lpetrich

One argument against radioisotope dating is that how can really know what their decay rates were in the past. However, here is an argument that suggests otherwise:

Relative rates of radioactive decay are constant to within experimental error, even for the oldest rocks. This is because some rocks can be dated using more than one radioisotope, and such ages have a tendency to agree. Different decay rates would produce systematic discrepancies between different isotopes' ages, which is not observed.

There are two main decay modes utilized in this work, alpha and beta decay, which have different sensitivites to physical constants.

Alpha decay proceeds by quantum-mechanical tunneling; if one follows the helium-4 nucleus back to the nucleus, it will stop outside, because of electrostatic repulsion. To go the rest of the way, it must act like a wave, tunneling through that potential until it reaches the nucleus. Spotaneous nuclear fission is closely related, and proceeds by the same mechanism.

To lowest approximation, the decay rate

r ~ r0*exp(-T)

where r0 is 1/(nucleus crossing time) and T = 2*pi*sqrt(2*m/E)*(Z1*Z2*alpha),

where alpha = e^2, the fine-structure constant, Z1 and Z2 are the (relative) electric charges of the nuclei, m is the reduced mass of the two nuclei or (A1*A2*mn)/(A1 + A2) -- slightless than that of a helium nucleus, E is the energy released by the decay, and (hbar = c = 1) units were used.

This is clearly very sensitive to changes in parameter values such as nuclear energy levels.

Beta decay proceeds by a different mechanism. A neutron in a nucleus produces a virtual W- particle that lasts for 10^-25 seconds before it becomes an electron and an antineutrino. Likewise, a proton can produce a neutron and a short-lived W+ particle that becomes a positron (antielectron) and an (ordinary) neutrino. Also, that W+ can combine with a nearby electron, producing a neutrino and an electron capture, the main "slow" beta-decay process.

For E (decay) much greater than me (electron mass), the beta decay rate is

r ~ Gf^2 * E^5

For E - me much less than me (electron comes off nonrelativistically),

r ~ Gf^2 * E^2*sqrt(me*E)^3

For electron capture,

r ~ Gf^2 * N * E^2

where N is the number density of atomic electrons at the nucleus. It is approximately (Z/a0)^3, where a0 is the Bohr radius, 1/(me*alpha), and Z is the relative charge of the nucleus. The constant Gf is the Fermi weak-decay constant, and is related to the mechanism that produces W and Z masses.

Beta-decay rates are also sensitive to fundamental-constant changes, but their sensitivities are different from alpha-decay sensitivities.

The next question is nucleus energies -- what fundamental constants are they dependent on. If alpha = 0 (no electromagnetic force) and up and down quarks had small and equal mass, then nucleons and nuclei would still exist and be massive, mostly due to the quantum-chromodynamic interaction between the quarks (QCD), which has a well-defined energy scale. QCD has the odd property that its counterpart of alpha, the fine-structure constant, gets smaller for higher-energy interactions; for low-energy ones, it gets large, leading to quark confinement.

Now add the odd fact that down quarks are heavier than up quarks, and also add electromagnetic interactions. The up-down mass difference makes neutrons (udd) more massive than protons (uud), while the protons' electrostatic repulsion increases the mass/energy of a collection of them. These effects influence the amount of energy available for radioactive decay, with beta decay being especially influenced by the up/down mass difference.

So one could work out the changes in various fundamental physical constants from variations in radioactive-decay rates over time -- if nonzero variations were observed. But they are not.

[ April 27, 2002: Message edited by: lpetrich ]</p>

lpetrich

I hope that my decay-rate formulas had not gone over too many people's heads; however, they do illustrate why one would not expect different decay rates to change by the same relative amounts if fundamental constants change.

But here is an indirect piece of evidence: continental-drift rates. One can measure these rates at the present day with techniques like VLBI (Very Long Baseline Interferometry radio astronomy) and GPS (Global Positioning Satellites), and compare with rates deduced over the past few million years -- rates calibrated with radioisotope dating of rocks formed in that time.

