A Re-Evaluation of Schrodinger s Cat Paradox Wells Lucas Santo 5 December 2012 PL2293 Philosophy of Quantum Mechanics Professor Jonathan Bain 1
1 Introduction This paper is a re-examination of the famous Cat Paradox proposed by Erwin Schrodinger in 1935. Today, Schrodinger s Cat is discussed almost synonymously with the Measurement Problem of Quantum Mechanics. However, I posit that Schrodinger s Cat also proposes an equally important challenge of the literal interpretation of Quantum Mechanics by offering a mystifying view of Quantum Superposition. In order to show this, I will trace the discussion of Schrodinger s Cat from its inception to the present over the course of this paper. In Section 2, I will take an etiological move back to Schrodinger s paper, The Present Situation in Quantum Mechanics, where the Cat Paradox was originally proposed, and re-examine his original intentions associated with introducing the Cat Paradox. In conjunction with looking at Schrodinger s paper, I will also look at the 1935 EPR Argument, which Schrodinger admits to be a key motivator for his own work. In Section 3, I describe the Measurement Problem that arises as a result of the Cat Paradox and discuss how later interpretations of Quantum Mechanics, such as Wigner s Friend, have tried to solve the Measurement Problem in relationship with Schrodinger s Cat. In Section 4, I will then put Schrodinger s Cat in conversation with the Many Worlds Interpretation of Quantum Mechanics. In Section 5, I introduce a potential solution to Schrodinger s Cat offered earlier this year by Professor Art Hobson of the University of Arkansas, Fayetteville, who molds his discussion around the phenomenon of Quantum Decoherence. Finally, in Section 6, I conclude this paper with a quick discussion on what a complete resolution of Schrodinger s Cat promises. 2 The Cat Paradox -By-Itself 2.1 Historical Context When Erwin Schrodinger imagined the Cat Paradox in 1935, one of the most hotly debated topics of the day was whether Quantum Mechanics (QM) could be taken as a successful ontologically literal physical theory. Earlier that year, Einstein, Podolsky, and Rosen (EPR) contended that in order for a physical theory to be successful, or satisfactory, it had to be both correct and complete (1935, pg. 777). While the 2
correctness of Quantum Mechanics can simply be tested by comparing the result of an a priori model with the a posteriori empirical result, EPR believed that completeness could only be fulfilled when every element of the physical reality must have a counterpart in the physical theory (1935, pg. 777). From here, EPR argued quite famously that the wave function (otherwise written as ψ-function) was incomplete: if it were actually complete, it would allow for non-locality, which they could not bear to accept. It is this that motivated Schrodinger to posit the Cat Paradox, in an attempt to make an argument for the incompleteness of QM without having to invoke the ideas of locality and we now refer to as entanglement (1935, pg. 163). For Schrodinger, the ψ-function is defined to be complete in the sense that it does not at all lack precision, but rather adds precision to our efforts at describing the world. With the ψ-function, we can calculate with certainty a fully determined statistical distribution to every variable, thus outlining exactly what outcomes are probable, and excluding all other outcomes that are not at all possible (1935, pg. 154). Even then, definite values of properties cannot be predicted by the ψ-function, and can only be obtained through direct measurements of the system. This is what deeply disturbs Schrodinger. How can we assume QM to be complete and take it ontologically seriously when the ψ-function merely describes a system as an ensemble of states in superposition (1935, pg. 155)? Without resolving this issue, the dynamics of the ψ-function cannot properly describe our reality by itself. Schrodinger thus devises the famous Cat Paradox in order to add weight this troubling issue of both measurement and superposition. 2.2 Coins Versus Cats In his thought experiment, Schrodinger describes a cat that is locked in a steel chamber with a Geiger counter that measures a radioactive substance, whose atoms have a 50-50 chance of decaying after a certain period of time. If an atom decays, the Geiger counter releases a hammer that breaks a vial of hydrocyanic acid and kills the cat (1935, pg. 157). The question then becomes, if we leave this cat alone for a period of time, how do we know if it is alive or dead? The obvious answer would be to open the steel chamber and simply check that is, to make a measurement. But before we make such a measurement, can we know and say which state that the cat is in? 3
In order to better explain the spookiness of the Cat Paradox, I would like to relate it to the flipping of an ideal and fair coin. Let us say that I flip a fair coin and immediately cup my hand over it such that I do not observe which side it has landed on. Because I have not yet measured the outcome of the flip, I am epistemically uncertain whether the coin has landed heads or tails. Like with the aliveness of Schrodinger s Cat, there is a 50-50 chance that either event has occurred. When I take my hand off the coin, I am then able to see which of the two outcomes has actually happened. However, with the flipping of the coin, I can be certain that the coin definitely landed on either heads or tails before I looked at it. In this case, my measurement did not cause the coin to become either heads or tails. With a literal QM interpretation, I cannot be so certain that this holds true for the aliveness of Schrodinger s Cat, for the state of the cat is in a superposition an ontological uncertainty. It seems to me that it is the issue of superposition, or