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Clearly this is all subjective, but Pilot Wave theory (De Broglie & Bohm) is the simplest least "crazy" of all the explanations. Horribly simplified: Space isn

Clearly this is all subjective, but Pilot Wave theory (De Broglie & Bohm) is the simplest least "crazy" of all the explanations. 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.

jostylr 9y ago
While one can take a bit of issue with using the ether as analogy for a number of reasons, the most important difference to keep in mind is that the wave function exists in configuration space. For 10^80 particles, this is a space with 3^(10^80) dimensions. This is the source of nonlocality. 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.
- BoiledCabbage 9y ago
  So here I may be stepping past my knowledge, but I thought that the reason for appearing to require so many would be simply due to using the wrong "basis" to calculate the wave function. Or separating the concept of how to generate the wave function from the values it produces. 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.
  - jostylr 9y ago
    Error: Yes, it should be 310^80. I think my brain was half-writing the dimension and half-writing the more useful view of (R^3)^10^80. Thanks for catching that. 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.
Simon_says 9y ago
The Pilot Wave Interpretation is one of the strangest contortions I've ever seen. You go to all the trouble to set up the wave equation acting on phase space of the entire universe, but then you remember that you think particles are fundamental elements of reality, so you drop them in and say they're guided by your wave equation. 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.
- BoiledCabbage 9y ago
  > 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.
  - Simon_says 9y ago
    Copenhagen isn't even a proper theory, because it never tells you precise criteria for when wavefunction collapse occurs. It's not a surprise that nobody noticed this at the time, because the Copenhagen Interpretation was invented prior to the foundational work on computation and formalization of what an algorithm is. But looking at it now, it should be clear that there's no formal definition of what a "measurement" is. As soon as you give precise criteria for wavefunction collapse, then you have a difference in predictions between Copenhagen and MW. 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.

jostylr 9y ago

While one can take a bit of issue with using the ether as analogy for a number of reasons, the most important difference to keep in mind is that the wave function exists in configuration space. For 10^80 particles, this is a space with 3^(10^80) dimensions. This is the source of nonlocality. 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.

BoiledCabbage 9y ago
So here I may be stepping past my knowledge, but I thought that the reason for appearing to require so many would be simply due to using the wrong "basis" to calculate the wave function. Or separating the concept of how to generate the wave function from the values it produces. 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.
- jostylr 9y ago
  Error: Yes, it should be 310^80. I think my brain was half-writing the dimension and half-writing the more useful view of (R^3)^10^80. Thanks for catching that. 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.

Simon_says 9y ago

The Pilot Wave Interpretation is one of the strangest contortions I've ever seen. You go to all the trouble to set up the wave equation acting on phase space of the entire universe, but then you remember that you think particles are fundamental elements of reality, so you drop them in and say they're guided by your wave equation. 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.

BoiledCabbage 9y ago
> 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.
- Simon_says 9y ago
  Copenhagen isn't even a proper theory, because it never tells you precise criteria for when wavefunction collapse occurs. It's not a surprise that nobody noticed this at the time, because the Copenhagen Interpretation was invented prior to the foundational work on computation and formalization of what an algorithm is. But looking at it now, it should be clear that there's no formal definition of what a "measurement" is. As soon as you give precise criteria for wavefunction collapse, then you have a difference in predictions between Copenhagen and MW. 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.