Schrödinger’s Cat


The famous paradox of Schrödinger’s cat is a thought experiment by the eminent physicist Erwin Schrödinger. He discovered the fundamental mathematics of quantum mechanics and was awarded the Nobel Prize in 1933. He described this idea in order to demonstrate the absurdity of quantum theory. It means the cat has to be alive and dead at the same time.

Essentially, a cat in a closed box has a fifty-fifty chance of being killed by a quantum device. According to standard quantum mechanics, the cat is then in a superposed state of dead and alive at the same time, as in the first picture below. Which does not make sense. As we know, as is obvious, in the ordinary world such a thing is always one way or the other.

Schrödinger's cat cartoon with 2 panes. First shows cat alive. Second shows cat alive and dead superposed.
Schrödinger’s cat

Then, according to the physics, when Schrödinger observes the state of the cat, it thereby becomes determinate. And this too of course makes no sense. How can looking at something change what is physically real.

No Collapse

In the many-worlds universe of Everett’s famous theory, both versions of the outcome become real. They exist in different parallel versions of an ordinary world. This was Everett’s solution to the measurement problem. It was a stroke of genius. Central to Everett’s theory is that there is no collapse. Every possible version of the world comes to exist. So in this case, each version of the outcome comes to exist, each one existing in the corresponding version of the world.

Illustration of Schrödinger's cat showing parallel realities in which the cat is dead and alive
Schrödinger’s cat in two parallel realities

This was confirmed by the pioneering physicist Bryce DeWitt. He was the first to take a significant interest in Everett’s work. He challenged Everett on various points but eventually confirmed his theory. As he stated:

Schrodinger felt that the wave mechanics that led to this paradox presented an unacceptable description of reality. However, Everett, Wheeler and Graham’s interpretation of quantum mechanics pictures the cats as inhabiting two simultaneous, noninteracting, but equally real worlds. (1970, 31)

What has never been resolved is that the strange collapse seems to happen on observation. So there is a great mystery about this process, the process that determines what is real. The superworld provides the solution.

The Superworld Solution

The key point is that Schrödinger is in both these versions of the ordinary world. So in his superworld, the cat is indeed both alive and dead, as in the first picture. Then, as he makes the observation of the state of the cat, say the cat is alive, he exists only in worlds in which the cat lives. This diagram, originally by Michael Lockwood, helps to make clear the ontology proposed in Avant Garde Science.

Diagram of the class of worldlines in Schrödinger's cat (Lockwood, 1989)
The class of worldlines in Schrödinger’s cat (Lockwood, 1989)

The cylinder represents the class of all the worlds in Schrödinger’s superworld. The two lines stand for a specific world in each class. The blue section is the class of worlds in which he observes the cat dead, and the yellow section the class of those in which he observes it alive.

At the bottom, where it is green, before he observes the outcome, Schrödinger sees only the outside of the box. So he exists both in worlds where the cat is alive and worlds where it is dead. So in the physical reality of his superworld, the cat really is alive and dead at the same time. This looks like the top picture, but it is actually the two versions of the world in the second picture, superposed.

Then, once the observation is made, his superworld includes only the worlds in which, say, the cat is alive, the sunny yellow version. His superworld is all that changes, but for him the effect is the collapse dynamics – change of the quantum state of the physical reality, on observation.

This resolves the central paradox of quantum theory, the measurement problem. The problem is that the world seems to change when an observation is made. The resolution is that the world itself does not change. What changes is the class of worlds in which the individual exists.

Probability

With this diagram of the class of worlds by Lockwood, the origin of probability becomes perfectly clear. Probability is how likely something is to happen. The probability of getting ‘tails’ when you toss a coin is a 1 in 2 chance, so the probability is 1/2. It seems obvious, but the basis of probability has never been fully understood.

In the superworld of the mind the nature of probability is self evident. It is the percentage of worlds in which a particular event will happen. As illustrated in the third diagram, Schrödinger exists in an equal number of worlds where the cat lives and the cat dies. This is the green section of the image.

Then, when he makes the crucial observation, his class of worlds becomes half of these worlds. When he observes inside the box, say the cat is alive, his superworld contains only worlds in which the cat lives. This is the yellow section of the image. So the chance of his making an observation in a world where the cat lives is 50 / 50 , 1/2.

If the experiment was modified so that the cat had a only a 30% chance of survival, then the yellow section would be much smaller, being 30% of the total, and the blue section much larger, 70% of the total, as in the diagram below. In this case, the probability of Schrödinger finding himself in a world where the cat survived 30% because only 30% of the worlds he is in have a live cat.

Probability of events in the superworld is simply the percentage of worlds in which a specific event happens.

Diagram of the class of worldlines in Schrödinger's cat with 30/70 probability (Lockwood, 1989)
Schrödinger’s cat with 30/70 probability (Lockwood, 1989)