Atom in a Decayed / Non-Decayed State

[Thecla]

TL;DR Summary

QM description of radioactive atom

In Sheldon Glashow's critical review of "What is Real? The Unfinished Quest for the Meaning of Quantum Physics" by Adam Becker, there is one paragraph I don't understand. In Glashow's thought experiment of a single radioactive atom in a box:

My thought experiment is like Schrödinger’s, but without the cat. A single X atom is placed in a sealed box. Four hours later, the box is opened. The atom survives in roughly half the times the experiment is repeated. Is the confined atom in a superposition of having decayed or not decayed until the box is opened? Does the act of opening the box collapse the wave function?No, and no again.

I always thought that the wave function of the atom in a box can be described as a linear combination of decayed and non decayed states, but Dr. Glashow seems to say no.

 

[Nugatory]

In Sheldon Glashow's critical review of "What is Real? The Unfinished Quest for the Meaning of Quantum Physics" by Adam Becker,...

You mean https://inference-review.com/article/not-so-real ?
If you’re going to quote something, provide a link to the source please.

 

[Demystifier]

I always thought that the wave function of the atom in a box can be described as a linear combination of decayed and non decayed states, but Dr. Glashow seems to say no.

To some extent it depends on the interpretation, but I will try to give an answer that minimally depends on it. If the atom in the box does not interact with its environment, then it can be said that it's in superposition (until we open the box). But if it interacts (which usually is the case), then atom is better described as being in the mixed state, which is not a coherent superposition.

 

[vanhees71]

If you just have an isolated nucleus being prepared in a pure state at time $t=0$ it will stay in a pure state. If it's instable, i.e., if it can undergo an radioactive decay you have a superposition of many states. The standard calculation is the Wigner-Weisskopf approximation, leading to the known exponential-decay law for the survival probability, $P(t)=\lambda \exp(-\lambda t)$, where $\tau=1/\lambda$ is the mean lifetime of the nucleus.

 

[atyy]

Glashow is wrong. Under the ideal circumstances of the thought experiment, the atom is in a superposition of decayed and not decayed, and the cat is in a superposition of dead and alive. And yes, the wave function collapses only when the observer gets a definitive report as to whether the atom has decayed or died.

Glashow claims to defends shut and up and calculate, but he betrays it by denying its absurdities. A true shut and and calculate believer would say,"Who cares? The probabilities of the measurement outcomes predicted by quantum mechanics match those that are observed.

 

[vanhees71]

I agree for the atom, if it is totally isolated from the environment, but not for the cat used as a measurement device, because the cat must be interacting with the environment if it shouldn't simply die by suffocation when isolated against the environment completely. The cat+atom as a closed system makes the cat thus not a proper measurement device for the state of the atom.

The so established necessity to let the cat breath, i.e., being coupled to the "environment" (the air) is also the reason, why Schrödinger's gedanken experiment is not correct, because the cat is not in a pure state, because it's an open quantum system coupled to the environment and thus always in a mixed state and thus always definite in a state of "alive" or "dead" (which represent very much coarse grained macroscopic observables about the cat).

 

[atyy]

I agree for the atom, if it is totally isolated from the environment, but not for the cat used as a measurement device, because the cat must be interacting with the environment if it shouldn't simply die by suffocation when isolated against the environment completely. The cat+atom as a closed system makes the cat thus not a proper measurement device for the state of the atom.

The so established necessity to let the cat breath, i.e., being coupled to the "environment" (the air) is also the reason, why Schrödinger's gedanken experiment is not correct, because the cat is not in a pure state, because it's an open quantum system coupled to the environment and thus always in a mixed state and thus always definite in a state of "alive" or "dead" (which represent very much coarse grained macroscopic observables about the cat).

Yes, in the ideal experiment we have to consider the system as "cat + air", and that is what is in the pure state, which we can still label as "dead" or "alive" since that is the observable we are interested in.

