QM Intro: Questions on Copenhagen, Feynmann and Many Worlds

[jms5631]

Hi, I'm a college student who is taking an introductory QM course, therefore I obviously have very little background in the subject. Forgive me if the questions seem non-sensical to those of you who have far more knowledge of the subject. I have only recently discovered this forum and have found the all the responses, and in those by particular Zapper Z and Vanesch, very edifying.

1) Recently we have learned about the leading interpretations of QM- in the "standard" Copenhagen Interpretation, the wavefunction represent our knowledge of a quantum system. Would Feynmann's sum of all histories approach contradict this, or are the two compatible. Does Tony Leggett's Ston Brook experiments shed any light on the nature of superpositions?(I'm sure this has to do with wave/particle duality, but I can't get a consensus on whether the wavefunction is an objectively real entity).

2) How do Zurek's Quantum Darwinism approach differ from Many Worlds? Does he explain what happens to the other potentialities in a quantum superposition?

Thank you in adavance for any help you can give me.

 

[Ken G]

1) Recently we have learned about the leading interpretations of QM- in the "standard" Copenhagen Interpretation, the wavefunction represent our knowledge of a quantum system. Would Feynman's [sic] sum of all histories approach contradict this, or are the two compatible.

To my knowledge, quantum mechanical "interpretations" are all required to fit the same data. So they are indeed "compatible" in regard to what is now known. Whether or not some esoteric new experiment could be attempted to distinguish them is less clear-- I've never seen a convincing case made for such an experiment.

Does Tony Leggett's Ston Brook experiments shed any light on the nature of superpositions?

Sure, it underscores the value of the concept in situations where it was less obvious the idea would be helpful.

(I'm sure this has to do with wave/particle duality, but I can't get a consensus on whether the wavefunction is an objectively real entity).

You'll never get a consensus on something that is not testable.

2) How do Zurek's Quantum Darwinism approach differ from Many Worlds? Does he explain what happens to the other potentialities in a quantum superposition?

In my opinion, there are no meaningful differences among any of the interpretations that make the same predictions for experiments we can actually do. I see a lot of baggage being attached to understanding imaginary processes that are actually unconstrained by experiment. Much ado about nothing, if you ask me- wait until there is actually some data that is not well treated with the minimal interpretation (which is that the axioms of physics are chosen to follow reality, not the other way around).

 

[ZapperZ]

1) Recently we have learned about the leading interpretations of QM- in the "standard" Copenhagen Interpretation, the wavefunction represent our knowledge of a quantum system. Would Feynmann's sum of all histories approach contradict this, or are the two compatible. Does Tony Leggett's Ston Brook experiments shed any light on the nature of superpositions?(I'm sure this has to do with wave/particle duality, but I can't get a consensus on whether the wavefunction is an objectively real entity).

The Stony Brook/Delft experiments were initiated by the theoretical suggestion by Tony Leggett. What they show is that even with a "glob" of object having as many as 10^11 particles, that object can still be in a superposition of states, i.e. the Schrödinger Cat-state. This is where the supercurrent (in which ALL of the condensed Cooper pair electrons form a single, coherent state) exhibit the superposition of the direction that it flows. So not only were these experiments added another verification to the principle of superposition, they also showed that "size" doesn't matter as along as one can maintain coherence for every part of the object in question (which isn't easy to do at our classical scale). This implies that if one can have a "large" object that can maintain such coherence, then quantum phenomena can still be observed.

The question on whether something is "real" or not is something I can't answer, because it depends on what you mean by "real". Does the ability to make uncannily accurate predictions of the outcome of a measurement implies that such a thing is real? In my case, I only care about such empirical results, because at the end of the day, that's the only thing that I can measure and verify. Everything else is simply a matter of tastes.

Zz.

 

[Ken G]

The Stony Brook/Delft experiments were initiated by the theoretical suggestion by Tony Leggett. What they show is that even with a "glob" of object having as many as 10^11 particles, that object can still be in a superposition of states, i.e. the Schrödinger Cat-state.

