# What evidence would there be if radioactive decay changed 7,000 years ago?

I know we generally operate - or religiously operate - on the principle that fundamental things don't change over time. It's the bedrock of geology - Uniformitarianism. I also believe it is unprovable (which may be bad for my question).

However, assume 14C was a more unstable isotope 7,000 years ago and decayed with $$\lambda$$ = 100a. There are other changes in my world as well - but for this question I want to know what our geologic table would look like if the 14C radioisotope became more stable only 7,000 years ago. In a nutshell I'm trying to hide the true age of the biosphere by making organisms look older, however someone has learned how to detect this.

Oh one more detail - the change was not precipitous. Over 500 years or so the $$\lambda$$ increased from 100a $$\longrightarrow$$ 5730a.

Running through a half-life calculator a 7,500 year old sample will 14C date to 38,900 years old if this change occurred. From comments it appears the overlapping rings from BC 5k~9k will look anomalous.

Other dating methods also exist as noted - DNA mutation rates, magnetic seabed ridges, other radioisotopes - if the evidence left behind by these comparisons could be included in an answers it would help greatly. For example, noncontinuous tree ring calibration curves can be assumed.

My only other thoughts are that maybe some of the $$\beta ^-$$ particles would be captured in nearby elements showing exotic compounds. E.g., maybe more copper or neon in zinc and sodium deposits. Would we see that or just assume it was normal?

Purpose
This change is "theorized" by only one special scientist, and is a prelude to something worse approaching. The greater scientific community is skeptical because his evidence is "not compelling." I am hoping answers include what evidence such a change would leave behind in the various other disciplines, while also hoping such evidence is "sloppy enough" to discredit my character's theory even though it is true. I need to use your evidence to patch the plot holes, or at least make them sloppy enough that everyone else could realistically miss this.

• Comments are not for extended discussion; this conversation has been moved to chat. – Monty Wild Oct 28 '19 at 5:51
• far away stars would look really weird. – John Oct 31 '19 at 21:17

Anthropologists and paleontologists are never happy with a single method of estimating the age of any item.

As has been mentioned there are tree rings. This leads to a large area of study called Dendrochronology. It is not just counting tree rings. Consider finding a fragment of wood in a building site or some such. It has rings. You line up those rings with other fragments of wood, looking for patterns of width. Because trees from the region will have experienced the same weather, the growth rings will be similar size. So you can then line up fragments from many different locations, both those worked by humans and those found in other locations. This means you can build a chronological record far longer than the life of the longest living tree in the area.

As has been mentioned, there are other radioactive isotopes. There are several different isotopes that are used. Different isotopes have different half lives, and enter organisms in different methods. By comparing the results of different methods you get additional information.

There are several other methods. For example, the temperature in the area has an effect on the isotopic ratios of a variety of chemicals. Just as an example, Oxygen is mostly O-16, but O-17 and O-18 appear in trace amounts. The exact amount is affected by the temperature. People build historical records of the isotopic ratios. Then they get such things as organic remains and check the isotope ratios. This can give them some information as to when the organism was alive. It's more difficult than C-14 in some ways. The isotope ratios can be affected by a lot of things. And it's not a straightforward monotonically-decreasing-with-time thing as C-14 decay is.

Other methods are also important over the historical period and the just-before-written-history period. For example, digging through the waste dumps of a community can give you a lot of information. Along with finding fragments of wood you find all kinds of other stuff. This kind of waste only appears on top of that kind of waste, for example. That tells you that the activities that produced it came later. Perhaps the people started using a particular kind of pottery or leather or some such. Or they started getting trade goods that included ocean products that had not reached that far inland. By mapping such things carefully you can get sequences. Then you line that up with other methods, like isotopic analysis or tree rings, that can give you a year estimate.

In some cases, we can see drastic events. For example, if a city is invaded the culture is likely to change radically. That will produce a horizon in the waste dumps. Roman garbage above this layer only, Germanic style waste only below. That tells you that the Romans invaded at that layer. And you can then try to estimate the date of that invasion, and so put bounds on dates for other material in the waste pile.

