Superpositons of a uranium atom

[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.

 

[malawi_glenn]

no this has nothing to do with quantum states to do

 

[SW VandeCarr]

no this has nothing to do with quantum states to do

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?

 

[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

 

[Bob_for_short]

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

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.

 

[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

 

[SW VandeCarr]

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

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.

 

[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?

 

[Vanadium 50]

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

Why is this relevant?

 

[malawi_glenn]

Bob S is the master of irrelevancy

 

[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.

 

[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?

 

[conway]

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

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

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?

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.

 

[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.

 

[SW VandeCarr]

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?

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?

 

[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.

 

[SW VandeCarr]

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

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.

 

[Vanadium 50]

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.

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

I have a number of books that treat the subject(s) in one way or another. "Quantum Reality" by Nick Herbert...

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.

 

[conway]

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.

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.

 

[malawi_glenn]

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.

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.

 

[Vanadium 50]

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.

The fact that a bunch of people with no training in physics but who have read books on QM - books not written by physicists - get excited about something does not mean that people who do understand it get excited about it.

I very much doubt that any working physicist today really believes the cat is in a superposition of states. There are such systems, as malawi_glenn points out, but cats are not one of them.

 

[Count Iblis]

The fact that a bunch of people with no training in physics but who have read books on QM - books not written by physicists - get excited about something does not mean that people who do understand it get excited about it.

I very much doubt that any working physicist today really believes the cat is in a superposition of states. There are such systems, as malawi_glenn points out, but cats are not one of them.

This is not true. Of course, cats can also be in a superposition, although it will decohere very rapidly (i.e. get entangled with tyhe environment) and you then get a global superposition that cannot be distinguished from a classical state. In my experience, it are manly the condensed matter folks who resist this idea, saying that that if you can't measure it, it doesn't exist.

But people who work on fundamental physics are more sympathetic to the idea, because to them the difference between a pure state and a mixed state, even if you can't measure it in practice, has profound theoretical implications.

Instead of considering Schrödinger's cat, today's theorists are considering black holes that evaporate by emitting Hawking radiation and are asking if this process is unitary, because Hawking's theory suggested that this process may not be unitary.

Most physicists who have studied this do now accept that this process does not violate unitarity or that it does not necessarily violate unitarity. One can formulate the problem as follows. You have an intitial pure state consisting of particles that are going to collide and form a black hole. The final state will contain Hawking radiation.

According to quantum mechanics, the final state is obtained by applying some unitary S-matrix to the initial state. But this picture is then hugely more weird that Schrödinger's cat. E.g., it is well known that there is always a probability that the particles won't form a black hole at all and it turns out that that you need to include the amplitude for that to see that the whole process is indeed unitary.

 

[Vanadium 50]

Okay, you say it's not true. Can you name a working physicist who believes the cat is in a superposition of states?

 

[Count Iblis]

Okay, you say it's not true. Can you name a working physicist who believes the cat is in a superposition of states?

Well, I'm a working physicist too, so let's change the criterium. Let's consider only physicists who have more than 100 published peer reviewed articles.

Then Max Tegmark would qualify. He would certainly agree that the cat plus rest of the universe ends up in a entangled superposition of the form:

|dead cat>|rest of universe_1> + |alive cat>|rest of universe_2>

and to a very good approximation:

<rest of universe_1|rest of universe_2> = 0

 

[SW VandeCarr]

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

What does my book have to do with this discussion? The book is not about quantum mechanics.

Is it fair then to say you haven't studied quantum mechanics?

In terms of taking formal courses in QM, it's fair to say that. Does that mean I can't ask questions? If it's a dumb question, feel free to say so.

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.

I did not express an opinion about the science. Interpretations that can't, in principle, be falsified are not science.

 

[conway]

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

Nor is it something to sneer at.

 

[Vanadium 50]

and to a very good approximation:

<rest of universe_1|rest of universe_2> = 0

Which is the point. Arguing that the cat is still in a superposition is a little like arguing that all the air molecules can suddenly move to one side of the room. Yes, the probability is non-zero, but when you have probabilities like 10^-1000, there is simply no risk in making a mistake by treating it as zero.

The cat never acts as if it's in a superposition.

What does my book have to do with this discussion? The book is not about quantum mechanics.

You were asked what your background is, so an answer could be crafted that was neither over nor under your head. In response, you pointed people to your profile, 2/3 of which is about your book. You brought it up - indeed, and still haven't answered the question. "Trained in medicine" may mean anything from "has an MD" to "took a class on first aid once". Even that is not all that relevant - the issue is how much QM you have studied, since that's the question

Nor is it something to sneer at.

I am not sneering. However, I don't believe it is evidence of expertise.

In any event, the OPs question has been asked and answered. It's clear that Mr. Conway doesn't believe it, and it's not clear to me what Mr. VandeCarr believes. Fair enough. I can only provide answers; I can't make someone believe them.

 

[conway]

In any event, the OPs question has been asked and answered. It's clear that Mr. Conway doesn't believe it, and it's not clear to me what Mr. VandeCarr believes. Fair enough. I can only provide answers; I can't make someone believe them.

You explain Schroedinger's cat by saying that the collapse occurs at the point of decay. Why should I believe that? The only reason you've given is the fact (implied) that you haven't self-published your own book.

If it were that easy to explain Schroedinger's cat, people wouldn't still be talking about it after seventy-five years. Saying you're not worried about it doesn't make you special.

 

[Count Iblis]

Which is the point. Arguing that the cat is still in a superposition is a little like arguing that all the air molecules can suddenly move to one side of the room. Yes, the probability is non-zero, but when you have probabilities like 10-1000, there is simply no risk in making a mistake by treating it as zero.

The cat never acts as if it's in a superposition.

That's not the point. The point is that the cat is in an entangled superposition with the rest of the universe. The ampilitude of both terms are large. There is no known accepted theory in physics that explains from first principles how a pure state can involve into a mixed state. The pure state is a superposition, the mixed state is a probability distribution over the two terms in the superposition.

Penrose has proposed such a theory based on the idea that gravitational interactions would cause such a state reduction, but this is not widely accepted and, more importantly, it hasn't been demonstrated in experiments.