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The notion of the wave function collapse is very specific to Copenhagen interpretation of quantum mechanics that tries to reconcile classical and quantum world. But everything is quantum so there is no classical measurement device, just its wave function interacting according to fully deterministic equations with the wave function of the electron.

The catch is that appearance of classical objects is still unsolved problem in QM. There are various approaches that in theory can explain the experimental results, but in practice explaining, say, quantum split experiments from pure QM view of multiple interacting wave functions still not possible.

> The catch is that appearance of classical objects is still unsolved problem in QM.

What? Decoherence explains classical objects.

While quantum decoherence explains appearance of classical objects in simple models, predicting the results of real experiments still not possible. And given this has not changed much as far as I know for the last 20 years, I started to suspect that decoherence alone may not be enough.

Objective collapse theories are being worked on.

https://youtu.be/FP6iyVJ70OU

No, it doesn't. Decoherence explains why self-interference of a single wave-function doesn't happen after interaction with the environment. But it doesn't explain two important things.

1, which is very practical, is that it doesn't explain why the wave function always decoheres in the same way. In experiments, you can always chose the basis of measurement, and get some definite results in that particular basis, while the properties in another basis remain indefinite. But, in classical reality, all objects have definite properties in the same basis (say, positions in the same Cartesian coordinate system). This is known as the preferred basis problem, and decoherence can't explain it.

2, which is somewhat more philosophical, decoherence doesn't explain the quantitative relationship between the wave function and the probability of observing a particular outcome. Indeed, in MWI it's very hard to even define probability in a coherent way, since all outcomes actually happen and there is an uncountable (in the mathematical sense) number of outcomes.

> In experiments, you can always chose the basis of measurement, and get some definite results in that particular basis, while the properties in another basis remain indefinite.

Can you give some examples of such bases? Position is one, for sure. In "Quantum Mechanics 101" we are told that momentum is another, but I'm sceptical that there is a real experiment that can measure momentum without also measuring position.

Even for position, you can measure less than a point-like position. For example, you can check if a particle is inside this box or outside it. After this measurement, the particle will either be inside the box or outside it, but it will not be at some fixed position inside the box (or some fixed position outside it). For example, if it's determined to be outside the box, it will definitely not interact with any particle that was inside the box at the same time, but it may interact with any particle anywhere else in the entire universe - and according to MWI, it WILL interact with every other particle everywhere else in the universe, in some part of state-space.

The many worlds interpretation works better with quantized probability. Imagine a huge computer running a monte carlo simulation with a probabilistic current state, and a set of transition states (the wave function). With quantized probability and a universe with finite "memory" the amplitude of the wave function basically maps to the amount of system memory being utilized for a portion of the simulated state space.

Well, quantized probability doesn't really make sense, there are extraordinarily improbable events happening every second. It's easy to create an event that has less probability than many things that have never been observed (flip 10,000 coins - whatever result you get has probability 1/2^10k).

You could perhaps create a version of QM with a quantized amplitude for the wave function in some basis.

It's also important to remember that the Schrodinger equation of a system has an infinity of solutions - for any solution, any linear function of that solution is also a solution. You need to choose a particular basis of measurement - choose a decomposition of the solutions - to be able to apply the Born rule and get from the wave function to a probability distribution.

Why is quantized probability nonsensical? Isn’t it equivalent to asserting the universe is not a continuum?

By quantized probability, I assume you mean something like "there is a minimal probability p for any possible event; if the probability we compute for some event is q < p, then that event is impossible".

If this is the right definition, then it's easy to disprove: for any p you chose, I can construct a series of events that each have probability q < p, but one of which is guaranteed to happen. This was the meaning of the examples I gave with the 10 thousand coins - the probability of any particular result after flipping the coins is extraordinarily small, and yet one of the results is guaranteed to happen.

Edit to add: to be clear, even if the universe itself were quantized, all measurable physical quantities, probability still wouldn't need to be quantized, as it's not a physical quantity, it's just a mathematical abstraction. Still, even in QM, not all physical quantities are quantized. For example, space (position) is not quantized in QM, and neither is time. They are both continuous quantities in all of the equations normally used. Planck time and Planck distance are only the shortest possible distances to measure precisely, given the Heisenberg uncertainty principle, but that doesn't require them to actually be quantized. In contrast, the quantization of mass, energy, spin etc are actually necessary for the theory to work, they are not just measurement artifacts.

