Given T-symmetry, what limits non-locality?

[.Scott]

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:

 

[mfb]

The condition of that landing spot would be determined by everything within a 1-lightyear light cone for planet B.

In the original time order, yes.
In the reverse time-order, this is no longer true. The 1-lightyear cone is now the set of objects you can influence if you start at B at the photon emission time. You don't need it to describe what happens at B.

There are local time-symmetric interpretations of quantum mechanics. And they do work.

 

[maline]

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.

This argument would apply just as well in a classical universe, which we know is local and time-symmetric. There must be a mistake here, but I admit confusion. Perhaps try articulating this argument in full detail. What do you mean by "neighborhood of interest"? Sure, anything can be described as "an effect of a cause of an effect of a cause" of something on the other end of the universe, but what are the implications of this?

 

[maline]

Okay, here's an example of a time reversible & local "life" game: a row of squares with 4 colors. At each move, the color in each square is determined by those to the left & right of it (ignoring its own color), according to these rules:
r r/ r b/ g r/ g b =>red
g g/ g y/ r g/ r y =>green
b b/ b r/ y b/ y r =>blue
y y/ y g/ b y/ b g =>yellow
To time-reverse, flip the board from left to right.
The way it works is that the information of color- one of 4 possibilities- is split into two bits, one going right & one left. Each new square's color is determined by two bits without losing information by confusing the two, as would happen with three colors or if the rules were left/right symmetrical. In classical mechanics, I believe the equivalent idea is Liouville's theorem.

 

[.Scott]

Okay, here's an example of a time reversible & local "life" game: a row of squares with 4 colors. At each move, the color in each square is determined by those to the left & right of it (ignoring its own color), according to these rules:
r r/ r b/ g r/ g b =>red
g g/ g y/ r g/ r y =>green
b b/ b r/ y b/ y r =>blue
y y/ y g/ b y/ b g =>yellow
To time-reverse, flip the board from left to right.
The way it works is that the information of color- one of 4 possibilities- is split into two bits, one going right & one left. Each new square's color is determined by two bits without losing information by confusing the two, as would happen with three colors or if the rules were left/right symmetrical. In classical mechanics, I believe the equivalent idea is Liouville's theorem.

Okay. It works. I even set it up in Excel and got this:

So I fumbled this in two ways:

First, I misstated the problem. I presumed the cells old value would be included in its new value. What I posted was:

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 its neighbors, to keep TRI, I needed to include the state of my entire universe in the determination of each cell.

What I should have said was:

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 more than one cell, to keep TRI, I needed to include the state of my entire universe in the determination of each cell.

That eliminates universes that simply shift left or right by some fixed number of pixels.

But of course, that is also not sufficient. I also need to say that if the rules create a situation where there are two or more independent bodies of information that have no potential to influence one another, that the information belonging to at least one of those independent universes must follow the rule that says its information in one cell is determined from information from at least two cells in the previous time slot.

After all, if our universe was like you universe, we would be essentially frozen in time.

I think we need to define some terms.
Universe is a system where the physical laws are the same at all locations and those laws do not result in multiple completely independent non-interacting sets of information.

In the Excel spreadsheet world:
Immediate means that each cell is determined by the value of exactly one cell of the previous time slice.
Local means that each cell is determined by the value of more that one cell - but not most cells.
Non-local means that each cell is determined by the value of most of the previous cells.

I'll leave the definitions open for a QM/Relativistic world. After all, it's possible there is no direct analogy. But if we can't find a better "life" world or a good reason for breaking the analogy to the real world, we may be in trouble.

 

[maline]

I also need to say that if the rules create a situation where there are two or more independent bodies of information that have no potential to influence one another, that the information belonging to at least one of those independent universes must follow the rule that says its information in one cell is determined from information from at least two cells in the previous time slot.

After all, if our universe was like you universe, we would be essentially frozen in time.

