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!).