Copenhagen Automata

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Copenhagen Automata

Postby hyksos on May 26th, 2017, 2:02 pm 

The Copenhagen Interpretation of quantum mechanics is a metaphysics which makes claims about scientific measurement and how states of the physical world relate to each other over time. We can build up a recipe for a Copenhagen universe, by starting from traditional cellular automata, and then making consecutive modifications until we reach something closer to what quantum mechanics suggests.

For the sake of digestibility, we will pretend our "universe" is a 1D strip of cells which take on states. Time runs downwards in the usual fashion, and each row corresponds to a singe time slice ; a snapshot of the universe at time t.

Multiple Futures

Traditional CA metaphysics says that the state of the world is a precise configuration given by the cell values, and the present state uniquely determines the future state.

traditionalCA..png


The first modification is to give up on a unique future, instead have our CA rule merely suggest a future state as a probability over a large set of states. The tallness of the green arrow is a probability that the future cell will take on a black or white value. It can literally be either one, and over many time cycles the relative sizes of the arrows will bear out.

suggeststate.png


Superposition
So far it is obvious that measurement will always produce an exactly white or exactly black cell value, as this is the only admissible values for a cell at any time. To step closer to Copenhagen, we will now allow the cells to take on partial grey values between black and white, and call those superpositions. The rule now maps exact neighbor states to some distribution over greyish values transitioning from black to white.

superposition.png


Now that grey values are permitted, a conceptual problem emerges. How do we apply a rule to say, a collection of 3 mostly grey cells? The answer is strange. We change the rules so that they only apply when some person is taking a measurement of the world. In the cycles of time in which the cells are not measured, we allow cells to cycle between black and white and back again. This splits the "rules" into two contradictory phases. One in which the cells are not being measured and they smoothly oscillate, and one in which they were measured at time cycle (=t), in which case they undergo the traditional rule. The oscillations can best be viewed as going from black to white, and passing through a reddish region in between.

quantumoscillator.png
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Re: Copenhagen Automata

Postby hyksos on May 26th, 2017, 2:13 pm 

Quantum Measurement
In the Copenhagen Interpretation, the act of measuring the cell values "does something" to them, which in turn effects their future values. While the system is not being looked at by anyone, it is left 'undisturbed' and cells are a mish-mash of blacks, whites, and various shades of red.

copenhagenstates.png


Whenever a lab tech measures the (or "looks at") the cells, he never sees an iota of red. Worse, all cells he ever sees are either completely black or completely white. These are the so-called Stationary States of the system.

stationarystates.png


A more exacting algorithm for this process goes as follows : The world begins in a strict stationary state (pure blacks, pure whites), provided nobody measures, the cells drift and oscillate. A measurement occurs at time Tm, wherein a translation must be made between the superposed cells and their pure values. This is done randomly where the continuous shade "suggests" the probability of finding the cell in a pure color. At the next time step (Tm+1), the rule is applied (probability sampling from under the Guassians). The cells take on continuous values again, and start to oscillate once more. That continues at each time cycle until another 'measurement' happens.

This could be programmed, possibly in some language like python. I have not done this myself, but I welcome others if they are curious. A random number generator would be used at several steps, particularly when the act of measuring "snaps" the cells back to pure values.
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Re: Copenhagen Automata

Postby bangstrom on May 26th, 2017, 6:11 pm 

This model answers Schroedinger’s objection that a particle can’t be in two states at once just as a cat can’t be both dead and alive at the same time. If you have two or more particles smoothly oscillating among themselves in linked pairs or linked collections of pairs, then anything that stops this oscillation will freeze the oscillation leaving one particle ‘black’ and the other ‘white’ so there is never a single cell that is both black and white at the same time in isolation.

To an observer looking at only one cell (particle) the observation would be that the cell is both white and black at the same time but there is always more than one cell involved so, when one cell is fixed as white, another cell is fixed at black and blackness and whiteness are conserved in the system.

I understand this is just a simple model used to represent real-world effects but I find the explanations of both to be somewhat in reverse and misleading because they imply that there is some magic to measurement or observation when neither of these can cause a change in the way things work.

For example, you said,”Now that grey values are permitted, a conceptual problem emerges. How do we apply a rule to say, a collection of 3 mostly grey cells? The answer is strange. We change the rules so that they only apply when some person is taking a measurement of the world. “

Speaking of both the real-world and possibly the game. Gray values are permitted in both and the only conceptual problem is that we do not expect gray values to exist because we only observe black and white. We don’t change the rules when we make a measurement because the rule that says gray values exist is already there. This makes measurement an effect- rather than the cause of anything.

I think of “measurement” as the act of a cell at the measurement end merging with a remote cell at the observed end to form two gray calls oscillating between black-red-white and, when the connection is lost, the oscillation stops and the black and white colors return at random. That is, they may not return to the same locations as before. If chance happens that the colors are reversed from what they were before, we have what is called a “measurement” but the measurement is the effect and not the cause of so we can’t say measurement “causes” a change in the particle observed. The changes that take place simultaneously at both ends are what we call measurement.

