I’m not wrong… but I’m not even right!
I just enjoy quoting my favorite Wolfgang Pauli line.
Seriously now - “but it’s not an electron at that time” - is quite a doozy of a way of… erm… looking at it.
Goddamn it, I looked at it! Again! Which goddamn collapsed the goddamned wave function! I can’t seem to get anything done around here with my Newtonian/classical physics tools (level, pincers and a pendulum) and these here fancy, tiny subatomic particles.
What is it then? If you say it’s a wave, well, that wave is in Hilbert space which is infinitely dimensional, not in spacetime which is four dimensional, so what does it mean to say the wave is “going through” the slit if it doesn’t exist in spacetime? Personally, I think all the confusion around QM stems from trying to objectify a probability distribution, which is what people do when they claim it turns into a literal wave.
To be honest, I think it’s cheating. People are used to physics being continuous, but in quantum mechanics it is discrete. Schrodinger showed that if you take any operator and compute a derivative, you can “fill in the gaps” in between interactions, but this is just purely metaphysical. You never see these “in between” gaps. It’s just a nice little mathematical trick and nothing more. Even Schrodinger later abandoned this idea and admitted that trying to fill in the gaps between interactions just leads to confusion in his book Nature and the Greeks and Science and Humanism.
What’s even more problematic about this viewpoint is that Schrodinger’s wave equation is a result of a very particular mathematical formalism. It is not actually needed to make correct predictions. Heisenberg had developed what is known as matrix mechanics whereby you evolve the observables themselves rather than the state vector. Every time there is an interaction, you apply a discrete change to the observables. You always get the right statistical predictions and yet you don’t need the wave function at all.
The wave function is purely a result of a particular mathematical formalism and there is no reason to assign it ontological reality. Even then, if you have ever worked with quantum mechanics, it is quite apparent that the wave function is just a function for picking probability amplitudes from a state vector, and the state vector is merely a list of, well, probability amplitudes. Quantum mechanics is probabilistic so we assign things a list of probabilities. Treating a list of probabilities as if it has ontological existence doesn’t even make any sense, and it baffles me that it is so popular for people to do so.
This is why Hilbert space is infinitely dimensional. If I have a single qubit, there are two possible outcomes, 0 and 1. If I have two qubits, there are four possible outcomes, 00, 01, 10, and 11. If I have three qubits, there are eight possible outcomes, 000, 001, 010, 011, 100, 101, 110, and 111. If I assigned a probability amplitude to each event occurring, then the degrees of freedom would grow exponentially as I include more qubits into my system. The number of degrees of freedom are unbounded.
This is exactly how Hilbert space works. Interpreting this as a physical infinitely dimensional space where waves really propagate through it just makes absolutely no sense!
But there really is an interference pattern. Whatever is happening is physical, not metaphysical, and is happening “through” or “because of” both slits at the same time.
Unless you’re trying to argue that the statistical behavior of electrons is somehow decoupled from the behavior or each individual electron, which would seem to me to be a very odd metaphysical position.
I am saying that assigning ontological reality to something that is by definition beyond observation (not what we observe and not even possible to observe) is metaphysical. If we explain the experiment using what we observe then there is no confusing or contradiction, or any ambiguity at all. Indeed, quantum mechanics becomes rather mechanical and boring, all the supposed mysticism disappears.
It is quite the opposite that the statistical behavior of the electron is decoupled from the individual electron. The individual electron just behaves randomly in a way that we can only predict statistically and not absolutely. There is no interference pattern at all for a single electron, at least not in the double-slit experiment (the Mach–Zehnder interferometer is arguably a bit more interesting). The interference pattern observed in the double-slit experiment is a weakly emergent behavior of an ensemble of electrons. You need thousands of them to actually see it.
This isn’t right.
It’s not even wrong.
(if you think you understand quantum physics, you don’t understand quantum physics)
That damn electron is NOT going through both slits at the same time! It’s doing something that we can’t even describe with words, only math!
