I guess they are somehow an animation of complex points in 3 real dimensions?
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.
If you can’t compute the next state of a “world” from how it looks now but have to look at the neighbours in configuration space doesn’t this mean that world evolution is inherently not a “private” fact?
It’s a local fact. Knowing just that point won’t work; it only gives you the positions of the particles, but having an arbitrarily small neighborhood will give you the derivative, which gives you the momentums of the particles.
And in stationary wavefunctions while each individual wave moves outward the shape of the wave function is the same after one cycle. That is such wavefunctions don’t “shatter” and they have the quality of reforming the same shape. I don’t have a good detail to point to but it seems it must converge just as fast as it splits.
In stationary waves, you’re dealing with something that only has a small set of states. It has to converge as fast as it splits, since there’s nowhere else to go. If you stick a particle in an infinite universe, there’s no stationary wavefunction.
Woudn’t the “converging worlds” be us much of a big deal as “splitting worlds”?
It doesn’t happen as much thanks to increasing entropy. Everything starts from the big bang, but it can end anywhere.
That’s not to say it doesn’t happen. The double slit experiment works because the universe where the photon passes through the left slit and the one where it passes through the right slit intersect again. It doesn’t work when you record which slit the photon passes through, since one universe now has a detector saying “left” and the other one has one saying “right”, so they’re not the same universe.
And wouldn’t it be quite possible that instead of looking like a tree or balloon on the macro level your world line would look more like a line.
As long as it’s stable it will. Once something chaotic happens, it will start splitting.
Doesn’t the preservation of measure mean that worlds don’t “dissipate into ambivalence”. A common take on many worlds where each decision splits your world would in my mind imply such a dissipation.
Imagine you’re putting a drop of dye into a pool. It doesn’t break down or otherwise stop being dye, but it does dissipate. It’s the same deal with quantum physics. The measure is preserved, but later on it’s just spread out more.
The bomb tester experiment reads to me as if you blow up the bomb in another world to gain info on the version in your world.
Also a good example of converging worlds. If the bomb doesn’t explode, the universes can converge again, causing destructive interference in places. If it does explode in one universe, they can’t converge, so those places that would have had destructive interference can still happen, and if they do, that proves the bomb exploded in another universe.
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.
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.
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.
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.
If you can’t compute the next state of a “world” from how it looks now but have to look at the neighbours in configuration space doesn’t this mean that world evolution is inherently not a “private” fact?
It’s a local fact. Knowing just that point won’t work; it only gives you the positions of the particles, but having an arbitrarily small neighborhood will give you the derivative, which gives you the momentums of the particles.
Even if I knew the neighbors in space in this configuration wouldn’t I still need to know the other configurations state? Depending on whether interference is enabled or disabled by monitoring the path in the double slit experiment I could be spatially close but far in configuration space in the middle receiving point. There is off course a linkage with the spatially close neighborhood as it too is influenced by the same offworlds. But isn’t it so that an event such as a bomb going off in another world will not have (perfect) precursor trace in this world but will have some point of first effect.
And in stationary wavefunctions while each individual wave moves outward the shape of the wave function is the same after one cycle. That is such wavefunctions don’t “shatter” and they have the quality of reforming the same shape. I don’t have a good detail to point to but it seems it must converge just as fast as it splits.
In stationary waves, you’re dealing with something that only has a small set of states. It has to converge as fast as it splits, since there’s nowhere else to go. If you stick a particle in an infinite universe, there’s no stationary wavefunction.
I was thinking off solid classical stuff that quantum mechanically still pulses. Like if I stick atom in a empty universe the electron will hang around the nucleus. I guess the direction of wandering of the whole atom would still spread. Does stuff not evaporating from your hands need a converging contribution from the environment? I find the idea a little spooky.
That’s not to say it doesn’t happen. The double slit experiment works because the universe where the photon passes through the left slit and the one where it passes through the right slit intersect again. It doesn’t work when you record which slit the photon passes through, since one universe now has a detector saying “left” and the other one has one saying “right”, so they’re not the same universe.
How come the effects of light on the air is not enough to “break the spell”? The splitting of worlds is not pointlike but I have very much trouble imagining what is “halfsplitting” like.
Doesn’t the preservation of measure mean that worlds don’t “dissipate into ambivalence”. A common take on many worlds where each decision splits your world would in my mind imply such a dissipation.
Imagine you’re putting a drop of dye into a pool. It doesn’t break down or otherwise stop being dye, but it does dissipate. It’s the same deal with quantum physics. The measure is preserved, but later on it’s just spread out more.
I was thinking if it more like oil that does form droplets as it is interacted with but sticks together instead of dissolving when left to it’s own.