I would say that this is not a Shrodinger Cat-state (I prefer kittenstate). The issue was never bean counting the particles, it was the presence of noise. It is untraceable couplings that make a cat a classical system, not the number of atoms it contains. When I use the term "macro system", I really mean "coupled to macroscopic concepts of noise". Ultra noise-free systems are inherently quantum mechanical, because they simply copy the same information over and over, like Bose-Einstein condensates or the Fermi sea. No one would think you don't need the Exclusion Principle to understand white dwarf stars, but the cat still has no useful quantum mechanical description. It's all about the role of coupling, and the action by the physicist of choosing how this is going to be treated. We don't ask "does a cat have a wavefunction", that's angels on a pin-- we ask "can we use a wavefunction to learn something interesting about a cat". I'd say the answer to that is a resounding "no", but I stand ready to be shown a contrary example.

This implies that if one can have a "large" object that can maintain such coherence, then quantum phenomena can still be observed.

Right, and that is interesting but I do not find it surprising. Quantum mechanics doesn't make wrong predictions, but there are situations where it makes no testable predictions, and when that's true, it cannot be applied by a scientist. The best example of this is thermodynamics and irreversibility-- we don't apply reversible physics to systems that we are treating as irreversible. It's not that we know we can't reverse it in principle, it's that irreversibility is itself a principle-- it all depends on what is the useful way to analyze things.

In my case, I only care about such empirical results, because at the end of the day, that's the only thing that I can measure and verify.

I completely agree-- and apply that logic to the concept of kittenstates.

 

[ZapperZ]

I would say that this is not a Shrodinger Cat-state (I prefer kittenstate). The issue was never bean counting the particles, it was the presence of noise. It is untraceable couplings that make a cat a classical system, not the number of atoms it contains. When I use the term "macro system", I really mean "coupled to macroscopic concepts of noise". Ultra noise-free systems are inherently quantum mechanical, because they simply copy the same information over and over, like Bose-Einstein condensates or the Fermi sea. No one would think you don't need the Exclusion Principle to understand white dwarf stars, but the cat still has no useful quantum mechanical description. It's all about the role of coupling, and the action by the physicist of choosing how this is going to be treated. We don't ask "does a cat have a wavefunction", that's angels on a pin-- we ask "can we use a wavefunction to learn something interesting about a cat". I'd say the answer to that is a resounding "no", but I stand ready to be shown a contrary example.

I'm not quite sure of what your point is here. The presence of the coherence gap in the Delft/Stony Brook experiments is definitely one property of "the cat", which in this case, is the supercurrent going in both directions through the SQUID. That coherence gap is a measureable property, and a direct consequence of the QM description/wavefunction of the system (i.e. the BCS ground state wavefunction).

Zz.

 

[Ken G]

I'm not quite sure of what your point is here. The presence of the coherence gap in the Delft/Stony Brook experiments is definitely one property of "the cat", which in this case, is the supercurrent going in both directions through the SQUID.

That is an example of a useful application of the concept of a wave function. I await an example involving a cat. You see, the issue is not if a macro system can behave quantum mechanically (we already knew that since Chadrasekhar and white dwarfs), it is if you can get a macro system that does not behave quantum mechanically to do so by attaching it to a quantum system. I say the answer is no, indeed that is the whole point of "measurement" as part of the scientific method. So saying a cat is in a superposition state when you hook it up to a nucleus is "not even wrong"-- it is contrary to the very process used to establish the value of the concept of superposition: hooking quantum systems up to classical ones because you understand how the latter act, in order to understand how the former act. Indeed, I'll bet dollars to donuts the same technique was applied to that SQUID!

 

[ZapperZ]

That is an example of a useful application of the concept of a wave function. I await an example involving a cat. You see, the issue is not if a macro system can behave quantum mechanically (we already knew that since Chadrasekhar and white dwarfs), it is if you can get a macro system that does not behave quantum mechanically to do so by attaching it to a quantum system. I say the answer is no, indeed that is the whole point of "measurement" as part of the scientific method. So saying a cat is in a superposition state when you hook it up to a nucleus is "not even wrong"-- it is contrary to the very process used to establish the value of the concept of superposition: hooking quantum systems up to classical ones because you understand how the latter act, in order to understand how the former act. Indeed, I'll bet dollars to donuts the same technique was applied to that SQUID!