There are other methods of getting ideas about chronology that are now becoming important. We are mapping genomes of many people. That can give ideas about when various people arrived at various locations. Which can in turn give estimates of the age of various other things that are produced by those people.

So far this is all based on the last few thousand years, say back about 30K or 40K. Longer term similar methods apply, just with slightly different items and emphasis and time scale. For example, part of the story on why the fossil Lucy was estimated to be the age it was, was isotopes. The rocks above and below the fossil were dated using, if I recall, the Argon-Argon method. But another method was to search out fossils of a variety of organisms in those rocks and fit them into the known history of evolution of those animals. You find this kind of tooth here and identify that as a wild boar from this age, that dates that layer of rock. This tooth over here is from an ibex from this era, and that dates this other rock. This fossil leaf in this other layer gets you this layer. This gets you fairly good information out to a few million years. A lot of work, but what are graduate students for?

For much longer periods we have a very interesting thing. There are natural nuclear reactors in Gabon. They are roughly 2 billion years old. By carefully examining these formations it is concluded that, 2 billion years ago, the various physical constants involved in nuclear activity were pretty much identical to their values today. Even very small changes in any of the nuclear parameters would have resulted in these reactors either not functioning at all, or in them completely exploding.

So over age ranges of a few thousand, a few million, and 2 billion years, all the evidence we have is cross referenced and compared. And it all seems to be consistent.

• Natural reactors are a very important point. There are a couple of people (namely John Webb) who think they've found astronomical evidence of spatial variation in the fine structure constant from telescope data, implying that it's changed throughout the life of the universe. Oklo is one of the things that makes this doubtful – llama Oct 25 '19 at 20:39
• It's the Dirac large number hypothesis. The Oklo reactors are roughly 2 billion years old. The cosmological ideas extend to something like 14 billion years. The crucial thing is the fraction of the age of the universe, specifically, the fraction between the big bang and the event you are looking at. The variation in things like the fine structure are thought to have occurred possibly a few million years after the big bang, and so from our era, a minute fraction of the age of the universe. So, interestingly, the Oklo reactors don't preclude something going on that early. – puppetsock Oct 28 '19 at 13:59

Tree ring sequences extend back further than 7000 years. A tree ring sequence for an area is derived from a series of pieces of wood whose growth periods overlapped.

C14 dating has to be calibrated to account for changes in isotope ratios in the atmosphere. That can be done, for the time range in question, by measuring the carbon isotope ratio in a piece of wood whose age has been determined from tree rings.

For purposes of getting correct dates, it does not matter whether the change in radioactive decay is noticed or not. A sample with the same ratio as a piece of a tree that was felled 7,500 years ago would be dated to 7,500 years ago.

• Running through a half-life calculator a 7,500 year old sample will $^{14}$C date to 38,900 years old if this change occurred. The overlapping rings from BC 5k~9k will look anomalous, and that is a problem for this story. I think this trick can't be done with a precipitous $\lambda$ change. It will have to be more gradual - which makes a new problem... – Vogon Poet Oct 25 '19 at 13:29
• @Patricia Shanahan Actually the oldest known living tree, "Methuselah", is calculated to be "only" 4,851 years old. en.wikipedia.org/wiki/List_of_oldest_trees If you know of older living trees that are 7,000 years old please inform the scientific community of the details. – M. A. Golding Oct 25 '19 at 17:33
• @PatriciaShanahan In response to your comment on my post, here is evidence that I found rather surprising: "As of 2013, the oldest tree-ring measurements in the Northern Hemisphere are a floating sequence extending from about 12,580 to 13,900 years" – Punintended Oct 25 '19 at 19:30
• @M.A.Golding: The tree doesn't necessarily have to be alive anymore, as long as you can accurately estimate when it died. – Mooing Duck Oct 26 '19 at 0:04
• @M.A.Golding: Tree ring sequences do not have to come from the same tree to be connected. At present the longest continuous tree ring sequences go back over 12,000 years in Europe, and about 8,500 years in North America. The problem arises when archaeologists find a piece of wood 10,000 years old according to the tree rings and carbon dating strongly disagrees. – AlexP Oct 28 '19 at 20:53

There are dozens of different radiometric dating methods available using a range of different isotopes

If the half-life of C-14 changed 7000 years ago Carbon would give dating results which were at variance to that of all of the other methods. This would be a puzzle but would not change much in practice. There are also many other non-radiometric methods for dating which can also be used which would corroborate the non C-14 based radiometric dating such as ice core measurements, magnetic measurements across oceanic ridges and mutation change rates in DNA to name but three.

