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Author Topic:   Spontaneous fission, decay rates, and critical mass
NoNukes
Inactive Member


Message 4 of 29 (647196)
01-08-2012 1:09 PM
Reply to: Message 1 by DWIII
01-08-2012 6:28 AM


That's just about right...
Thanks for doing the work for starting this thread.

I have a nit to pick with one statement in the OP.

The statements "You can't affect decay rates without affecting fission decay" and "When you reduce the nuclear binding energy or lower the barrier for radioactive decay to occur, and reduce the decay rate, you would increase the occurrence of all forms of radioactive decay, including fission" and "the critical mass required to reach a sustained reaction is reduced" collectively imply some sort of correlation between decay rates and critical mass.

I don't think the statements have the implication stated above. I am willing to accept that lowering the barrier for decay will have an affect on the spontaneous fission rate. But accepting that hypothesis does not imply a correlation between decay rates and critical mass.

I'd also question the relevance of your plutonium evidence. A Pu 238 nucleus behaves very differently in nuclear reactions from a Pu 239 nucleus. Comparing isotopes may not be a good indicator of what would happen if the binding energy for a particular nucleus were to be supernaturally reduced.

But you have accurately capturing my position on the matter.


Under a government which imprisons any unjustly, the true place for a just man is also in prison. The proper place to-day, the only place which Massachusetts has provided for her freer and less desponding spirits, is in her prisons, to be put out and locked out of the State by her own act, as they have already put themselves out by their principles. Thoreau: Civil Disobedience (1846)

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 Message 1 by DWIII, posted 01-08-2012 6:28 AM DWIII has responded

Replies to this message:
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NoNukes
Inactive Member


Message 5 of 29 (647200)
01-08-2012 1:51 PM
Reply to: Message 3 by RAZD
01-08-2012 8:48 AM


Re: Decay rates, change, and atomic stability
Because the atoms are less stable (to allow the increased decay rate) they are more susceptible to fission, and have a lower threshold to energy increases that result in induced fission.

No one disputes that the spontaneous fission rate would increase.

But essentially every low energy neutron (upwards of 96 per cent) captured by a U235 atom already produces an induced fission. There simply isn't much room for improvement in this area. In the six factor formula, this ratio is wrapped up into "eta" which is the neutron yield per captured neutron.

Thus lower energy neutrons would induce fission rather than just be absorbed (as often happens today), AND induced fission would release more neutrons than now (an "average of 2.52 for U-235, and 2.95 for Pu-239" today)

I note that this is the first time you have made this argument. Most (if not all) of your previous arguments haven't dealt with chain reactions. We are at last on the same page.

As I argued above, it is not true that absorption of a thermal neutron in U235 often fails to produce fission. Fast neutrons, on the other hand have a lowered probability of being captured by a U235 nucleus. I'm curious to see what use you make of this information.

I am aware of no good reason why the products from fission would necessarily include more neutrons simply because the binding energy changes.

A typical split of a U235 atom yields two big roughly equal sized fragments, with some alpha particles and some neutrons and a bunch of energy in the form of gamma rays and kinetic energy of the fragments. I will accept the values you provide as average values for the produced neutrons. But who knows what the mix might be if we introduce supernatural meddling? More alphas? More neutrons? Slightly bigger fragments and fewer neutrons? Slightly more energy per fission than before with the same fission products? A lower percentage of neutron pre-cursors among the fission products reducing the number of delayed neutrons produced so that keff is actually lowered rather than increased?

I'll admit that I don't know enough atomic physics to speculate. But I do know enough to be skeptical. I can suggest that it is not inevitable that more neutrons would be produced per fission. But I'd welcome your explanation of why there is likely to be more neutrons produced.

... neglecting for now that this could result in 238U and other elements being able to support a chain reaction, the inevitable result is that smaller critical mass would be the case.

You haven't established an inevitable result for at least the reasons I've discussed above. I don't dispute that changing the nuclear binding energy might make other nuclei capable of sustaining a chain reaction, but I don't see the link to your conclusion of more neutrons from U235.

Finally I ask, how do we change properties of atomic nuclei without PFM?

Edited by NoNukes, : Change fusion to fission. Minor corrections.

Edited by NoNukes, : Fusion ain't fission, sigh.


