevations. They're in this room. Or if you prefer, they're in space near a planet. The things we call reference frames are "artefacts of measurement" that have no physical existence. And those clocks don't actually measure time. There is no time flowing through those clocks. Can you see it whooshing through? No. What they actually do is clock up some form of regular motion, and display a cumulative total that you call the time.

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I responded thus: "But, if what clocks "actually do is clock up some form of regular motion", according to you, does that mean that you cannot - even in principle - build a clock based on the nuclear decay of an unstable isotope (to take one example)?"

I got wondering, is it possible to build a clock, which measures time in some reasonably accurate fashion, but does not "clock up some form of regular motion"? To be sure, I do not know what Farsight means by that phrase, but still ...

First, what do I want my no-moving-parts-clock to do? Well, I want to be able to glance at it and get an answer to this question: 'what time is it, now?' And by "glance" I mean "sense"; for example, I could 'tell the time' by touching the clock, and feeling how warm it is, or I could tell the time by listening to the clock and hearing how loud it is.

An RTG, a radioisotope thermoelectric generator^WP, could be such a clock. With a suitable choice of radioisotope and cladding, the brightness and color of the clock would tell the time, once t=0 was set (the fainter and redder the clock, the greater t is). The outside could also be painted with temperature-sensitive paint, making the clock more easy to read. By having a clock with several different modules - each with a different radioisotope - even finer gradations and/or spans of time may be possible.

With a suitable choice of radioisotope - the daughter isotope being an element with a low boiling point perhaps - the clock could tell time by being weighed; "if it's this heavy it must be Tuesday". More precision might be possible by putting the clock on a pressure-sensitive surface, one which changes color with pressure - "if it's blue it must be Wednesday".

Hooked up to some sort of Geiger counter, the clock could tell time by the volume of sound coming from the loudspeaker; "if it's this loud, it must be 13:30".

Of course, there are lots of practical challenges to building a robust, reliable no-moving-parts radioisotope clock! Especially if you want a clock that tells date (over a period of a decade or two, say) as well as time (both hour and minute).

What do you think?

I think I also pointed out something similar a while back, but I proposed a collection of muons. Since they have no internal structure but still decay with a half-life it's much easier to claim the clock has no need of moving parts to measure time.

I certainly see no fundamental problem with the argument anyway.

I guess almost any particle decay process would do. Radioisotope decay is surely the most convenient, from a practical perspective.

If something e/m-based were needed, perhaps the mean lifetime of the positronium ¹S₀ could be a contender? There's no motion (in the classical sense) determining the lifetime.

DeiRenDopa said:

So I started a thread, Radioisotope clocks, to see what others think (at least about a radioisotope clock).

There's also this interesting aspect: why should the universe care about human-scale stuff? A clock based on C-14 would indeed be useless for day-to-day timekeeping. So would one based on Cn-284 (an isotope of copernicium, half-life 97 ms^WP). But, from the point of view of physics, clocks, and timekeeping, that's irrelevant, right?

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Not necessarily useless, there's a different way of creating a radioisotope clock. Place the carbon-14 in a sealed chamber with a scintillation detector, and use the output of the detector as a trigger for a counter. You'd then calibrate it based on the average number of counts per second to convert the count to time.

(And program it to continually adjust the calibration based on the half-life of carbon-14.)

This kind of clock would be useful for timekeeping on a day-to-day basis, but I'm not sure how accurate it'd be.

ETA: While the length of the second might vary, if you calibrate it properly, it could possibly be very accurate in the long run. You might end up with something like 10.500,001 ticks per second, where you'd have it alternating between 10 and 11 ticks for it to advance one second, plus an extra tick every 1,000,000 seconds.

Brian-M said:

ETA: While the length of the second might vary, if you calibrate it properly, it could possibly be very accurate in the long run. You might end up with something like 10.500,001 ticks per second, where you'd have it alternating between 10 and 11 ticks for it to advance one second, plus an extra tick every 1,000,000 seconds.

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I'm not entirely sure what you are suggesting, but if the true mean number of ticks per second were 10.500,001, you'd only get ten ticks in a second around 12.4% of the time and 11 ticks 11.8 % of the time. You're almost as likely to get 9 ticks as 11. The chance of getting less than ten ticks in a second is about 40 %. That's all because the ticks will be Poisson distributed with variance equal to the mean.

Tubbythin said:

I'm not entirely sure what you are suggesting, but if the true mean number of ticks per second were 10.500,001, you'd only get ten ticks in a second around 12.4% of the time and 11 ticks 11.8 % of the time. You're almost as likely to get 9 ticks as 11. The chance of getting less than ten ticks in a second is about 40 %. That's all because the ticks will be Poisson distributed with variance equal to the mean.

