I had a similar prompt for knowledge seeking in wanting to figure out how the math supports or doesn’t support “converging worlds” or “mangled worlds”. The notion of a converging world is also porbably of note worthy intuitive reference point in thought-space. You could have a system that is in a quantum indeterministic state each state have a different interaction so that the futures of the states are identical. At that point you can drop the distinguising of the worlds and just say that two worlds have become one. Now there is a possibility that a state left alone first splits and then converges or that it does both at the same time. There would be middle part that would not be being able to be “classified” which in these theories would be represented by two worlds in different configurations (and waves in more traditional models).
Some times I have stumbled upon an argument that if many worlds creates extra worlds whether that forms as a kind of growing block ontology (such as the flat splitters in the sequence post). Well if the worlds also converge that could keep the amount of “ontology stuff” constant or able to vary in both directions.
I stumbled upon that |psi(x)^2| was how you calculated the evolution of a quantum state which was like taking a second power and then essentailly taking a square root by only careing about the magnitude and not the phase of the complex value. For a double slit wtih L being left and R being R it resulted in P(L+R)^2= ^2+C+^2 (where C was either 1, 2 or sqr(2) don’t remember and didn’t understand which) . The squarings in the sum I found was claimed to be the classical equivalent of the two options. The interference fridges would be great and appear where the middle term was strong. I also that you could read as something like “obtain X if situation was/is y”. Getting L when the particle went L is thus very ordinary and all. You can also note that the squaring have the same form as the evolution of a pure state. However I didn’t find anything in whether the middle term was interpretable or not. If you try to put it into words it looks a lot like “probability of getting L when the situation was R” which seems very surprising that it could be anything else than zero. But then again I dont’ know what imaginary protoprobabilties are. Because it’s a multipication of two “chains of events” it’s clear you can’t single out the “responcible party”, it can be a contribution from both. I somehow suspect that this correlates that if your “base” is |L> then the |R>|L> base doesn’t apply, ie you can’t know the path taken and still get interference. I get that many worlds posits the R world and the L word but it seems there is like a bizarre combination world also involved. One way I in my brute naivity think migth be goign on is taht the particle started in the L world but then “crossed over” to the R world. If worlds in contact can exchange particles it might seem as particles “mysteriously jumped” while the jumping would be loosely related where the particle was. They would have continous trajectories when tracked within the multiverse but they get confused for each other in the single worlds.
However I was unable to grasp the intuition how bras and kets work or what they mean. I pushed the strangeness to wavefunctions but was unable to reach my goal.
It still seems mysterious to me how the single photon state turns into two distinct L and R. I could imagine the starting state to “do a full loop” be a kind of spiral where the direction that photon is travelling is a superpositon of it travelloing in each particular direction with each direction differing from it’s neighbour by the phase of the protoprobability phase with their magnitudes summing to 1. That way if the photon has probability one at L it can’t have probability 1 as the real part of the protoprobability at R can’t be 1 as it is known to differ in phase. I know these intuitions are not well founded, I know the construction of them is known to be unsafe. However intuitive pictures are more easy for me to work with even if it means needing to reimagine them rather than just have them in the right configuration (if somebody know s a more representative way to think about it please tip me about it).
I am also using a kind of guess that you can take a protoprobaility strip it of imaginary parts an dyou get a “single world view” and I am using a view of having 2 time dimensions: a second additional clock makes the phases of the complex values sweep forward (or sweep equal surface areas) even if the “ordinary clock time” would stay still. The undeterminancy under this time would be that a being that is not able to measure the meta-time would be ignorant on what part of the cycle the world is in. Thus you would be ignorant of the phases, but the phases would “resonate”. I am assuming one could turn this into a equivalent view where the imaginary component would just select a spatial world in a 1-time multiverse (in otherwise totally real-part only worlds).
I don’t have known better understanding but I have a bunch of different understadnings of unknown fittness.
I don’t quite understand this topic, but maybe this could be useful:
The problem with “converging / mangled worlds” is statistical. To make two worlds interact (and become the same world, or erase each other, depending on mutual orientation of their amplitudes), those worlds must have all their particles in the same position. In usual circumstances, this seems unlikely. Imagine the experiment with the cat, where in one world the cat is dead, and in other world the cat happily walks away. How likely is it that at some moment in the future, both universes will have all particles in the same positions?
So, in usual circumstances two worlds interact only if a moment ago they were the same world, and the only difference was one particle going two different paths. (Yes, there are also all the other particles in the universe, also splitting all the time. But this happens the same way in both branches, so it cancels out.)
