How does carbon 14 have such a perfect halflife?

[mfb]

Theoretically, if one started with 1,000 atoms and were able to identify, separate and isolate the 500 atoms that were going to decay sometime within 5700 years

If you violate the laws of physics in our universe then you can do whatever you want, but it will have little relevance for the universe we live in.

 

[Nugatory]

[Hypothetically] if one started with 1,000 atoms and were able to identify, separate and isolate the 500...
I am proposing that to maintain that these two atoms are identical physically, electromagnetically and in every nuclear-atomic way, is illogical.

You may find that assumption to be implausible, but that's not the same thing as illogical. I'm not sure why you find this assumption to be so implausible though.

Imagine that we have a large number of coins. We'll call the heads-up state "undecayed" and the "tails-up" state "decayed". Initially they are all in the heads-up undecayed state. Once every minute we toss all the coins into the air so that each one comes down heads-up (undecayed) or tails-up (decayed) with 50% probability. We will find that the half-life of a collection of undecayed coins is one minute; on average half the coins will decay every minute.

We could assume that the process is not in fact random. Maybe each coin contains an internal trigger that counts tosses and cause the coin to land tails after N tosses; if when we start half the coins have N=1, one-quarter have N=2, one-eighth have N=3 and so forth we would see this behavior. Under this assumption, we could in principle identify ahead of time the 500 out of 1000 that will decay during the first half-life as you suggest - they're the ones for which N=1. However, we don't need that assumption to explain the decay behavior; random every toss works just as well and is much more consistent with our understanding of how coin tossing works.

A further difficulty with your seemingly "logical" idea that the decay times come from some internal property of the atoms is that the initial conditions have to be tuned very carefully to match the observed results. If we don't start with half the coins having N=1, one-quarter N=2, one-eighth N=3 and so forth we won't get results that match the observed results - and the more we try to imagine how that might happen, the more implausible and contrived the idea seems.

 

[jbriggs444]

If we don't start with half the coins having N=1, one-quarter N=2, one-eighth N=3 and so forth we won't get results that match the observed results - and the more we try to imagine how that might happen, the more implausible and contrived the idea seems.

Suppose that we program all the coins according to an exponential distribution of flips-until-the-first-tails. And we speculate that the internal timer that is so-programmed is hidden. The only way to query it is to flip the coin until the first tails.

What observable difference is there between this description of the situation and a description that says it's just 50/50 at each flip?

In the absence of an observable difference the distinction between the two possibilities is no longer a matter of science. It is a matter for Occam's Razor to hack at.

 

[Auston Louis]

You may find that assumption to be implausible, but that's not the same thing as illogical. I'm not sure why you find this assumption to be so implausible though.

Imagine that we have a large number of coins. We'll call the heads-up state "undecayed" and the "tails-up" state "decayed". Initially they are all in the heads-up undecayed state. Once every minute we toss all the coins into the air so that each one comes down heads-up (undecayed) or tails-up (decayed) with 50% probability. We will find that the half-life of a collection of undecayed coins is one minute; on average half the coins will decay every minute.

We could assume that the process is not in fact random. Maybe each coin contains an internal trigger that counts tosses and cause the coin to land tails after N tosses; if when we start half the coins have N=1, one-quarter have N=2, one-eighth have N=3 and so forth we would see this behavior. Under this assumption, we could in principle identify ahead of time the 500 out of 1000 that will decay during the first half-life as you suggest - they're the ones for which N=1. However, we don't need that assumption to explain the decay behavior; random every toss works just as well and is much more consistent with our understanding of how coin tossing works.

A further difficulty with your seemingly "logical" idea that the decay times come from some internal property of the atoms is that the initial conditions have to be tuned very carefully to match the observed results. If we don't start with half the coins having N=1, one-quarter N=2, one-eighth N=3 and so forth we won't get results that match the observed results - and the more we try to imagine how that might happen, the more implausible and contrived the idea seems.

Thanks for your valuable insight into my perception of why I believe that two atoms, one that will decay within the next hour and one that will decay in more than 5,000 years are not identical. In the excellent analogy of tossing coins, one realizes that in reality, there are multiple factors that actually determine if the coins will land heads or tails. These factors include the way each coin was tossed, involving friction from the hand, the height of the toss, the spin of the coin based upon the angle of the hand and action of the wrist/fingers and environmental conditions surrounding each coin, and finally, slight differences in coin shape, thickness and weight, and surface imperfections from wear and tear. In other words, all these factors determine if the coin will land heads or tails. My proposal is similar to your analogy of the tossed coins in that there are factors that have yet to be determined, both within the atom awaiting decay and the immediate environment surrounding the atom, that determine if the atom will decay now or in another 5,000 years.