Under a government which imprisons any unjustly, the true place for a just man is also in prison. The proper place to-day, the only place which Massachusetts has provided for her freer and less desponding spirits, is in her prisons, to be put out and locked out of the State by her own act, as they have already put themselves out by their principles. Thoreau: Civil Disobedience (1846)

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NoNukes
Inactive Member


Message 8 of 29 (647233)
01-08-2012 6:59 PM
Reply to: Message 6 by foreveryoung
01-08-2012 3:39 PM


Does anybody know what factors determine how fast or slow any particular unstable isotope decays?

I'd like to clarify what types of comparisons you are asking about.

Are you referring to nuclear factors that determine why one isotope of oxygen is stable or long lived while another isotope of oxygen has a short decay half life, and a third isotope has a long decay half-life ?

Or are you referring to factors that might affect the decay rate of a particular isotope such as K40 or Carbon 14?


Under a government which imprisons any unjustly, the true place for a just man is also in prison. The proper place to-day, the only place which Massachusetts has provided for her freer and less desponding spirits, is in her prisons, to be put out and locked out of the State by her own act, as they have already put themselves out by their principles. Thoreau: Civil Disobedience (1846)

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 Message 6 by foreveryoung, posted 01-08-2012 3:39 PM foreveryoung has responded

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NoNukes
Inactive Member


(1)
Message 11 of 29 (647284)
01-08-2012 11:54 PM
Reply to: Message 10 by RAZD
01-08-2012 9:12 PM


Re: Decay rates, change, and atomic stability
But even a 1% increase would cause more induced fission than now would it not? This would translate to less critical mass needed to achieve a sustained chain reaction would it not?

I agree that such a change might have the effect you describe, but maybe not. When a U235 nucleus absorbs a neutron and forms U236, the U236 nucleus may either fission or emit a gamma ray. If we lowered the binding energy, why wouldn't the gamma ray emission probability be increased?

What we can say for sure is that an enormous increase in the decay rate could correspond to only a tiny effect on criticality through this mechanism. Surely this effect cannot be used to demonstrate that no rapid decay occurred in the past because of the lack of more natural reactors.

Compared with the other effects that are postulated to have resulted in the natural reactors at Oklo going critical, the theoretical maximum contribution to keff from increasing the probability that a captured thermal neutron will cause fission is quite small, making it impossible to say that we would have seen more such natural reactors if the creationists were right.

For example this effect could not overcome the changes in enrichment that make it impossible for a natural critical reactor to form today. Consider that immersing a mass of U235 in ordinary water produces a substantial increase in reactivity.

That this is why the occurrence of spontaneous fission would increase, not just decay events, yes?

Spontaneous fission is very like decay. I am supposing that the rate of spontaneous fission increases for reasons very similar to the reasons why K40 decay would increase. But many of the other events that effect a chain reaction are quite dissimilar to decay. I believe it is necessary to make an independent case for each effect that dialing down the binding energy of nuclei results in the effect in a helpful direction. One method for doing this would be to look at the effect on each of the six factors in the keff formula. (Where keff is the ration between neutrons populatin in a generation and the neutron population in the previous generation. keff=1 means a critical reactor). For example, what would you expect would be the effect on the probability of absorption of a neutron in some material other that U235. If that probability were to increase then the margin below criticality (or negative reactivity) would increase.

With increased decay rates and atomic stability it would seem highly likely that the numbers of alpha particles (bound by the same laws and forces as the ones involved in alpha decay events, after all) would increase in number in these events as well.

Give me an argument for the above.

Coincidentally, I had to tutor a high school student on nuclear reactions including fission this afternoon. It turns out that fission fairly rarely produces alpha particles directly. However, I think this is actually a side issue. With respect to sustaining a chain reaction, the important fission products are neutrons, and the production of those particular fission fragments that beta decay to produce neutron emitters.

The reduced stability of the atoms necessary to achieve a reduction in decay rate would affect this proportion and logically result in more neutrons than we see today.

Maybe. But perhaps fewer neutrons might be produced than we see today. My gut feeling is that there would be no significant effect, but I'm not professing to know the answer.

Would you not agree that a slight shift in the proportions of these events, that raised the average number, say by 1% (+0.03 neutrons on average), would cause more induced fission than now, yes? And this would translate to less critical mass needed to achieve a sustained chain reaction would it not?