It still seems mysterious to me how the single photon state turns into two distinct L and R.
My intuition is that this “single state” was never literally one point, but always a small interval (wave? hump?). An interval can break into two parts, and those can travel in different directions. There is no such thing as a single point in quantum physics.
(Disclaimer: I don’t really understand quantum physics; I am just interpreting the impression I got from looking at Eliezer’s drawings. If you have better knowledge, feel free to ignore this.)
What forces the worlds to be same in order to interact? You could also have merely adjacent worlds where the “collisions angle” could compensate for small differences. It is just a little harder to imagine how worlds of unrelated state would interact. Maybe dark energy is the sum total of gravity from other worlds?
It’s also that two worlds won’t long stay singular, but branch all the time into subworlds. The probability of some of the pairwise worlds being close enough is higher.
edit: Also there are settings where splitting doesn’t mean lack of structure. For example in the mirror experiements the two paths will systematically intersect and this is a pretty stable result of the mirror positionings.
It’s also that two worlds won’t long stay singular, but branch all the time into subworlds. The probability of some of the pairwise worlds being close enough is higher.
If something branches in a limited space, soon the branches will touch each other. The question is, how soon is “soon”. If we imagine a real 3D tree in a 3D world, the branches will touch before dozen splits. But if the tree would be extremely large (a few kilometers) and the branches extremely tiny (a few milimeters), there could be more splits.
If we imagine the history of the whole universe as a branching tree in a many-dimensional world, we have to realize there are many dimension (I guess approximately six dimensions for each particle: position and momentum), and compared with the size of the dimension, the branches are really tiny (take two random particles in the whole universe, what is their probability of hitting each other). So there is a lot of time for the tree to grow.
Eventually, the branches will run out of space and start hitting each other all the time. But I think this will happen at the “heat death” of the universe. Then the branches will hit each other so much that the whole concept of time or even reality may become meaningless. But I think this is not happening now, yet. There is still a lot of space for the universe to grow without intersecting with other branches.
What forces the worlds to be same in order to interact? … Maybe dark energy is the sum total of gravity from other worlds?
This seems to me like a new hypothesis, outside of the quantum physics as we know it yet, not supported by experimental results. Maybe it is so; maybe it isn’t. Without good evidence for it the prior probability seem small (there are many possible new hypotheses we could make to explain dark energy, this is just one of them, why should it be preferred to the alternatives).
I had a similar prompt for knowledge seeking in wanting to figure out how the math supports or doesn’t support “converging worlds” or “mangled worlds”. The notion of a converging world is also porbably of note worthy intuitive reference point in thought-space. You could have a system that is in a quantum indeterministic state each state have a different interaction so that the futures of the states are identical. At that point you can drop the distinguising of the worlds and just say that two worlds have become one. Now there is a possibility that a state left alone first splits and then converges or that it does both at the same time. There would be middle part that would not be being able to be “classified” which in these theories would be represented by two worlds in different configurations (and waves in more traditional models).
Some times I have stumbled upon an argument that if many worlds creates extra worlds whether that forms as a kind of growing block ontology (such as the flat splitters in the sequence post). Well if the worlds also converge that could keep the amount of “ontology stuff” constant or able to vary in both directions.
I stumbled upon that |psi(x)^2| was how you calculated the evolution of a quantum state which was like taking a second power and then essentailly taking a square root by only careing about the magnitude and not the phase of the complex value. For a double slit wtih L being left and R being R it resulted in P(L+R)^2= ^2+C+^2 (where C was either 1, 2 or sqr(2) don’t remember and didn’t understand which) . The squarings in the sum I found was claimed to be the classical equivalent of the two options. The interference fridges would be great and appear where the middle term was strong. I also that you could read as something like “obtain X if situation was/is y”. Getting L when the particle went L is thus very ordinary and all. You can also note that the squaring have the same form as the evolution of a pure state. However I didn’t find anything in whether the middle term was interpretable or not. If you try to put it into words it looks a lot like “probability of getting L when the situation was R” which seems very surprising that it could be anything else than zero. But then again I dont’ know what imaginary protoprobabilties are. Because it’s a multipication of two “chains of events” it’s clear you can’t single out the “responcible party”, it can be a contribution from both. I somehow suspect that this correlates that if your “base” is |L> then the |R>|L> base doesn’t apply, ie you can’t know the path taken and still get interference. I get that many worlds posits the R world and the L word but it seems there is like a bizarre combination world also involved. One way I in my brute naivity think migth be goign on is taht the particle started in the L world but then “crossed over” to the R world. If worlds in contact can exchange particles it might seem as particles “mysteriously jumped” while the jumping would be loosely related where the particle was. They would have continous trajectories when tracked within the multiverse but they get confused for each other in the single worlds.
