When you study radioactivity in high school or anything that relates to radioactive dating, you’re drilled in the fact that any and every radioactive (unstable) nuclei decay at a fixed mathematical rate called the half-life. Each ‘brand’ of nuclei has its own half-life that’s applicable or unique to those particular nuclei. What’s probably not drilled into you is that unstable nuclei decay for no reason at all and that tends to make a bit of a hash of the half-life relationship which in turn can’t be explained. Something is screwy somewhere.
Is there a relationship between causality and radioactive decay and the precise pattern to that decay? Why is this important or interesting? Because, at least in IMHO, there’s something screwy somewhere between the three that needs resolution. Radioactivity – exactly when something decays, in this case unstable (i.e. – radioactive) nuclei, is totally random. There is no rhyme or reason for the when. There is no cause according to quantum or particle physicists; therefore there should be no pattern according to me. If, contrary to scientific opinion, cause and effect operate at the quantum level (the micro realm where unstable nuclei go poof) then there are plausible mechanisms, again according to me*, that could account for a pattern – the half-life pattern – which is what we observe. So there’s a conflict here, or as I have stated, there’s something screwy somewhere.
The central theme here is why do unstable nuclei decay according to a precise mathematical relationship termed the half-life? There are potentially dozens of other precise mathematical possibilities, and a near infinite ones if you abandon any mathematical symmetry altogether. Let’s explore a few of those.
For the sake of what follows, let’s assume a barrel full of 1000 marbles. Each marble represents one of the 1000 identical unstable radioactive nuclei ‘marbles’ or atomic ‘marbles’ that sooner or later will go poof and decay giving off, radioactivity – Alpha, Beta and/or Gamma Rays. The barrel is just to keep all of them in place – say like a 1000 atom lump of uranium. The decay or the poof will originate when someone removes a marble or the marble from the barrel.
Now how many ways can one remove marbles from the barrel – how many ways can unstable radioactive nuclei be made to decay.
For the standard half-life relationship to hold, you are restricted to pulling out half of the marbles that are in the barrel per fixed unit of time. You remove one half of the original lot of 1000 marbles per unit of time; then one half of the remaining 500 marbles per unit of time; then one half of the remaining 250 marbles per unit of time; then one half of the remaining 125 marbles, and so on and so forth – 62, 31, 16, 8, 4, 2, 1 and finally all 1000 marbles have been removed and there is no more instability left. All the 1000 radioactive atoms have now gone poof and decayed. You can plot that on a graph and get a nice pattern. That’s what’s in the textbooks.
Since the half-life works on an ever diminishing scale, one-half of the original, then one-half of what remains, then one-half of what remains after that, and so on, why that and why not other possible but similar relationships?
What about three-quarter lives? If you start with 1000 unstable marbles, after one unit of time you decay 750, leaving 250. Three-quarters of 250 is 188 that bite the dust after another identical interval of time leaving 62 to go. Three-quarters of 62 is 46 more who have decayed. That just leaves 16 radioactive marbles in the barrel. 12 of them go poof in the next time interval, leaving a bare quartet. One more time interval sees just one lone radioactive marble left, which of course will give up the ghost in the next (and final) time interval.
Now what about two-third lives? If you start with 1000 unstable marbles, after one unit of time you decay 667, leaving 333. Two-thirds of 333 are 222 that bite the dust after another identical interval of time leaving 111 to go. Two-thirds of 111 are 74 more who have decayed. That just leaves 37 radioactive marbles in the barrel. 25 of those go poof in the next time interval, leaving a bare 12. One more time interval sees just four lone radioactive marbles left, three of which of course will give up the ghost in the next to last round, the lone and final survivor going down the gurgler in that next (and final) time interval.
For another example, why a one-half life relationship in favour of an ongoing diminishing reciprocal to the above one-third relationship? Remove one-third of the 1000 marbles leaves 667. One-third now removed from those 667 leaves behind 445 ‘radioactive’ marbles. Remove one-third of those 445 marbles and you’re left with 297. One-third taken away from 297 leaves 198, then 132, then 88, then 59, then 39, then 26, then 17, then 11, then 7, then 5, then 3, then 2, then one is left which goes poof at that last pick of the draw; in that final unit of uniform time.
In a similar sort of exercise to a third-life, you can substitute the standard half-life for a quarter-life (1000, 750, 562, 421, 316, etc.) or a half-life for a fifth-life (1000, 800, 640, 512, 410, etc.).
Another variation on the theme might revolve around why does not Mother Nature decide, per fixed unit of time, on one-half of the original then one-third of the remaining then one-quarter of what remains after that, hence one-fifth, one-sixth, etc. In our 1000 marble in the barrel analogy, that’s one-half of the 1000 removed or 500 left, then one-third removed of the 500 or 333 remain, then one-quarter removed of the remaining 333 leaves 250 remaining, then one-fifth removal of the 250 leaves 200 remaining, then remove one-sixth of the 200 leaves 167, and so on down the diminishing line.