more specifically the literal interpretation of it, that primarily distinguishes the quantum weirdness of Schrodinger s Cat with the uncertainty of a simple coin toss. 2.3 The Blurriness What is so spooky about superposition is that I cannot adopt any of the four classically logical descriptions of the cat s aliveness. In superposition, the cat is not dead, not alive, not both alive and dead, and not neither alive nor dead. So what can I say of the cat s state before I make a measurement? If the literal interpretation of superposition is to be taken seriously, Schrodinger asks, Have [systems in superposition] then no reality, perhaps a blurred reality? (1935, pg. 155) For things at the atomic level, this blurriness does not seem to pose a great challenge for physicists. However, when extended to the macroscopic scale, as with Schrodinger s Cat, it seems nonsensical and unacceptable to allow for a blurring of reality. For anyone who wishes to adopt any sort of ontologically, or ontic, literal interpretation of Quantum Mechanics, I propose that they must first be able to more adequately explain what occurs when a system is in a superposition of states. Of course, this is not what most physicists and philosophers find about Schrodinger s Cat that is most troubling rather, for them, the trouble comes from the Measurement Problem. 3 The Measurement Problem 4
After describing the Cat Paradox, Schrodinger continues by explaining that the macroscopic indeterminacy can then be resolved by direct observation, or in other words, by measurement (1935, pg. 157). This then brings about the core of the Measurement Problem what exactly does a measurement entail? More importantly, when does a measurement occur? And finally, is measurement the only thing that can cause a superposition to collapse? For Schrodinger s Cat, it would be quite odd to say that if we never look inside the steel chamber, the cat will forever be in a blurred reality. However, if a theory were to propose that the state of the cat does collapse to either being alive or dead before measurement, it would still need to describe when and how that collapse occurs. Many interpretations of quantum mechanics since 1935 have sought to resolve the paradox of Schrodinger s Cat. Wigner s Friend, for example, leads to the idea that there are two fundamentally different sorts of physical systems in the world, and introduces the philosophical notion of Cartesian mind-body dualism into mainstream physics (Albert 1994, pg. 82). In his interpretation, Wigner believes that collapse only occurs when a conscious being observes a system in superposition. The cat becomes either alive or dead when the first conscious being observes the state of the cat. However, this requires of Wigner a great undertaking to discuss what exactly consciousness is defined as, and whether it can actually be said to exist or not. 1 As a result, it seems that most contemporary philosophers and physicists adopt the Many Worlds interpretation, as it offers them a seemingly clever solution to the Cat Paradox. 4 Many Worlds and Many New Cats In the Many Worlds interpretation, which was originally proposed by Hugh Everett in 1957 and expanded on by Bryce DeWitt in 1970, each term in a superposition given by the ψ-function corresponds literally to a different physical world (Albert 1994, pg. 113). For instance, if an electron in the state black > is sent through a Hardness measuring box, the resulting superposition of hard > and soft > terms would correspond to two wholly different worlds: one where the electron is found to be hard, and the other where the electron is found to be soft. 1 The materialist Daniel Dennett would surely propose, then, that collapse never occurs, while the panpsychist Galen Strawson would argue that collapse always occurs. 5
An advocate of the Many Worlds interpretation would thus say that in performing the Schrodinger s Cat experiment, our world would split into two separate, non-interacting worlds, where the cat is alive in one world and dead in the other. It seems at first glance that this interpretation of QM successfully avoids the sort of blurriness that bothers Schrodinger, but as Albert points out, the Many Worlds interpretation still leads to many new problems. For instance, what does it mean for there to be a 50% chance of Schrodinger s Cat being alive or dead, if both cases necessarily will occur in different worlds (Albert 1994, pg. 115)? Furthermore, Hughes (1992, pg. 293) points out that experimentally, the Many Worlds interpretation still leads to the same predictions as a literal interpretation of QM. For when a measurement occurs, we cannot perceive the phenomenon of world splitting, and as a result, the wave packet has collapsed no less mysteriously (Hughes 1992, pg. 293). Though Schrodinger s Cat may not suffer from any blurring of reality due to world splitting, we still do not know whether the cat is alive or dead until we open the steel chamber and look inside. In addition, I must ask when exactly this phenomenon of world splitting occurs. If we believe that world splitting semantically replaces the phenomenon of a measurement, then we still run into all of the same problems as before. For instance, at which point in time during the Schrodinger s Cat experiment does the world split? Splitting cannot occur right when we close the steel chamber with the cat inside, for we could simply open the chamber back up and save the cat before any radioactive atoms have the chance to decay. Similarly, splitting cannot only occur when we open up the steel chamber to check on the cat, because that would still leave the cat in a blurred reality prior to checking on the cat just as the Measurement Problem did. In conclusion, it seems that trying to pinpoint the time when a world splits is quite similar a task as trying to define when a measurement occurs, and perhaps the Many Worlds interpretation as commonly understood is not enough to address the Cat Paradox. 5 Hobson and Decoherence In an article published earlier this year, Art Hobson argues for a solution to Schrodinger s Cat that utilizes both entanglement and Quantum Decoherence. First, Hobson makes the claim that the common description of Schrodinger s Cat as being in the state cat> = a life> + b death> is incorrect, and instead, the cat 6