One finds very good agreement, suggesting that radioactive-decay rates have not changed.

wdog

Ip,

The creationists also have used the argument that since life in the universe is dependent on some very finely tuned physical constants, that proves that god created it. then they turn around and say that these constants could have changed in the past to produce different decay rates,....hmmm,.... can you see a problem?

I liked your post, thanks

btw, do you work at lawrence livermore?

[ April 27, 2002: Message edited by: Optics Guy ]</p>

RufusAtticus

In my experience, most "profesional" creationists stick to one or the other.

However, the little misguided lambs have a harder time staying consistent.

-RvFvS

lpetrich

Interesting discrepancy. I think that this fine-tuning question deserves further comment, however.

And yes, I do work at LLNL, but I don't like to talk about that or what I do there.

wdog

Ip,

ok, I understand about remaining anonymous.

rufus,

I didn't know that. Are you elevating creationism to a 'profession'?

Coragyps

Hovind, Ham, and Morris certainly seem to be making a living off it - but I will stop short of comparing it to the "world's oldest profession."

Re variation in decay rates: I am in a discussion with some young goober on another board who dug up the following "facts" in his websurfing:
* Beryllium-10 decay rates (by electron capture) have been observed to vary by as much as 1.5%
* This means that they might vary by 40%
* Therefore, all radiometric dating is a fraud.
And this from a person who claimed that the isochron method was flawed because you couldn't be sure how fast those isochrons decayed.

lpetrich

Actually, there is a reason why such variations can happen -- the electron-capture rate is proportional to the number of density of electrons at the nucleus, and that can change when an atom gets into a different chemical combination. Thus, when beryllium combines with oxygen to make BeO, its two outer electrons tend to get attracted to the oxygen atom, lowering the electron density at the beryllium nuclei.

So do such results include what chemical states the beryllium was in when it was measured?

However, it is only the outer valence electrons that tend to be lost or added, and these do not contribute as much to the nucleus's electron density as the inner-shell electrons do, especially the innermost or K-shell electrons (about ~ Z^3 * valence-electron density).

For these reasons, one expects very little effect on the decay rate of potassium-40 and other long-lived electron capturers. First, the density of K-shell electrons is much greater than that of valence-shell ones, and second, the atoms are often in the same chemical state all the time, usually being oxidized (tending to lose some valence electrons; potassium loses its one valence electron).

Here's a nice URL: <a href="http://math.ucr.edu/home/baez/physics/ParticleAndNuclear/decay_rates.html" target="_blank">http://math.ucr.edu/home/baez/physics/ParticleAndNuclear/decay_rates.html</a>

Coragyps

Thanks for the info and links, lpetrich.
Beryllium only occurs in the +2 state in the lithosphere, anyway, so I seriously doubt that it's worth worrying about WRT dating anyway.

lpetrich

Here's another page on the subject of electron capture: <a href="http://www.talkorigins.org/origins/postmonth/mar01.html" target="_blank">http://www.talkorigins.org/origins/postmonth/mar01.html</a>

And here's a collection of isotope data: <a href="http://isotopes.lbl.gov/education/isotopes.htm" target="_blank">http://isotopes.lbl.gov/education/isotopes.htm</a>

As to pressure effects, they've only been noticed for beryllium-7, most likely because its innermost electron wavefunctions are relatively easy to squeeze, because of the beryllium nucleus having charge 4. One can estimate the properties of atom K-shells by assuming that the other atom electrons do not exist, resulting in a hydrogenlike atom; the typical pressure of the K-shell electrons increases as Z^5 (Z^2 for the energy, one Z each for the space dimension, since pressure ~ energy density).

I've been unable to track down which way the Be-7 pressure effect went -- I expect that the decay rate would increase with increasing pressure and decreasing volume.

So under pressures that are likely in the Earth's crust and upper mantle (up to a few hundred kilobars), K-40 atoms' decay rates are not likely to change by any noticeable amount.