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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 functi

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.

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.