4 ms·

There would be a tiny tiny bias here, right? There are fewer atoms available to decay for the second interval (because the first two that decayed no longer exi

There would be a tiny tiny bias here, right? There are fewer atoms available to decay for the second interval (because the first two that decayed no longer exist), so the expected time to see two more decays would be slightly longer. You could compensate for this mathematically - you'd look at the intervals relative to the expected interval for the current radioactive mass, rather than relative to each other. (Of course, the bias would be on the order of the reciprocal of Avogadro's number, and probably ignorable for all practical uses.)

shagie 4y ago
That change in "fewer atoms" would likely be beyond the detection of clock jitter. If you've got a mole of cesium, that's 132 grams and contains on the order of 10^23 atoms. Even after one half life (33 years), that's still on the order of 10^23 atoms. The difference between 10^23 and (10^23) - 1 isn't going to be noticeable. The statistical tests of some hotbits data - https://www.fourmilab.ch/hotbits/statistical_testing/stattest.html https://www.fourmilab.ch/hotbits/statistical_testing/stattes... The test that you're likely most interested in is ent ( https://www.fourmilab.ch/random/ https://www.fourmilab.ch/random/ ) and the entropy per byte and serial correlation test Entropy = 7.999975 bits per byte. Serial correlation coefficient is -0.000053 (totally uncorrelated = 0.0). From the docs: > Serial Correlation Coefficient > This quantity measures the extent to which each byte in the file depends upon the previous byte. For random sequences, this value (which can be positive or negative) will, of course, be close to zero. A non-random byte stream such as a C program will yield a serial correlation coefficient on the order of 0.5. Wildly predictable data such as uncompressed bitmaps will exhibit serial correlation coefficients approaching 1. See [Knuth, pp. 64–65] for more details. If you had a sufficiently precise clock where the difference between the 10^23 and 10^23 - 1 became noticeable, you'd likely see other effects. Cesium 137 decays via beta decay which is influenced by the weak force and neutrino. There is evidence that solar neutrinos slightly perturb the rate of beta decay ( https://physicsworld.com/a/do-solar-neutrinos-affect-nuclear-decay-on-earth/ https://physicsworld.com/a/do-solar-neutrinos-affect-nuclear... ) > Further evidence that solar neutrinos affect radioactive decay rates on Earth has been put forth by a trio of physicists in the US. While previous research looked at annual fluctuations in decay rates, the new study presents evidence of oscillations that occur with frequencies around 11 and 12.5 cycles per year. The latter oscillation appears to match patterns in neutrino-detection data from the Super-Kamiokande observatory, in Japan. Other physicists, however, are not convinced by the claim. ... and if you are capable of measuring the differences between N and N-1 atoms in the decay rate or the influence of neutrinos in the decay rate your clock is way too expensive to be used for generating random numbers. ---- (late edit) https://www.fourmilab.ch/hotbits/how3.html https://www.fourmilab.ch/hotbits/how3.html specifically addresses this though: > For example, you might worry about the fact that the intensity of the radiation source is slowly decreasing over time. Cæsium-137's 30.17 year half-life isn't all that long. One half-life in the future, we'll measure T1 and T2 intervals, on the average, twice as long as today. This means, then, that even on consecutive measurements there is a small bias in favour of T2 being longer than T1. How serious is this? Well, expressed in seconds, the half-life is about 9.5×108 and we receive count pulses at a rate of 1000 per second or so. So the time needed to perform the measurements to produce one random bit is on the order of 10−12 half-lives, and T2 will then tend to be longer by a factor of the same magnitude. Since the inter-count interval is around a millisecond, this means T2 will be, on average, 10−15 seconds longer than T1. This is comparable to the long-term accuracy of the best atomic time standards and is entirely negligible for our purposes. The crystal oscillator which provides the time base for the computer making the measurement is only accurate to 100 parts per million, or one part in ten thousand, and thus can induce errors ten million times as large as those due to the slow decay of the source. (This is, again, unlikely to be a real problem because most computer clocks, while prone to drifting as temperature and supply voltage vary, do not change significantly on the millisecond scale. Still, jitter due to where the clock generator happens to trigger on the oscillator waveform will still dwarf the effects of decay of the source during one measurement.)