Or what about an inverse square relationship which is a common relationship in physics. So the diminishing relationship is one quarter, followed by one ninth of what remains, followed by one sixteenth of that, followed by one twenty-fifth, followed by one thirty-sixth, etc. That is, start with 1000 marbles, then removing one quarter of those 1000 leaves 750, then removing one ninth of those 750 leaves 667, and removing one sixteenth of those 667 leaves 625, then removing one twenty-fifth of those 625 leaves 600, then removing one thirty-sixth of those 600 leaves 583, and so on. Why didn’t Mother Nature opt for that mathematical relationship for radioactive decay?
Now consider the near infinite number of alternatives or possibilities.
You could grab out all 1000 marbles in one fell swoop.
You could equally grab out 500, catch your breath, then grab out 500 more.
You could pull out 1 or 2 or 5 or 10, etc. marbles per unit of time. From say the initial 1000, pull out 25 each grab: 1000, 975, 950, 925, 900, 875, etc. Or, one could pull out any random number of marbles every 25 seconds.
You could pull out 1, then 2 then 3 then 4 then 5, etc. per unit of time. Starting with 1000, you’d have 1000, 999, 997, 994; 900; 985; 979; 972, etc. Or, pull out 1, then 2 then 4 then 8 then 16 then 32 then 64, etc. doubling each time. Or 1, then 4, then 9, then 16, then 25, then 36 more, then 47 more, then 64 more, then 81 more, then 100 more, etc., the squares of 1, 2, 3, etc. Or there’s the cubes of 1, 2 3, etc. – 1, 8, 27, 64, 125 and so on until all the marbles have been grabbed. Another relationship could be pulling out 1, then 2 more, then 3 more, then 5 more, then 8 more, then 13 more, then 21 more, then grab another 34, then another 55, etc. where what you grab out is the sum of the previous two grabs. Then there are the primes – grab 1, then 2 then 3 then 5 then 7 then 11 then 13 then 17, etc. There’s no end to the possible mathematically related sequences that have nothing to do with a half-life.
If radioactive nuclei go poof for absolutely no reason at all – there’s no cause for the effect – as scientists claim**, then all radioactive nuclei decay should be absolutely random. It just so happens that mathematically the most probable way is a totally random way, a totally random selection of marbles from the barrel since there are way more ways of doing something (removing marbles from the barrel) randomly than doing something by the mathematical book – engineering some precise mathematical relationship that one can put down in equation form and graph as a symmetrical line or curve.
Take say two decks of cards, each numbered 1 to 52 and each shuffled well – then each shuffled again. A randomly chosen card from Deck A decides the number of marbles to be removed; a randomly chosen card from Deck B decides the time before you remove them. Picked cards are re-entered back into their respective decks and the decks shuffled again.
Now this is just a convenient-sized quasi-random number generator one can apply to our 1000 ‘radioactive’ marble sample. In reality, the first ‘deck of cards’ would have to represent every possible positive whole number, and the second time generator ‘deck of cards’ every possible increment of the smallest possible time unit – the Planck unit of time – in which anything meaningful can take place, like a nucleus decaying and going poof. Both random number generating ‘decks’ together then can deal with every radioactive nucleus that ever was and is in the entire cosmos.
Meantime, back to the 1000 marbles in the barrel and the two finite shuffled deck of cards from which numbers of marbles and time frames are picked randomly. I think you’d agree that if you followed the logic of picking and removing the number of marbles from the barrel based on a random shuffling of one deck of cards and doing so at time intervals based on the random shuffling of a second deck of cards, you are unlikely in the extreme to end up with the standard half-life relationship. Something is indeed screwy somewhere.
In conclusion, if you buy say a 24-can case of beer, there will come a point in time when half the contents (12 cans) have been consumed. But you couldn’t call that time interval the half-life of that case of beer since there is no reason to assume that the next six cans (half of the remaining 12 cans) will be consumed in the next identical time interval and the next three cans in an identical time interval following that. The same argument applies to radioactive (unstable) nuclei. The fact that the half-life relationship exists and has been verified in defiance of all that is logical given the lack of causality is suggestive evidence IMHO for the reality of, our reality being; the Simulated (Virtual Reality) Universe scenario. It’s all just software programming done from a higher reality.
* In the nanosecond that separates no decay from decay, something must of happened IMHO to trigger the decay event. I’ve gone on record elsewhere that a plausible mechanism might be neutrinos slam-banging into unstable nuclei, the impact being the tipping point that triggers the decay event.
**Scientists probably conclude that because nothing they do to radioactive nuclei, either chemically or physically makes any difference to the poof rate of that specific type of unstable nuclei. You can hammer them, boil them in oil, piss on them, feed them to bacteria, give them the evil eye, soak them in Holy Water, oxygenate then, play heavy metal music to them, shine a laser beam on them, freeze them, put them in a vacuum, and for all the good those things do, nothing changes.
Further Reading:
Malley, Marjorie C.; Radioactivity: A History of A Mysterious Science; Oxford University Press, Oxford; 2011:
