Collapse Postulates

Macroscopic decoherence—also known as “many-worlds”—is the idea that the known quantum laws that govern microscopic events simply govern at all levels without alteration. Back when people didn’t know about decoherence—before it occurred to anyone that the laws deduced with such precision for microscopic physics might apply universally—what did people think was going on?

The initial reasoning seems to have gone something like:

When my calculations showed an amplitude of (−1/3)i for this photon to get absorbed, my experimental statistics showed that the photon was absorbed around 107 times out of 1,000, which is a good fit to 1/9, the square of the modulus.

to

The amplitude is the probability (by way of the squared modulus).

to

Once you measure something and know it didn’t happen, its probability goes to zero.

Read literally, this implies that knowledge itself—or even conscious awareness— causes the collapse. Which was in fact the form of the theory put forth by Werner Heisenberg!

But people became increasingly nervous about the notion of importing dualistic language into fundamental physics—as well they should have been! And so the original reasoning was replaced by the notion of an objective “collapse” that destroyed all parts of the wavefunction except one, and was triggered sometime before superposition grew to human-sized levels.

Now, once you’re supposing that parts of the wavefunction can just vanish, you might think to ask:

Is there only one survivor? Maybe there are many surviving worlds, but they survive with a frequency determined by their integrated squared modulus, and so the typical surviving world has experimental statistics that match the Born rule.

Yet collapse theories considered in modern academia only postulate one surviving world. Why?

Collapse theories were devised in a time when it simply didn’t occur to any physicists that more than one world could exist! People took for granted that measurements had single outcomes—it was an assumption so deep it was invisible, because it was what they saw happening. Collapse theories were devised to explain why measurements had single outcomes, rather than (in full generality) why experimental statistics matched the Born rule.

For similar reasons, the “collapse postulates” considered academically suppose that collapse occurs before any human beings get superposed. But experiments are steadily ruling out the possibility of “collapse” in increasingly large entangled systems. Apparently an experiment is underway to demonstrate quantum superposition at 50-micrometer scales, which is bigger than most neurons and getting up toward the diameter of some human hairs!

So why doesn’t someone try jumping ahead of the game, and ask:

Say, we keep having to postulate the collapse occurs steadily later and later. What if collapse occurs only once superposition reaches planetary scales and substantial divergence occurs—say, Earth’s wavefunction collapses around once a minute? Then, while the surviving Earths at any given time would remember a long history of quantum experiments that matched the Born statistics, a supermajority of those Earths would begin obtaining non-Born results from quantum experiments and then abruptly cease to exist a minute later.

Why don’t collapse theories like that one have a huge academic following, among the many people who apparently think it’s okay for parts of the wavefunction to just vanish? Especially given that experiments are proving superposition in steadily larger systems?

A cynic might suggest that the reason for collapse’s continued support isn’t the physical plausibility of having large parts of the wavefunction suddenly vanish, or the hope of somehow explaining the Born statistics. The point is to keep the intuitive appeal of “I don’t remember the measurement having more than one result, therefore only one thing happened; I don’t remember splitting, so there must be only one of me.” You don’t remember dying, so superposed humans must never collapse. A theory that dared to stomp on intuition would be missing the whole point. You might as well just move on to decoherence.

So a cynic might suggest.

But surely it is too early to be attacking the motives of collapse supporters. That is mere argument ad hominem. What about the actual physical plausibility of collapse theories?

Well, first: Does any collapse theory have any experimental support? No.

With that out of the way…

If collapse actually worked the way its adherents say it does, it would be:

  1. The only non-linear evolution in all of quantum mechanics.
  2. The only non-unitary evolution in all of quantum mechanics.
  3. The only non-differentiable (in fact, discontinuous) phenomenon in all of quantum mechanics.
  4. The only phenomenon in all of quantum mechanics that is non-local in the configuration space.
  5. The only phenomenon in all of physics that violates CPT symmetry.
  6. The only phenomenon in all of physics that violates Liouville’s Theorem (has a many-to-one mapping from initial conditions to outcomes).
  7. The only phenomenon in all of physics that is acausal / non-deterministic / inherently random.
  8. The only phenomenon in all of physics that is non-local in spacetime and propagates an influence faster than light.

What does the god-damned collapse postulate have to do for physicists to reject it? Kill a god-damned puppy?

Distinct Configurations

Top

Book

Sequence

Decoherence is Simple