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Space-time quantization and its philosophical aspect


Spathi

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Modern physics describes matter by floating numbers. This means that an absolutely accurate description of any particle requires an infinite amount of information.

Intuitively, it seems that this should not be so, and the model of the Conway's Game of Life looks more close to reality. In this game, the state of the system is described by discrete values, i.e. a finite amount of information is sufficient to describe the system. The question arises, are there any analogs of the Game of Life (cellular automata), in which the laws of conservation and the laws of thermodynamics work?

The Game of Life clearly reproduces reality very poorly, since it does not contain any of this. In addition, this game has a different arrow of time. In our reality, we experrience a psychological arrow of time: we remember the events of the past and predict the events of the future, and this knowledge about the past and the future is very asymmetric - information about the past is much more voluminous, more specific, detailed, more reliable than the information about the future. In the game Life, if there were intelligent beings, it would be the opposite: according to the state of the system at the moment of the present, it is possible to accurately predict the state of the system in the future, but it is impossible to recreate the state of the system in the past.

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12 hours ago, Spathi said:

Modern physics describes matter by floating numbers. This means that an absolutely accurate description of any particle requires an infinite amount of information.

That's not physics at all, or even mathematics. Computers (IEEE in particular) define and use floating point numbers, and yes, they're very much discreet, unlike actual numbers referred to by physics and mathematics.

The vast majority of real numbers are not expressible in any discreet form. The ones that are are countable, but the real numbers are not countable. So I can express an irrational number like √2 with a couple keystrokes, but most numbers like the mass of my pencil are expressible only as approximations.

12 hours ago, Spathi said:

the model of the Conway's Game of Life looks more close to reality.

Hardly. Yes, it uses discreet mathematics. It is 2D, or 3D with time added. It has a preferred frame and even a preferred orientation for the spatial axes. Like all cellular automata, it has a fixed 'speed of light', but only relative to that one absolute frame. Unlike our physics, it is entirely deterministic in one direction, which gives it an arrow of time, but for a different reason than the direction of our arrow of time.

12 hours ago, Spathi said:

The question arises, are there any analogs of the Game of Life (cellular automata), in which the laws of conservation and the laws of thermodynamics work?

I've never seen an attempted definition for an analog version of a cellular automata. Sure, it can easily be done. Far more difficult would be trying to find a rule that yields concepts of momentum, force, etc that are meaningful in our universe. I can't see why it isn't possible, or why it would need analog values to do so, but good like finding one. In particular, those concepts are insanely difficult to implement in physics with preferred spatial axes, and I cannot think of a way to implement a cellular arrangement and rules that don't do that.

12 hours ago, Spathi said:

The Game of Life clearly reproduces reality very poorly, since it does not contain any of this.

Of course. It was never intended as a model of our reality. It being two dimensional is a big clue about that.

12 hours ago, Spathi said:

In the game Life, if there were intelligent beings...

CGoL can implement a Turing machine. A Turing machine is capable of simulating our classical physics to a finite but arbitrarily large degree of precision. Hence intelligent life can exist in CGoL, but it would be a simulation of different physics running on a CGoL engine, not the CGoL physics itself in any way resembling our physics.

 

Edited by Halc
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