This really bugs me.

For any single nucleus (of an isotope that undergoes spontaneous decay), while a large population will decay at a characteristic rate related to half life and population, a single nucleus may decay instantly, or survive for an infinite time before decay. But, given any two of these nuclei (and we might take tritium as a simple one): if they are in the same quantum state to start with, they are absolutely identical - they are in some ways quantum clones.

How can a nucleus “know” when to decay? I understand there are incomprehensible behaviours of the strong and weak nuclear forces, and the probability functions of quantum mechanics at play.

I propose an experiment in which nuclei (with a known probability/frequency of spontaneous decay) are accelerated to a significant proportion of c, to see whether their decay frequency is affected by time dilation.

The mechanics of the experiment would be really quite simple.
-- Frankx, Nov 18 2019

Muons https://en.wikipedi...ng_of_time_dilation
A test of time dilation [DenholmRicshaw, Nov 19 2019]

Toroidal croissant Toroidal_20croissant
There's no end to it ... [8th of 7, Nov 21 2019]

Where is the observer in relation to the sample ?

The relativistic frame of reference determines the observed result, shirley ?
-- 8th of 7, Nov 18 2019


My design would be a simple linear accelerator with sensors distributed along its length. A population of atoms of known half-life are ionised and accelerated to a significant proportion of c. Depending on their velocity, a shift should be observed (for a static observer or sensor) in their rate of decay. So, sensor/observer is “static”.
-- Frankx, Nov 18 2019


You're going to have a population of nucleii with a range of velocities, even with the tightest engineering controls. That will affect your data.

The nucleii and the observer need to be in the same reference frame, and the sample needs to be cooled to near 0K to minimize translational velocity within the population.
-- 8th of 7, Nov 18 2019


//How can a nucleus “know” when to decay? // It doesn't. The chances of its decaying in the next second are (for any given isotope) the same whether it's just been formed or its been sitting around for many half-lives.

Also, unstable particles (including unstable nuclei) have longer half-lives when accelerated to relativistic velocities. So, if your particles have a half-life of a microsecond at rest (relative to the observer), and you send them round an accelerator for a microsecond, a lot more than half will remain and come out the far end. It's been done, and in fact is a common factor in many accelerator experiments.
-- MaxwellBuchanan, Nov 18 2019


Muons produced 20km up in the upper atmosphere by cosmic radiation impact have a half life of 2.2 microseconds and yet more are observed at the Earth's surface because of time dilation effects. See link...
-- DenholmRicshaw, Nov 19 2019


// have longer half-lives when accelerated to relativistic velocities. //

No, they don't.

Their half life ** measured by a "stationary" observer ** is longer, but that's because time passes more slowly for the particles at their high relativistic velicity.

It's an example if the well-known "twin paradox".

As you correctly point out, the statistical probability of decay is a constant. If the observer is in the same reference frame as the sample, then the observed decay rate should be the same independent if their translational velocity. But if the observer and sample are in different reference frames, then relativistic time distortion has to be factored in.

[Frankx]'s original question is valid but only if the sample and observer travel together. It can't be resolved experimentally by s "static" observer.
-- 8th of 7, Nov 19 2019


OK, I'm moving this to Halfbakery Archive, as the effect has been experimentally measured as noted.

Rossi–Hall experiment and others [link]

How does a nucleus "know" when to decay: it seems to be down to the probability function for quantum tunneling. It's a random event, but with a defined probability (over a certain period of time)
-- Frankx, Nov 19 2019


"Gosh; hold on to your protons, chaps: here goes!"
- Arthur Ransome, We Didn't Mean to Go to c
-- pertinax, Nov 21 2019


//We Didn't Mean to Go to c// [@]*

*I propose [@] to indicate that an annotation has been awarded a notional bun.
-- MaxwellBuchanan, Nov 21 2019


In terms of patisseriological topology, [@] looks more like a Danish Pastry or a Cinnamon Roll than a bun. Although, in the grand Linnaean taxonomy of baked goods, are these sub-classes of 'bun'?
-- hippo, Nov 21 2019


"©" to denote a Notional Croissant would be an alternative.
-- 8th of 7, Nov 21 2019


...and "&" for a broken pretzel
-- hippo, Nov 21 2019


//[@] looks more like a Danish Pastry or a Cinnamon Roll//

However, if you cut a croissant in half, the exposed face looks quite @ish.
-- MaxwellBuchanan, Nov 21 2019


If you don't like an annotation you could award a cat's arse: "*"
-- hippo, Nov 21 2019


That's just a blatant and shameless act of elf-promotion, [MB].

<link>
-- 8th of 7, Nov 21 2019


//probability function for quantum tunneling// So if God doesn't play craps, an energy valley of the space-time fabric. Another variable not isolated by current technology or theory.
-- wjt, Nov 22 2019


//God doesn't play craps//

There's no 'craps' when 'all' possibilities exist.
There are just means to ends.
-- 2 fries shy of a happy meal, Nov 22 2019


True, the lowest possible, amongst all possible, is quite difficult to get to.
-- wjt, Nov 22 2019


// I'm moving this to Halfbakery Archive //

TIL that exists. I have at least one idea to move, then.

// are these sub-classes of 'bun'? //

Around here, I hear "cinnamon bun" said often, so I'd say yes for that one.
-- notexactly, Nov 24 2019


// I'm moving this to Halfbakery Archive //

An excellent example of a quantum effect; the idea is observed, its wave function collapses, and its position is fixed in Halfbakery:Archive.

Sadly, due to Heisenberg's law, it is then impossible to know its momentum.
-- 8th of 7, Nov 24 2019


Nowhere really fast...
-- 2 fries shy of a happy meal, Nov 25 2019


But can't stop the waves of unseen subtleties, though.
-- wjt, Nov 28 2019



random, halfbakery