I think what you mean is as follows: In my game, we could replace the colors with two separate variables,
yellow= black with a dot in the center
blue= black with no dot
green= white with a dot
red= white with no dot
Then we would see the dots simply shifting to the left, and the black/white pattern shifting to the right.
By "frozen in time", you mean that this model has a very short recurrence time, equal to the length of the row.

I don't see why any of this should be a problem. A classical-mechanics universe would in fact have a finite recurrence time, if not for the expansion. Separate sets of information do not have to be obviously visible, or even simple to work with.
Perhaps you will like this version better. The two bits are somewhat harder to separate out.
r r/ r b/ g r/ g b =>red
g g/ g y/ r g/ r y =>green
b b/ b g/ y b/ y g =>blue
y y/ y r/ b y/ b r =>yellow
To time-reverse, flip left-right and switch red & green, or blue & yellow.
BTW, thanks a lot for the pretty pictures! I did spend a bit of time thinking of this solution, so it feels good to see it "in the flesh".

 

[.Scott]

I think what you mean is as follows: In my game, we could replace the colors with two separate variables,
yellow= black with a dot in the center
blue= black with no dot
green= white with a dot
red= white with no dot
Then we would see the dots simply shifting to the left, and the black/white pattern shifting to the right.
By "frozen in time", you mean that this model has a very short recurrence time, equal to the length of the row.

I don't see why any of this should be a problem. A classical-mechanics universe would in fact have a finite recurrence time, if not for the expansion. Separate sets of information do not have to be obviously visible, or even simple to work with.
Perhaps you will like this version better. The two bits are somewhat harder to separate out.
r r/ r b/ g r/ g b =>red
g g/ g y/ r g/ r y =>green
b b/ b g/ y b/ y g =>blue
y y/ y r/ b y/ b r =>yellow
To time-reverse, flip left-right and switch red & green, or blue & yellow.
BTW, thanks a lot for the pretty pictures! I did spend a bit of time thinking of this solution, so it feels good to see it "in the flesh".

The problem only occurs when information is combined across a region of space. In the model you presented, this didn't really happen. The left-shifting information was superimposed on the right-shifting information. If that was happening in our QM/Relativistic universe, we would never know it. We could not affect it, it could not affect us, and we would not consider that other set of information to be part of our universe.

It is a given that you will get time reversal whenever each cell is determined from exactly one previous cell - either its value or some other simple function of it. The result will be a universe where the information either remains stationary or shifts at a constant rate to the left or right. But such a universe never combines state information from from multiple sources - so it is fundamentally unlike our QM/Relativistic universe.

Also, it is given that you can superimpose the information from multiple shifting universes, but you still haven't created anything that would look like the particle interactions we get in this universe - because such a mechanism applied to our universe would simply result in overlapping universes each with no interactions.

So the central problem is to create a "life" game that:
* exhibits time reversal;
* combines states from multiple cells to generate a cell from the next generation;
* does not isolate information into superimposed but independent universes;
* determines new cell values from only local cells - where the locality is substantially smaller than the entire universe.

What I am discovering is that you can't do this with a "life" game - and the reasons would seem to apply to any similar universe including our own QM/Relativistic one. It's not clear to me at all what sort of device or rule could be used by the QM/Relativistic universe to avoid having to use most of the information in the universe to determine, for example, where individual photons will land in an interference pattern.

 

[maline]

Also, it is given that you can superimpose the information from multiple shifting universes, but you still haven't created anything that would look like the particle interactions we get in this universe - because such a mechanism applied to our universe would simply result in overlapping universes each with no interactions.

I don't see why. What we see would be the equivalent of the colors, not each bit of information on its own. If there were 2^9 different colors, encoding bits from the square in question & its neighbors, you wouldn't see any color repeated often enough to even find the pattern. Would you still call that "no interaction"?

How about my new version? There the sets of information are not completely isolated from one another.
The bottom line is that as long as any particular pattern of colors can only be produced around one previous color, there is no information loss, and you can describe a (possibly very complicated) reversal rule.