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I guess that's what happens when I post numbers on impulse without thinking it through or checking up on details.

You can get elapsed time from an RTG by measuring its electrical output against a constant load, adjusting for the heat sink temperature and thermoelectric decay rate. Of course, the usual Pu-238 generator has a very slow decay rate (ETA) so it's not so good for measuring short intervals of time.

sts60 said:

You can get elapsed time from an RTG by measuring its electrical output against a constant load, adjusting for the heat sink temperature and thermoelectric decay rate. Of course, the usual Pu-238 generator has a very slow decay rate (ETA) so it's not so good for measuring short intervals of time.

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Yes, and that output can be measured, confidently, to ~±0.001% (1 part in 100,000), would you say?

The range of time that we'd like to be able to 'tell time accurately' might be 1 second to 1 century. A century is ~3 billion seconds. Assuming that 'tell time accurately' means, approximately, '±0.5s over periods of up to 1 million seconds, ±0.5 hours over periods of up to 1 century', how many different kinds of RTG-based radioisotope clock would we need? Of course, the one(s) for measuring shorter periods would need to be started anew, periodically; there may not be a suitable radioisotope with a desired half-life; etc ...

Tubbythin said:

I'm not entirely sure what you are suggesting, but if the true mean number of ticks per second were 10.500,001, you'd only get ten ticks in a second around 12.4% of the time and 11 ticks 11.8 % of the time. You're almost as likely to get 9 ticks as 11. The chance of getting less than ten ticks in a second is about 40 %. That's all because the ticks will be Poisson distributed with variance equal to the mean.

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Thinking it over again, I believe we're talking about different things. I'll stand by what I originally wrote, and try and explain what I meant more clearly. For simplicity, I'll drop the 0.000,001 from the example and make it exactly 10.5 "ticks" per second.

If you measure an average of 10.5 "ticks" (detected particles) per standard second, then you could program the clock to advance one second after ten "ticks", then advance another second after eleven "ticks", then start back at ten "ticks" again.

This way, both the radioisotope clock and a standard clock will measure exactly the same average number of "ticks" from the scintillation detector per second.

Even though the exact length of the second as measured by the the radioisotope clock will vary considerably compared to the standard second, these will average out over minutes and hours, resulting in the time displayed by the radioisotope clock closely corresponding to the time displayed by the standard clock.

What you'd end up with is a clock with an irregular length second, but still keeps good time. If the advance of the second were audible, but not the "ticks", it would sound like the irregular-ticking clock kept in the waiting room of Discworld's Lord Vetinari, intended to distract and irritate people waiting to see him.

Apparently someone has made their own real-life version of Vetinari's clock...

Brian-M said:

Thinking it over again, I believe we're talking about different things. I'll stand by what I originally wrote, and try and explain what I meant more clearly. For simplicity, I'll drop the 0.000,001 from the example and make it exactly 10.5 "ticks" per second.

If you measure an average of 10.5 "ticks" (detected particles) per standard second, then you could program the clock to advance one second after ten "ticks", then advance another second after eleven "ticks", then start back at ten "ticks" again.

This way, both the radioisotope clock and a standard clock will measure exactly the same average number of "ticks" from the scintillation detector per second.

Even though the exact length of the second as measured by the the radioisotope clock will vary considerably compared to the standard second, these will average out over minutes and hours, resulting in the time displayed by the radioisotope clock closely corresponding to the time displayed by the standard clock.

What you'd end up with is a clock with an irregular length second, but still keeps good time. If the advance of the second were audible, but not the "ticks", it would sound like the irregular-ticking clock kept in the waiting room of Discworld's Lord Vetinari, intended to distract and irritate people waiting to see him.

Apparently someone has made their own real-life version of Vetinari's clock...

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This makes more sense. However, since it is never going to be a reliable clock down to a second, I think you might as well just advance the clock 2 seconds every 21 ticks.
I might, if I find the time, do some Monte Carlo simulations of this at some point in the next few days.

Tubbythin said:

This makes more sense. However, since it is never going to be a reliable clock down to a second, I think you might as well just advance the clock 2 seconds every 21 ticks.
I might, if I find the time, do some Monte Carlo simulations of this at some point in the next few days.

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I was thinking that you could make it more precise by using a more radioactive material or a more sensitive detector. If the scintillation detector "ticks" an average a thousand times a second, then it would be much more precise than one where it only ticks ten times a second.

Brian-M said:

I was thinking that you could make it more precise by using a more radioactive material or a more sensitive detector. If the scintillation detector "ticks" an average a thousand times a second, then it would be much more precise than one where it only ticks ten times a second.

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Agreed.