Yes, if this were the only effect. And maybe the effect is even larger than you postulate. But you need to give me a reason to believe that the effect would occur, and be in the direction you say. I still maintain that I haven't yet seen an argument that a higher average number of neutrons would be produced from fission.

Edited by NoNukes, : Discuss 236


Under a government which imprisons any unjustly, the true place for a just man is also in prison. The proper place to-day, the only place which Massachusetts has provided for her freer and less desponding spirits, is in her prisons, to be put out and locked out of the State by her own act, as they have already put themselves out by their principles. Thoreau: Civil Disobedience (1846)

This message is a reply to:
 Message 10 by RAZD, posted 01-08-2012 9:12 PM RAZD has responded

Replies to this message:
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NoNukes
Inactive Member


(1)
Message 12 of 29 (647285)
01-09-2012 12:33 AM
Reply to: Message 9 by foreveryoung
01-08-2012 8:37 PM


Off topic.
I'll join you in that radioactive decay thread.

Under a government which imprisons any unjustly, the true place for a just man is also in prison. The proper place to-day, the only place which Massachusetts has provided for her freer and less desponding spirits, is in her prisons, to be put out and locked out of the State by her own act, as they have already put themselves out by their principles. Thoreau: Civil Disobedience (1846)

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NoNukes
Inactive Member


(1)
Message 14 of 29 (647348)
01-09-2012 11:21 AM
Reply to: Message 13 by DWIII
01-09-2012 10:28 AM


Re: Decay rates, change, and atomic stability
Again, for all we know, the specifics of neutron emission rates via fission (such as average number of neutrons released, and/or the energy spectrum of those neutrons, not even to mention rates of subsequent neutron absorption and/or rates of subsequent induced fissioning) may very well be extremely sensitive to small changes in overall nuclear stability, and not always in the same directions.

Another way to frame this idea.

Fission of U235 can be thought of as not a single specific reaction but as a large set of competing reactions with products varying in both the number of neutrons released, and in the exact fission fragments produced. The distribution of fission fragments for fission of U235 looks like the illustration below:

Even if we accept that decreasing the binding energy makes fission of U235 easier, how can we say that a particular fission product result is favored since the different possible outcomes compete with one another? And if we cannot answer that question, then we cannot say whether on average more or fewer neutrons would be released per fission.

We also know that certain fission fragments (such as Xe135) are strong neutron absorbing nuclei which compete with U235 in absorbing neutrons, while other fission products release delayed neutrons after beta-decay. How can we predict whether reducing U235 binding energy will favor or disfavor producing chain reaction poisoning or neutron creating fission products?

Edited by NoNukes, : No reason given.


Under a government which imprisons any unjustly, the true place for a just man is also in prison. The proper place to-day, the only place which Massachusetts has provided for her freer and less desponding spirits, is in her prisons, to be put out and locked out of the State by her own act, as they have already put themselves out by their principles. Thoreau: Civil Disobedience (1846)

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NoNukes
Inactive Member


Message 16 of 29 (647496)
01-10-2012 12:29 AM
Reply to: Message 15 by RAZD
01-09-2012 1:57 PM


Re: Decay rates, change, and atomic stability
I don't think it would be the case of one or the other, but both would be affected. If the number of absorptions increases then both more fission and more gamma ray emission could occur, and quite possibly in the same ratio.

If both increased in the same ration, there would be no effect on k. It would mean that the lifetime of a generation of neutrons is shorter, but that would not affect criticality.

Curiously, when we are talking about changing the age of the earth from 4.55 billion years to 10,000 years we are talking about an enormous increase in the decay rate, yes?

Yes, but we are discussing a parameter (fraction of neutrons absorbed by U235 that result in fission) that is already fairly close to 1, and which cannot increase above 1.

Or it could correspond to a significant effect. You need to show why you think there would only be a small effect, yes?

I think I just did. I'm pretty sure that I made the same argument in a previous post.

If the binding energy holding alpha particles is reduced to allow more rapid decay, then it is also reduced for holding alpha particles within a nucleus, and they are more likely to be released under impact.

I don't see a reason to chase this down. Creating more alpha particles does not give us more neutrons. It might even result in fewer neutrons because alpha particles are such a stable and preferred arrangement. I've also argued that changing the fission product mix can produce results that lower criticality even if more neutrons are produced directly from fission. (See comments on Xe135 and neutron pre-cursors).