 

[mfb]

@.Scott: What you see are just the laws of the universe. Sure, they are simple in this case and you have tons of conserved quantities, but there is interaction happening. You are just able to find a basis where those interactions are factored out. You can do the same in our real world, such a basis is just much more complicated (and impossible to find once you get macroscopic systems).

 

[Khashishi]

Maybe a 1+1 D universe isn't big enough to have complex patterns. Have you tried a 2+1 D game?

 

[.Scott]

@.Scott: What you see are just the laws of the universe. Sure, they are simple in this case and you have tons of conserved quantities, but there is interaction happening. You are just able to find a basis where those interactions are factored out. You can do the same in our real world, such a basis is just much more complicated (and impossible to find once you get macroscopic systems).

I certainly don't doubt that there is interactions in our universe. The problem I am seeing is that it seems that in order to make the results time reversible, the results of those interactions would have to be determined not just non-locally, but non-locally in the extreme. The reason is that if you place a boundary on the region affecting the result of the interaction, that exact boundary must also hold for the time-reverse interaction. In the case of a pixelated "life"-type universe, that is not possible. The reason is that at the end of a time step, some of the needed information has escaped from the original boundary and has been replaced with different information - so an attempt to reverse the interaction with the same rules will be based on different information - and so the reversal may not be accurate.

It's not clear to me why QM would not suffer from this same problem. Once a QM interaction has completed, the information that determined the QM result would have escaped any fixed region presumed to contain "all the information needed" to determine that result. So if QM is entirely time-reversible, it would seem there can be no limit of the size of the region containing the information needed to reverse the interaction.

I can try to think of reasons that might exempt QM. For example, perhaps all QM interactions occur instantly - or the part of them involving non-locality happens in zero time. This would allow the non-local interaction to be reversible since there would be no time for the boundary of the non-local information to change during the interaction. As long as these interactions could be unwound in the reverse order in which they occurred, they would be time-reversible.

 

[.Scott]

Perhaps you will like this version better. The two bits are somewhat harder to separate out.
r r/ r b/ g r/ g b =>red
g g/ g y/ r g/ r y =>green
b b/ b g/ y b/ y g =>blue
y y/ y r/ b y/ b r =>yellow
To time-reverse, flip left-right and switch red & green, or blue & yellow.

Given red=0, green=1, blue=2, yellow=3:
In your first universe, the Excel value at cell C3 was =CHOOSE((B2*4+D2+1),0,1,0,1,0,1,0,1,2,3,2,3,2,3,2,3).
This time, it is =CHOOSE((B2*4+D2+1),0,1,0,1,0,1,0,1,3,2,2,3,3,2,2,3)
On the time reversal, I switched the 2/3 colors from blue/yellow to yellow/blue.
This is what it looked like:

The fact that we have diagonal bands of all 0s and 1s or 2s and 3s is a pretty convincing indication that there are two independent bit fields.

In my last post, I speculated that if the QM interactions were done is zero time, the problem would be resolved.
If we go back to your first universe and add an extra step between every two consecutive steps, we should be able to create interactions while preserving time reversibility. The extra step I will add is to change all 313's to 323's and vice versa. It should cause our right-shifting and left-shifting universes to interact while remaining time-reversible.
Here is the result:

The reason that this extra step cannot be combined with the original step is that you need to stop time in mid step in order to reverse it.

 

[mfb]

it would seem there can be no limit of the size of the region containing the information needed to reverse the interaction.

That is not what "local" means. To study future or past at your location for t=3 seconds, all you need is the volume ct = 1 million kilometers around you. If you want to study the next or past nanosecond, it is sufficient to consider a radius of 30cm, and so on. that is "local". And it works in both directions - that is T reversal.

 

[.Scott]

That is not what "local" means. To study future or past at your location for t=3 seconds, all you need is the volume ct = 1 million kilometers around you. If you want to study the next or past nanosecond, it is sufficient to consider a radius of 30cm, and so on. that is "local". And it works in both directions - that is T reversal.