• Can you suggest what trails would be found in methods like DNA mutation rates or ice core samples? Can I assume ice cores would be noncontinuous like tree rings? – Vogon Poet Oct 25 '19 at 16:14
• No, you could not. Dome C cores from Antarctica give a climate record from the present to 800,000 years ago. The West Antarctic Ice Sheet cores, due to high annual accumulation, provides high-resolution data from the present to 62,000 years ago. NorthGRIP in Greenland has single cores from the present to 123,000 years ago, and North Greenland Eemian Project to 128,500 years ago. – Keith Morrison Oct 25 '19 at 22:31

C-14 dates are already problematic because atmospheric C-14 levels have varied over time. While raw C-14 dates always come out in the right order they can be substantially off. In practice we calibrate C-14 dates against tree rings and ice cores, both of which give dates to the exact year for as far back as the data exists.

Nobody would realize C-14 decay rates had changed, they would just assume a change in atmospheric C-14 and look for an astrophysical explanation. A modern paleontologist would not be fooled for a second.

• I assumed this but now I have conflicting answers. When you say "not be fooled" you mean a paleontologist would still accurately determine that a sample which $^{14}$C dates 38,000 years, was actually only 7,500 years old? – Vogon Poet Oct 25 '19 at 16:11
• @VogonPoet What conflicting answers? Everything I see says mostly the same thing--that the correct date would be found anyway by other means. The only thing different about my answer is that I said they would figure the C-14 levels had been different and start looking for why they were different. – Loren Pechtel Oct 25 '19 at 23:15
• You’re saying no one would notice (which would be great) but most others say everything else would point out the change in decay rate. That’s the way I read your post at least – Vogon Poet Oct 25 '19 at 23:17
• @VogonPoet I'm saying they would go for the simpler answer--C-14 levels were lower in the past. That's much more believable than somehow C-14 decay rates changed in the past. – Loren Pechtel Oct 25 '19 at 23:23

Based on your comment as to your goal, no, changing the decay rate of C14 (which would itself require a change in the fundamental nature of the universe) would not by itself have provided a false date range for the Pleistocene, because carbon dating is far from the only method used for dating. Dendrochronology has been mentioned, other radioisotope dating methods. There's ice cores which have been calibrated to tree ring and other dating methods which line up with data from varves from lake deposits, which line up with ashfall from major volcanic eruptions which line up with archeological data...

Carbon-14 ain't going to cut it as an attempted one-size-fits-all explanation.

• Sounds like a lot of plot holes to fill. "By far the most common numerical ages applied to varve sequences are from radiocarbon $^{14}$C dating" - It appears that no carbon dating at all would occur in glacial varves if all $^{14}$C decayed before 10k years ago, unless the glacial varves are also younger than they seem, and their years do not layer in carbon years. Difficult... – Vogon Poet Oct 25 '19 at 16:26
• More generally, there is a lot of cross-checking between different dating methods based on different lines of evidence. – Patricia Shanahan Oct 25 '19 at 16:58

I'm no geologist, but it seems this would be pretty noticeable with technology similar to or more advanced than ours.

