Superpositons of a uranium atom

1. Jun 27, 2009

SW VandeCarr

As I understand it, a uranium atom should exist in a superposition of its three isotopes (U238,U235,U234). Is this correct?

If so, the probability of any isotope being observed should be related to its natural abundance. But this would mean that the probabilities are time dependent, which is nonsense. Where I am I going wrong here?

What are the states of a uranium atom? According to what I've read about the famous Schrodinger Cat Gedanke the decay of a uranium atom is the critical event. This is taken as the 'realization' of a single quantum state (decayed) although that single state could be U235 or (rarely) U234.

Last edited: Jun 27, 2009
2. Jun 27, 2009

malawi_glenn

no this has nothing to do with quantum states to do

3. Jun 27, 2009

SW VandeCarr

I pretty much figured that out if you read the post. I asked what are the quantum states? The point in time when a particular uranium atom decays is unpredictable. This is the trigger for the execution of the cat. I understand this is a consequence of the wave function collapse (if you choose to view it that way.) Can you or someone else give me better answer?

4. Jun 27, 2009

malawi_glenn

"As I understand it, a uranium atom should exist in a superposition of its three isotopes (U238,U235,U234). Is this correct?"

No

5. Jun 27, 2009

Bob_for_short

If your initial atom is U238 and it can decay into U235 and into U234, then it is right. The initial populations (probability amplitudes) of the latter two states are zero but they grow up with time. I am not good in U238 decay channels, though.

Bob_for_short.

6. Jun 27, 2009

Bob S

In 1972, the remains of a natural nuclear reactor was discovered at the Oklo site in Gabon. The reactor had sufficlent concentration of U235 and a water moderator, and ran at over 100 kilowatts for over 100,000 years. After the reactor ran out of fuel (sufficient concentration of U235), it stopped running. The "natural concentration" of uranium-235 depends on where you mine it.
https://netfiles.uiuc.edu/mragheb/www/NPRE%20402%20ME%20405%20Nuclear%20Power%20Engineering/Natural%20%20Nuclear%20Reactors,%20The%20Oklo%20Phenomenon.pdf [Broken]

Last edited by a moderator: May 4, 2017
7. Jun 27, 2009

SW VandeCarr

So we all agree that the probability that a given U238 atom will decay in some period of time can be estimated from the half-life of U238. The probability that a given uranium atom will be identified as U238 depends on the distribution of isotopes in the relevant sample.

Now malawi_glenn says that the decay of an isotope has nothing to do with quantum states. However, it's treated as an example of the collapse of a wave function (under the Copenhagen interpretation) in all of the descriptions of the Schrodinger Gedanke that I've read. The idea of superposition was the motivation for this thought experiment.

Last edited by a moderator: May 4, 2017
8. Jun 28, 2009

malawi_glenn

The decay is governed by the transition matrix element between two quantum states yes, but maybe not in that sense you think, you seem to think of uranium as a spin-1 particle which have 3 states (spin_z up, spin_z 0 and spin_z -1), in an unpolarized beam, now here we can talk of the beam as a superposition of the three spin_z states.

You are mixing this quantum ensamble with how isotopes are related to each other, the superposition of states is a REAL probability, but your uranium 238 sample will, after a very very long time, have changed it's compositness - even WITHOUT an observation in the quantum mechanical sense.

For instance the spin-1/2 beam, in e.g. Sakurais books, you can measure the spin_x then the spin_z and get a certain result, that the spin_z component is -1/2 for all particles, then you measure spin_y and then spin_z again and will find that all particles have spin_z +1/2 (or something like that, I can give you the full treatment later once you understand these differences).
Now that was en example on how a quantum ensemble behaves under the superposition principle.

The process U238 -> U235 + other particles is not even reversible, and they are not even identical particles.

Now you can ask "what are the states of a Uranium XXX nuclei", in the same way as we can ask what states a hydrogen atom etc have, with respect to energy spectra etc.

But, yes, the decay of U-238 to something is governed by QM, but maybe not in the way you think of... Why is this question interesting to you? are you a student or?

9. Jun 28, 2009

Staff Emeritus
Why is this relevant?