 

[phinds]

See, @Nugatory, you've proved his point

@Auston Louis, your confirmation bias is showing.

 

[WWGD]

I Think I get it, this only works for HUGE Amounts of Atoms, if we were to Try and Carbon Date a Sample with only 100,000 atoms half life it wouldn't work...what would be the smallest sample we could carbon date, like how many atoms for the Statistics to work because it has to be large numbers of atoms or we can get the popcorn effect I am only guessing...

Look up ROC, Receiver Operating Curve to see relation between sample size and power of the test.

 

[Nugatory]

My proposal is similar to your analogy of the tossed coins in that there are factors that have yet to be determined, both within the atom awaiting decay and the immediate environment surrounding the atom, that determine if the atom will decay now or in another 5,000 years.

You’re proposing that there is an as-yet-undiscovered hidden variable theory (that’s the standard terminology and you’ll occasionally see the acronym HVT) that explains the apparent randomness of quantum mechanics the same way that classical mechanics can in principle explain the apparent randomness of a tossed coin. That is a plausible enough conjecture, and it would not be completely amazing if such a theory were eventually discovered. However...

Bell’s theorem (google, and also look for the web page maintained by our own @DrChinese) and the experiments it motivated shows that any correct hidden variable theory must be at least as weird and offensive to our classical intuition as QM itself. So although you may feel that the random black box model of QM “can’t be right”, you’re not going to like the alternatives any more. In particular, you can’t have a theory that offers the same “if we just knew the exact values of...” certainty that Laplace’s demon promised us and that you’re finding in a tossed coin.

 

[mfb]

@Auston Louis: It's an analogy, and if you take analogies too far you always end up with wrong results. Coins will never fully simulate quantum mechanics, but something you can take away here: When you have the coins in your hand there is nothing relevant that would distinguish the coins. You can inspect the coins as much as you want, you still can't predict on which side they will land. There is nothing that would make one coin a heads-coin, and in fact if you throw the same coin many times you'll get different results.
All this is not needed in quantum mechanics, where you can show that atoms of the same nuclide in the ground state are exactly identical by observing the statistics they follow.

 

[PeroK]

My proposal is similar to your analogy of the tossed coins in that there are factors that have yet to be determined, both within the atom awaiting decay and the immediate environment surrounding the atom, that determine if the atom will decay now or in another 5,000 years.

The main contender for this is Bohmian mechanics (aka Pilot Wave theory). See here, for example:

https://plato.stanford.edu/entries/qm-bohm/

As others have said, although this provides essentially a realist-deterministic interpretation of QM, it requires the pilot wave to be non-local in order to explain observed experimental phenomena. In particular, "classical" hidden variables have been shown to be inconsistent with experiment.

 

[Auston Louis]

If you violate the laws of physics in our universe then you can do whatever you want, but it will have little relevance for the universe we live in.

Thanks for your time and insight in assisting me gain an improved perspective of my proposal.
The radioactivity decay law can be stated that the probability per unit time that a nucleus will decay is a constant, independent of time, or the number of atoms likely to decay in a given infinitesimal time interval (dN/dt) is proportional to the number of atoms present.

@Auston Louis: It's an analogy, and if you take analogies too far you always end up with wrong results. Coins will never fully simulate quantum mechanics, but something you can take away here: When you have the coins in your hand there is nothing relevant that would distinguish the coins. You can inspect the coins as much as you want, you still can't predict on which side they will land. There is nothing that would make one coin a heads-coin, and in fact if you throw the same coin many times you'll get different results.
All this is not needed in quantum mechanics, where you can show that atoms of the same nuclide in the ground state are exactly identical by observing the statistics they follow.

mfb, thanks much for your explanation. How about atoms that are not in the ground state?

 

[Auston Louis]

You’re proposing that there is an as-yet-undiscovered hidden variable theory (that’s the standard terminology and you’ll occasionally see the acronym HVT) that explains the apparent randomness of quantum mechanics the same way that classical mechanics can in principle explain the apparent randomness of a tossed coin. That is a plausible enough conjecture, and it would not be completely amazing if such a theory were eventually discovered. However...

