The Rule Behind Quantum Probabilities

Why it attracts me

The Born rule is where quantum physics stops being abstract and meets data. One short rule turns the theory's arrows into numbers that experiments confirm.

The idea

Each possible result has an amplitude, an arrow-like number. Square the arrow's length and you have the chance of that result. Repeat the experiment thousands of times and the share of each result settles close to that chance. Max Born proposed this in 1926 and shared the 1954 Nobel Prize in Physics, awarded especially for this idea. In Everett's view (Hugh Everett: Quantum Measurement Without Collapse), every result happens, so the meaning of "chance" becomes a real puzzle. Some physicists argue it can be recovered as the rational way to bet on what you will see. Others are not convinced.

Where it connects

This rule is the main reason I keep quantum chances apart from the chances in my decisions (Probability, Risk & Uncertainty). A decision tree (Mapping the Futures a Choice Opens) uses probabilities that are my own estimates, and they should never be dressed up as quantum branch weights. Updating beliefs as evidence arrives (Adjusting My Confidence as Evidence Arrives) is about beliefs, not amplitudes.

An example

My Queueing Simulation Lab draws random arrival times. Its running averages wobble early, then settle toward what the formula predicts, much as quantum statistics settle over many runs. The difference is instructive. The lab's randomness comes from a seed, so pressing Reset replays the exact run. Experiments have ruled out the simplest, local kinds of hidden seed for quantum results. Whether anything like one lies behind them at all is a question the interpretations answer differently (Comparing Views of What Quantum Physics Means).

Questions I'm still exploring

• If every result happens in Everett's picture, what does a 30 percent chance refer to?
• Why should the chance be the square of an amplitude, and not some other rule?
• When I call a decision risky, which kind of probability am I using?

Sources and further reading

• The Nobel Prize in Physics 1954: Max Born, facts page, NobelPrize.org — Shared with Walther Bothe; Born's citation reads "for his fundamental research in quantum mechanics, especially for his statistical interpretation of the wavefunction". Confirmed by search; the page blocks automated loads.
• Stanford Encyclopedia of Philosophy: Everettian Quantum Mechanics — Section 3 discusses the problem of probability in Everett's picture.