ZD writes:

NN writes:

... Surely this effect cannot be used to demonstrate that no rapid decay occurred in the past because of the lack of more natural reactors.


We have evidence of several natural reactors in Oklo, so the question is not whether natural reactors could form, but the number of reactors that could form and the number that should form under reduced binding energy that would allow faster decay to occur.

Didn't I argue exactly that point? My point is that the contribution, if any, from affecting the number of captured neutrons that cause fission is far less than the other sources of positive reactivity that we believe contributed to the forming of natural reactors, such that we cannot say that there should be more natural reactors than we currently find if the binding energy were lowered in the past.


We can start with η, the production factor

η = υ•σFf/σFa
where
υ = the average number of neutrons produced per fission in the medium
σFf = the microscopic fission cross section
σFa = the microscopic absorption cross section

If we start here, we aren't going to get very far. We currently disagree on how u is affected. I have been arguing that the effect on the cross section ratio must be small given that the ratio is already close to 1 and cannot exceed 1.

Interestingly, the wiki table here lists 2.43 for the average number of neutrons produced per fission in Uranium-235, where previously we had 2.52.

Actually I cited 2.4+.


Under a government which imprisons any unjustly, the true place for a just man is also in prison. The proper place to-day, the only place which Massachusetts has provided for her freer and less desponding spirits, is in her prisons, to be put out and locked out of the State by her own act, as they have already put themselves out by their principles. Thoreau: Civil Disobedience (1846)

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NoNukes
Inactive Member


Message 19 of 29 (647784)
01-11-2012 10:02 AM
Reply to: Message 18 by RAZD
01-10-2012 7:23 PM


Re: Decay rates, change, and atomic stability
I think we can agree though, that IF ν increased - and nothing else occurred - that THEN the scenario I have proposed for decreased critical mass and more frequent occurrence of natural reactors should result, yes? If it doubled it would have a significant effect, yes?

Absolutely. Increasing u has the potential for being a highly significant effect.

Zen Deist writes:

NN writes:

Yes, but we are discussing a parameter (fraction of neutrons absorbed by U235 that result in fission) that is already fairly close to 1, and which cannot increase above 1.


Is this is the f factor, the thermal utilization factor (the probability that a neutron that gets absorbed does so in the fuel material, with typical values 0.71, 0.799), that you are talking about?

No. Here I was still talking about the cross section ratio in the equation for η.

Now it should be evident that this would have a maximum value of 1 (ie everything is fuel), so a maximum effect would be on the order of ~20% increase in fission or reduction in critical mass. We can agree that this would not be significant, yes?

I don't think we can make that assumption. The cross section ratio in the η formula is for a single material, U235 and is primarily a characteristic of U235 alone. In contrast, cross section ratio in the formula for f depends on the relative amounts of all absorbing materials in the reactor. In a commercial operating nuclear reactor a typical value might be .8, but in a natural mix of materials, f might be any value less than or equal to 1. This factor is one of the parameters through which lowered enrichment makes it impossible for a natural U235 reactor to form today.

Further, the neutron absorption reaction is nothing like a decay reaction. I don't think Gamow's formula would help us predict how absorption rates would be affected by the change in energy. Similarly the factor p is also difficult to analyze.

I did take a look at Gamow's formulas, and I thought I would say something about the variables involved.

The Z values are the number of units of charge on a particle, and in the formula Zalpha = 2, and ZD is the number of protons in the decaying nucleus.

ε0, is the permittivity of free space, which is a constant.
http://en.wikipedia.org/wiki/Vacuum_permittivity. A dependency on the speed of light might be introduced via this constant.

R and b are constant distances used to parametricize the potential felt by an alpha particle escaping the nucleus. I have no idea how to calculate R but it must be on the order of the size of the nucleus. Gamow gives a relation for b.

I think the remaining variables in the equations are pretty straight forward. In the end, Gamow lumps all of the constants and gives a pretty simply relation between binding energy and the decay constant.