 

[atyy]

At the end of the article Glashow quotes Dirac, but Dirac did not dismiss the measurement problem as important. He thought it not worth attacking it at his moment in history, because it is difficult. And he thought that new physics that replaces quantum mechanics might solve it.

https://blogs.scientificamerican.com/guest-blog/the-evolution-of-the-physicists-picture-of-nature/
"There will have to be some new development that is quite unexpected, that we cannot make a guess about, which will take us still further from Classical ideas but which will alter completely the discussion of uncertainty relations. And when this new development occurs, people will find it all rather futile to have had so much of a discussion on the role of observation in the theory, because they will have then a much better point of view from which to look at things. So I shall say that if we can find a way to describe the uncertainty relations and the indeterminacy of present quantum mechanics that is satisfying to our philosophical ideas, we can count ourselves lucky. But if we cannot find such a way, it is nothing to be really disturbed about. We simply have to take into account that we are at a transitional stage and that perhaps it is quite impossible to get a satisfactory picture for this stage."

 

[vanhees71]

Yes, in the ideal experiment we have to consider the system as "cat + air", and that is what is in the pure state, which we can still label as "dead" or "alive" since that is the observable we are interested in.

I'd not say that it makes sense to attribute the system "cat+air" the states "dead" and "alive", it's the cat only. The closed system is of course "nucleus+geiger counter+bottle with poison+cat+air". I think it's completely illusory to think that this can be described by a pure state. You cannot even write down the pure state due to the sheer amount of microscopic degrees of freedom you'd have to consider. It's also completely irrelevant to prepare this macroscopic system in a pure state.

 

[atyy]

I'd not say that it makes sense to attribute the system "cat+air" the states "dead" and "alive", it's the cat only. The closed system is of course "nucleus+geiger counter+bottle with poison+cat+air". I think it's completely illusory to think that this can be described by a pure state. You cannot even write down the pure state due to the sheer amount of microscopic degrees of freedom you'd have to consider. It's also completely irrelevant to prepare this macroscopic system in a pure state.

It's fine as a thought experiment.

 

[martinbn]

Given the paragraph before the quote, it seems that he is using an ensemble interpretation ( he calls it Copenhagen). In this interpretaion what he said is correct.

 

[WernerQH]

(quoting Sheldon Glashow:)

Is the confined atom in a superposition of having decayed or not decayed until the box is opened? Does the act of opening the box collapse the wave function?

Glashow is talking of two different things here: one that happens in the real world (nuclear decay), and one that happens only in the minds of some theoreticians (wave function collapse). Nuclear decay occurs on a time scale much shorter than microseconds, the time it takes the emerging neutrino to leave the scene. The atom is definitely in the non-decayed state a millisecond before, and in the decayed state a millisecond after the event. The wave function, on the other hand, is envisioned to evolve more slowly, in Glashow's example on the time scale of hours. Because this gradual evolution is at odds with the definite clicks registered by a Geiger counter, some people adduce "measurement" and "wave function collapse" (which are theorized to happen in an instant). A Geiger counter supposedly "measures" nuclear decay. But it does not cause or trigger it. An unstable atom will not decay twice as fast if it is "observed" by two Geiger counters. The collapse of the wave function is fictitious.

Freeman Dyson has explained it well:
"Unfortunately, people writing about quantum mechanics often use the phrase "collapse of the wave-function" to describe what happens when an object is observed. This phrase gives a misleading idea that the wave-function itself is a physical object. A physical object can collapse when it bumps into an obstacle. But a wave-function cannot be a physical object. A wave-function is a description of a probability, and a probability is a statement of ignorance. Ignorance is not a physical object, and neither is a wave-function. When knowledge displaces ignorance, the wave-function does not collapse; it merely becomes irrelevant.
(https://www.edge.org/response-detail/25350)

 

[PeterDonis]

Nuclear decay occurs on a time scale much shorter than microseconds, the time it takes the emerging neutrino to leave the scene.

