Radioactive decay and relativity

[curiousOne]

Does the half life of a particular radioactive decay change if the sample is accelerated close to the speed of light ?
Didn't Hawking answer that question in the 1980's ?
Shouldn't the half life itself change over time ? (since the normal pdf is the one with the most entropy of information and radioactive decay increases the entropy of the material, I'm concluding the pdf itself should bias after a while. )
J.D.

 

[jtbell]

Does the half life of a particular radioactive decay change if the sample is accelerated close to the speed of light ?

Sure. The half-lives of unstable elementary particles increase as their speed increases, exactly according to relativistic time dilation. This is routinely observed and taken account of at particle-accelerator laboratories.

When I was in grad school, one of my friends worked on an experiment that studied sigma and xi hyperons, using beams that were a meter or two long (before decay) because of time dilation. Without the time dilation, the experiment would have been impossible because the beams would have decayed before they even entered the detector!

Shouldn't the half life itself change over time ?

As far as we know, the probability that a particular individual particle decays during the next second is contstant, regardless of how long the particle has already "lived," or whether the other particles in a sample have decayed or not. This leads to a constant half-life. I don't remember ever seeing any evidence to the contrary.

 

[akhmeteli]

As far as we know, the probability that a particular individual particle decays during the next second is contstant, regardless of how long the particle has already "lived," or whether the other particles in a sample have decayed or not. This leads to a constant half-life. I don't remember ever seeing any evidence to the contrary.

On the other hand, it might be noteworthy that, strictly speaking, the exponential law is incompatible with quantum mechanics (this is an old result by Khalfin). It is very difficult to observe the deviations from the exponential law though. Some details and a reference to Khalfin's work can be found in Nature vol. 335, p. 298 (22 September 1988)

 

[Vanadium 50]

this is an old result by Khalfin

But not really relevant to the question.

 

[akhmeteli]

But not really relevant to the question.

One of the questions the original poster asked and jtbell answered was "Shouldn't the half life itself change over time ?" Nonexponential decay means the half life is not constant in time. So why do you believe my post was irrelevant?

 

[Dadface]

The predicted exponential decay is based on probability which only works well if there are a large number of radioisotopes.As this number reduces the probability assumptions become less valid as does the definition of half life.

 

[Vanadium 50]

Nonexponential decay means the half life is not constant in time. So why do you believe my post was irrelevant?

First, the Misra and Sudarshan effect is negligibly small. I don't believe it has even been observed in nuclear transitions (although it has in atomic transitions). Second, no matter how you define a lifetime in the case of the practically-but-not-theoretically exponential decay, the answer to the OP's question is clearly "yes".

Splitting hairs like this doesn't make the answer to the OP's any clearer.

 

[akhmeteli]

First, the Misra and Sudarshan effect is negligibly small. I don't believe it has even been observed in nuclear transitions (although it has in atomic transitions).

Google search for the exact phrase "Misra and Sudarshan effect" or "Misra-Sudarshan effect" gave nothing but your post. If, however, you mean "Quantum Zeno effect", this is not exactly what I had in mind. Khalfin's results on decay nonexponentiality (which precede Misra-Sudarshan work by 10-20 years) are applicable both to very short times, which may be relevant to the Quantum Zeno effect, and to very long times, which does not seem relevant to QZE. Furthermore, I said myself that "It is very difficult to observe the deviations from the exponential law though", so what's your point?

Second, no matter how you define a lifetime in the case of the practically-but-not-theoretically exponential decay, the answer to the OP's question is clearly "yes".

If you mean that for a "practically exponential decay" half-life "practically" does not change with time, this sounds pretty much like a tautology. My point, however, was that theoretically there is no such thing as precisely exponential decay.

Splitting hairs like this doesn't make the answer to the OP's any clearer.

It makes the answer more precise though. The OP's question was "Shouldn't the half life itself change over time ?", and the correct answer is "Yes, it should." Furthermore, OP used the following interesting argument: "since the normal pdf is the one with the most entropy of information and radioactive decay increases the entropy of the material, I'm concluding the pdf itself should bias after a while." This is a purely theoretical argument, so if you answer "No, half life should not change over time" based on practical considerations, such an answer may be not just imprecise, but also confusing and misleading.

Anyway, you could accuse me of hair-splitting (although I said myself that decay nonexponentiality is very difficult to observe), but not of irrelevancy.

 

[curiousOne]

Thanks for the replies. That was very informative.
Now a related question:
With a large sample, across a horizon, I think the decay pdf would change dramatically, so the exponential law should fail outside the horizon, but not inside, i.e. the half life would take on different values across the horizon.
Is that reasonable ?