Sunday, May 2, 2010

Schrödinger's Cat: A Semi-Classical Mistake

I'm sure that anyone who is reading this blog has heard of Schrödinger's Cat and can at least give a brief synopsis of the famous thought experiment. So I will not do that here, but I will discuss some of the implications and misconceptions about Schrödinger's Cat (if you are not familiar with it then read then you can read more here). For my part I have heard Schrödinger's Cat explained in classes on quantum mechanics many many times. The most recent being my graduate quantum class, and previously from my physics classes at BYU. In ALL of these explanations the general approach is to tell the thought experiment (with a few variations) and then finish up by proclaiming "Therefore the cat is both alive and dead, AT THE SAME TIME!!!"

Occasionally the effort is made to point out that Schrödinger was trying to show how ridiculous the Copenhagen interpretation is but this explanation is always half-hearted and does not really consider the problem fully. Mostly it is treated as a brain teaser without any attempt to actually answer the questions involved, or to draw any significant physical conclusions. This stands in stark contrast to other famous thought experiments that fundamentally changed the way we view the world. The problem with this is that Schrödinger's Cat is one of the few parts of physics where the technical, philosophical conversation diverged from what is taught in standard physics classes to the point that most physicists are not even aware that the paradox posed by Schrödinger has been answered and resolved.

To give you an idea of what I mean I will use an analogy. In the beginning of the last century people were starting to wonder about the nature of the universe, especially when it was found that one of the implications of general relativity was that, without at least a corrective term, the universe would be expanding. This was backed up by Hubble's observations. Over the years the nature of the expanding universe has been debated, calculated, recalculated, considered, proved, disproved, reproved, recalculated, recalibrate, observed, reobserved and recalculated. The point is the conversation has moved on significantly from the beginning of the 1900's, and the issues involved have grown and have become more complex.

Now imagine sitting in on an astronomy class and the professor says something to the effect, "It is possible that the universe is expanding. There are some theories that say that the stars, galaxies and everything else are moving away from each other, but when we look out into the night sky we don't actually observe anything moving. All the stars are just fixed and immovable, so these theories present a paradox, because how can the universe be expanding if we don't see it moving?"

Assuming that this professor is not trying to make the students think critically and eventually learn how to reconcile observations with theories, most of us would be wondering how in the world this guy got his job in the first place. If the professor asked this question and left it like that without ever trying to explain to the students the changes and advancements in our understanding over the last 100 years then we should be concerned about the level of education that these students were receiving.

Several years ago that may have been a valid question, but the scientific conversation has moved on since then as our understanding has changed to accommodate our new understanding, and what is taught in basic physics and astronomy classes has also changed to reflect this. Unfortunately the same has not happened with Schrödinger's Cat. The way it is presented in physics classes is the same way it has always been approached, and that approach does not reflect the shift in the physical or philosophical conversation over that last 70-80 years. Essentially physics teachers are still talking about Schrödinger's Cat like a paradox when there is none.

One of the main problems lies with the strict Copenhagen interpretation. The Copenhagen interpretation asserts that before a measurement is made the system exists simultaneously in all possible states (i.e. the cat is both alive and dead, or the particle is in both energy states 1 and 2). The problem with this is that a statement such as, "The cat is alive", fundamentally assumes that an observation has already been made. But no observation has been made. Insisting that the cat is either alive or dead or both before an observation is made fundamentally misunderstands what it means to be alive or dead. It would be like asking the question, "What is the mass of a certain rock on the far side of the moon?". It is a valid question and there are upper and lower bounds to what the mass might be but to insist that the mass of the rock is a simultaneous superposition of all possible masses does not make sense. Essentially the problem with saying that the particle (cat) exists in all possible states is that we would be insisting on knowing something that we do not know.

So when someone says, "The cat is both alive and dead at the same time." then they are effectively saying, "There exists some knowledge that I do not have, and that falls outside the realm of knowledge altogether, but I will now make a definitive statement about that thing and what it is, even though I do not know." In other words, "I know something that I do not know."