Looking at this page, you could corroborate C-14 dating (t-1/2 = 5740 years) with Uranium-Thorium (t-1/2 = 80,000 years) and/or Uranium-Proactinium (t-1/2 = 32,760 years) - if not precisely, at least the rough date. The soft limit of C-14 dating is described as ~70,000 years, which overlaps reasonably well with U-Th and U-Pa

It might take a while for folks to discover this. Apparently U-Pa and U-Th are mainly used in seabed dating, as Pa and Th precipitate out of seawater. If you had a lake that was large and stable enough, you might be able get these data by dredging it, which is quite a bit more accessible than much of the undisturbed seafloor

• OK did I say this correctly? - the C14 today is still 5740 years, we did not see a change. I am arguing that 7,000 years ago, c14 decayed with 100y t-1/2. So any evidence of change would have to be from over 7,000 years ago. And that page is actually the result of that corroboration you talk about. What this change does is make fossils with no carbon look as if they are over 70ka old, but I'm saying they lived only 10,000 years ago, and C14 has changed. Maybe I don't understand exactly what you mean by corroborate. – Vogon Poet Oct 24 '19 at 22:59
• Ahh I see, I'd misunderstood your "100y t-1/2". I think you could still notice this discrepancy, depending on what samples you're able to gather. Something that is 8,000 years old would look 60,000 by C-14 but 8,000 by U-Pa. U-Th might be tricky with this recent of a sample, but you could be verify your general U-Pa assay fidelity with something ~30,000 years old. Regardless, compare a 8,000 year-old sample to a 5,000 year-old one: the C-14 difference will be massive, the U-Pa won't – Punintended Oct 24 '19 at 23:01
• Why organisms? Just look for uranium in carbonaceous rocks, such as certain types of shale. Seafloor sediment or shale at the very top of its strata may be young enough? Again, not a geologist :) – Punintended Oct 24 '19 at 23:48
• Isn't this much too complicated. Why not count tree rings to check C14 dating? – Patricia Shanahan Oct 25 '19 at 1:22
• I'm sort of wondering why you need to go to this whole effort when relatively recent human civilization did overlap with megafauna: the last mammoths on Earth died out about 500 years after the Great Pyramid at Giza was built. It would be a lot easier to postulate a refugium in Siberia then try to change the fundamental nature of the freaking universe. – Keith Morrison Oct 30 '19 at 17:22

There are too many checks and balances behind dating techniques for them to go unnoticed unless ALL of your measurements are messed up. Instead of focusing on carbon dating, let's look at creating the kind of plot point you are looking for based on outcome.

the ramifications are that it’s going to happen again and basic physics we are used to will all be changing. This event is a foreshadowing, but I’m trying not to fly in the face of well-established science too much. I can make the change less dramatic or less abrupt, but one person still has to “figure it out”. Ideally the change can hide in the slop of our recent history.

I think the the answer you are looking for is that time itself speeds up or slows down. This is much harder to trace than a single case of radioactive decay. It affects everything on Earth the same: radioactive decay, tree rings, ice cores, etc. From our perspective, this 7000 years is the same as the last 7000 years even if one technically took a lot longer to happen than the other according to outside observation.

To "see" a change in the speed of time, one must be able to observe a reference point that is moving at a different speed of time. Since all of Earth (and maybe our solar system) is effected, the only place to see this change is in space. We take certain things for granted in astrophysics that actually don't add up like how the the period of rotation on the outside of a galaxy can be the same as the inside whereas inside planets need to move faster for a solar system to work, or how we need to introduce invisible matter & energy into our calculations to make anything add up. Perhaps your physicist can mathematically prove that these things aren't lining up because the local coefficient of time itself is distorted... or better yet, maybe there really IS invisible matter and energy, and he's just the guy to prove it once and for all.

What you need is Dark Matter!

Ughhh... I know, I know, dark-matter is the end all handwavium of science fiction. It's often used to explain the unexplainable in outrageous and down right stupid ways, but in this case, it would actually explain your phenomenon according to accepted sciences.

Dark matter is a source of mass and gravity that we simply have no instruments for measuring. In the presence of gravity, our perception of time slows down; so, if our solar system were to periodically pass through dark matter nebulas, then our experience of time would speed up and slow down accordingly.

As long as our local time distortion stays constant, we would perceive space exactly the same no matter where we look, but if something happened 7000 years ago, then things at 7000 light years would be lensed. Because we can not see it "from the side" we can't tell that it is distorted, but maybe at 7000 light years there is some kind of slight banding in the red-shift, or maybe the apparent density of stars slightly changes, or maybe the change was too gradual to notice; so we just assume the galaxy is stretched out a little bit differently than it really is.