Under a government which imprisons any unjustly, the true place for a just man is also in prison. The proper place to-day, the only place which Massachusetts has provided for her freer and less desponding spirits, is in her prisons, to be put out and locked out of the State by her own act, as they have already put themselves out by their principles. Thoreau: Civil Disobedience (1846)

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NoNukes
Inactive Member


(1)
Message 21 of 29 (647862)
01-11-2012 4:34 PM
Reply to: Message 20 by RAZD
01-11-2012 3:45 PM


Re: Decay rates, change, and atomic stability
Greetings Zen Deist,

Zen Deist writes:

So that is A possibility to investigate further.

Yes. It is likely to be the most important one.

Zen Deist writes:

Wouldn't R be the nucleus\charge radius?

Gamow models the potential acting on an alpha particle leaving the nucleus as a square potential well up to radius R and a coulombic (eletrostatic) potential outside of that distance. So R is related to the distance over which a nuclear attractive force holds a nucleon in place. I think it is likely that R is related to the radius of the nucleus or the number of nucleons in the nucleus in some complex way. I don't know if it is worth the effort to investigate it any further than that.

Just in simple terms (1/0.8) = 1.25, or a 25% increase possible if ALL the material were included. This would not be a significant increase to the overall fission equation, correct?

IMO, that proposition is not correct. There is no reason to expect that the f cannot decrease to zero or that f is nominally 0.8 in a natural critical reactor. The value of f varies strongly and directly with the enrichment ratio and indirectly with the amount of reactivity poisons. The argument used to limit excursions of the cross section ratio in η does NOT apply to f.

So can we assume that the f factor would not be affected by the YEC factor?

I think that's a good first guess. At this point, if I were to propose a negative effect or an uncertain effect, I think I'd owe you an explanation. I think factor "p" is likely to be a different story. I'm still considering my position on "p".

Some of the factors in the keff formula can be greater than one, although that possibility does not apply to the factors we've discussed so far absent some pretty funky mechanisms.

ABE
oops. the reproduction factor in a critical reactor is of course greater than 1.

Edited by NoNukes, : No reason given.

Edited by NoNukes, : No reason given.


Under a government which imprisons any unjustly, the true place for a just man is also in prison. The proper place to-day, the only place which Massachusetts has provided for her freer and less desponding spirits, is in her prisons, to be put out and locked out of the State by her own act, as they have already put themselves out by their principles. Thoreau: Civil Disobedience (1846)

This message is a reply to:
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NoNukes
Inactive Member


(1)
Message 22 of 29 (647984)
01-12-2012 1:04 PM
Reply to: Message 20 by RAZD
01-11-2012 3:45 PM


More thoughts about Gamow's equations or "When nuclides decay"
I was doing some more thinking about Gamow's derivation, and I think that we cannot say that his result applies to situations where uncharged particles are emitted from a nucleus, or where the nucleus that does not remain largely intact.

As previously discussed Gamow models the potential which the emitted particle as a combination of a square well potential and a coulombic field. A neutron, having no charge is not affected by coulombic forces. I doubt that it is appropriate to simply substitute zero into the equations for Zalpha, but doing so result in there being no binding energy dependency on the decay constant.

Secondly, if the nucleus splits or becomes significantly smaller during decay then the characterization of the nucleon attractive force using R and Zd from the original nucleus would seem to be entirely inappropriate.

Let's consider the application of Gamow's model to nuclear absorption. Neutrons experience essentially no barrier to entering a nucleus. We haven't discussed exactly how the modification of the binding energy is accomplished, but I would expect that all of the energy states of the nucleus are effected. Thus the probably absorption of fast neutrons and the resulting fissions, which includes absorption at resonance peaks based on the energy states of the nucleus is likely to be affected in some way. I have yet to figure out how to characterize this.

Finally, let's take a crude look at a possibility that an increased in the speed of light might have an affect on alpha decay rates. The speed of light is inversely proportional to the square root permittivity of free space. So changing the speed of light could result from a change in permittivity. While the speed of light also depends on the permeability of free space, permeability does not affect the decay constant. I think we can ignore this latter possibility, since we are not trying to claim that halo data proves that the speed of light is constant.

The problem for this hypothesis is that according to Gamow's work, both the decay energy and the decay constant are strongly dependent on the permittivity of free space. This means that changing the permittivity of free space should disturb halo production.

Finally I note that changing the decay rate without changing the decay energy does not seem to be a great way of resolving the issue of what happens to all of that heat when nuclides decay.
One might also ask why someone who believes in a fine tuned universe would make such an argument.