When put like this the paradox seems rather ridiculous. But to be fair to the original issue I will mention that both Schrödinger's Cat and the Copenhagen interpretation were trying to address a very interesting issue that presented itself with the advent of modern quantum mechanics. Under a classical consideration everything was self-existent with a definite state, but one of the conclusions of quantum mechanics was that nothing had a definite state until it was observed. This seemed to fly in the face of how we understood the world to work because originally the state of a particle (or anything for that matter) was inextricably linked to its existence. So, classically, it did not make sense to have a particle not be in a specific state, because that would imply that, at least until it was observed, it did not exist. The chain of logic can be characterized in the following syllogism:

All things that exist have a definite state and all things that have a definite state, by definition, exist. Quantum mechanics tells us that before an observation is made a particle is not in one specific state but exists in a range of possibilities. But in order for the particle to exist it must be in some state, so in order to preserve the existence of the particle we must assert that it exists in all possible states at the same time.

This particular syllogism leads to the conclusion that Schrödinger's Cat is both alive and dead at the same time, which is absurd, and it was this point that Schrödinger wished to make with his thought experiment. The original argument used by Schrödinger (and Einstein) dealt with the last statement in the syllogism which is the conclusion that the particle (cat) must exist in all possible states. While their argument may have been insightful it did not deal with the root of the problem, which comes from the original statement that in order for something to exist it must be in a specific state. Essentially the problem is that the original statement fundamentally assumes a classical view of the world and thus the conclusion, which is central to the Copenhagen interpretation, contains a mixture of both classical and modern views. You might call it a semi-classical view.

One way of thinking about this problem was expressed by Steven Weinberg.
"Bohr's version of quantum mechanics was deeply flawed, but not for the reason Einstein thought. The Copenhagen interpretation describes what happens when an observer makes a measurement, but the observer and the act of measurement are themselves treated classically. This is surely wrong: Physicists and their apparatus must be governed by the same quantum mechanical rules that govern everything else in the universe."
Essentially we cannot mix classical views with modern views. We must think of everything acting quantum mechanically, which means that we cannot assert that existence is determined by being in a particular state. If we take this approach then it completely removes the paradox presented by Schrödinger's Cat and the Copenhagen interpretation (but not the math, or the probabilities given by it!).


  1. "Unfortunately the same has not happened with Schrödinger's Cat. The way it is presented in physics classes is the same way it has always been approached, and that approach does not reflect the shift in the physical or philosophical conversation over that last 70-80 years. Essentially physics teachers are still talking about Schrödinger's Cat like a paradox when there is none."

    How true! I don't know why so many physicists continue to talk about quantum mechanics as if it is weird and not well understood. It is! We've made predictions confirmed by measurements from quantum physics to more significant figures than anything else in all of science.

    In fact, one of my pet peeve's is when people quote Bohr saying "Anyone who says they understand quantum mechanics doesn't know the first thing about quantum mechanics."

    Bohr's quote made sense 80 years when quantum mechanics was at the cutting edge of theoretical physics ago. But today???

    *Today even chemists have a good understanding of quantum mechanics!*

    One again, Weinberg correctly sets the record straight: the Copenhagen people were confused because they tried to understand quantum physics classically. Classic misstake. (pun?)

  2. "I will now make a definitive statement about that thing and what it is, even though I do not know."

    That sure isn't a problem limited to quantum mechanics!

    Thanks for the write-up. Now when I hear someone talk about the cat I can smugly think, "That's sooo yesterday." Unfortunately, my understanding of QM is pre-med level at best, so it will be an empty smugness.

  3. I would like to point out that I did not come to this realization about Schrödinger's Cat by myself. When I learned about it I learned it in the way I described above ("It is both alive and dead at the same time!"), but I never thought about it after that. I just grouped it with all the other weird "paradoxes" they like to throw at us (like Zeno's paradox...interestingly enough that one also has a simple answer but they never give the answer...I guess most people have never heard of a geometric series, but I digress). It was not until I took a class from Dr. Michael Arts (a rather black sheep in the Philosophy department at BYU, he actually thinks that Philosophy should produce knowledge! The nerve...) that I learned the answer to Schrödinger's Cat. His response was from a epistemological approach (the approach I took to introduce the idea, the "I will now make a definitive statement about that thing and what it is, even though I do not know." approach). It was that class that started me thinking about it and lead me to the realization that Schrödinger's Cat (and all of quantum mechanics) was consistently being misrepresented.