Space as seen from the side:

The shift is so small that instruments are barely sensitive enough to detect it. Every other metric of chronological dating tells your scientist nothing happened 7000 years ago. Other astronomers write off his findings as instrument error or a statistical anomaly. Even your scientist himself might dismiss it at first... until he starts looking into the Planet Nine controversy and realizes that a new dark-matter wave is already affecting the outer reaches of our solar system.

The best part here is that there are already competing and non-verifiable pieces of evidence that something massive is at the edge of our solar system; so, his theory could very believable enter into this stack, be scientifically sound(ish), and also be easily dismissed by other scientists in favor of "more believable" opinions which would work great with your story.

• OK I admit this creates the plot point exactly as intended - thinking Star Trek Voyager Blink of An Eye type time differential. But I do so hate time paradoxes! Oddly my universe does agree with this possibility if you’ve seen my other questions. I’ve used “time breaking” on a small scale, this is now the solar system. Requires much deep thought... – Vogon Poet Oct 25 '19 at 19:58
• @VogonPoet You can speed up or slow down time all you want without creating a paradox as long as you don't try going backwards. This is really no different than the gravitational lensing that happens near major sources of gravity. – Nosajimiki - Reinstate Monica Oct 28 '19 at 14:09
• @VogonPoet A possible explanation of these time shifts occurred to me this morning that I think would really fit the bill of what you are looking for. Updated answer accordingly. – Nosajimiki - Reinstate Monica Oct 30 '19 at 14:53
• I really appreciate the work here and I just finished Split Second by Douglas Richards which uses dark matter and the "quintessence" theory to distort time, much like you did. This does help me with a different question however my question here does require a noticeable change in physics. The fact that "we would perceive space exactly the same no matter where we look" sort of makes my entire crisis vanish. Thanks again tho – Vogon Poet Oct 30 '19 at 15:17

It sounds like you're conflating two questions: (1) "What would the geologic record look like if 14C decay changed 7000 years ago?", and (2) "What evidence might there be that the rate had changed?"

I'll ignore the first question and focus on the second. The only way to detect this sort of change is to see it happening now, which means precision measurements over a sufficiently long period of time (or otherwise accounting for some other indirect effect). These precision measurements aren't easy, and they always have some degree of uncertainty associated with them.

An example is the question of whether radioactive decay rates are affected by neutrino flux, see https://www.sciencedirect.com/science/article/pii/S0969804317303822. This particular article presents evidence that they aren't, but if they were, then this could be an example of an indirect effect. In other words, if you could make up some reason why neutrino flux was higher 7000 years ago, then this could be a reason for a shift in decay rates that would be very hard to measure today. And in any case, the fact that these measurements were made in 2018 tells you that there is room for small, previously unobserved effects that could be consistent with a long-term slowly-varying time-dependence.

By the way, you are right in that we operate on an assumption that the laws of physics do not change as a function of time. The laws may have some time-dependence built into them, but the laws themselves do not change. This assumption does have some supporting evidence, based on observations of galaxies millions of light-years away (which means the events we're observing occurred millions of years ago), but it's still fundamentally an assumption. However, it's one that you do not want to violate. If you did, it would be no different from saying "it's that way because God make it that way". If you go that route then you may as well throw up your hands and give up on science altogether, because science can no longer be used to predict anything. So to the degree that science works, that assumption holds.