You’re wrong, it’s definitely going through both slits at the same time, but it’s not an electron at that time.
I’m not wrong… but I’m not even right!
I just enjoy quoting my favorite Wolfgang Pauli line.
Seriously now - “but it’s not an electron at that time” - is quite a doozy of a way of… erm… looking at it.
Goddamn it, I looked at it! Again! Which goddamn collapsed the goddamned wave function! I can’t seem to get anything done around here with my Newtonian/classical physics tools (level, pincers and a pendulum) and these here fancy, tiny subatomic particles.
What is it then? If you say it’s a wave, well, that wave is in Hilbert space which is infinitely dimensional, not in spacetime which is four dimensional, so what does it mean to say the wave is “going through” the slit if it doesn’t exist in spacetime? Personally, I think all the confusion around QM stems from trying to objectify a probability distribution, which is what people do when they claim it turns into a literal wave.
To be honest, I think it’s cheating. People are used to physics being continuous, but in quantum mechanics it is discrete. Schrodinger showed that if you take any operator and compute a derivative, you can “fill in the gaps” in between interactions, but this is just purely metaphysical. You never see these “in between” gaps. It’s just a nice little mathematical trick and nothing more. Even Schrodinger later abandoned this idea and admitted that trying to fill in the gaps between interactions just leads to confusion in his book Nature and the Greeks and Science and Humanism.
What’s even more problematic about this viewpoint is that Schrodinger’s wave equation is a result of a very particular mathematical formalism. It is not actually needed to make correct predictions. Heisenberg had developed what is known as matrix mechanics whereby you evolve the observables themselves rather than the state vector. Every time there is an interaction, you apply a discrete change to the observables. You always get the right statistical predictions and yet you don’t need the wave function at all.
The wave function is purely a result of a particular mathematical formalism and there is no reason to assign it ontological reality. Even then, if you have ever worked with quantum mechanics, it is quite apparent that the wave function is just a function for picking probability amplitudes from a state vector, and the state vector is merely a list of, well, probability amplitudes. Quantum mechanics is probabilistic so we assign things a list of probabilities. Treating a list of probabilities as if it has ontological existence doesn’t even make any sense, and it baffles me that it is so popular for people to do so.
This is why Hilbert space is infinitely dimensional. If I have a single qubit, there are two possible outcomes, 0 and 1. If I have two qubits, there are four possible outcomes, 00, 01, 10, and 11. If I have three qubits, there are eight possible outcomes, 000, 001, 010, 011, 100, 101, 110, and 111. If I assigned a probability amplitude to each event occurring, then the degrees of freedom would grow exponentially as I include more qubits into my system. The number of degrees of freedom are unbounded.
This is exactly how Hilbert space works. Interpreting this as a physical infinitely dimensional space where waves really propagate through it just makes absolutely no sense!
But there really is an interference pattern. Whatever is happening is physical, not metaphysical, and is happening “through” or “because of” both slits at the same time.
Unless you’re trying to argue that the statistical behavior of electrons is somehow decoupled from the behavior or each individual electron, which would seem to me to be a very odd metaphysical position.
I am saying that assigning ontological reality to something that is by definition beyond observation (not what we observe and not even possible to observe) is metaphysical. If we explain the experiment using what we observe then there is no confusing or contradiction, or any ambiguity at all. Indeed, quantum mechanics becomes rather mechanical and boring, all the supposed mysticism disappears.
It is quite the opposite that the statistical behavior of the electron is decoupled from the individual electron. The individual electron just behaves randomly in a way that we can only predict statistically and not absolutely. There is no interference pattern at all for a single electron, at least not in the double-slit experiment (the Mach–Zehnder interferometer is arguably a bit more interesting). The interference pattern observed in the double-slit experiment is a weakly emergent behavior of an ensemble of electrons. You need thousands of them to actually see it.