state must be written cat> = a live cat> undecayed nucleus> + b dead cat> decayed nucleus> in order to express an entanglement between the cat and the radioactive atom (2013, pg. 4). This description of the Cat Paradox in terms of entangled states seems to be wholly valid if we perform the thought experiment with some slight modifications. Let us imagine that our steel chamber is technologically advanced, and allows us to separate the chamber in half, while keeping the contents of the two halves hidden. If we run the Schrodinger experiment for a certain period of time, we can then separate the chambers and bring them a great distance apart from one another, before opening either of the chambers and looking inside. If we look inside the chamber with the radioactive atom and see that the nucleus has decayed, then we know that the cat is no longer alive. Conversely, if we see that the nucleus has not decayed, then we know that the cat is still alive. Following a conventional explanation of entanglement, we can say that both the cat and the nucleus are in superposition states until a measurement is made on either one of the two. It is only at this point that collapse occurs. However, Hobson does not stop here. By operating on the idea that an entangled system necessarily interacts with its environment, Hobson claims that environmental interactions cause the entangled system to decohere, which for him, is equivalent to superposition collapse (2013, pg. 1). He believes, then, that we do not need to wait until a measurement is performed in order for an entangled system to collapse. In fact, Hobson boldly states that looking at the outcome changes nothing, beyond informing the observer of what has already happened (2013, pg. 4). Given that his interpretation of Quantum Decoherence is accurate, Hobson s solution to Schrodinger s Cat Paradox would essentially escape the Measurement Problem and the issue of blurriness by reducing the ontic uncertainty of all entangled states to mere epistemic uncertainty. Not knowing whether the cat is alive or dead would be no more mysterious or distressing than whether a coin landed heads-up or tails-up. But can we accept Hobson s interpretation of Quantum Decoherence? For all practical purposes, it may be acceptable to say that Decoherence and collapse are equivalent, but for Hobson to unequivocally equate the two seems to be too bold of an assertion, especially considering that it may be ideally possible to distinguish between a decohered and a collapsed state. Furthermore, if Decoherence does equate to collapse, we must still ask when Decoherence exactly occurs, and whether the 7
system will still suffer from blurriness at any point in time. Nonetheless, Hobson s attempt at solving Schrodinger s Cat and escaping the Measurement Problem can be learned from, especially in considering the cat state as an entanglement of states, rather than a mere superposition. If we choose to do this, however, we will be forced to abandon Schrodinger s original goal of challenging the literal interpretation of Quantum Mechanics without having to deal with entanglement, as EPR did. 6 Conclusion: What A Complete Resolution Promises In conclusion, we can trace the origin of Schrodinger s Cat Paradox as an attempt to question the literal, ontic interpretation of Quantum Mechanics. By proposing a sort of reductio ad absurdum argument, Schrodinger showed how quantum superpositions could be amplified from a microscopic to macroscopic scale, and that a literal interpretation of QM would lead to an unacceptable blurriness of reality. What exactly does this blurriness mean, and what does it entail for those experiencing it? In addition, the Cat Paradox raises the question of when a measurement occurs and what exactly a measurement is defined as. Therefore, in order for an interpretation of QM to be seriously considered, it must first answer the questions posed by Schrodinger s Cat for both the Measurement Problem and the Superposition Problem. While looking at different proposed solutions to the Cat Paradox, we may also consider whether that interpretation is complete as defined by EPR. While both the Wigner s Friend and Many Worlds interpretations seem to explain current problems of physical reality quite well, the mind-body duality of Wigner s Friend and the phenomena of world-splitting in Many Worlds seem to introduce more unanswered problems that do not necessarily solve Schrodinger s Cat. Finally, as Hobson shows, considering Schrodinger s Cat as a question of entanglement seems to slightly aid our task of escaping the Cat Paradox, but we must be very careful when adopting certain theories such as Decoherence. Perhaps, once we understand more about Decoherence can we move closer to addressing both the Superposition and the Measurement Problems. 8
References Albert, D.Z. (1994). Quantum Mechanics and Experience. Harvard University Press. Einstein, A., Podolsky, B., & Rosen N. (1935). Can Quantum-Mechanical Description of Physical Reality Be Considered Complete? Physical Review, 47, pp. 777-780. Hobson, A. (2013) Two-photon interferometry illuminates quantum state collapse. Physical Review A, 88, 022105. Hughes, R.I.G. (1992). The Structure and Interpretation of Quantum Mechanics. Harvard University Press. 9