This is another possibility that I think exists in the real world but possibly not in the model and that is a condition where a black cell can spontaneously merge with a remote white cell to become two gray cells and, when the connection is lost, the two gray cells return to black and white but not necessarily in the same location. That is, the cells can swap colors to the perception that they have swapped locations and this is the quantum mechanics behind what we call a “measurement.”
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Re: Copenhagen Automata

Postby someguy1 on May 26th, 2017, 9:53 pm 

hyksos » May 26th, 2017, 12:02 pm wrote:The Copenhagen Interpretation of quantum mechanics is a metaphysics which makes claims about scientific measurement and how states of the physical world relate to each other over time. We can build up a recipe for a Copenhagen universe, by starting from traditional cellular automata ...


I read over the Wiki page at https://en.wikipedia.org/wiki/Copenhagen_interpretation. It said nothing to the effect that the Copenhagen interpretation relates to or entails that the universe is a CA. Can you clarify this point for me please?
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Re: Copenhagen Automata

Postby hyksos on June 2nd, 2017, 10:33 am 

someguy1 » May 27th, 2017, 5:53 am wrote:
hyksos » May 26th, 2017, 12:02 pm wrote:The Copenhagen Interpretation of quantum mechanics is a metaphysics which makes claims about scientific measurement and how states of the physical world relate to each other over time. We can build up a recipe for a Copenhagen universe, by starting from traditional cellular automata ...


I read over the Wiki page at https://en.wikipedia.org/wiki/Copenhagen_interpretation. It said nothing to the effect that the Copenhagen interpretation relates to or entails that the universe is a CA. Can you clarify this point for me please?

You are currently reading a forum thread about a cellular automata that "acts like" the Copenhagen interpretation of quantum mechanics. This is a toy system meant to diagram and idea for pedagogical purposes. In particular, the main take away point here is what quantum mechanics says about how the future relates to the past. To boil it down -- there are multiple futures which can emerge from a particular present moment.

Perhaps some particular regular on this forum will pass through here and read this thread. Maybe pick up something. Hopefully that person is affected by what they pick up. (Yes I am thinking of a particular person).

It said nothing to the effect that the Copenhagen interpretation relates to or entails that the universe is a CA.

Yes. That's expected. A corollary that is trying to be communicated here (not the 'main point' by any means) is that our universe is very likely not a CA.
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Re: Copenhagen Automata

Postby hyksos on June 2nd, 2017, 10:39 am 

bangstrom » May 27th, 2017, 2:11 am wrote:I understand this is just a simple model used to represent real-world effects but I find the explanations of both to be somewhat in reverse and misleading because they imply that there is some magic to measurement or observation when neither of these can cause a change in the way things work.

Let it be known that this is not supposed to be a quantum ab initio simulation of a quantum field. There is something I am trying to communicate that a certain someone here who has a certain background should be able to pick up.

But if you want to get more technical about this, see the part where I sample under green Gaussian curves. If you wanted to get this closer to "physically correct" what actually would happen is that you would sample that constantly, and the gaussians would be set up in such a way that a wave-like oscillation would "naturally" emerge. That's too complicated to explain and would have caused a wall of text .. further it would have obscured the principle take-away points.
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Re: Copenhagen Automata

Postby hyksos on June 2nd, 2017, 10:41 am 

take-away point : There is no The One Single Future that is cleanly derivable from The One Single Past.

( If that is your working definition of the word "determinism" , then the universe we inhabit is mostly likely not deterministic. )
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Re: Copenhagen Automata

Postby someguy1 on June 2nd, 2017, 1:00 pm 

hyksos » June 2nd, 2017, 8:33 am wrote:Perhaps some particular regular on this forum will pass through here and read this thread. Maybe pick up something. Hopefully that person is affected by what they pick up. (Yes I am thinking of a particular person).



Ah ... I took the bait intended for someone else.
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Re: Copenhagen Automata

Postby Dave_Oblad on June 2nd, 2017, 2:25 pm 

Hi Hyksos,

Bait taken.. lol.

Hyksos wrote:The first modification is to give up on a unique future, instead have our CA rule merely suggest a future state as a probability over a large set of states.

This is a form of Fuzzy Logic, which is still utterly Deterministic.

Pretty neat trick (impossible) to take a deterministic Boolean rigid logic and imbue it with any quality approaching a probability function.

The fallacy I see is that in the realm of absolute Logic, where there can exist no such thing as a Grey Scale Probability aspect.. for the same reason we can not mathematically generate a Truly Random number.

Any mathematical argument auto forces absolute determinism into the picture (even with fuzzy logic).

Best wishes,
Dave :^)
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Re: Copenhagen Automata

Postby hyksos on June 2nd, 2017, 3:49 pm 

Now that you mention it, this does look eerily similar to fuzzy logic.
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