Roger Maioli

# Did Schrödinger think that a cat can be dead and alive at the same time?

Schrödinger’s cat is one of the most popular thought experiments in the history of science and philosophy. Proposed in 1935 by the Austrian-Irish physicist Erwin Schrödinger (1887–1961), the experiment shows that, on a certain interpretation of quantum mechanics, a cat locked in a steel chamber could be said to be simultaneously dead and alive.

The image of a cat that is simultaneously dead and alive is surely gripping. But did Schrödinger really believe that this was possible?

**He did not.**

Schrödinger’s thought experiment is an example of a *reductio ad absurdum *— a way of discrediting a theory or argument by showing that it leads to absurd consequences. The dead-and-alive cat, for Schrödinger, invalidates a certain way of interpreting quantum mechanics, known today as the Copenhagen interpretation.

What is an “interpretation” of quantum mechanics? It is a hypothesis regarding what quantum theory reveals about the **physical** world. Since the 1920s physicists have disagreed on what quantum mechanics implies about the actual state of the universe.

Quantum mechanics originally emerged less as a theory about the world than as a set of mathematical tools for making predictions in areas where classical physics failed. Early quantum ideas were developed to solve problems related to emission and absorption of electromagnetic radiation (light) and the motion of subatomic particles like electrons inside the atom, then newly discovered. Applying Newtonian physics to understand these systems led to results that increasingly diverged from the observations, prompting the development of a new theory.

The problem, in part, had to do with the observed behavior of waves and particles. Classical physics made a clear distinction between the behavior of waves and the behavior of particles. Particles are localized: they have position, they move in straight lines, and they bounce off other particles. Waves, on the other hand, are extended: they zig-zag, they cancel or amplify each other, they travel as ripples in ponds and spread like rainbows in the sky. However, early twentieth-century experiments showed results that could be better explained if light, which classical physics regarded as a wave, was instead localized and bouncing around like a particle. Conversely, as experiments probed deeper into the heart of matter, the electron showed distinct ripples as it moved past a narrow slit, a classical wave-like phenomenon. This made classical physics unable to make reliable predictions in this brave new micro-world.

The equations of quantum mechanics — including, notably, the one discovered by Schrödinger himself — enabled physicists to make accurate predictions about this new wave-like behavior of matter and the particle-like behavior of light, by means of what is called a **wave function**. A wave function is a mathematical description of a physical system, a description that combines the particle’s position and velocity into an extended, non-localized entity. Just as the laws of motion had enabled scientists to make predications within a Newtonian model, Schrödinger’s equation allows us to calculate the evolution of the wave function over time.

Here then was a new mathematical tool for calculating the outcomes of experiments that classical physics was unequipped to handle. This new tool, on the influential interpretation proposed by the German-Jewish physicist and mathematician Max Born, was a statistical one. The wave function, for Born, is the probability amplitude of finding the particle in a given state. In other words, instead of predicting the exact position or velocity of a given particle at time *t*, the wave function maps out a range of possible positions and velocities and determines the chances that the particle will be *here* or *there*, with *this* or *that* velocity, at time *t*. On this view, quantum mechanics is a probabilistic theory. It yields probable rather than definite predictions about the properties of a physical system.

Born’s statistical interpretation of the wave function prompted a further question: what do these predictions mean about the actual state of things in the real world? Do they mean that, at any given time, the particles themselves lack a definite position and velocity? Or do they mean that the equations involved are incomplete approximations that leave out important information about the world? Interpretations of quantum mechanics emerged as ways of addressing these questions. They try to spell out what the mathematic formalism of quantum theory reveals about physics.

The so-called Copenhagen Interpretation of quantum mechanics, developed among others by Niels Bohr (1885–1962) and Werner Heisenberg (1901–1976), derives unsettling conclusions from the theory. According to this interpretation, which exists in various (and sometimes incompatible) versions, particles only acquire definite classical properties like position and velocity once they are observed (or “measured”); prior to measurement, **particles exist in a state of superposition**, which combines the many probable positions and velocities mapped out by the wave function. A particle is neither *here *nor *there*, but in a combination of both. This is the crux of the matter as far as Schrödinger’s cat is concerned.

