Maybe There’s Just One Universe And The Cat Is Just Alive (Or Dead)

Asserting that [Schrödinger’s] cat is both alive and dead is akin to a baseball fan saying that the Yankees are stuck in a superposition of both won and lost until he reads the box score. It’s an absurdity, a megalomaniac’s delusion that one’s personal state of mind makes the world come into being.

Hans Christian von Baeyer, Quantum Weirdness? It’s All In Your Mind, Scientific American 308:54-61.

There are a number of different interpretations of quantum mechanics, but the two most popular (and the ones most found in science fiction) are the Copenhagen Interpretation and the Many-Worlds interpretation. In the Copenhagen Interpretation, developed principally by physicists Niels Bohr and Werner Heisenberg in 1920, a quantum particle doesn’t exist in one state or another, but in all possible states at once. It isn’t until we observe its state that a quantum particle is forced to choose one probability, and that’s the state that we observe. This is still the orthodox and most popular interpretation.

In the Many-Worlds interpretation, first developed by physicist Hugh Everett in 1957, for each possible outcome of any given action, the universe splits to accommodate each one, and everything that could have possibly happened in the past, but didn’t, has occurred in some other universe or universes. This interpretation removes the observer from the equation, and appears to reconcile the observation of non-deterministic events, such as random radioactive decay, with the fully deterministic equations.

But now there’s a relatively new interpretation called Quantum Bayesianism (or QBism) that combines quantum theory with Bayesian probability theory in an effort to eliminate the paradoxes found in previous interpretations, or at least put them in a less troubling form. It does this by redefining the wave function – a mathematical expression of objects in the quantum state. In earlier interpretations, the wave function is a real property of the object. But under QBism, the wave function is simply a mathematical tool and nothing more. The wave function has no bearing on the reality of the object being studied, just as the long-division problem to calculate your car’s fuel consumption has no effect on the gas mileage. Remove the wave function, and paradoxes – particles seem to be in two places at once, information appears to travel faster than the speed of light, cats can be dead and alive at the same time – vanish.

The notion that the the wave function isn’t real goes back to Danish physicist Niels Bohr, who considered the wave function a computational tool: it gave correct results when used to calculate the probability of particles having various properties, but there wasn’t a deeper explanation of what the wave function is. Einstein also favored a statistical interpretation of the wave function. But Qbism’s interpretation began in a short paper published in January 2002 under the title “Quantum Probabilities as Bayesian Probabilities,” by Carlton M. Caves of the University of New Mexico, Christopher A. Fuchs, then at Bell Labs in Murray Hill, N.J., and Ruediger Schack of the University of London.

QBism begins with Bayesian probability, which basically says, “I don’t know how the world is. All I have to go on is finite data. So I’ll use statistics to infer something from those data about how probable different possible states of the world are.” (For more on Bayesian probability, see my post “What, Exactly, Is Probability?“) It then applies this to determine the result of the wave function.

Let’s see how this differs by looking at the famous Schrödinger’s cat thought experiment devised by Austrian physicist Erwin Schrödinger in 1935. Schrödinger wrote:

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 that 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 of the entire system would express this by having in it the living and dead cat mixed or smeared out in equal parts. It is typical of these cases that an indeterminacy originally restricted to the atomic domain becomes transformed into macroscopic indeterminacy, which can then be resolved by direct observation.

In traditional interpretations, before an observer looks inside the box, the wave function describing the system is in a superposition where the stat of the cat is both “alive” and “dead.” When an observer is introduced, the wave function collapses the cat into one state or another (or the universe splits and the cat collapses into both states, one in each of the universes.) But QBism says that the wave state is simply a description of the observer’s mental state – their experience of the world in which they live in, as opposed the the reality that is that world, and these personal degrees of belief can be described using Bayesian probability.

Is there any evidence to support this interpretation? One of the key principles of quantum mechanics is the Born rule, which tells observers how to calculate the probability of a quantum event using the wave function. The Born rule states that the probability to find a quantum object at a certain place at a certain time equals the square of its wave function. Recently, Christopher Fuchs was able to demonstrate that the Born rule could be rewritten almost entirely in terms of Bayesian probability theory without referring to a wave function. This means that it’s possible to predict the results of experiments using probabilities without and no wave function, providing evidence that the wave function is just a tool that tells observers how to calculate their personal beliefs, or probabilities, about the quantum world around them. Additionally, QBism is currently being used in quantum computer science for Quantum Bayesian networks.

References

Appleby, D.M.; A. Ericsson; and C. A. Fuchs, 2011. “Properties of QBist state spaces”. Foundations of Physics 41 (3): 564–79. arXiv:0910.2750. Bibcode:2009arXiv0910.2750A

Fuchs, Christopher A., 2011. Coming of Age With Quantum Information: Notes on a Paulian Idea. Cambridge, UK: Cambridge University Press

Fuchs, Christopher A., 2010. QBism, the Perimeter of Quantum Bayesianism. http://arxiv.org/abs/1003.5209

Griffiths, Robert B. Measured responses to quantum Bayesianism. Phys. Today 65(12), 8 (2012); doi: 10.1063/PT.3.1798

Gomatam, Ravi Niels Bohr’s Interpretation and the Copenhagen Interpretation – Are the two incompatible? Philosophy of Science, 74(5) December 2007

Schrödinger, Erwin, Die gegenwärtige Situation in der Quantenmechanik (The present situation in quantum mechanics), Naturwissenschaften (translated by John D. Trimmer in Proceedings of the American Philosophical Society)

Tucci, Robert R., 2012. An Introduction to Quantum Bayesian Networks for Mixed States. http://arxiv.org/abs/1204.1550

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