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Slider comments on Open thread, 9-15 June 2014 - Less Wrong Discussion

3 Post author: Tenoke 09 June 2014 01:07PM

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Comment author: Slider 12 June 2014 01:13:24PM 0 points [-]

A set of n entangle particles is a function from R^(3n) to C. It's assigning a complex number to each configuration of particles. Since there are n particles, and each particle has three real dimensions, it comes out to 3n real dimensions.

But won't the physcial underlying reality still be contrained to a fixed dimensionality space (if it is not R3)? That is can the function be composed as a R^(3n) function to R^3 to C? I thought particles are bumps in a field not that each bump makes it's own field to contain it.

Comment author: DanielLC 12 June 2014 05:59:50PM 0 points [-]

But won't the physcial underlying reality still be contrained to a fixed dimensionality space (if it is not R3)? That is can the function be composed as a R^(3n) function to R^3 to C?

I'm not sure what you're trying to say here. Are you suggesting that it's a function that maps a point on R^(3n) onto functions from R^3 to C? Like you plug in a point in R^(3n), and you get a function from R^3 to C?

I thought particles are bumps in a field not that each bump makes it's own field to contain it.

If you have one particle, it can be in any position in R^3, so you have a function from R^3 to C. If you have two particles, then they can be in any combination of positions with their own values. For example, if one is a proton and one's an electron, and there's not enough energy in the system to split them, then either of the particles can be anywhere, but they still have to be close to each other. If they each had their own distinct wave function, that wouldn't be possible. It works because the system as a whole has one wave function, and it's close to zero for any configuration where the proton and electron are not close together.

Does that help at all?

Comment author: Slider 12 June 2014 09:36:25PM 0 points [-]

If they are of the same type then a point (A,0,0,B,0,0) would result in the same state as (B,0,0,A,0,0) I would understand this as those points mapping to a same R^3->C function. I thought there was no billiard balls and that the wavefunction has ontological priority? If I had two separate particles of different kinds in the same position I could tell from the R^3->C undulations on which kind of particle it is. I can understand it might be handy to order the undulations by their centers point-like shorthands. I thought that the real mechanics happen on the R^3->C and if there are mechanics on the higher dimensional structure they are an emergent consequence of that level.

Like I can index me throwing a rock on the lake by where my rock lands. However this kind of description can not describe any two simultanoues throws or things like throwing a stick sideways into the water. The wierder throws I make the more things I need to spesify. However if I somehow manage convey the shape of the water there is no way it can be inadeqaute picture of the wave (such as if I make a topographical map). And in no way of splashing can I add or remove water or make it do anything but go up or down. The quantum field takes on value of C so it has "more room" than simply going up or down. However in no way of taking on those C values does the lake change in volume or dimensionality.

Comment author: DanielLC 12 June 2014 11:20:35PM *  0 points [-]

If they are of the same type then a point (A,0,0,B,0,0) would result in the same state as (B,0,0,A,0,0)

If they're bosons. If they're fermions it would be opposite state.

I would understand this as those points mapping to a same R^3->C function.

They map to the same (or opposite) C value.

I thought that the real mechanics happen on the R^3->C and if there are mechanics on the higher dimensional structure they are an emergent consequence of that level.

The real mechanics happen on the R^(3n)->C. If they're not very entangled, you can separate it approximately into f(x,y) ~= (g(x),h(y)), where x and y are the positions of the points in R^3, f is a wave function from R^6 to C, and g and h are wave functions from R^3 to C.

Like I can index me throwing a rock on the lake by where my rock lands. However this kind of description can not describe any two simultanoues throws or things like throwing a stick sideways into the water. The wierder throws I make the more things I need to spesify. However if I somehow manage convey the shape of the water there is no way it can be inadeqaute picture of the wave (such as if I make a topographical map). And in no way of splashing can I add or remove water or make it do anything but go up or down. The quantum field takes on value of C so it has "more room" than simply going up or down. However in no way of taking on those C values does the lake change in volume or dimensionality.

I'm not sure what you mean by this.

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