• OK I genuinely did not see those as different. Reading... – Vogon Poet Oct 25 '19 at 19:36
• OK, good points. But you’re asking me to fundamentally change radioactive decay into a causal event which can be influenced by some trigger, such as antineutrinos. That has vast ramifications and the whole universe changes if there were some actual method to control a half-life. Antineutrinos are a wonderful scapegoat because we would never see it happening, however I’m not ready to invalidate atomic clocks, which invalidates every test of general relativity we’ve ever made LOL! In universe, $\lambda$ remains a mystery - it just changed. – Vogon Poet Oct 25 '19 at 19:46
• Radioactive decay is already a causal event. It's caused by weak nuclear interactions (which is one of the 4 fundamental forces: electromagnetic, strong nuclear, weak nuclear, and gravity). So what you're really asking is whether something can affect the weak force. Current theories say no, and all experimental evidence also says no. But one could potentially modify the theory to get a small dependence on something. The only way to test that is precision measurements of carbon half-life. And btw, don't confuse relativity (i.e., gravity) with weak interactions - they're very different. – Richter65 Oct 28 '19 at 15:07
• ? What do you know that your not telling us? The radioactive decay of any atom is completely random. It is also spontaneous by definition. If your saying it is also causal, then whatever cause it has violates the general theory of relativity (because the cause for a spontaneous event must travel faster than the speed of light). How can an event simultaneously be completely random and causal and spontaneous?? Mind. Blown. – Vogon Poet Oct 28 '19 at 15:37
• I think what you mean is that the weak force allows radioactive decay, rather than causes it. In other words, radioactive decay could not happen within the standard model of particle physics unless some new force existed. We gave this force the name weak force, but the force itself doesn’t cause anything. It fills a hole in our math so whatever makes decay work doesn’t violate the standard model. The decay itself is still a random event. – Vogon Poet Oct 28 '19 at 15:56

There seems to be a lot of confusion and misunderstandings in the comments, so I thought a brief description of radioactive decay may be worthwhile. My goal is to explain how radioactive decay is tied to the fundamental laws of physics.

I'll start with a (very) brief description of the Standard Model of Particle Physics, which represents our best current understanding of matter and forces. In the Standard Model, there are 12 fundamental particles: six quarks and six leptons. The quarks are what make up nuclear matter; in particular, the two lowest-energy (and therefore stable) quarks are called up ($$u$$) and down ($$d$$). Similarly, the two stable leptons are electrons ($$e$$) and electron neutrinos ($$\nu_e$$). Each particle has an associated anti-particle which has opposite charge and opposite "lepton number" (for leptons) or "baryon number" (for quarks), but everything else is the same. The anti-particle of an electron is called a positron, and the anti-particle of a neutrino is imaginatively called an anti-neutrino. An interesting property of anti-particles is that, mathematically, they are equivalent to regular particles going backwards in time.

A proton is made up of $$uud$$ (each up quark has charge +2/3; each down quark has a charge -1/3). A neutron is made up of $$udd$$.

Of the four fundamental forces in the universe (electromagnetic, strong nuclear, weak nuclear, and gravity) the Standard Model talks about the first three and ignores gravity. Gravity, by the way, is described by General Relativity, which is a non-quantum theory that is fundamentally different from any quantum field theories such as those that form the basis of the Standard Model. In the Standard Model, the three forces are mediated (or, in a sense, caused or described by) by an exchange of a particle called a (vector) boson. Each of the forces has its own set of associated vector bosons:

• The electromagnetic force has one associated boson, called a photon. Photons only interact with electrically charged particles.
• The weak force has three bosons: $$W^+$$, $$W^-$$, and $$Z$$. These interact with all particles.
• The strong force has eight bosons, collectively called gluons. These only interact with quarks.

So, for example, an electromagnetic interaction happens when a photon is exchanged between two charged particles. Likewise, a weak interaction happens when a W or Z is exchanged between two particles. However, Weak interactions are a bit different in that, uniquely among all forces/interactions, they can change a particle from one type to another. So if a particle emits or absorbs a W boson, it will become a different type of particle.

For radioactivity, the most important example is a process called beta decay (https://en.wikipedia.org/wiki/Beta_decay), in which a down quark emits a $$W^-$$ boson and becomes an up quark; the $$W^-$$ then decays to an electron and an anti-neutrino. Equivalently, you can say the $$W^-$$ mediates a weak interaction between a $$u$$/$$d$$ and a $$\nu_e$$/$$e$$. There's also a variant in which a proton becomes a neutron via $$u \to d \,\nu_e \, e^+$$ mediated by a $$W^+$$ exchange. (The former is called $$\beta^-$$, and the latter $$\beta^+$$). The relevant Feynman diagram for $$\beta^-$$ decay is:

In the most general terms, radioactive decay is governed by all three forces in the Standard Model: strong nuclear, weak nuclear, and electromagnetic interactions. To quote the Wikipedia page (https://en.wikipedia.org/wiki/Radioactive_decay), "the combined effects of these forces produces a number of different phenomena in which energy may be released by rearrangement of particles in the nucleus, or else the change of one type of particle into others." However, for most unstable nuclei, beta decay is the most common cause of radioactivity.