But the probability of the nuclear decay occurring is not $1$ over the time scale Glashow is talking about--which means the wave function of the atom, over the time scale Glashow is talking about, will have amplitudes for both "decayed" and "not decayed". So the fact that, if nuclear decay occurs, it occurs quickly, is irrelevant to the point Glashow is trying to make.

The collapse of the wave function is fictitious.

This depends on which interpretation of QM you adopt. In some interpretations collapse is not fictitious.

 

[WernerQH]

But the probability of the nuclear decay occurring is not $1$ over the time scale Glashow is talking about--which means the wave function of the atom, over the time scale Glashow is talking about, will have amplitudes for both "decayed" and "not decayed". So the fact that, if nuclear decay occurs, it occurs quickly, is irrelevant to the point Glashow is trying to make.

The decay probability per unit time is the inverse of the lifetime, and everybody agrees that after 4 hours the probability that a decay has occurred is 1/2. If a decay has occurred, it is certain to have happened quickly. Just before the box is opened, the average physicist would expect the atom to be either decayed or non-decayed, but not in a superposition. Perhaps you have misunderstood Glashow's point.

 

[PeterDonis]

Just before the box is opened, the average physicist would expect the atom to be either decayed or non-decayed, but not in a superposition.

This will depend on which interpretation of QM you adopt.

Perhaps you have misunderstood Glashow's point.

Perhaps you have misunderstood my point. My point is not that Glashow is right or wrong--the claim he is making (which is basically the same one you make about "the average physicist") is interpretation-dependent, so it is right on some interpretations and wrong on others. My point is that the interpretation-dependent claim that Glashow is making has nothing to do with how long the nuclear decay takes to happen, if it happens. So your point about how long nuclear decay takes to happen is irrelevant to Glashow's claim.

 

[hutchphd]

I am suddenly struck by the endless arguments regarding transubstantiation in Christian doctrine. This entire subject seems terribly similar, right down to "when does the transformation take place".
I don't mean to single out Christianity but it is what I know. (Although in truth I only know the word " transubstantiation" from listening to Tom Lehrer.)
Is this discussion similarly relevant, or am I being too dismissive?

 

[StevieTNZ]

Just before the box is opened, the average physicist would expect the atom to be either decayed or non-decayed, but not in a superposition.

Bolded part, what caused the wave function to collapse then (whether physical or updating our knowledge etc)? That doesn't seem like unitary evolution of the fundamental Schrodinger equation to me.

 

[atyy]

I am suddenly struck by the endless arguments regarding transubstantiation in Christian doctrine. This entire subject seems terribly similar, right down to "when does the transformation take place".
I don't mean to single out Christianity but it is what I know. (Although in truth I only know the word " transubstantiation" from listening to Tom Lehrer.)
Is this discussion similarly relevant, or am I being too dismissive?

The Copenhagen interpretation was of course first discovered in that subject area.

 

[Demystifier]

The Copenhagen interpretation was of course first discovered in that subject area.

When I click on the blue, I get nonsense.

 

[atyy]

When I click on the blue, I get nonsense.

The Golden Rule is an operational rule across religions, just like the Copenhagen interpretation is an operational rule across interpretations.

 

[Demystifier]

The Golden Rule is an operational rule across religions, just like the Copenhagen interpretation is an operational rule across interpretations.

I like analogies, even farfetched ones, but that's too much even for me.

 

[WernerQH]

So your point about how long nuclear decay takes to happen is irrelevant to Glashow's claim.

Why do you dismiss the time scales as irrelevant? Do you really think of nuclear decay as a gradual process (possibly taking millions of years) as suggested by Schrödinger's equation? Is the click of a Geiger counter merely a trick played on us by our senses?

We seem to disagree on what Glashow's claim actually is. You may not find it convincing, but he is certainly entitled to his own view of quantum theory, and is under no obligation to think of all interpretations of QM as "created equal." He would probably reject the fine print that you are trying to add as irrelevant.

