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Schrödinger’s cat, aka quantum measurement problem

It’s been 116 years since Max Planck introduced the Quantum idea, yet experts still disagree about quantum fundamentals. My previous post on the wave-particle duality problem argued the universe is made of fields, not particles, and that photons, electrons, and other quanta are extended bundles of field energy that often act in particle-like ways.

Here, I am proposing a solution to the measurement problem. To avoid getting lost in abstractions, I’ll illustrate it with the double-slit example. When many photons pass one at a time through the slits, the overall pattern made on the screen by the many tiny impacts is an interference pattern, implying each photon is an extended field passing through both slits.

Suppose we place a “which-slit detector” at the slits: a device that detects each photon as it comes through the slits. Such a device always detects the photon coming through just one, not both, slits. The macroscopic read-out of the detector always indicates either “slit 1” or “slit 2,” not both. This read-out is a “quantum measurement,” meaning “any process in which a quantum phenomenon (the photon coming through the slits) causes a macroscopic response (the detector registering slit 1 or 2).” The detection process causes a new pattern on the screen: rather than an interference pattern, the screen shows a simple “sum” of two single-slit patterns; each single-slit pattern is a scatter-shot distribution of individual impacts, centered directly behind one slit and falling off in intensity on both sides.

Therefore, a which-slit detector causes each photon to “collapse” from a state of going through both slits to a state of going through one or the other slit. In fact, if a which-slit detector suddenly switches on while a stream of photons passes through the slits, the screen shows a sudden transition — a quantum jump — from the two-slit interference pattern to the sum of two single-slit patterns precisely when the detector switches on.

Standard quantum theory predicts the which-slit detector causes the photon’s quantum state to “entangle” with the detector’s quantum state. Such an entangled state is subtle. Most quantum physicists interpret it as follows:

“Photon comes through slit 1 and detector reads slit 1” superposed with “photon comes through slit 2 and detector reads slit 2.”

The term “superposed with” means both situations occur simultaneously. Above, we saw a simpler example of superposition: a single photon coming through both slits with no which-slit detector present is a superposition of two states, namely “photon comes through slit 1” and “photon comes through slit 2.”

Erwin_Schrödinger_(1933)
Erwin Schrödinger (1933) by the Nobel Foundation. Public domain via Wikimedia Commons.

The entangled state is odd. Erwin Schrödinger dramatized this in his famous example: A cat is connected to a Geiger counter (which detects individual radioactive decays of a nucleus) which is connected to a radioactive Nucleus in such a way that, if the nucleus decays (a quantum process) the Geiger counter triggers a mechanism that kills the cat (a macroscopic response). This is a quantum measurement; theoretically, its result is the following entangled state:

“Nucleus doesn’t decay and cat lives” superposed with “nucleus decays and cat dies.”

This describes a cat that is both alive and dead! That’s impossible. This is the measurement problem.

The solution: physicists have misread entangled states. These states were poorly understood in Schrodinger’s day, but theory and experiments since 1964 have carefully dissected them. The experiments typically work with entangled photon pairs rather than a macroscopic detector such as a cat. The beauty of these experiments is that photons are easier to manipulate than cats. The experiments can manipulate each photon’s so-called “phase angle” (I won’t try to define this term here), something that’s impossible with cats.

In these experiments, each photon (call them “A” and “B”) makes a random choice between two states (call them “1” and “2”). Thus there are four possible two-photon states: (A1, B1), (A1, B2), (A2, B1), (A2, B2). It turns out that, with both phase angles set at zero, quantum theory predicts (A1, B1) is superposed with (A2, B2). If we regard A as a radioactive nucleus and B as a cat, this superposition is just the dead-and-alive cat dilemma.

But when experimenters vary the photon’s phases, something new appears: surprisingly, the states of the photons don’t vary. However, the correlations between the photons do vary. For example, suppose we set A’s phase at zero and then vary B’s phase smoothly from zero to all the way around to 180 degrees. The following table gives selected outcomes:

Phase of B (degrees) Correlation between A and B
0 100% same, 0% different
45 71% same, 29% different
90 50% same, 50% different
135 29% same, 71% different
180 0% same, 100% different

For example, when B’s phase is 45 degrees, 71% of the outcomes are the same (both 1 or both 2) and 29% are different (if one photon is in state 1, the other is in state 2).

The table demonstrates an interference effect. Just as the simple double-slit experiment shows smooth variation from “constructive” to “destructive” as we scan across the viewing screen, the photon pair shows smooth variation from “correlated” to “anti-correlated” as we proceed from 0 to 180 degrees. This is interference, but of a different sort than in the simple double-slit experiment. It’s only the correlations between the states, not the states themselves, that are interfering. Thus neither photon is superposed. Only the correlations between the photons are superposed.

Returning to Schrodinger’s cat: the experiments show this seemingly paradoxical state is merely a superposition of different correlations between the nucleus and the cat, not a superposition of the nucleus or of the cat. The Schrodinger’s cat state should be read this way:

“An undecayed nucleus is 100% correlated with a live cat” and “a decayed nucleus is 100% correlated with a dead cat.”

Think about this. It’s totally equivalent to “the cat is alive if the nucleus is undecayed, and the cat is dead if the nucleus is decayed.” That’s not paradoxical. It’s exactly what we want. Problem solved.

Featured image credit: Brush by geralt. CC0 public domain via Pixabay.

The post Schrödinger’s cat, aka quantum measurement problem appeared first on OUPblog.



This post first appeared on OUPblog | Oxford University Press’s Academic Ins, please read the originial post: here

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