shagie 4y ago

That change in "fewer atoms" would likely be beyond the detection of clock jitter. If you've got a mole of cesium, that's 132 grams and contains on the order of 10^23 atoms. Even after one half life (33 years), that's still on the order of 10^23 atoms. The difference between 10^23 and (10^23) - 1 isn't going to be noticeable. The statistical tests of some hotbits data - https://www.fourmilab.ch/hotbits/statistical_testing/stattest.html https://www.fourmilab.ch/hotbits/statistical_testing/stattes... The test that you're likely most interested in is ent ( https://www.fourmilab.ch/random/ https://www.fourmilab.ch/random/ ) and the entropy per byte and serial correlation test Entropy = 7.999975 bits per byte. Serial correlation coefficient is -0.000053 (totally uncorrelated = 0.0). From the docs: > Serial Correlation Coefficient > This quantity measures the extent to which each byte in the file depends upon the previous byte. For random sequences, this value (which can be positive or negative) will, of course, be close to zero. A non-random byte stream such as a C program will yield a serial correlation coefficient on the order of 0.5. Wildly predictable data such as uncompressed bitmaps will exhibit serial correlation coefficients approaching 1. See [Knuth, pp. 64–65] for more details. If you had a sufficiently precise clock where the difference between the 10^23 and 10^23 - 1 became noticeable, you'd likely see other effects. Cesium 137 decays via beta decay which is influenced by the weak force and neutrino. There is evidence that solar neutrinos slightly perturb the rate of beta decay ( https://physicsworld.com/a/do-solar-neutrinos-affect-nuclear-decay-on-earth/ https://physicsworld.com/a/do-solar-neutrinos-affect-nuclear... ) > Further evidence that solar neutrinos affect radioactive decay rates on Earth has been put forth by a trio of physicists in the US. While previous research looked at annual fluctuations in decay rates, the new study presents evidence of oscillations that occur with frequencies around 11 and 12.5 cycles per year. The latter oscillation appears to match patterns in neutrino-detection data from the Super-Kamiokande observatory, in Japan. Other physicists, however, are not convinced by the claim. ... and if you are capable of measuring the differences between N and N-1 atoms in the decay rate or the influence of neutrinos in the decay rate your clock is way too expensive to be used for generating random numbers. ---- (late edit) https://www.fourmilab.ch/hotbits/how3.html https://www.fourmilab.ch/hotbits/how3.html specifically addresses this though: > For example, you might worry about the fact that the intensity of the radiation source is slowly decreasing over time. Cæsium-137's 30.17 year half-life isn't all that long. One half-life in the future, we'll measure T1 and T2 intervals, on the average, twice as long as today. This means, then, that even on consecutive measurements there is a small bias in favour of T2 being longer than T1. How serious is this? Well, expressed in seconds, the half-life is about 9.5×108 and we receive count pulses at a rate of 1000 per second or so. So the time needed to perform the measurements to produce one random bit is on the order of 10−12 half-lives, and T2 will then tend to be longer by a factor of the same magnitude. Since the inter-count interval is around a millisecond, this means T2 will be, on average, 10−15 seconds longer than T1. This is comparable to the long-term accuracy of the best atomic time standards and is entirely negligible for our purposes. The crystal oscillator which provides the time base for the computer making the measurement is only accurate to 100 parts per million, or one part in ten thousand, and thus can induce errors ten million times as large as those due to the slow decay of the source. (This is, again, unlikely to be a real problem because most computer clocks, while prone to drifting as temperature and supply voltage vary, do not change significantly on the millisecond scale. Still, jitter due to where the clock generator happens to trigger on the oscillator waveform will still dwarf the effects of decay of the source during one measurement.)