However I was unable to grasp the intuition how bras and kets work or what they mean. I pushed the strangeness to wavefunctions but was unable to reach my goal.
It still seems mysterious to me how the single photon state turns into two distinct L and R. I could imagine the starting state to “do a full loop” be a kind of spiral where the direction that photon is travelling is a superpositon of it travelloing in each particular direction with each direction differing from it’s neighbour by the phase of the protoprobability phase with their magnitudes summing to 1. That way if the photon has probability one at L it can’t have probability 1 as the real part of the protoprobability at R can’t be 1 as it is known to differ in phase. I know these intuitions are not well founded, I know the construction of them is known to be unsafe. However intuitive pictures are more easy for me to work with even if it means needing to reimagine them rather than just have them in the right configuration (if somebody know s a more representative way to think about it please tip me about it).
I am also using a kind of guess that you can take a protoprobaility strip it of imaginary parts an dyou get a “single world view” and I am using a view of having 2 time dimensions: a second additional clock makes the phases of the complex values sweep forward (or sweep equal surface areas) even if the “ordinary clock time” would stay still. The undeterminancy under this time would be that a being that is not able to measure the meta-time would be ignorant on what part of the cycle the world is in. Thus you would be ignorant of the phases, but the phases would “resonate”. I am assuming one could turn this into a equivalent view where the imaginary component would just select a spatial world in a 1-time multiverse (in otherwise totally real-part only worlds).
I don’t have known better understanding but I have a bunch of different understadnings of unknown fittness.
I don’t quite understand this topic, but maybe this could be useful:
The problem with “converging / mangled worlds” is statistical. To make two worlds interact (and become the same world, or erase each other, depending on mutual orientation of their amplitudes), those worlds must have all their particles in the same position. In usual circumstances, this seems unlikely. Imagine the experiment with the cat, where in one world the cat is dead, and in other world the cat happily walks away. How likely is it that at some moment in the future, both universes will have all particles in the same positions?
So, in usual circumstances two worlds interact only if a moment ago they were the same world, and the only difference was one particle going two different paths. (Yes, there are also all the other particles in the universe, also splitting all the time. But this happens the same way in both branches, so it cancels out.)
My intuition is that this “single state” was never literally one point, but always a small interval (wave? hump?). An interval can break into two parts, and those can travel in different directions. There is no such thing as a single point in quantum physics.
(Disclaimer: I don’t really understand quantum physics; I am just interpreting the impression I got from looking at Eliezer’s drawings. If you have better knowledge, feel free to ignore this.)
What forces the worlds to be same in order to interact? You could also have merely adjacent worlds where the “collisions angle” could compensate for small differences. It is just a little harder to imagine how worlds of unrelated state would interact. Maybe dark energy is the sum total of gravity from other worlds?
It’s also that two worlds won’t long stay singular, but branch all the time into subworlds. The probability of some of the pairwise worlds being close enough is higher.
edit: Also there are settings where splitting doesn’t mean lack of structure. For example in the mirror experiements the two paths will systematically intersect and this is a pretty stable result of the mirror positionings.
If something branches in a limited space, soon the branches will touch each other. The question is, how soon is “soon”. If we imagine a real 3D tree in a 3D world, the branches will touch before dozen splits. But if the tree would be extremely large (a few kilometers) and the branches extremely tiny (a few milimeters), there could be more splits.
If we imagine the history of the whole universe as a branching tree in a many-dimensional world, we have to realize there are many dimension (I guess approximately six dimensions for each particle: position and momentum), and compared with the size of the dimension, the branches are really tiny (take two random particles in the whole universe, what is their probability of hitting each other). So there is a lot of time for the tree to grow.
Eventually, the branches will run out of space and start hitting each other all the time. But I think this will happen at the “heat death” of the universe. Then the branches will hit each other so much that the whole concept of time or even reality may become meaningless. But I think this is not happening now, yet. There is still a lot of space for the universe to grow without intersecting with other branches.
This seems to me like a new hypothesis, outside of the quantum physics as we know it yet, not supported by experimental results. Maybe it is so; maybe it isn’t. Without good evidence for it the prior probability seem small (there are many possible new hypotheses we could make to explain dark energy, this is just one of them, why should it be preferred to the alternatives).