Twin paradox in SR and its applicability to radioactive decay

[Scott444]

Hi, thanks to a different thread/question on this forum I've come to appreciate time dilation ..somewhat. And from that I wondered if, given the range of locally measured times aboard any and all particles in the universe, given their different trajectories and histories since the big bang ..wouldn't, when they coalesce, form a normally distributed bell curve of time passed clocks? ...And wouldn't then the decay likeyhood of each of these (imagine we're considering some particular radioactive element) well wouldn't the half life calculation/radioactive -ness of such stuff be a function of each atom's clocks ...or of that time passed distribution ? So, does a normal distribution of times passed for each atom, in a radioactive element, generate the observed decay curve?

I found this but ...it's over my head. (http://www.umich.edu/~ners311/CourseLibrary/bookchapter13.pdf)

But if this is true is there not a case to generalise it further and make some argument that the stochastic nature of quantum dynamics isn't a random - utterly unpredictable albeit normally distributed thing but is actually a function of the relative age of subatomic particles or the age of quarks? ..Thank you for any thoughts or guidance.

 

[russ_watters]

And from that I wondered if, given the range of locally measured times aboard any and all particles in the universe, given their different trajectories and histories since the big bang ..wouldn't, when they coalesce, form a normally distributed bell curve of time passed clocks?

No, there is an infinite number of valid frames with no preferred distribution. And even if there were:

...And wouldn't then the decay likeyhood of each of these (imagine we're considering some particular radioactive element) well wouldn't the half life calculation/radioactive -ness of such stuff be a function of each atom's clocks ...or of that time passed distribution ?

Yes...

So, does a normal distribution of times passed for each atom, in a radioactive element, generate the observed decay curve?

No. Radioactive decay has a certain rate, but each atom is not on a schedule. There is randomness in that distribution.

But if this is true is there not a case to generalise it further and make some argument that the stochastic nature of quantum dynamics isn't a random - utterly unpredictable albeit normally distributed thing but is actually a function of the relative age of subatomic particles or the age of quarks?

Right; that's not how it works. The randomness is real, not a function of the "age" of particles.

 

[Scott444]

Hey thanks Russ, might just need to get to grips with the first part of what you say ...

there is an infinite number of valid frames with no preferred distribution

Is that true? How can something with a beginning (big bang) and a process (particle - planet - galaxy formation) in a finite time not have a normal distribution? Wouldn't the paths and histories of any of the bits of the universe (in a gas cloud - form a star - supernova - be in galaxy - - flung from a galaxy etc ) not amount to a normalish distribution of time taken paths? some sped some didn't - but many did much the same and a few did less etc - doesn't the fact that there is - at smaller scales - heterogeniety - require a normal dist? ...I mean okay - maybe then - I'm struggling with a flat distribution though. :)

 

[Scott444]

okay russ (accepting the details of the elements age distribution and thank you,) - each individual atom's time path/age does affect the individuals liklyhood of decay ...doesn't it? ...by the following

If you put half a piece of some element with a particular decay half life in a spaceship and did the twin paradox trip with its other half staying home - then there will be different percetages of decay products in the two pieces when they meet again, right? ...because the individual atoms were aged at differing rates (or followed differering space-time paths). And their collective propensity to produce decay products is then different - the two pieces will sit at different points on that elements decay curve. It must follow that individual atoms are more likely to decay if they're older ...surely?
- is it saying anything different to say more decay over time?

Then can't I argue that while we may not be able to determine an atoms age - its propensity to decay is a function of its age ..and that while decay appears random with respect to the individual, and we can only statistically define it - it is not inherently random - we just lack information about it... ..??

 

[Dale]

So, does a normal distribution of times passed for each atom, in a radioactive element, generate the observed decay curve?

No, the decay times are exponentially distributed, not normally distributed. The exponential distribution has the memoryless property. What that means is that if a particle has a half life of one hour then the probability that it decays in the next hour is 0.5 regardless of whether it is already 1 minute old or 1 week old. There is no memory of how long it has already been around.

 

[Scott444]

No, the decay times are exponentially distributed, not normally distributed. The exponential distribution has the memoryless property. What that means is that if a particle has a half life of one hour then the probability that it decays in the next hour is 0.5 regardless of whether it is already 1 minute old or 1 week old. There is no memory of how long it has already been around.

Ahhh, cheers Dale or as my daughters used to say, and in this case they'd be dead right "that's so random!"
I'd say horribly random. c'mon - how do you people ever finish a physics course with having common sense assaulted like this at every turn. :)
But thank you - ..

 

[Dale]

how do you people ever finish a physics course with having common sense assaulted like this at every turn. :)

I understand the feeling. The answer is to use the mathematical formulas consistently and carefully and trust the result of the math even if the result is surprising. Then repeat on many, many problems until the feeling of surprise goes away. At that point your intuition is correct.

 

[russ_watters]

Perhaps Dale already got the message through, but...

okay russ (accepting the details of the elements age distribution and thank you,) - each individual atom's time path/age does affect the individuals liklyhood of decay ...doesn't it? ...

No. Radioactive decay does not depend on particle age.

If you put half a piece of some element with a particular decay half life in a spaceship and did the twin paradox trip with its other half staying home - then there will be different percetages of decay products in the two pieces when they meet again, right?

Yes.

...because the individual atoms were aged at differing rates (or followed differering space-time paths). And their collective propensity to produce decay products is then different - the two pieces will sit at different points on that elements decay curve. It must follow that individual atoms are more likely to decay if they're older ...surely?

No. Radioactive decay rate is a bulk property that has no memory of the past whatsoever. But moving forward, the decay rate is defined as a function of the passage of time.

- is it saying anything different to say more decay over time?

Well, you are trying to describe a memory effect, so in that context no.

 

[Scott444]

Yes thanks Russ, it's, in an intuitive sense, frustrating - but I kinda see what's up.
cheers,
Scott