Bell’s theorem (google, and also look for the web page maintained by our own @DrChinese) and the experiments it motivated shows that any correct hidden variable theory must be at least as weird and offensive to our classical intuition as QM itself. So although you may feel that the random black box model of QM “can’t be right”, you’re not going to like the alternatives any more. In particular, you can’t have a theory that offers the same “if we just knew the exact values of...” certainty that Laplace’s demon promised us and that you’re finding in a tossed coin.

Nugatory, thanks for your helpful explanations.

 

[Nik_2213]

Tangential, there's the 'X17' hypothesis. (Based on limited data: Due Care, Please ??)
https://en.wikipedia.org/wiki/X17_particle

As I understand it, the as-yet undetectable flux of such shy 17 MeV bosons may 'nudge' vulnerable 'nuclear' neutrons unto decay at a slightly different half-life to them 'solo'.

Potentially new science if can be proven, a candidate for 'Shrug' gallery if not...

 

[Vanadium 50]

@Nik_2213 , it sounds to me like you are proposing an undetectable flux of an unconfirmed particle is producing an unneeded effect.

 

[mfb]

How about atoms that are not in the ground state?

They are different from atoms in the ground state. Nothing mysterious. For nuclear decays this rarely matters.

 

[Nik_2213]

@Nik_2213 , it sounds to me like you are proposing an undetectable flux of an unconfirmed particle is producing an unneeded effect.

But, as I cautioned, based on limited data: Due Care, Please ??

Like those many 'Ghost Islands' that frequented old charts, but eluded confirmation as misplaced, mis-identified or eroded back to a reef / sea-mount, a few may yet surprise with the equivalent of a pumice raft...

I've seen plate tectonics, quarks and exo-planets confirmed, neutrinos detected and weighed (< ~1.1 eV ??), Higgs' proven. Plus, like super-symmetry, a lot of real-neat stuff with beautiful math that remains stubbornly, stubbornly elusive.

IMHO, until Dark Matter & Dark Energy are resolved, there's some wriggle room for weirdness. Like the recent work on proton charge radius, a different approach may expose a small but under-estimated systematic error...

As ever, Due Care, Please ??
;-)

 

[WWGD]

But, as I cautioned, based on limited data: Due Care, Please ??
As ever, Due Care, Please ??
;-)

I really due care.

 

[Vanadium 50]

why I believe that two atoms, one that will decay within the next hour and one that will decay in more than 5,000 years are not identical.

I'm surprised we are discussing this, since this is pretty clearly a personal theory and we don't discuss that topic here. Especially in this thread, since physics as it is understood and practiced has a different answer. We wouldn't answer a question with "phlogiston" or "caloric" would we? I'm also surprised that someone who states he is a physicist would propose such a thing.

Everyone else is discussing Bell. This is a fine argument, but I think there are better ones.

As you've described it, radioactive nuclei "wear out" over time. This wearing out (experimentally) is exponential, with the same constant independent of sample and environment.

This leads to a number of questions:

1. Why do some nuclei decay immediately after production? (The most probable lifetime in an exponential is zero) - why is the initial resistance to wear distributed in a fashion that appears to be random and exponential. In short, all you have done is move the question of randomness up one level so you haven't gained anything but one more question. (Why exponential)
2. Why are nuclear half-lives the same for the same species of nucleus produced at different times, different places or by different mechanisms?
3. Why can't we accelerate or retard this wear?

So I would say you answered one question by pushing it back a level and adding three more questions. You argued that your theory was superior "philosophically". I think I demonstrated it isn't. The only "philosophical" improvement seems to be that you like it better. I maintain that nature is the way it is whether or not anyone of us likes it.

But there is an even bigger problem, and that's thermodynamics. You are arguing that radioactive atoms are distinguishable. If that were true, we would have the Gibbs paradox and could use it to construct perpetual motion machines. We would not have Bose-Einstein or Fermi-Dirac statistics, at least not in atoms. Even if we didn't understand - or even observe - radioactive decay, we could tell that this theory is not right, because it leads to a very different thermodynamics than we observe.

 

[phinds]

I'm surprised we are discussing this, since this is pretty clearly a personal theory and we don't discuss that topic here.

+1 on that. I don't understand why this thread is still open.

 

[PeroK]

@Vanadium 50

Maybe we were awaiting the definitive rebuttal, and now that you've provided it the thread can be closed with a flourish!

 

[DrClaude]

@Vanadium 50

Maybe we were awaiting the definitive rebuttal, and now that you've provided it the thread can be closed with a flourish!

Indeed, time to close. Thanks to all that have participated.