Even if I knew the neighbors in space in this configuration wouldn’t I still need to know the other configurations state?
I’m not sure I understand.
Are you saying that, in addition to knowing what the nearby universes are, you need to know the value of the waveform there?
I was just talking about the value of the waveform. You automatically know what the nearby universes are. They’re the ones just like yours, but with a few particles moved by epsilon.
Like if I stick atom in a empty universe the electron will hang around the nucleus.
In principle, the electron can go anywhere, but it’s being forced near the atom, so almost all of the waveform will be there. There’s not enough room for it to spread out.
How come the effects of light on the air is not enough to “break the spell”?
It interacts with nearby universes. The universe where the photon changes the direction of a molecule of air on the way to the sensor array interferes with a universe where the photon took a different path and the air was already going that direction.
This doesn’t happen with a sensor, because any sensor that’s likely to say the photon went through the left slit when it really went through the right one isn’t very good at sensing.
I was thinking if it more like oil that does form droplets as it is interacted with but sticks together instead of dissolving when left to it’s own.
You said that multiple splitting of worlds seems like it would reduce measure. I showed an example of something dispersing but not reducing, showing that dispersion does not imply reduction. The fact that there are many things that don’t disperse or reduce is irrelevant.
Placing oil in droplets results in the droplets sticking together, but this is due to the cohesive force of the water. It has nothing to do with conservation of oil.
The wavefunction is the same object shared by all universes, correct? Thus a point’s spatial neighborhood in one universe is not the full neighborhood of the point. I would imagine (if it’s a coherent notion) taking a derivate only “within one universe” would have a different result than taking it with the full wavefunction.
Wouldn’t an air molecule already going one way need a separate cause to be going that way (as in something that pushes it that way (probably another air molecule))? And wouldn’t that put it simply further in configuration space (ie make interference less likely)? I have still trouble imagining when interference happens and when not. You need a path in configuration space to connect two points to have interference? And if the distance is big there are more chances for the intervening configurations to spoil the interaction?
It seems the air gets scrambled. I guess any device that could detect the scrambling would be as good as detecting the particle directly?
The wavefunction is the same object shared by all universes, correct? Thus a point’s spatial neighborhood in one universe is not the full neighborhood of the point. I would imagine (if it’s a coherent notion) taking a derivate only “within one universe” would have a different result than taking it with the full wavefunction.
I meant the universe’s neighborhood, at taking the derivative of the universe’s wavefunction at that point.
Wouldn’t an air molecule already going one way need a separate cause to be going that way (as in something that pushes it that way (probably another air molecule))?
Since the wave function is continuous, if you look at a universe with a particle nudged just a little bit, the wave function won’t change much. It’s not like you’re moving that particle very far.
I guess any device that could detect the scrambling would be as good as detecting the particle directly?
No. If the air only ended up in that orientation if the particle went in a particular direction, then the system would decohere, and the detector would be unnecessary. Since the air can end up in the same orientation either way, there’s no way to detect it.
Since the wave function is continuous, if you look at a universe with a particle nudged just a little bit, the wave function won’t change much. It’s not like you’re moving that particle very far.
If the photon is going through the other slit it’s several molecule lengths away. So the molecule just curves/collides with empty space as if the photon was there? I don’t understand how it can touch the air and not decohere.
The interactions are weak. If we had some super-sensitive air pressure detector that could tell which slit the photon had gone through, we’d get the same results as when we measure which slit the photon has gone through (that is to say, no interference). But actually such a thing is impossible; maybe a few air molecules close to the photon path will get their state entangled with the photon state, but they don’t interact enough with other air molecules for the entanglement to spread through the whole room. So you get a case rather like the one where you record which slit the photon went through but then destroy that information without reading it—and you do see the interference.
There’s another universe where the air was already going in that direction. Since the photon isn’t going to nudge it much, it’s a really similar universe, so it has about the same wavefunction as the universe you were looking at to begin with.
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.
It’s a local fact. Knowing just that point won’t work; it only gives you the positions of the particles, but having an arbitrarily small neighborhood will give you the derivative, which gives you the momentums of the particles.
In stationary waves, you’re dealing with something that only has a small set of states. It has to converge as fast as it splits, since there’s nowhere else to go. If you stick a particle in an infinite universe, there’s no stationary wavefunction.
It doesn’t happen as much thanks to increasing entropy. Everything starts from the big bang, but it can end anywhere.
That’s not to say it doesn’t happen. The double slit experiment works because the universe where the photon passes through the left slit and the one where it passes through the right slit intersect again. It doesn’t work when you record which slit the photon passes through, since one universe now has a detector saying “left” and the other one has one saying “right”, so they’re not the same universe.