To me, his viewpoint makes perfect sense, and hopefully the discussion has relieved the initial poster's bafflement.

 

[WernerQH]

what caused the wave function to collapse then?

If you think of the wave function as a physical object, you have a problem.
But you don't have to. And unitary evolution is only a part of the story.

 

[EPR]

Bolded part, what caused the wave function to collapse then (whether physical or updating our knowledge etc)? That doesn't seem like unitary evolution of the fundamental Schrodinger equation to me.

Zeilinger explains it thus(though I have no idea how a particle would know that information about it is being transmitted to an observer):"The superposition of amplitudes ... is only valid if there is no way to know, even in principle, which path the particle took. It is important to realize that this does not imply that an observer actually takes note of what happens. It is sufficient to destroy the interference pattern, if the path information is accessible in principle from the experiment or even if it is dispersed in the environment and beyond any technical possibility to be recovered, but in principle still ‘‘out there.’’ The absence of any such information is the essential criterion for quantum interference to appear."

https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.71.S288

 

[vanhees71]

The Golden Rule is an operational rule across religions, just like the Copenhagen interpretation is an operational rule across interpretations.

Yes, the believe in collapse is religion ;-)).

 

[atyy]

Ten Commandments of the Church of the Smaller Hilbert Space
http://mattleifer.info/wordpress/wp-content/uploads/2008/11/commandments.pdf
http://mattleifer.info/2006/04/13/the-church-of-the-smaller-hilbert-space/

 

[PeterDonis]

Do you really think of nuclear decay as a gradual process (possibly taking millions of years) as suggested by Schrödinger's equation?

No, that is not what Schrodinger's equation says. Schrodinger's equation says that the state of the atom is a superposition of "not decayed" and "decayed", with the relative amplitudes of the two terms in the superposition varying with time.

Whether or not this is a complete and correct description of the entire process involved depends on which interpretation of QM you adopt.

Is the click of a Geiger counter merely a trick played on us by our senses?

No, but in the scenario under discussion, there is no equivalent of anything like a click by a Geiger counter until the box is opened.

 

[PeterDonis]

We seem to disagree on what Glashow's claim actually is. You may not find it convincing, but he is certainly entitled to his own view of quantum theory, and is under no obligation to think of all interpretations of QM as "created equal." He would probably reject the fine print that you are trying to add as irrelevant.

If any of this is true, that's all the more reason to let the OP know that Glashow's claims are interpretation dependent.

 

[vanhees71]

No, that is not what Schrodinger's equation says. Schrodinger's equation says that the state of the atom is a superposition of "not decayed" and "decayed", with the relative amplitudes of the two terms in the superposition varying with time.

Whether or not this is a complete and correct description of the entire process involved depends on which interpretation of QM you adopt.
No, but in the scenario under discussion, there is no equivalent of anything like a click by a Geiger counter until the box is opened.

What's objectively observable doesn't depend on any interpretation. You can measure the radioactive decay of a large amount of nuclei, and that's what's done in practice: You have a macroscopic amount of a radioactive substance and can measure the decay rates. Quantum mechanically it's described as you say, and all there is quantum mechanically are the probabilities for an atomic nucleus, being present at $t=0$ ("preparation") to be still there at time $t$ ("measurement"). There's nothing interpretation dependent here concerning these probabilities, but you can just objectively measure these probabilities on an large ensemble of these nuclei. Of course, this is "an interpretation", namely the ensemble interpretation, but any other interpretation doesn't say anything different from it as long as you are only concerned with what's objectively observable. Whether or not there is a collapse, whether of not the "state is really in a superposition", etc. etc. is nothing you can empirically test and thus irrelevant for the scientific question whether QT is correct or not. As far as the physics is concerned the theoretical formalism and its relation to measurable/observable facts about nature is unique and independent on "interpretation".

 

[PeterDonis]

What's objectively observable doesn't depend on any interpretation.