Hum... I think I'm beginning to see what you're trying to say.

I've never bought into the actual Schrödinger Cat scenario. The cat itself is a classical system, and the orthorgonal states of "dead" and "alive" is undefined as far as a "measurement" goes, i.e. what would be the observable to be measured when it is in superposition of dead and alive states. The SQUID experiments are very clear in this sense, because it is measuring an observable that "does not commute" to the observable measuring the direction of the current. Thus, the superposition of direction of the current is preserved. One can't do that with the cat.

I invoked the "Schrödinger Cat state" phrase not because I consider this as an illustration of the Schrödinger Cat thought experiment, but rather as a generic term for the superposition of 2 orthorgonal states, a term commonly used in many of these papers. Now whether one can take a classical system and couple it to a quantum system and get that classical system to behave quantum mechanically, that I haven't seen.

On the other hand, and I'm not sure how this would be relevant here, there is the proximity effect in dealing with superconductivity. This is where the superconducting wavefunction penetrates into a non-superconducting material, making that material behave as if it is a superconductor. This is a well-known phenomena and in fact, is used to characterize certain materials.

Zz.

 

[jms5631]

Thanks guys for the informative posts, they are very elucidating. I guess the origin of the hangup I'm having right now is understanding the difference between the original conception of the Born probability wave, and the Feynman path integral. In the former, can you say that a system was in a superposition of state (i.e. particle is at both left and right slit)? I'm assuming you can based on Schrödinger's cat though experiment, which existed long before Feynmann, but I don't understand how.

Ken G, I agree with you about interpretations. I'm of the opinion that my class is focusing too heavily on interpretational and metaphysical aspects. Given that we don't have a complete theory of quantum gravity, and all interpretations are empirically identical, I think it's very presumptuous to assign ontological reality to any of these interpretations. Thus I prefer an instrumentalist approach until something changes. However, I've been criticized for not trying to apply QM to reality and sidestep it. Anyway, thanks again for your help.

 

[Ken G]

The cat itself is a classical system, and the orthorgonal states of "dead" and "alive" is undefined as far as a "measurement" goes, i.e. what would be the observable to be measured when it is in superposition of dead and alive states. The SQUID experiments are very clear in this sense, because it is measuring an observable that "does not commute" to the observable measuring the direction of the current. Thus, the superposition of direction of the current is preserved. One can't do that with the cat.

That's pretty much all I'm saying, with the additional point that at some point even the SQUID system had to be brought into contact with something that we could count on to act classically. Science is built around classical action, and quantum behavior is always seen through the "lens" of classical couplings. That's what leads to all the "paradoxical" behavior, I think we really shouldn't be so surprised. If our predictions about how that coupling plays out, we should be content, that's all we can reasonably expect.

I invoked the "Schrödinger Cat state" phrase not because I consider this as an illustration of the Schrödinger Cat thought experiment, but rather as a generic term for the superposition of 2 orthorgonal states, a term commonly used in many of these papers.

Perhaps that is the terminology, maybe invoking a sense of "color", but I would view it as especially unfortunate, for all these reasons.

On the other hand, and I'm not sure how this would be relevant here, there is the proximity effect in dealing with superconductivity. This is where the superconducting wavefunction penetrates into a non-superconducting material, making that material behave as if it is a superconductor. This is a well-known phenomena and in fact, is used to characterize certain materials.

That sounds like an interesting application of the concept of "quantum/classical transition". I'm not saying there is no value in looking at such hybrid concepts, I'm just saying that we choose how we wish to treat things. Like our choice to study quantum systems by coupling them to classical ones-- we couldn't simply leave them alone because that's just not how we do science. So I find all the machinations people go through to try and "resolve the paradoxes" to be curious-- the paradoxes are created by our approach to science, why would we need to "resolve" how unitary transformations collapse wave functions? That would be like resolving how the classical dynamics of air molecules leads to irreversibility-- there's nothing to resolve, it's all about what we want to know about a system.