Horribly simplified: Space isn't empty, there is an "ether". Matter moving through the ether interacts with it and produces waves just like a very light boat in a lake - these crests and troughs exactly line up with the magical waveform. All of the quantum behavior we see is explained by the waves in this "ether".
Ie the waveform is no longer this crazy math thing its a real thing. And just like "air" was considered empty until we discovered a vacuum, space itself is considered empty until we fully define the "ether". It matches up with all of the results of Copenhagen, but was dismissed because physicists like "locality" and it gives up locality.
But guess what? The surface of a lake is non-local. Your boat is affected by boats far away via waves, the effect just diminishes over distance.
And the double slit experiment is so straightforward now that it makes Copenhagen and many-worlds look kinda silly.
While PWT is the most sensible to me, it is strange though solely because of the wave function which is common to all theories, including MW. The novel part of PWT, that of particles having definite locations at all times being guided by the wave, is quite ordinary.
Via analogy, let's imaging the perfectly still lake. In the lake at an (x,y) position is a mechanical oscillator which moves up and down and continuously produces waves. Knowing the position of the oscillator and it's phase I can calculate the position of crests and troughs of waves on the surface and the height of the water at any location.
If now I had 100 oscillators spread on the surface of the lake, I would need 100 inputs of x,y coordinates of where the oscillators are and each their phases. In this case i'd need 3100 inputs/dimensions to calculate the wave function.
At first, this seems like a lot; but I don't need 3100 dimensions to describe the resultant wave function. It still is simply the surface of a lake. It can always be described at any moment in time in 2 dimensions (x,y) with a height value for each point of the surface. If you want to capture it changing over time you need 3 dimensions (x,y,t) with height values for each.
The fact I'd need to go through all 3100 inputs to calculate the wave, doesn't mean I need 3100 values to store the results of that calculation. This it what I mean by using the wrong "basis" to describe the wave function.
In programmer terms you can describe a resultant value as either a function, and all of its required parameters. Or you can just describe the output value. 310^80 is describing all of the inputs and the "function" to call.
And one note, on the math. I believe there be 3(10^80) dimensions as inputs. Which would mean R^(3*(10^80)) possible configurations. You wrote 3^(10^80) which is significantly larger.
As for your analogy, I don't quite follow. The actual physical model is that of the oscillators, more or less. The wave is the mathematical abstraction that does allow us to replace it with a function. In terms of information, the wave has more detail, but it is abstracted into a nice form. I think we agree on this.
But the quantum wave function is serving a different role. The water wave is something that varies over the 2d space. As we look at different values, we change the x and y coordinates to see the new values. In that sense, it is 2d.
For the quantum wave function, if we keep all but one of the 10^80 particles in the same exact position, but we vary the position of that one particle, we do get different values of the wave function and it does matter to all the particles as it will affect the gradient vector defining the velocity vector of each of the particles. The change is not localized to just the one particle that is changing, but impacts all particles.
Of course, most of the time, practically speaking, changes by one particle will not make a difference, but situations such as present in Bell's Theorem and quantum computing are exceptions to this.
Fundamentally, the current state of all the particles is needed to be known in order to know what part of the wave function is needed. That is the sense in which the dimension is not 3, but 310^80.
If you take Pilot Wave Interpretation and just take out the particles, you're left with the Many Worlds Interpretation with exactly the same predictions. To paraphrase Netwon, there's no need for that hypothesis.
And if you take Many World and simply add a particle you have Pilot Wave hypothesis. No need for the crazy multiple universes nonsense. All 3 produce (including Copenh) the exact same predictions, so that's not gonna be the distinguishing factor.
Which is more contorted? Waves are physical and particles exist? Or we live in a countless number of simultaneously subdividing universes?
It's fascinating to hear people discuss PW vs MWs - because (in my opinion) it becomes very clear which they became comfortable with first.
If you were to stop a random person on the street and give them a summary of the two theories it's pretty clear that someone unfamiliar with both would say the PW is a ton simpler. But it's fascinating to see that a good number of people who are comfortable with many worlds will argue that it's less complex. My view is obviously their opinion is shaped by what they've been exposed to first.
And PW is strictly more complicated than MW, because you still need to track the same wavefunction on phase space, but then you add this particle to have something to point to and say "this is reality". But all the complexity of the wavefunction is still there. If you try to reduce this complexity by collapsing the wave function, you're back to having the same problems as Copenhagen.
The problem here is that you want an explanation that is intuitive and easy for you to grasp. What if the true answer is one that is too hard for you (or maybe any human) to easily understand?
Our brains aren't evolved for understanding the true nature of the universe, they're evolved for reproducing and surviving in a very simple world. We're using re-purposed hardware for a very different task- we shouldn't be surprised that it's difficult.
Absolutely. For survival-to-reproduction -- and for quite a bit more than that -- Aristotle's physics are enough; but they're full of absurdities and strange edge cases when you look at them more carefully. To explain the flight of an arrow, you need Newton... and then you start noticing that Newton has edge cases too.
I don't pretend to understand quantum mechanics, but I'm fine with cheering from the sidelines on that one. Whatever the answers are at that level, they certainly seem to be shaping up to be something deeply unlike our intuitions...
QM does not line up with human intuition at all. It looks like this is a fundamental issue with how the universe works, not a problem with our explanations. And really, that shouldn't be any surprise. There's no reason to expect the universe's workings to match our intuition in any situation that's substantially different from what our intuition evolved in.
MWI may or may not be correct, but an adherent definitely would not say they "don't understand" QM.
The Copenhagen Interpretation has a pretty big theoretical hole in that the condition for when a wavefunction collapse occurs is not defined within the theory itself. Supposedly collapse occurs during a "measurement". Well, what's a measurement? Your measuring apparatus are all made up of matter that supposed to be following the same fundamental physical laws. I think you'd be hard pressed to write a computer program that takes as input a description of all the particles and their wavefunctions and compute when a measurement occurs. In practice, scientists doing calculations under the Copenhagen Interpretation will choose the points in time to perform a collapse so that the calculations match experimental results. This is what I mean when I say that Copenhagen is non-algorithmic. That's a forgivable mistake if you invent your theory before the idea of an algorithm is formalized (as was CI), but today it's not a forgivable mistake.
If you decide to fix the problem with Copenhagen Interpretation by explicitly defining that a measurement is when X happens for some X, then you've allowed for an experiment whose results can differentiate between Copenhagen and Many Worlds. MWI says that different parts of the wave function can affect each other no matter how distant, though the effect size decreases exponentially with distance. So set up an experiment so that X occurs and then be able to measure interference from distant parts of the wavefunction that are either present (in MWI) or not present (in CI). That distinguishes the interpretations via experiment.
OK so far...
> and the reason they behave like that is because they're interacting with parallel universes.
No longer OK. You consider that the simple explanation? You don't think that's obfuscating at least as much as "there are no photons" does?
If you still don't understand, consider this: MWI only works if photons are kept in a coherent superposition of states.
Supposedly this means each universe defines a state.
But... the photons have to be isolated from their respective universes. Otherwise coherence is broken and you no longer have your coherent superposition.
Given that, what's the rationale for inventing an entire universe around a quantum particle if the math only works if you keep that particle isolated from everything else in that universe?