Furthermore, under the Copenhagen interpretation, the superposition is not directly observable. This is because the wave function that describes the world in terms of probabilities *collapses* when the system is observed, eliminating the superposition between probable states to reveal one single, definite set of properties. Once observed, the particle is either *here* or *there*, but not both.

Schrödinger had a very different interpretation of quantum mechanics, according to which equations like his own provided incomplete descriptions of physical reality; the probabilities governing the properties of quantum systems, in his view, were mathematical (or epistemological) but not physical (or ontological). In other words, we can at best make probabilistic statements about the physical world; but this is not to say that the physical world itself is probabilistic, in the sense of lacking definite properties.

Schrödinger accordingly rejected the Copenhagen Interpretation in a 1935 paper entitled “The Present Situation in Quantum Mechanics.” This paper regards the notion of superpositions, which Schrödinger called “a blurred reality,” as unacceptable. Blurriness may seem tolerable, he points out, while we confine superposition to the realm of subatomic particles: “Inside the nucleus blurring doesn't bother us.” And yet “serious misgivings arise if one notices that the uncertainty affects macroscopically tangible and visible things, for which the term ‘blurring’ seems simply wrong.”

Schrödinger found a forceful way to illustrate this point. He imagined a scenario where the “blurriness” of microscopic particles (in his example, one atom) would extend to the macroscopic level. What if, he asked, the properties of a single atom had consequences for the properties of large objects? Then, if it were true that the atom, prior to observation, exists in a state of superposition, the large objects affected by it would also have to be in a state of superposition.

This is where the cat comes in. Schrödinger imagines a complicated contraption in which a single atom has an equal probability of decaying or not decaying; if it decays, it will release poison and kill a cat locked in a steel chamber; if it does not decay, the cat will survive; and if we believe that the atom, prior to observation, can be in a superposition as both decayed and undecayed, then we should accept that the cat, prior to observation, can equally be simultaneously dead and alive:

“One can even set up quite ridiculous cases. A cat is penned up in a steel chamber, along with the following device (which must be secured against direct interference by the cat): in a Geiger counter there is a tiny bit of radioactive substance, so small, that perhaps in the course of the hour one of the atoms decays, but also, with equal probability, perhaps none; if it happens, the counter tube discharges and through a relay releases a hammer which shatters a small flask of hydrocyanic acid. If one has left this entire system to itself for an hour, one would say that the cat still lives if meanwhile no atom has decayed. The psi-function [i.e. the wave function] of the entire system would express this by having in it the living and dead cat (pardon the expression) mixed or smeared out in equal parts.”

Through this example, Schrödinger concludes, “an indeterminacy originally restricted to the atomic domain becomes transformed into macroscopic indeterminacy” — and the macroscopic consequences are absurd enough to call into question the assumptions of the Copenhagen Interpretation. The cat paradox, according to Schrödinger, “prevents us from so naively accepting as valid a ‘blurred model’ for representing reality.”

Neither Bohr nor Heisenberg would commit to strong claims about what the universe is like prior to observation; on their view, what cannot be observed simply does not matter. Schrödinger, however, feared that the notion of superposition would have disturbingly misguided implications about the physical world. Whether he was right is still debated by modern physicists and philosophers of science. But one thing we know for sure: Schrödinger did not believe in cats that were simultaneously dead and alive.

*This post has revised for accuracy by my friend Wladimir Lyra, Assistant Professor of Astronomy at New Mexico State University, to whom I*’*m grateful. You can read about his fascinating work here: *http://www.wladimirlyra.com/research.html.

The quotations above are from John D. Trimmer’s English translation of Schrödinger essay. Trimmer’s translation was originally published in *Proceedings of the American Philosophical Society*, 124, 323-38, and subsequently in J.A. Wheeler and W.H. Zurek, eds. *Quantum Theory and Measurement *(Princeton university Press, New Jersey 1983).* *