Edited by NoNukes, : One two many "finally"s


Under a government which imprisons any unjustly, the true place for a just man is also in prison. The proper place to-day, the only place which Massachusetts has provided for her freer and less desponding spirits, is in her prisons, to be put out and locked out of the State by her own act, as they have already put themselves out by their principles. Thoreau: Civil Disobedience (1846)

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NoNukes
Inactive Member


Message 24 of 29 (648042)
01-12-2012 7:09 PM
Reply to: Message 23 by RAZD
01-12-2012 5:45 PM


Re: More thoughts about Gamow's equations or "When nuclides decay"
The probability of neutron emission would then be a result of the probability of the particle being a neutron when the time comes to be emitted.

I think this is a rather curious thing to say. I don't think there is a time for a nucleus to emit a neutron.

IF induced fission is unaffected or negatively affected, THEN the decay of materials should be affected by decay disproportionately to the effects of induced fission.

I didn't address this argument. The problem see with the argument is that we need to know the crank that was actually turned so that we can model the change in each nuclide. Was the binding energy of each nuclei changed by a constant factor, decremented by a constant amount, is it possible was some other independent parameter was varied in a consistent way for each atom so that decay rates changed by constant ratios? I am not sure exactly where to start.

I'll ponder this some more, but I won't spend any more time on keff.

Edited by NoNukes, : No reason given.


Under a government which imprisons any unjustly, the true place for a just man is also in prison. The proper place to-day, the only place which Massachusetts has provided for her freer and less desponding spirits, is in her prisons, to be put out and locked out of the State by her own act, as they have already put themselves out by their principles. Thoreau: Civil Disobedience (1846)

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NoNukes
Inactive Member


Message 26 of 29 (648142)
01-13-2012 12:01 PM
Reply to: Message 25 by RAZD
01-12-2012 10:34 PM


Re: More thoughts about Gamow's equations or "When nuclides decay"
Another way would be to calculate the change in binding energy to double the rate, and then see if that makes some fissionable isotopes (238U for instance) become fissile in average concentrations known today.

My point is that once magic is invoked, any and all rules might be broken. I don't see any possible way for binding energy to be changed without some supernatural intervention.


Under a government which imprisons any unjustly, the true place for a just man is also in prison. The proper place to-day, the only place which Massachusetts has provided for her freer and less desponding spirits, is in her prisons, to be put out and locked out of the State by her own act, as they have already put themselves out by their principles. Thoreau: Civil Disobedience (1846)

This message is a reply to:
 Message 25 by RAZD, posted 01-12-2012 10:34 PM RAZD has responded

Replies to this message:
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NoNukes
Inactive Member


Message 28 of 29 (648420)
01-15-2012 4:56 PM
Reply to: Message 27 by RAZD
01-13-2012 9:44 PM


Re: decay energy, the speed of light, the strong force, Uranium haloes and 238U fission
Changing c would be invoking magic, and changing the strong force would be invoking magic. The question is whether or not we can eliminate any "natural" change to c or the strong force in some distant past through the evidence available.

Yes, as best we know. Further, there is no evidence that "c" has ever changed. Thank goodness we foreveryoung isn't dragging us down that rabbit hole.

In my view, the difficult is to deny the link between decay constant and decay energy. Gamow not only shows that they are linked, but it also provides one technique for looking at the strength of the link with other constants (charge on electron, nuclear masses, permittivity, etc.)

But that said, we know that Gamow's relations are based on an approximating model, and we might well question it's predictions based on the equation that are not verified by experiment. For example, Bohr's planetary model of the atom worked pretty well to explain the known spectra of the Hydrogen atom, but there are lots of details regarding even hydrogen that the Bohr model cannot explain. Quantum based models of hydrogen explain essential all of hydrogen's chemical behavior.

Further, a creationist is very unlikely to accept that any of this science means anything. "With man this is impossible, but with God all things are possible."


Under a government which imprisons any unjustly, the true place for a just man is also in prison. The proper place to-day, the only place which Massachusetts has provided for her freer and less desponding spirits, is in her prisons, to be put out and locked out of the State by her own act, as they have already put themselves out by their principles. Thoreau: Civil Disobedience (1846)

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