Schrödinger’s Cat

Erwin Schrödinger’s intention for his infamous cat-killing box was to discredit certain non-intuitive implications of quantum mechanics, of which his wave mechanics was the first mathematical formulation.
Albert Einstein originated the suggestion that the superposition of Schrödinger’s wave functions implied that two different physical states could exist at the same time. This is correct for so-called “entangled” states, but it applies only for atomic level phenomena and over limited distances that preserve the coherence of the wave functions.

Einstein wrote to Schrödinger with the idea that the decay of a radioactive nucleus could be arranged to set off a large explosion. Since the moment of decay is unknown, Einstein argued that the superposition of decayed and undecayed nuclear states implies the superposition of an explosion and no explosion. Many years later, Richard Feyman made this a nuclear explosion! (What is it about some scientists?)

Einstein and Schrödinger did not like the fundamental randomness implied by quantum mechanics. They wanted to restore determinism to physics. Indeed Schrödinger’s wave equation predicts a perfectly deterministic time evolution of the wave funcion. Randomness enters only when a measurement is made and the wave function “collapses.”

Schrödinger devised a variation in which the random radioactive decay would kill a cat. Observers could not know what happened until the box is opened.The details of the tasteless experiment include:

  • a bit of radioactive material with a decay half-life likely to emit an alpha particle during a time T
  • a Geiger counter which produces an avalanche of electrons when the alpha particle passes through it
  • an electrical circuit energized by the electrons which drops a hammer
  • a flask of a deadly hydrocyanic acid gas, smashed open by the hammer.

The gas will kill the cat, but the exact time of death is unpredictable and random because of irreducible quantum indeterminacy.This thought experiment is widely misunderstood. It was meant to suggest that quantum mechanics describes the simultaneous (and obviously contradictory) existence of a live and dead cat. Here is the famous diagram with a cat both dead and alive.

What’s wrong with this picture?

Quantum mechanics claims only that the time evolution of the Schrödinger wave functions for the probability amplitudes of nuclear decay accurately predict the proportion of nuclear decays that will occur in a given time interval.More specifically, quantum mechanics provides us with the accurate prediction that if this experiment is repeated many times (the SPCA would disapprove), half of the experiments will result in dead cats.

Note that this is a problem in epistemology. What knowledge is it that quantum physics provides?

If we open the box at the time T when there is a 50% probability of an alpha particle emission, the most a physicist can know is that there is a 50% chance that the radioactive decay will have occurred and the cat will be observed as dead or dying.

If the box were opened earlier, say at T/2, there is only a 25% chance that the cat has died. Schrödinger’s superposition of live and dead cats would look like this.

If the box were opened later, say at 2T, there is only a 25% chance that the cat is still alive. Quantum mechanics is giving us only statistical information – knowledge about probabilities.

Schrödinger is simply wrong that the mixture of nuclear wave functions that accurately describes decay can be magnified to the macroscopic world to describe a similar mixture of live cat and dead cat wave functions and the simultaneous existence of live and dead cats.

What do exist simultaneously in the macroscopic world are genuinealternative possibilities for future events. This is what bothered physicists like Einstein, Schrödinger, and Max Planck who wanted a return to deterministic physics. It also bothers determinist and compatibilistphilosophers who have what William James calls an “antipathy to chance.”

Until the information comes into existence, the future is indeterministic. Once information is macroscopically encoded, the past is determined.

How does information physics resolve the paradox?

As soon as the alpha particle sets off the avalanche of electrons in the Geiger counter (an irreversible event with a significant entropy increase), new information is created in the world.For example, a simple pen chart recorder attached to the Geiger counter could record the time of decay. Notice that as usual in information creation, the energy expended by a recorder increases the entropy more than the increased information decreases it, thus satisfying the second law of thermodynamics.

Even without a mechanical recorder, the cat’s death sets in motion biological processes that an equivalent, if gruesome, recording. When a dead cat is the result, a sophisticated autopsy can tell when Schrödinger’s cat died because the cat’s body is acting as an event recorder. There never is a superposition of live and dead cats.

The paradox points clearly to the Information Philosophy solution to the problem of measurement. Human observers are not required to make measurements. The cat is the observer.

In most physics measurements, the new information is captured by apparatus well before any physicist has a chance to read any dials or pointers that indicate what happened. Indeed, in today’s high-energy particle interaction experiments, the data may be captured but not fully analyzed until many days or even months of computer processing establishes what was observed. In this case, the experimental apparatus is the observer.

See Erwin Schrödinger on I-Phi 

Leave a Reply

Fill in your details below or click an icon to log in: Logo

You are commenting using your account. Log Out / Change )

Twitter picture

You are commenting using your Twitter account. Log Out / Change )

Facebook photo

You are commenting using your Facebook account. Log Out / Change )

Google+ photo

You are commenting using your Google+ account. Log Out / Change )

Connecting to %s