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A video on time reversal inspired me to attempt a version of Conway's "life" that would share QM's T-symmetry. If you have never hear of Conway's life, it is described here:
http://en.wikipedia.org/wiki/Conway's_Game_of_Life
My thought was that instead of the two colors (black and white) in Conway's game, mine would have three. And by reversing any two of the three colors, the same rules would cause my version of the game to run backwards.
In Conway's game, non-locality was limited to the eight cells to the North, South, East, West, NE, NW, SE, and SW of a cell.
My original hope was that I could use a similar constraint on my Time-Reversal-Invariant (TRI) rules. Surprisingly, I cannot. Once I allowed the new value of any cell to be determined, in part, by one or more of it's neighbors, to keep TRI, I needed to include the state of my entire universe in the determination of each cell.
Moreover, the reasoning behind it seemed to very fundamental - support TRI and even a little non-locality and the cat's out of the bag. This is not to say that you can't have a weighted locality - with near objects much more likely to affect the new state than far objects. You can.
Although the logic behind this is pretty clear when you apply it to an array of cells with time occurring in discrete steps, working the same logic through using real-world QM and relativity is less obvious. But here's my attempt to describe that:
Let's say our QM/relativity-based universe has two planets: A and B. Let's also say that a photon is transmitted from A and a year later arrives at B. For this to happen, quite a large region of space had to be felt out by the photon - not limited to the direct path from A to B. For example, the photon needed to know that the spot it landed on did not fall within a dark interference band caused by interplanetary debris.
Now we will time-reverse our universe. What will happen is that the photon will depart B enroute to A - but only because of the environment it sees from B. But the A-to-B trajectory has to be made based on the same information as the B-to-A trajectory. Otherwise the proper time-reversed path may not be followed. Of course, when the photon departed A, it's landing spot may not have even existed on B. The condition of that landing spot would be determined by everything within a 1-lightyear light cone for planet B. So the photon's path must also be determined by everything in that light cone - and so also everything withing the corresponding planet A light cone. Ans as you flip back and forth from the A-to-B and B-to-A trajectory, the region of interest continues without bound.
It's easier to see this in a pixelated universe. In order for pixel A to affect pixel B, pixel A has to be within range of B - say within 1-pixel of B. And everything else within 1-pixel of B also has the potential to affect B. But when time-reversal is applied, the neighborhood of interest becomes A's neighborhood. So it's everything within 1 pixel of A - potentially 2 pixels from B. Then reverse it again and it's potentially 2 pixels from A as well. No limit is ever enough because no limit ever includes the same information for both A and B - so the entire universe is included before the "same information" criteria is met. There is always a possibility for some condition on one side of the universe to affect a transition on the other side.
Back to our unpixelated QM/relativity-based universe, certainly entanglement is an example of this effect. But I doubt that it is enough.
Do QM equations (or anything else) suggest this open-ended non-locality?
By the way. What got me set on this line of thought was a 1-hour presentation by David Wallace where he zeroed in on the main issues affecting the apparent asymmetry of time. From what I can tell, it's pretty main-stream. In case anyone's interested, here's that link:
http://en.wikipedia.org/wiki/Conway's_Game_of_Life
My thought was that instead of the two colors (black and white) in Conway's game, mine would have three. And by reversing any two of the three colors, the same rules would cause my version of the game to run backwards.
In Conway's game, non-locality was limited to the eight cells to the North, South, East, West, NE, NW, SE, and SW of a cell.
My original hope was that I could use a similar constraint on my Time-Reversal-Invariant (TRI) rules. Surprisingly, I cannot. Once I allowed the new value of any cell to be determined, in part, by one or more of it's neighbors, to keep TRI, I needed to include the state of my entire universe in the determination of each cell.
Moreover, the reasoning behind it seemed to very fundamental - support TRI and even a little non-locality and the cat's out of the bag. This is not to say that you can't have a weighted locality - with near objects much more likely to affect the new state than far objects. You can.
Although the logic behind this is pretty clear when you apply it to an array of cells with time occurring in discrete steps, working the same logic through using real-world QM and relativity is less obvious. But here's my attempt to describe that:
Let's say our QM/relativity-based universe has two planets: A and B. Let's also say that a photon is transmitted from A and a year later arrives at B. For this to happen, quite a large region of space had to be felt out by the photon - not limited to the direct path from A to B. For example, the photon needed to know that the spot it landed on did not fall within a dark interference band caused by interplanetary debris.
Now we will time-reverse our universe. What will happen is that the photon will depart B enroute to A - but only because of the environment it sees from B. But the A-to-B trajectory has to be made based on the same information as the B-to-A trajectory. Otherwise the proper time-reversed path may not be followed. Of course, when the photon departed A, it's landing spot may not have even existed on B. The condition of that landing spot would be determined by everything within a 1-lightyear light cone for planet B. So the photon's path must also be determined by everything in that light cone - and so also everything withing the corresponding planet A light cone. Ans as you flip back and forth from the A-to-B and B-to-A trajectory, the region of interest continues without bound.
It's easier to see this in a pixelated universe. In order for pixel A to affect pixel B, pixel A has to be within range of B - say within 1-pixel of B. And everything else within 1-pixel of B also has the potential to affect B. But when time-reversal is applied, the neighborhood of interest becomes A's neighborhood. So it's everything within 1 pixel of A - potentially 2 pixels from B. Then reverse it again and it's potentially 2 pixels from A as well. No limit is ever enough because no limit ever includes the same information for both A and B - so the entire universe is included before the "same information" criteria is met. There is always a possibility for some condition on one side of the universe to affect a transition on the other side.
Back to our unpixelated QM/relativity-based universe, certainly entanglement is an example of this effect. But I doubt that it is enough.
Do QM equations (or anything else) suggest this open-ended non-locality?
By the way. What got me set on this line of thought was a 1-hour presentation by David Wallace where he zeroed in on the main issues affecting the apparent asymmetry of time. From what I can tell, it's pretty main-stream. In case anyone's interested, here's that link: