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.
The individual electron just behaves randomly in a way that we can only predict statistically and not absolutely.
That’s the non-boring part, for lack of a better expression. Quantum Mechanics only predicts the outcome for an ensemble, and that imperfectly. It can say nothing at all about the outcome for a single particle.
Well, what is boring and non-boring I guess is in the eye of the beholder. What I moreso was referring to is what is difficult to wrap your head around.
The nondeterminism is kind of unavoidable as long as you don’t want to change the mathematics of the theory itself, but I also don’t really consider nondeterminism to be that unintuitive or difficult to “understand.” I mean, throughout most of human history, it wasn’t that common for humans to actually believe in determinism in the Laplacian sense of being able to make absolute prediction to the future based on complete knowledge of the past, that was largely popularized with the rise of Newtonian mechanics, and even by the 19th century you had even a lot of materialist philosophers calling it into question on grounds of logical consistency. Personally, I think the strong desire to maintain Laplacian determinism is really a physicist thing. They work with Newtonian mechanics first and it becomes so intuitive some don’t want to let it go when it comes to quantum mechanics. But I doubt if you went and talked to the average person, most probably wouldn’t be that strongly adherent to Laplacian determinism.
The kinds of views I was talking about are more things like people who try to interpret the state vector as literally representing a physical wave spreading out in space that collapses like a house of cards when you perturb it, or try to envision a literal multiverse where everything is just a big “universal wave function.” A lot of these bizarre views are not only unintuitive but literally impossible to visualize, and they run into a lot of problems in logical consistency and there have been mountains papers and books published on the subject trying to work out all the conceptual issues. If you are a person just learning QM and the philosophical interpretation around it bothers you, if you listen to people who talk about these weird things, you will need to read through dozens of books and maybe even hundreds of papers just to get a general idea of what is going on, and even then most of these interpretations still have not resolved their mountain of conceptual issues.
To me this really bothered me when I got into quantum computing for the first time. I wanted to not just learn the math but have some sort of intuition of what is actually going on. I then went down a rabbit hole of reading tons and tons and tons of books and academic papers to try and find some way to make the math make sense on a philosophical level. Most of the mainstream views you see in the popular media just overcomplicate things for no reason because the person wants to make QM sound more mystical than it actually is. What I ultimately came to realize is that most of this confusion is just self-imposed in the sense that they are based on assumptions which are not actually demanded by the mathematics and entirely optional (such as interpreting a list of probability amplitudes a literal entity in a physical space) and thus most can be stripped away.
You can’t strip away every aspect of QM that makes it unique, because it clearly does differ from classical mechanics, but by dong this you do really hone down on what actually makes QM unique and what is genuinely an unavoidable consequence of the mathematics. And what you get down to is just interference effects, which arise from the fact that probability amplitudes are complex-valued, thus can cancel each other out, which can’t occur in classical probability theory. Nondeterminism and context-dependence then follow from this as a necessity for the theory to be logically consistent, but both of those are fairly easy to have an intuition for.
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.
That’s the non-boring part, for lack of a better expression. Quantum Mechanics only predicts the outcome for an ensemble, and that imperfectly. It can say nothing at all about the outcome for a single particle.
Well, what is boring and non-boring I guess is in the eye of the beholder. What I moreso was referring to is what is difficult to wrap your head around.
The nondeterminism is kind of unavoidable as long as you don’t want to change the mathematics of the theory itself, but I also don’t really consider nondeterminism to be that unintuitive or difficult to “understand.” I mean, throughout most of human history, it wasn’t that common for humans to actually believe in determinism in the Laplacian sense of being able to make absolute prediction to the future based on complete knowledge of the past, that was largely popularized with the rise of Newtonian mechanics, and even by the 19th century you had even a lot of materialist philosophers calling it into question on grounds of logical consistency. Personally, I think the strong desire to maintain Laplacian determinism is really a physicist thing. They work with Newtonian mechanics first and it becomes so intuitive some don’t want to let it go when it comes to quantum mechanics. But I doubt if you went and talked to the average person, most probably wouldn’t be that strongly adherent to Laplacian determinism.
The kinds of views I was talking about are more things like people who try to interpret the state vector as literally representing a physical wave spreading out in space that collapses like a house of cards when you perturb it, or try to envision a literal multiverse where everything is just a big “universal wave function.” A lot of these bizarre views are not only unintuitive but literally impossible to visualize, and they run into a lot of problems in logical consistency and there have been mountains papers and books published on the subject trying to work out all the conceptual issues. If you are a person just learning QM and the philosophical interpretation around it bothers you, if you listen to people who talk about these weird things, you will need to read through dozens of books and maybe even hundreds of papers just to get a general idea of what is going on, and even then most of these interpretations still have not resolved their mountain of conceptual issues.
To me this really bothered me when I got into quantum computing for the first time. I wanted to not just learn the math but have some sort of intuition of what is actually going on. I then went down a rabbit hole of reading tons and tons and tons of books and academic papers to try and find some way to make the math make sense on a philosophical level. Most of the mainstream views you see in the popular media just overcomplicate things for no reason because the person wants to make QM sound more mystical than it actually is. What I ultimately came to realize is that most of this confusion is just self-imposed in the sense that they are based on assumptions which are not actually demanded by the mathematics and entirely optional (such as interpreting a list of probability amplitudes a literal entity in a physical space) and thus most can be stripped away.
You can’t strip away every aspect of QM that makes it unique, because it clearly does differ from classical mechanics, but by dong this you do really hone down on what actually makes QM unique and what is genuinely an unavoidable consequence of the mathematics. And what you get down to is just interference effects, which arise from the fact that probability amplitudes are complex-valued, thus can cancel each other out, which can’t occur in classical probability theory. Nondeterminism and context-dependence then follow from this as a necessity for the theory to be logically consistent, but both of those are fairly easy to have an intuition for.