Physics Asked on May 2, 2021
There are lots of questions and answers on this site about wave function collapse (for example, How does a Wavefunction collapse?, Why does a wavefunction collapse when observation takes place?, How does wave function collapse when I measure position?, and others). However, after reading a few of them, I still don’t understand why this is such a difficult topic. Since I don’t know very much about quantum mechanics, I’m probably just missing a fundamental concept somewhere; I’m trying to figure out what it is.
As I understand it, in quantum mechanics, everything that exists is described by a wave function. A particle in a box has a wave function. Light in the double slit experiment has a wave function. I have a wave function, albeit an extremely complex one.
When two particles interact, one can use quantum field theory to write a wave function describing the system before and after the interaction. For example, if a free electron approaches a proton, one can write a wave function describing the time evolution of the system. At any given time in the future, there is a probability that the electron will be near the proton with a low energy, indicating that it has emitted a photon and has been captured into an atomic orbital. There is also a probability that it will be far away with a high energy, indicating that it remains free.
It seems to me that when we make a "measurement" of a quantum mechanical system, exactly the same thing happens. One particle interacts with another group of particles (the observer), and in principle, one could write a wave function describing the time evolution of the whole system.
For example, a physicist might measure the spin of an electron. After the measurement is made, there is some probability that the electron is spin-up and the atoms in the physicist’s brain rearrange themselves in such a way that the physicist believes the electron is spin-up. There is a probability that the electron is spin-down and the physicist believes it is spin-down. There is also a probability that the physicist makes an error, a (tiny) probability that the physicist is actually in the Andromeda Galaxy and didn’t make the measurement at all, and so on.
Indeed, the entire idea of the physicist "really" being in the Andromeda Galaxy is perhaps not very meaningful. It would be more precise to say that the physicist is really a giant wave function with a tiny amplitude a few million light years from the particle being measured.
Since everything is a wave function, both before and after the measurement, this explanation sidesteps the entire idea of the particle’s wave function "collapsing." Instead, the particle is just interacting with other particles.
Is this a valid way of thinking about wave function collapse? If so, what is missing? Why is the interpretation of quantum mechanics considered to be an interesting question?
Yes what you describe is a valid way of describe the wave function collapsing. On your account there is a universal wavefunction and it, at all times, evolves unitarily. There is in fact no collapse. Wavefunction collapse is an explicitly non-unitary time evolution of whatever wavefunction is under consideration and that is what is sometimes controversial. Schrodinger's equation tells us that systems evolve unitarily and wavefunction collapse tells us that systems evolve non-unitarily. One major criticism of the Copenhagen interpretation is that it doesn't clearly explain when the universe follows the unitary evolution and when it follows non-unitary evolution. That makes it an incomplete theory at best.
Anyways, what you describe --- only unitary evolution --- often goes under the name the Many Worlds Interpretation of quantum mechanics. However I think this is a pretty bad misnomer as it gets pretty scifi pretty quick and people start talking about divergent universes etc. when what is going on is really just as you describe, the universe is just undergoing unitary evolution which leads to entanglement and superposition states.
What is the problem with this approach? In an objective world there is no problem. However, as far as we* know the universe has subjective components as well. For example, I have a feeling or experience or qualia as to what it feels like to observe an electron in the spin up state (perhaps I have an apparatus that lights up a different colored light depending on the spin state measured by some spin measuring apparatus). But I do NOT have a feeling or experience of ever being in a superposition of having seen both spin up and spin down.
However on your account, the particles that make up my body, my brain etc. are in a superposition of having experienced both of those things.
I think most modern physicists probably harbor a tacit dualist perspective on the mind-body problem and would subscribe to the idea that our subjective thoughts are correlated with the physical state of our brains and bodies. In fact, we might go so far as to suppose that mental states a one to one with physical states.
Your interpretation is not compatible with this naive dualist perspective. On your interpretation a person's body would be in a superposition of having experienced both a spin up and spin down electron. What mental state would they be in? You could say it is random at the end of the measurement. Say the person's mind experiences spin up right after the measurement. Ok. But what about 10 seconds after the measurement? On your account the wavefunction should still be a superposition of the person's body having seen up and down. So do the dice get rolled again to determine what the person experiences in this new instant? Is it random from instant to instant which experience we have? That is a bit solipsistic.
Is there a rule that says if your mental state experiences spin down at the end of the experiment it will also experience spin down 10 seconds later despite the wavefunction having equal weight for both probabilities? If so our theory should probably be able to describe that rule.
Or is it somehow possible for a person to have multiple simultaneous, and contradictory experiences? This has implications for what is meant by one's personal identity.
What your, and the many worlds interpretation, fatally fails to do is provide any account whatsoever for how physical states are correlated with subjective experience. This comes for free in classical physical theories so we typically don't think of this as being a desiderata for physical theories. This comes for free in classical theories because we can say the E&M fields which hit our eyeballs move charges in our optical nerves which affect the neurons in our brain, and because our mental states are correlated with the physical state of our bodies (possibly in a 1:1 way) it is clear that measurement results should cause us to experience particular things. It is not so clear quantum mechanically however. What the copenhagen interpretation, or spontaneous collapse does is basically brutally jam this correlation between mental and physical states back into the theory by hand by demanding that the system collapses into one state or the other so that we avoid the conundrum of people having manifold simultaneous experiences.
In any case, there are many philosophical issues here that I won't be able to present in a very coherent way but I did want to share some of my thoughts and some references.
See
Maudlin, T. Three measurement problems. Topoi 14, 7–15 (1995). for a great introduction to the quantum measurement problem.
Decoherence and the Quantum to Classical Transition by Schlosshauer. A great intro to decoherence that can help you avoid some traps that come with thinking about decoherence in the context of unitary evolution and the many worlds interpretation generally.
*Or at least I
Correct answer by Jagerber48 on May 2, 2021
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