Why do you think this is a result of an unquantized wavefunction rather than due to the mathematical edifice we use to model it? It's not clear to me that things like the product rule for probabilities would still hold if you're not transforming and normalizing amplitudes.

Classical objects are not explained in Quantum Mechanics, they are a fundamental part of the theory itself. (Measurement is an interaction with an apparatus which is a classical object.)

The notion of a 'Classical Object' in this particular framework of QM is an assumption, not a prediction.

Since all objects are composed of quantum particles, all objects are quantum objects. So a complete theory of QM needs to be able to explain, not assume, why some objects behave classically.

To summarize: a measurement need not give enough information to convert a wavefunction into an impulse (point) function. Not all measurements give you point information. A measurement could provide enough information to constrain the wavefunction to a more restricted (knowledgeable) form (lower entropy if you use integrate over the wavefunction -- that is Integral(-P(x)*Log(P(x))))

This is especially the case with entanglement. By measuring one entangled observable, we often increase our knowledge but not absolutely like in the naive explanations that have you believe it is always an entangled pair of spin up and spin down..

All measurement does is reduce uncertainty/entropy of the wavefunction. The strange part is that one can actually undo this restriction by erasing any traces of the measurement. See the Delayed choice quantum eraser experiment. Collapse doesn't really exist.. It's more like expressions that can be reduced, appear reduced, until they cannot be reduced..thus they appear expanded. Imo, entanglement is evidence that all interactions are lazily computed and are copy-on-read or lisp expressions that gradually become larger as interactions continue, and are beta or alpha reduced when possible.

I like it. Dont confuse tgis entropy with the von neumann entropy which increases (or at least stasy the same) when a measurement is perfomed (pure state turning into mixed state)

> If you measure the exact position of an electron, the wave function collapses to a point.

Note, though, that in reality you can never measure the exact position of an electron (or anything else); the best you can do is to measure that the electron is inside some finite-sized (possibly very small) region. The "exact position" measurement is an idealization that can be useful for pedagogy but can't be realized in any actual experiment.

spin? things go one direction or the other in a magnetic field

I assume that by 'you can never measure the exact position of an electron (or anything else)', they meant 'you can never measure the exact position of an electron (or the exact position of anything other than an electron)', not 'you can never measure the exact position of an electron (or any other property of an electron)'.

As moonchild posted, I was only saying that you can't measure the position of an electron exactly. I was not saying that you can't measure any properties of electrons at all.

The more general statement is that you can't measure exact values for any observable with a continuous spectrum; you can only measure that a quantum system is within some finite range of values. Spin has a discrete spectrum, so you can measure exact values for spin.

This is all "operationally correct".

If you are intrigued as to what it means for the wave function to collapse, and related questions such as at which speed does it collapse, etc, you must consider what it means to measure something.

If you want to know the property of some particle you need to interact with it ... at least with another particle. The system of those two particles is described by a wave function. This wave function evolves according to the Schrödinger equation and it will tell you that after the interaction you have a superposition of two states: one where the particle you're measuring is inside the box and the measurement probe particle is carrying that information, and the other state that tells you that the particle is outside the box *and* the measurement probe tells is carrying that information.

The wave function of the system hasn't really collapsed to a single state.

Now, let's say that your measurement apparatus records the information of this test particle by e.g. printing it out to a piece of paper or whatever (bits in hard disk)

The wave function of the whole system now captures the superposition where the measured particle was in one state and the paper contains black ink in some places and not in other places, superimposed with the other state where the measured particle was in the other state and the paper carries ink in other locations.

Nothing has collapsed yet; you just have a very complicated wave function. By processing the measurement you effectively introduced a "causality amplification" process, but one that operates on the whole of the wave function.

But, you may protest: "I see only one outcome of the measurement!"

The wave function of the universe is in a superposition of your body (and thus brain) being in a state where you have observed ( and recorded such observation) one measurement outcome and another state where you have observed the other outcome.

Both states are equally real and present in the wave function of the universe. But each of the brain states in the superposition doesn't interact with the other states do each future though you have in one of the superimposed states are effectively independent from the others, giving the impression that the wave function has "collapsed".

Some people like to say that the "universe has split" into independent world lines or something like that. Some people find this terminology helpful, some find it confusing. But the thing is, this just follows from applying the Schrödinger equation without making arbitrary exceptions when humans get involved.

Thanks