This is what happens inside Carbon 14. Via beta decay, one of the neutrons in the nucleus becomes a proton (and therefore the carbon atom turns into a nitrogen atom), emitting an electron and anti-neutrino from the $$W^-$$ decay. The half-life is determined by strength of the weak force interaction, which is a function of the nucleons and their energy states. In principle, you could write down the Lagrangian and determine the half-life; in practice, this tends to be measured experimentally.

So if the half-life of carbon 14 were to change, it would mean some addition to the theory, i.e., you would have to add additional terms to the Lagrangian. This is not impossible -- there are many Beyond-the-Standard-Model theories that predict all sorts of changes, but the changes would have to be very subtle so as to have been missed all this time.

Edit

The process of actually calculating a half-life from first principles involves quantum field theory, which is too complex to fully explain here. However, I can explain some of the language that is used (with the perspective of someone with a particle physics background, however, rather than a nuclear physics background). Wikipedia links are included where appropriate.

In the language of QFT, radioactive beta ($$\beta^-$$) decay is a transition from an initial state ($$udd$$) to a final state ($$uud + e^- + \bar{\nu_e}$$). To calculate the transition rate (or half-life), we need to calculate the transition amplitude, which gives the probability of the transition between those two states. More specifically, we're interested in the S-matrix element, which is the transition amplitude from time $$t=-\infty$$ to $$t=+\infty$$. S-matrix elements are often expressed and visualized using Feynman diagrams. The transition rate can be calculated from the S-matrix element using a formula known as Fermi's Golden Rule.

Of course, for nuclear beta decay, the matrix element calculation isn't as simple as it is for free particles. There are complex nucleon-nucleon interactions that strongly affect the transition amplitude; these have to be modeled and accounted for in the QFT Lagrangian. Nuclear physicists have done this with good results, but it remains an area of active research (especially for isotopes far from stability). By the way, that same Lagrangian is where you would introduce any other interactions that might affect the half-life.

• I’m fairly certain that half lives can not be predicted at all from first principles and I would be interested in any link you can provide suggesting a Lagrangian (or did you mean Euler-Lagrangian) equation can successfully predict any nuclear isotope half-life using first principles. I am fairly certain from my own studies that the $\lambda$ of any radioisotope is itself an ab initio characteristic of that element. This post would benefit from a reference if you have one. – Vogon Poet Oct 28 '19 at 20:28
• Of course you can predict decay rates. That's what quantum field theory does: calculates transition amplitudes from an initial to final state. That's why people like Feynman diagrams; they're a visual representation of the S-matrix element. Complications arise for nucleons inside the nucleus, which is a bit outside my expertise, but a Google search reveals a mechanism known as pn-QPRA, explained in int.washington.edu/talks/WorkShops/int_06_2b/People/Vretenar_D/…, with some example results (that I haven't read) in doi.org/10.1016/0370-2693(88)91202-6 – Richter65 Oct 29 '19 at 3:56
• So bottom line you disagree with the determination that radioactive decay is spontaneous. OK. – Vogon Poet Oct 29 '19 at 4:12
• I don't know what you mean by "spontaneous". I think of it as a random variable (as in en.wikipedia.org/wiki/Random_variable), with a probability distribution that is obtained from quantum field theory calculations. In that sense, it's "randomness" is no different from any other observable in quantum mechanics. – Richter65 Oct 29 '19 at 18:34
• "Radioactive decay is the spontaneous breakdown of an atomic nucleus resulting in the release of energy and matter." This means that nothing in this universe causes it; it happens completely by itself. It is not on a timer, or hit by anything, or pushed out by some force. It has no cause. And it is random. – Vogon Poet Oct 29 '19 at 20:11