Interpreting Quantum Mechanics

In my last post, I discussed the mathematical intuition underlying Quantum Mechanics, which is the idea that particle configurations with probability amplitudes can cancel out when combined. That is because amplitudes can be positive, negative or complex numbers, not just positive numbers as classical probabilities are.

I also noted that when a photon arrives at the back screen in the double-slit experiment, we only see one of the slit detectors activated, which corresponds to one of the configurations. But how do we account for the configuration where the other detector was activated?

There are several interpretations, all disturbing, so therefore best described by reference to superheroes.

Copenhagen Interpretation: You, the conscious observer, create reality. If you look at the back screen, the photon will be a wave. If you look at the slits, the photon will instead be a particle. You don't feel like you're in a superposition, so you're an exception to the laws that those little particles follow.




De Broglie–Bohm (or pilot-wave) Interpretation: The photon surfs on a wave which carries it through one of the slits to a location on the back screen where destructive interference doesn't occur. Added bonus: Entangled particles can communicate faster than the speed of light in violation of special relativity.

Many-Worlds Interpretation: You observe one of the photons going through one slit while your twin observes the other photon going through the other slit. You are either observing a superposition on the back screen or participating in a branch of one when you become entangled with one of the photons. Also the entire universe is in a superposition. Things just look classical because you have to be standing in one configuration or another.





Instrumentalist Interpretation: Yada yada yada ... who cares? You can build really amazing stuff using quantum mechanics! Also affectionately called, "shut up and calculate!".

So there we have it. The Copenhagen Interpretation posits an observer-dependent reality and a mysterious wave function collapse. The Bohmian Interpretation requires information to travel faster than light.^[1] The Many-Worlds Interpretation causes incredulous stares. And, finally, the Instrumentalist Interpretation isn't an interpretation at all.^[2]

Since each interpretation uses the same mathematical formalism, is there any reason to prefer one to another on philosophical grounds? I think there is.

The famous Schrodinger's Cat thought experiment vividly demonstrates the logic of quantum behavior in terms of familiar, everyday things. The upshot is that the cat is in a superposition of being both dead and alive until we look in the box. But what does that mean? And why don't we normally observe such things?

To take the second question first, we actually can observe superpositions involving objects that are (just barely) visible to the naked eye. For example, a recent experiment demonstrated interference effects for the superposition of a tiny tuning fork vibrating and not vibrating. This is analogous to the double-slit experiment where photon amplitude flows through both slits and we observe an interference pattern on the back screen.

So what does this mean? It means that we have observed the effects of a single amplitude, and it is the sum of the amplitude for a vibrating tuning fork and the amplitude for a non-vibrating tuning fork.

How can this observation be explained in a coherent way? The idea that there is a single tuning fork that is both vibrating and not vibrating is a contradiction, so that fails. The idea that there is a single tuning fork that is either vibrating or not vibrating also fails, since possibilities can't cause interference effects. That leaves the idea that there is one tuning fork that vibrates and a second one that does not and that we are observing the combined effects of both.

If there are two tuning forks, what would explain the observation of a single tuning fork (that is either vibrating or not) when you try to detect the vibration? There are paths that entangle you with the vibrating tuning fork and paths that entangle you with the non-vibrating tuning fork and amplitude flows along both paths. Becoming entangled with one of the tuning forks destroys the interference pattern from your point-of-view (that is, you can no longer observe the effects of the other tuning fork because there are no amplitude paths from here to there).^[3]

The Many-World's Interpretation, despite its startling implications, seems to me to be the most coherent interpretation of both our everyday and quantum observations. That, of course, doesn't mean that it is true - that is ultimately an empirical question^[4]. However it is an intuitive and natural framework for conceptualizing our observed experience.

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[1] See Bells Theorem which rules out local hidden variables.

[2] The pragmatic and reasonable version of the Instrumentalist Interpretation is that the math works, whether or not we know what it means. In stronger versions, it asserts that there is no explanation to be had and that the math doesn't mean anything.

[3] This process is called decoherence and is only reversible in practice in microscopic environments where interactions with air and apparatus molecules can be controlled (it's easy to break an egg but difficult to put it back together again). So observing things in a single (or decohered) state is the everyday situation that corresponds to our classical intuitions. The difficult challenge for quantum computing just is how to reliably maintain quantum bits in a superposition of 1 and 0 values.

[4] Scott Aaronson has a great post explaining that while the Many-Worlds Interpretation is the obvious, straightforward reading of quantum mechanics, it is also provisional in a way that heliocentrism (as opposed to geocentrism) isn't. You could, in principle, fly a spaceship above the plane of the solar system and see the Earth and the other planets circling the sun. However you can't similarly travel to another world branch to meet your twin.