Last edited by a moderator: May 4, 2017
10. Jun 28, 2009

malawi_glenn

Bob S is the master of irrelevancy

11. Jun 28, 2009

conway

I have the basically the same opinion as VandeCarr, that uranium atoms exist in a superpositions of states. I am not that he's got exactly the correct superpositions: for example, the 4-billion year half life is the decay of uranium to lead, is it not?...so the atom should actually be in a superposition of uranium and lead.

12. Jun 28, 2009

malawi_glenn

we will then have aditional particles together with the lead state, and also time dependent wave function coefficients.

I have still not figured out why the OP is asking this and what hos background are, have he even done basic quantum nuclear physics classes or not?

13. Jun 28, 2009

conway

If I understand you correctly then you are agreeing that there is a superposition of the uranium and the lead states.

If I understand him correctly he's making the very good observation that the basic mysteries of Schroedinger's cat are already present at the level of the decay of the uranium atom.

14. Jun 28, 2009

malawi_glenn

we can make a state which is a superposition of allt the components of the entire universe if we want...

well not really, since the s-cat only demands the existence of pure random process.

in reality, the situation is as follows, take a uranium 238 nucleus, the state is then |psi> = |uranium 238>. Insert the cat and close the box.

now, since the uranium is unstable, it has a certain probability for each infinitesimal time to decay to something, these problem can be modeled by good ol' time dependent perturbation theory.

I can still not see why this is crucial, the s-cat only require a pure random process.

15. Jun 28, 2009

SW VandeCarr

Why shouldn't it be interesting to me? Does it matter as long as the is question reasonably well posed? I've seen less well posed questions in this forum which you've answered.

In any case, I indicated in the OP that I was a bit confused about this. That's why I asked the question. I understand that nuclear decay is not reversible and that the concept of superposition does not apply in the same way as it applies to spin states of, for example, a photon. Your last response to me helped clear up the difficulties and I appreciate it.

As far as my background is concerned, you can check "About Me" at my member site. My particular current interests are logic, probability theory and Bayesian statistics.

EDIT: Can I then take it that, in your view, the s-cat Gedanke is not an example of a Copenhagen type wave function collapse?

Last edited: Jun 28, 2009
16. Jun 28, 2009

malawi_glenn

The reason for why I asked why you wanted to know this is that these interpretation issues are already messed up by amateurs (and also professional physicists as well hehe) - I could not catch what was confusing for you.

When we open the box to see if the cat is alive or dead, we have performed a measurement and this the "cat" wave function has collapsed.

Tell me if you want reading material regarding different interpretations of QM.

17. Jun 28, 2009

SW VandeCarr

I have a number of books that treat the subject(s) in one way or another. "Quantum Reality" by Nick Herbert (which has had good reviews) is devoted entirely to QM interpretations. The Copenhagen and Many Worlds interpretations are frankly metaphysical. I don't know if this can be said about the Bohmian interpretation. I started a thread in this forum (June 20) regarding the Ensemble (or Statistical) Interpretation which generated some good discussion. I personally prefer this one to the others. I agree with a comment by Frederick that this interpretation essentially says that QM doesn't need an interpretation. Nevertheless, thanks for your offer.

Last edited: Jun 28, 2009
18. Jun 29, 2009

Staff Emeritus
I have to say that I do not find the fact that you have written a self-published book as evidence of expertise.

Is it fair then to say you haven't studied quantum mechanics? Reading popularizations is fine, but it's no substitute for actually studying the topic and doing the calculations yourself. You say you have an opinion - I would argue that until you have studied the subject yourself, rather than just reading what some writers have said about it, you don't get to have an opinion.

Now, onto the question at hand. Isotopes are not in a superposition of states. One can imagine a superposition of states between U-238 and Th-234 + alpha, but as a practical matter, I doubt you could ever prepare such a thing. In a very real sense, the decay itself collapses the wavefunction.

19. Jun 29, 2009

conway

Then what is all the hullabaloo over Schroedinger's cat? If you're right, then we can all stop worrying about it because if there's no superposition of atoms, there's no superposition of cats.

I'm not saying you're wrong. I'm just saying you do not make your point by stating this result as a fact without any justification.

20. Jun 29, 2009

malawi_glenn

but dude, there are other things that are in superposition.. have you done QM excerices with beams of spin-1/2 particle? (successive stern gerlach apparatus)?? That is perhaps the best illustration of superposition in QM.