As long as it’s stable it will. Once something chaotic happens, it will start splitting.
Imagine you’re putting a drop of dye into a pool. It doesn’t break down or otherwise stop being dye, but it does dissipate. It’s the same deal with quantum physics. The measure is preserved, but later on it’s just spread out more.
Also a good example of converging worlds. If the bomb doesn’t explode, the universes can converge again, causing destructive interference in places. If it does explode in one universe, they can’t converge, so those places that would have had destructive interference can still happen, and if they do, that proves the bomb exploded in another universe.
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.
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?
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?
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.
If they’re bosons. If they’re fermions it would be opposite state.
They map to the same (or opposite) C value.
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.
I’m not sure what you mean by this.
Even if I knew the neighbors in space in this configuration wouldn’t I still need to know the other configurations state? Depending on whether interference is enabled or disabled by monitoring the path in the double slit experiment I could be spatially close but far in configuration space in the middle receiving point. There is off course a linkage with the spatially close neighborhood as it too is influenced by the same offworlds. But isn’t it so that an event such as a bomb going off in another world will not have (perfect) precursor trace in this world but will have some point of first effect.
I was thinking off solid classical stuff that quantum mechanically still pulses. Like if I stick atom in a empty universe the electron will hang around the nucleus. I guess the direction of wandering of the whole atom would still spread. Does stuff not evaporating from your hands need a converging contribution from the environment? I find the idea a little spooky.
How come the effects of light on the air is not enough to “break the spell”? The splitting of worlds is not pointlike but I have very much trouble imagining what is “halfsplitting” like.
I was thinking if it more like oil that does form droplets as it is interacted with but sticks together instead of dissolving when left to it’s own.
I’m not sure I understand.
Are you saying that, in addition to knowing what the nearby universes are, you need to know the value of the waveform there?
I was just talking about the value of the waveform. You automatically know what the nearby universes are. They’re the ones just like yours, but with a few particles moved by epsilon.
In principle, the electron can go anywhere, but it’s being forced near the atom, so almost all of the waveform will be there. There’s not enough room for it to spread out.
It interacts with nearby universes. The universe where the photon changes the direction of a molecule of air on the way to the sensor array interferes with a universe where the photon took a different path and the air was already going that direction.
This doesn’t happen with a sensor, because any sensor that’s likely to say the photon went through the left slit when it really went through the right one isn’t very good at sensing.
You said that multiple splitting of worlds seems like it would reduce measure. I showed an example of something dispersing but not reducing, showing that dispersion does not imply reduction. The fact that there are many things that don’t disperse or reduce is irrelevant.
Placing oil in droplets results in the droplets sticking together, but this is due to the cohesive force of the water. It has nothing to do with conservation of oil.
The wavefunction is the same object shared by all universes, correct? Thus a point’s spatial neighborhood in one universe is not the full neighborhood of the point. I would imagine (if it’s a coherent notion) taking a derivate only “within one universe” would have a different result than taking it with the full wavefunction.
Wouldn’t an air molecule already going one way need a separate cause to be going that way (as in something that pushes it that way (probably another air molecule))? And wouldn’t that put it simply further in configuration space (ie make interference less likely)? I have still trouble imagining when interference happens and when not. You need a path in configuration space to connect two points to have interference? And if the distance is big there are more chances for the intervening configurations to spoil the interaction?
It seems the air gets scrambled. I guess any device that could detect the scrambling would be as good as detecting the particle directly?
I meant the universe’s neighborhood, at taking the derivative of the universe’s wavefunction at that point.
Since the wave function is continuous, if you look at a universe with a particle nudged just a little bit, the wave function won’t change much. It’s not like you’re moving that particle very far.
No. If the air only ended up in that orientation if the particle went in a particular direction, then the system would decohere, and the detector would be unnecessary. Since the air can end up in the same orientation either way, there’s no way to detect it.
If the photon is going through the other slit it’s several molecule lengths away. So the molecule just curves/collides with empty space as if the photon was there? I don’t understand how it can touch the air and not decohere.
The interactions are weak. If we had some super-sensitive air pressure detector that could tell which slit the photon had gone through, we’d get the same results as when we measure which slit the photon has gone through (that is to say, no interference). But actually such a thing is impossible; maybe a few air molecules close to the photon path will get their state entangled with the photon state, but they don’t interact enough with other air molecules for the entanglement to spread through the whole room. So you get a case rather like the one where you record which slit the photon went through but then destroy that information without reading it—and you do see the interference.
There’s another universe where the air was already going in that direction. Since the photon isn’t going to nudge it much, it’s a really similar universe, so it has about the same wavefunction as the universe you were looking at to begin with.