I probably did mix "local" with some other uncoined term that is closely related to locality. Here's my attempt to better work those terms:

First, I am presuming that QM is truly time-reversible. That requires absolute determinism - you never gain information, you never loose information, information simply becomes recoded by deterministic rules. Next, although I do not dispute HUP, as time advances things that were previously uncertain become certain. For example, in the Bell experiment, the orientation of particles are measured - so what had been inherently unknowable becomes known. Since it happens, there is a mechanism and I am looking at the properties of that mechanism.

If the moment that the Bell experiment performs a particle measurement is time-reversed, what happens is that certainty becoming unavailable. What had been the reaction to the particle detection becomes a mechanism for emitting information in the form of a particle and perhaps other forms. What's left behind is a mechanism probably devoid of any clue of what it had just transmitted. The key is that at every step in the process, there needs to be enough information around to drive time in either direction.

The next key is that the information that is required to create an interaction is exactly the same information that is required to reverse it. Whatever the "mechanism" is that is generating the interaction operates on a set of information that is either local or non-local. Whether it is entirely local or not doesn't matter. What is important is that when the transition happens, all the information about that transition remains unchanged and uncontaminated - so that the "mechanism" would use the same information for both time directions.

In my life game, I did that by freezing the universe and making only very local changes that could not interfere with any other very local changes. In the game of QM, that isn't what happens and perhaps nothing like that is what happens. From what I understand, QM seems to continue to allow a period of indecision where both possible detection states remain possible. So the information-collection period might be extended.

It's not clear to me what the underlying strategy is for QM to be both time-reversible and allow interactions that have potentially wide-ranging effects. My sense is that very QM "decision" is based on all the information in the universe - so whether it is derived locally or not is irrelevant.

 

[mfb]

I am presuming that QM is truly time-reversible.

The equations are time-reversible, but some interpretations add irreversible (and also nondeterministic) elements like collapses.

You cannot have both at the same time. If you want to reverse the evolution, you'll need a deterministic interpretation like Many Worlds. That allows to reverse every experiment, although the reversed experiment looks very odd - like a wavefunction starting at many places at once, converging at a small localized object (emitting photons in the original order, absorbing them with time reversal). But there is nothing certain that gets uncertain or vice versa.

 

[.Scott]

The equations are time-reversible, but some interpretations add irreversible (and also nondeterministic) elements like collapses.

So that David Wallace presentation is perhaps hog wash? Actually, I just Googled around at other articles. Apparently, only the wave equation is definitively T-symmetric. Collapses or measurements are usually suspected as being non-reversible.

You cannot have both at the same time. If you want to reverse the evolution, you'll need a deterministic interpretation like Many Worlds. That allows to reverse every experiment, although the reversed experiment looks very odd - like a wavefunction starting at many places at once, converging at a small localized object (emitting photons in the original order, absorbing them with time reversal).

The many-worlds notion of a universe constantly splitting into non-interacting parts does not conserve information. Instead, each split introduces "which world" information into each universe. Of course, if many-worlds was time reversible, we would expect to see situations where worlds merged even in normal forward time - an effect that would be as difficult to recognize as the splitting and one that would reduce the total information.

More to the point, explaining that time-reversal is possible only with help from other worlds is less than completely satisfying.

But there is nothing certain that gets uncertain or vice versa.

Since the result of a measurement is usually not known in advance, that result is unpredictable until the measurement is made. The measurement result would be unavailable.

 

[mfb]

The many-worlds notion of a universe constantly splitting into non-interacting parts does not conserve information.

It does.

Instead, each split introduces "which world" information into each universe.

If you know the current state, you can exactly predict the state of the universe at some point in the future - there is no information added (where would it come from?).

Of course, if many-worlds was time reversible, we would expect to see situations where worlds merged even in normal forward time

We would not, as there is no reason to expect two branches to exist in exactly the right way to merge in the future. And even if there would, it would not lead to anything you could observe.