True, but Glashow's claim is not about what is objectively observable. In his scenario, nothing is objectively observed until the box is opened; that's part of the specification of the scenario. Yet he makes claims about what happens before the box is opened. Any such claim, given his specification of the scenario, is interpretation dependent.

 

[StevieTNZ]

Zeilinger explains it thus(though I have no idea how a particle would know that information about it is being transmitted to an observer):"The superposition of amplitudes ... is only valid if there is no way to know, even in principle, which path the particle took. It is important to realize that this does not imply that an observer actually takes note of what happens. It is sufficient to destroy the interference pattern, if the path information is accessible in principle from the experiment or even if it is dispersed in the environment and beyond any technical possibility to be recovered, but in principle still ‘‘out there.’’ The absence of any such information is the essential criterion for quantum interference to appear."

https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.71.S288

I disagree, because the fundamental Schrodinger equation can't go from a pure state (that is, superposition) to a mixed state (no interference), without someone mucking around in the middle between the unitary evolution of the Schrodinger equation and destroying interference patterns and one state arising.

Unless you mean otherwise?

EDIT: even, if in principle the information is available, I would say, as Caslav Brunker has communicated to me, the interference pattern would be supressed but there in principle.

 

[vanhees71]

True, but Glashow's claim is not about what is objectively observable. In his scenario, nothing is objectively observed until the box is opened; that's part of the specification of the scenario. Yet he makes claims about what happens before the box is opened. Any such claim, given his specification of the scenario, is interpretation dependent.

True, and it's irrelevant as far as physics is concerned, because you cannot empirically check it, because when you empirically check it you have to open the box. So it's like discussing how many angels fit on the tip of a needle or whether the chicken or the egg was first... You can write tons of quantum-esoteric books about this subject and unfortunately they may sell better than good textbooks on the subject ;-)).

 

[WernerQH]

I disagree, because the fundamental Schrodinger equation can't go from a pure state (that is, superposition) to a mixed state (no interference), without someone mucking around in the middle between the unitary evolution of the Schrodinger equation and destroying interference patterns and one state arising.

Right, unitary evolution and the focus on the wave function appear to necessitate some "mucking around", because it can't be the whole story. But there is a decent way of combining unitary evolution and "measurements": the Schwinger/Keldysh closed time-path formalism.

"[K]nowledge of the transformation function referring to a closed time path determines the expectation value of any desired physical quantity for a specified initial state or state mixture."
(J. Schwinger, J.Math.Phys. 2, 407, 1961)

There is no talk of collapse, because in the Heisenberg picture the state vectors are constant. All that quantum theory is concerned with are operator products and traces over them.

 

[vanhees71]

The paper by Keldysh is much better readable to learn about the Schwinger-Keldysh real-time contour:

L. Keldysh, Diagram Technique for Nonequilibrium Processes,
Zh. Eksp. Teor. Fiz. 47, 1515 (1964), [Sov. Phys JETP 20 1965 1018],
https://www.jetp.ac.ru/cgi-bin/e/index/e/20/4/p1018?a=list

 

[WernerQH]

The paper by Keldysh is much better readable to learn about the Schwinger-Keldysh real-time contour:

L. Keldysh, Diagram Technique for Nonequilibrium Processes,
Zh. Eksp. Teor. Fiz. 47, 1515 (1964), [Sov. Phys JETP 20 1965 1018],
https://www.jetp.ac.ru/cgi-bin/e/index/e/20/4/p1018?a=list

True, Schwinger's paper is heavy going. I learned about the Keldysh formalism from the reviews by Chou et al (Physics Reports 118, 1-131) and Rammer and Smith (Rev.Mod.Phys. 58, 323-359), and I once even bought Rammer's book "Quantum Field Theory of Non-equilibrium States".
I think the method deserves to be much more widely known, but most presentations are extremely technical, and in standard cases the end result is just the Golden Rule.