The details of the tasteless experiment include:

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

This thought experiment is widely misunderstood. It was meant (by both Einstein and Schrödinger) 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.

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.

The kind of coherent superposition of states needed to describe an atomic system as in a linear combination of states (see Paul Dirac's explanation of superposition using three polarizers) does not describe macroscopic systems.

Instead of a linear combination of pure quantum states, with quantum interference between the states, i.e.,

quantum mechanics tells us only that there is 50% chance of finding the cat in either the live or dead state, i.e.,

Just as in the quantum case, this probability prediction is confirmed by the statistics of repeated identical experiments, but no interference between these states is seen.

What do exist simultaneously in the macroscopic world are genuine alternative possibilities for future events. There is the real possibility of a live or dead cat in any particular experiment. Which one is found is irreducibly random, unpredictable, and a matter of pure chance.

Genuine alternative possibilities is what bothered physicists like Einstein, Schrödinger, and Max Planck who wanted a return to deterministic physics. It also bothers determinist and compatibilist philosophers who have what William James calls an "antipathy to chance." Ironically, it was Einstein himself, in 1916, who discovered the existence of irreducible chance, in the elementary interactions of matter and radiation.

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

For example, a simple pen-chart recorder attached to the Geiger counter could record the time of decay, which a human observer could read at any later time. 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 constitute an equivalent, if gruesome, recording. When a dead cat is the result, a sophisticated autopsy can provide an approximate time of death, because the cat's body is acting as an event recorder. There never is a superposition (in the sense of the simultaneous existence) 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. In this case, 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.

And, in general, the universe is its own observer, able to record (and sometimes preserve) the information created.

The basic assumption made in Schrödinger's cat thought experiments is that the deterministic Schrödinger equation describing a microscopic superposition of decayed and non-decayed radioactive nuclei evolves deterministically into a macroscopic superposition of live and dead cats.

But since the essence of a "measurement" is an interaction with another system (quantum or classical) that creates information to be seen (later) by an observer, the interaction between the nucleus and the cat is more than enough to collapse the wave function. Calculating the probabilities for that collapse allows us to estimate the probabilities of live and dead cats. These are probabilities, not probability amplitudes. They do not interfere with one another.

After the interaction, they are not in a superposition of states. We always have either a live cat or a dead cat, just as we always observe a complete photon after a polarization measurement and not a superposition of photon states, as P.A.M.Dirac explains so simply and clearly.

According to quantum mechanics the result of this experiment will be that sometimes one will find a whole photon, of energy equal to the energy of the incident photon, on the back side and other times one will find nothing. When one finds a whole photon, it will be polarized perpendicular to the optic axis. One will never find only a part of a photon on the back side. If one repeats the experiment a large number of times, one will find the photon on the back side in a fraction sin²α of the total number of times.

Quantum mechanics similarly gives us only the probability of finding live cats (or dead cats) in a large number of identically prepared experiments (pace the SPCA)

Thus we may say that the photon has a probability sin²α of passing through the tourmaline and appearing on the back side polarized perpendicular to the axis and a probability cos²α of being absorbed. These values for the probabilities lead to the correct classical results for an incident beam containing a large number of photons.

In this way we preserve the individuality of the photon in all cases. We are able to do this, however, only because we abandon the determinacy of the classical theory. The result of an experiment is not determined, as it would be according to classical ideas, by the conditions under the control of the experimenter. The most that can be predicted is a set of possible results, with a probability of occurrence for each...

When we make the photon meet a tourmaline crystal, we are subjecting it to an observation. We are observing whether it is polarized parallel or perpendicular to the optic axis. The effect of making this observation is to force the photon entirely into the state of parallel or entirely into the state of perpendicular polarization. It has to make a sudden jump from being partly in each of these two states to being entirely in one or other of them. Which of the two states it will jump into cannot be predicted, but is governed only by probability laws. If it jumps into the parallel state it gets absorbed and if it jumps into the perpendicular state it passes through the crystal and appears on the other side preserving this state of polarization.

Superposition and Indeterminacy

The non-classical nature of the superposition process is brought out clearly if we consider the superposition of two states, A and B, such that there exists an observation which, when made on the system in state A, is certain to lead to one particular result, a say, and when made on the system in state B is certain to lead to some different result, b say. What will be the result of the observation when made on the system in the superposed state? The answer is that the result will be sometimes a and sometimes b, according to a probability law depending on the relative weights of A and B in the superposition process. It will never be different from both a and b.

There is no justification for assuming an intermediate (and absurd) condition of simultaneous live and dead cats. The thing that is "intermediate" is the probability, not the outcome.

The intermediate character of the state formed by superposition thus expresses itself through the probability of a particular result for an observation being intermediate between the corresponding probabilities for the original states,† not through the result itself being intermediate between the corresponding results for the original states.

† The probability of a particular result for the state formed by superposition is not always intermediate between those for the original states in the general case when those for the original states are not zero or unity, so there are restrictions on the 'intermediateness' of a state formed by superposition.

In this way we see that such a drastic departure from ordinary ideas as the assumption of superposition relationships between the states is possible only on account of the recognition of the importance of the disturbance accompanying an observation and of the consequent indeterminacy in the result of the observation. When an observation is made on any atomic system that is in a given state, in general the result will not be determinate, i.e., if the experiment is repeated several times under identical conditions several different results may be obtained. It is a law of nature, though, that if the experiment is repeated a large number of times, each particular result will be obtained in a definite fraction of the total number of times, so that there is a definite probability of its being obtained. This probability is what the theory sets out to calculate.

(The Principles of Quantum Mechanics, chapter 1, pp.5-14)

Decoherence theorists claim that they explain the "mysterious" non-appearance of macroscopic superpositions of states. But quantum mechanics does not predict such states, despite the popular idea of macroscopic superposition of live and dead cats.

The system is a substance in chemically unstable equilibrium, perhaps a charge of gunpowder that, by means of intrinsic forces, can spontaneously combust, and where the average life span of the whole setup is a year. In principle this can quite easily be represented quantum-mechanically. In the beginning the psi-function characterizes a reasonably well-defined macroscopic state. But, according to your equation [i.e., the Schrödinger equation], after the course of a year this is no longer the case. Rather, the psi-function then describes a sort of blend of not-yet and already-exploded systems. Through no art of interpretation can this psi-function be turned into an adequate description of a real state of affairs; in reality there is no intermediary between exploded and not-exploded. 

Schrödinger turned the gunpowder into his Cat.