The collapse of Wave function isn't a physical process - but then why hasn't everything blurred into complete uncertainty?

Question

Sabine Hossenfelder very coherently points out the "The real problem with quantum mechanics" in the following clip: https://www.youtube.com/watch?v=LJzKLTavk-w&t=583s

Shortly after second 583 she sais:

The vast majority of physicists today think the collapse of the wave-function isn’t a physical process. Because if it was, then it would have to happen instantaneously everywhere. Take the example of the electron hitting the screen. When the wave-function arrives on the screen, it is spread out. But when the particle appears on one side of the screen, the wave-function on the other side of the screen must immediately change. Likewise, when a photon hits the moon [Hyperion] on one side, then the wave-function of the moon has to change on the other side, immediately.

This is what Einstein called “spooky action at a distance”. It would break the speed of light limit. So, physicists said, the measurement is not a physical process. We’re just accounting for the knowledge we have gained. And there’s nothing propagating faster than light if we just update our knowledge about another place. But the example with the chaotic motion of Hyperion tells us that we need the measurement collapse to actually be a physical process!

Without it, quantum mechanics just doesn’t correctly describe our observations. But then what is this process? No one knows - and that’s the problem with quantum mechanics."

However the physicist Wojciech Zurek seems to have found the solution, showing how wavefunction collapse can be modelled with unitary evolution and entanglement alone, introducing concepts such as "einselection" and "pointer states". ( https://en.wikipedia.org/wiki/Einselection )

However criticism does exist about his idea, as for example pointed out in this short article: https://physicstoday.scitation.org/doi/10.1063/PT.3.2760

Whatever the case with Zurek's particular solution, my question is: How is it possible that Unitary-only evolution can EVER model wavefunction collapse - even just in principle?

The unitary evolution of a single particle, according to schroedinger's equation, is characterized by the position and the momentum of the particle to become gradually more and more uncertain - so giving enough time, the particle could be anywhere with any momentum...

How then is it possible, just in principle, that the probability distribution of a wavefunction of ANYTHING can sharpen up into a peak, rather then flat-line over time?

Can anyone explain how Zurek's theory (or any theory) can get around the constant increase in uncertainty, which seems to be associated with unitary-only evolution?

Is the answer maybe somewhat similar to the "trick" round the entropy-zero-sum game of the second law of thermodynamics? - You can reduce uncertainty locally, if you increase uncertainty at least as much or more somewhere else?

So is Zurek's idea that the universe will eventually "dissipate" into maximal uncertainty, but that we happen to have a classical world with sharply defined objects around us because we live in an "open system" where photons with "high certainty" from the sun entangle with us and our environment and then reflect into the dark sink of the universe, where they blur out into complete uncertainty, allowing us to stay "certain" and "classical" at their expense?

Answer 1

There is no evidence collapse is physical

Collapse as a linguistic shortcut

A "measurement" is actually a generation of entanglement between a system and environment, the joint wavefunction doesn't collapse. The homework problems ask you to compute the marginal spin-up and spin-down probabilities, which can be computed from the joint wavefunction. It is just easier for the problem sets to phrase their question as "probability of spin up".

Collapse as a numerical tool

Collapse is very useful to simplify a problem since it reduces the size of the system we are using. Invoking collapse assumes that the environment is very large and can "swallow" any entanglement it gets with the system. When is this assumption valid?

You can measure a qubit by letting it control the output of a CNOT gate. The other qubit can be thought of as the "environment". However, you can undo this measurement with a second CNOT gate with the same two qubits. The environment qubit, which would have reported "UP" or "DOWN", gets resorbed. You can't invoke "collapse" for this case.

But what about an LED screen which reports qubits as "UP" or "DOWN"? The screen emits trillions of photons which each contain which-path information. You can't undo this measurement just as you can't undo smashing a watermelon. You can safely invoke collapse without getting a wrong final answer.

Collapse as your metaphysical observation

why hasn't everything blurred into complete uncertainty?

This "obvious-fact" is quite literally a boring down-to-Earth concept. But it is actually metaphysics, not physics! This is because (as far as we know) it is impossible to build a machine that can detect itself being in a superposition. Or a machine that detects parallel universes.

Your quote states that your subjective self-awareness is 100% real, as is your macroscopic reality around you. But science doesn't address what it is like to be something: your subjective self-awareness, no matter how real it is, cannot be seen by outsiders and so is metaphysical.

Science can't provide an answer to metaphysical concepts. We have interpretations of what actually is happening at our deepest levels of reality, but we cannot design an experiment to tell us which interpretation is correct.

Searching for collapse as a physical event

There is no evidence it is, but people have tried.

One idea is that you can't super-position two spacetimes, which would make double-slit experiments fail above the Planck mass. We can't get anywhere near this mass in a double-slit experiment and I am skeptical that gravity would be so different at low energy to other forces.

Another idea is that collapse occasionally happens to wavefunctions at all times. The repeated localizations in position space will randomly perturb the momentum and so generate heat energy out of nowhere. This also seems very unlikely.

Answer 2

A measurement is an interaction that copies information from one system to another. If a measuring device $M$ is in a blank state $|0\rangle_M$ system $S$ is in some unsharp state then the overall state is $$ |\psi(0)\rangle = \sum_a\alpha_a|a\rangle_S|0\rangle_M $$ The measurement device $M$ measures the observable $\hat{A}_S$ with eigenstates $|a\rangle_S$ of $S$ onto an observable $\hat{A}_M$ of $M$ and the resulting state is $$ |\psi(0)\rangle = \sum_a\alpha_a|a\rangle_S|a\rangle_M. $$

So for each value of $\hat{A}_S$ there is a corresponding value of $\hat{A}_M$. And if some further system, like an environment $E$ reads the measuring device then the state is $$ |\psi(0)\rangle = \sum_a\alpha_a|a\rangle_S|a\rangle_M|a\rangle_E. $$

The different values of $\hat{A}_S$ can't undergo quantum interference anymore because the information required for that interference is spread across $M,S,E$. So the different versions of $M,S,E$ for each of the $a$ values evolve independently.

The result of this process is that physical reality on the macroscopic scale looks a bit like a collection of parallel universes. For reasons that aren't well explained, many physicists don't like this conclusion and it is commonly called the many worlds interpretation (MWI) of quantum mechanics. For more details see

https://arxiv.org/abs/quant-ph/0104033

https://arxiv.org/abs/0707.2832

I said that the world acts approximately like a collection of parallel universes, but that approximation isn't perfect because "classical" systems can carry quantum information and they do in experiments such as the EPR experiment and other experiments that are often wrongly described as evidence for non-locality:

https://arxiv.org/abs/quant-ph/9906007

https://arxiv.org/abs/1109.6223

Collapse isn't a consequence of quantum mechanics and leads to many problems, such as alleged instantaneous changes of systems and doesn't solve any problems so it isn't clear why anyone would insist on it, but some people do.