More to the point, explaining that time-reversal is possible only with help from other worlds is less than completely satisfying.

Blame the universe for being non-classical.

Since the result of a measurement is usually not known in advance

In MWI it is (assuming you know the initial state).

 

[.Scott]

The many-worlds notion of a universe constantly splitting into non-interacting parts does not conserve information.

It does.

Instead, each split introduces "which world" information into each universe.

If you know the current state, you can exactly predict the state of the universe at some point in the future - there is no information added (where would it come from?).

I meant in the individual worlds, not in the systems as a whole.
For example, if we started with a universe that contained nothing, but at each step in time added one bit of information - splitting into two worlds one with the bit set to 0 the other with the bit set to 0, then the system as a whole would not gain any information. Given any time, you would be able to described the entire system of worlds very concisely. For example, at time t=10, you would have 1024 worlds each with 10 bits. So the state of the entire system would simply be an encoding of the value of t. However, each of those 1024 worlds would have 10 bits of information. And a denizen of this system would experience a universe where information was not conserved - because they would experience a steady accumulation of which-world information.

Of course, if many-worlds was time reversible, we would expect to see situations where worlds merged even in normal forward time.We would not, as there is no reason to expect two branches to exist in exactly the right way to merge in the future. And even if there would, it would not lead to anything you could observe.

What would stop those other universes from existing? If it happened, it would lead to a reduction in which-world information. I am not convinced that the many-worlds model is useful in explaining anything.

Since the result of a measurement is usually not known in advance.

In MWI it is (assuming you know the initial state).[/QUOTE]But if MWI is not further developed, it creates an explanation that is not of any further use. It could only be demonstrated by disproving all other models.

 

[mfb]

I meant in the individual worlds, not in the systems as a whole.

That is as meaningful as saying "the set of natural numbers has tons of information because I consider only a specific number here and storing that number needs information". You need information to say which world you mean, but that is not a property of the universe, it is a property of what you look at.

And a denizen of this system would experience a universe where information was not conserved

Unless they discover MWI, de-Broglie-Bohm or other deterministic interpretations.

What would stop those other universes from existing?

Looks very unlikely, but it does not matter anyway.

MWI is an interpretation like many others - you can like them, you can dislike them, they all give the same predictions for practical experiments.

 

[.Scott]

I meant in the individual worlds, not in the systems as a whole.

That is as meaningful as saying "the set of natural numbers has tons of information because I consider only a specific number here and storing that number needs information". You need information to say which world you mean, but that is not a property of the universe, it is a property of what you look at.

That's close to the opposite of what I said. The set of natural numbers has very little information. But the average amount of information is each element in the set of all sets that contain only natural numbers would be infinite. Since the discriminating information is in what it takes to described the content, it is the content of these subsets themselves that specify the subset.
Likewise, it is the content of a world itself that specifies which world it is. Examining the content of our current world is the same as examining what makes it distinctive from other worlds. And since, with the MWI interpretation, the number of worlds is ever increasing, the amount of discriminating information (the content of each world) will be ever increasing.

What would stop those other universes from existing?

Looks very unlikely, but it does not matter anyway.

MWI is an interpretation like many others - you can like them, you can dislike them, they all give the same predictions for practical experiments.

MWI only gives the same predictions if you don't try to apply MWI rules more generally - for example, presuming that there are lots of worlds out there all interacting using the same rules - presumably T-symmetrical worlds.
However, the whole purpose of a new interpretation is to expand it to other cases so that it can be tested more generally. If this cannot be done with MWI, then MWI is a dead end of very limited purpose.

 

[mfb]

But the average amount of information is each element in the set of all sets that contain only natural numbers would be infinite.

I don't see how this would be relevant, in the same way as I don't see how a specific individual branch would be relevant if you want to reverse the time-evolution where you want to reverse all. QM with MWI is time-symmetric only if you take the whole wavefunction.