    The only problem with thinking of the world in quantum mechanical terms is that it is a radical change from how we normally look at it. But doing so is very interesting and exciting (philosophically). Unfortunately philosophy has not moved past Plato so it is in no position to consider our new understanding. But having said that I don't think that anyone has come up with a good way of explaining QM to those who don't have at least a bachelor's degree in physics.

  4. I've always thought the solution to Schrödinger's Cat was a function of Δt from when the cat was put into the box. And wasn't the guy putting the cat into the box making an observation? Doesn't this guy hold the key to the whole problem? We need to track him down. =:)

  5. You're right that there's no real problem in interpreting entangled states. But there is still a deep problem with Schrodinger's cat, which is the measurement problem. And I don't see how the Copenhagen interpretation has a prayer of solving it.

    When you open the box with the cat in it, the collapse postulate says you'll observe a collapsed eigenstate of the system with some probability. But the Schrodinger equation says that since you're a system of particles, you'll couple to the box and become a pure superposition of states (or, if you're a Copenhager, you'll join the "realm of the unknowable"). That's literally a logical contradiction in the foundations of quantum mechanics. One axiom says you'll be in eigenstate P. The other axiom says you won't.

    There are two main ways out of this -- you can modify the collapse postulate (e.g., Everett/many worlds), or you can modify the Schrodinger equation (e.g., Bohm, GRW). But these and all other proposals seem to be unsatisfactory in one way or another -- so this remains a huge problem in the foundations quantum theory.

  6. Nice post. It´s a problem that Schrodinger´s cat is such a famous thought experiment (often used instead as an analogy). In explaining quantum physics to lay audiences I don´t think it helps, and rather gives the impression of quantum physics being impossible to understand.

  7. Bryan,

    Thanks for your comment.

    You are only in a pure superposition of states if you turn off interactions. (Which in the real world you aren't.) These interactions destroy the superposition and therefore lead to a "collapse" of the wave function.

    A good article on this is "Quantum decoherence" article on the Wikipedia that says: "Decoherence occurs when a system interacts with its environment in a thermodynamically irreversible way. This prevents different elements in the quantum superposition of the system+environment's wavefunction from interfering with each other. Decoherence has been a subject of active research since the 1980s... A quantum state is a superposition of other quantum states, for instance, the spin states of an electron. In the Copenhagen interpretation, the superposition of states was described by a wave function, and the wave function collapse was given the name decoherence. Today, the decoherence program studies quantum correlations between the states of a quantum system and its environment. But the original sense remains, decoherence refers to the untangling of quantum states to produce a single macroscopic reality."

    In other words, interactions cause superpositions to "untangle" leading to a collapsed wave function, irregardless if whether there is some intelligent observer to observe it or not.

    This makes sense as the early universe went on existing in well defined states long before there was intelligent observers to "collapse" the wave functions. Irreversible interactions accomplish the same goal.

    Hence, Schrodinger's Cat could only be in a superposition of states if you turned all interactions of all the particles of the cat with themselves and outside sources off.

  8. Hey. Once again, great post. Personally, I guess I've never had a problem with Schrodinger's Cat, and I'm still kind of trying to see what the issue is. I think the difference is that I've never taught or learned it as a "paradox" per se. I've only really used it as an illustration of quantum superposition. Even though we all understand that a macroscopic cat can't occupy both an "alive" and "dead" state at the same time, it illustrates the fact that quantum mechanical objects do occupy multiple states at the same time -- in the form of a superposition. This is not a phenomenon that one sees in macro-objects and requires some form of illustration -- limited though it may be. For example, atoms are routinely in a superposition of multiple electronic states. This is kind of like it being both "excited and de-excited at the same time", even though what's really happening is it's just a superposition. The cat just works for me as an illustration for people who get scared at mathematical equations or the mention of a word like "superposition." (I only wish there were a good way of similarly illustrating the difference between $(|g> + |e>)/sqrt(2)$ and $(|g> - |e>)/sqrt(2)$, but I digress.) I guess I just haven't seen it presented as a serious paradox, only more as a memory hook or illustration of the concept. Anyways, great post.

  9. Decoherence is not enough to solve the measurement problem. Both Adler and Pearle have written excellent pieces on this.

    Look, the "decoherence program" you mention does provide a mechanism for the suppression of interference effects. But it never truly eliminates them. You've still got a partly-dead-and-partly-alive cat according to decoherence. The Copenhagen interpretation makes this bad situation even worse -- it means that systems are always in a superposition of eigenstates, and so you can never know anything at all!

  10. "Schrödinger was trying to show how ridiculous the Copenhagen interpretation is" -- actually the so-called 'Schrödinger's cat' paradox was first stated by Eugene Wigner (since he himself did not own a cat!)

  11. "Essentially we cannot mix classical views with modern views. We must think of everything acting quantum mechanically, which means that we cannot assert that existence is determined by being in a particular state. If we take this approach then it completely removes the paradox presented by Schrödinger's."

    This doesn't make sense to me. I get it at a basic level, but my question is how does this remove the paradox? The fact is that we experience the world classically, even though the classical world does not exist. What does it mean to accept the existence of something not in a particular state? Haven't we now just recreated the paradox back one step?

    I think Bryan has a point here.

    I don't see how the explanation above makes sense of Schrodinger's cat.

    Joseph's explanation would seem to resolve the paradox. But he seems to me to be saying that there are plenty of opportunities for the wave function to collapse at the cat level, so it has. But after reading Roger Penrose, I was under the understanding that this is at odds with current quantum theory. Penrose' twistor theory was meant in part to come up with a new theory where by the collapse of the wave function happens independent of observers. He threw his own theory into the "tentative" category and admits it didn't catch on. So I'm not sure I see that as a successful explanation of the cat paradox either.

  12. Bruce and Byran,

    You do bring up good points that this issue isn't 100% understood. I'm glad you've brought them up. Two things:

    1. Again, we know there has to be a solution as there were no intelligent observers during the early universe and wave functions seemed to be collapsed just fine. Or, even if you don't want to accept early universe physics, objects like distant stars seem to carry on just fine without intelligent observers collapsing their wave functions.

    2. Though ideas like "Quantum decoherence" aren't perfect, they've helped us make great strides into understanding how wavefunctions collapse on their own with interactions. Now, it could be that Penrose is correct and you need something further like twister physics.

    3. So, the fact that wave functions do seem to collapse just fine without intelligent observers around and the fact that we've made tremendous headway into resolving this issue leads me to believe that it isn't the "paradox" many make it out to be.

    But I could be wrong,

  13. Well Mr. Joseph Smidt, the question in this thought experiment seems to me not wether we need an intelligent observer to explain the wave function collapse but rather what the collapse itself means.
    That the intelligent observer bears no physical significance seems rather obvious aswell (I laugh at the Tao of Physics).
    And even though I only have basic quantum physics knowledge, it seems also plausible (note, plausible) from everyday experience that the cat is always either alive or dead and never alive and dead at the same time, which seems to contradict the quantum postulates, and hence the paradox.
    The more obvious statistical approach to the problem is ruled out I believe.
    I'd be more inclined to the decoherence approach to the problem in which the experiment-observer need not be counscious driven or related.
    An isolated system is always in a superposition of all possible states and when an interaction takes place, it "colapses". The cat is dead if and only if the system is triggered and always alive when it is in a superposition of triggered and not triggered or even if the system is collapsed into a not triggered state. Same as saying that the cat is dead only as long as the poisounous particle is defenly sent.

  14. Anonymous,

    "the question in this thought experiment seems to me not wether we need an intelligent observer to explain the wave function collapse but rather what the collapse itself means."

    I agree and think you are correct.

    "Same as saying that the cat is dead only as long as the poisounous particle is defenly sent."

    Yes, well said.

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