[Entropy and Newton's Third Law of Motion] - A New Kind of Science: The NKS Forum

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Entropy and Newton's Third Law of Motion

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Posted by: Gunnar Tomasson

I just checked out Philip Mintz' website and came across the following statement:

I would like to see some notions eradicated, like the idea that entropy makes things happen. Entropy is only a concept. It can't cause anything. Even if it can be shown mathematically that entropy increases in every interaction, there are no consequences. If you find it hard to comprehend what entropy means, it is no fault of yours. Nobody can describe entropy. It was originally conceived of when it appeared in an equation. It is a mathematical term with no physical manifestation.

Another notion that should be dispelled is the idea that something happens because it is statistically probable. If something is found to be statistically probable, it is after the fact. The event does not happen because it is probable. It happens because it is caused to happen. Discover the cause. As the event happens, it is observed, and the data are organized. Analysis of the data can be given statistical treatment. It is all in the mind.

A follow-up Internet search brought to light the following statement:

Entropy is a measure of possibilities. A messy room has high entropy because there are many possibly ways to be messy. Toys and clothes can be laying around anywhere within the room. A neat room has low entropy because there are few ways to be neat. All toys and clothes must be in their proper places.

A process can be driven, or forced to happen, only by increasing the entropy of the universe. A driven process is said to be "spontaneous". A few spontaneous processes are a falling brick, a bouncing ball, a crashing car, a melting ice cube on a warm day, a freezing lake on a cold day, or the chemical transformations of a burning match. The entropy of the universe increases during each of these spontaneous processes.

Hmmm?

Here is an Internet posting on Newton’s Third Law of Motion:

Sir Isaac Newton first presented his three laws of motion in the "Principia Mathematica Philosophiae Naturalis" in 1686. His third law states that for every action (force) in nature there is an equal and opposite reaction. In other words, if object A exerts a force on object B, then object B also exerts an equal and opposite force on object A.

Comment:

I don’t understand how “entropy” can be squared with Newton’s Third Law of Motion and would appreciate clarification thereof by NKSers who do understand it.

Gunnar


Posted by: Philip Mintz

The subject is matter in motion. When two bodies of matter collide, the repulsive force on them is equal. The bodies rebound, moving with as much total kinetic energy as the system had before the collision, except for a loss due to the fact that the bodies have internal structure. The bodies are aggregates of molecules and the molecules contain a nucleus and electrons. When the body collides, the nuclei and electrons are caused to oscillate. Now the kinetic energy is distributed between the moving bodies and the atoms they contain. So far there is no gain of entropy. because nothing has left the system. However, some of the motion is transfered to the surrounding atmosphere . The motion of the molecules of air is called kinetic energy, and its average kinetic energy per molecule is called temperature. Since the heated air is not going to return to the system, the entropy of the universe has risen.

The New York Times of Tuesday, Nov. 25 has an article titled "Big Step In Conductivity: More Sociable Particles" It is related to the prediction of the Bose-Einstein condensate. One of the researchers said, "Nobody has a good theory to describe these things. " To me it does not appear so difficult when I apply my theory of the fundamental particle of matter. When rubidium atoms are chilled to close to absolute zero, they get closer to each other than their radii should permit. (also closer than quantum mechanics permits) The answer is that the electrons and protons have internal structure, with a core surrounded by neg-pos pairs. (the fundamental particles)

When two electrons approach each other, the core of one electron attracts the pairs of the other electron. That is what happens when the temperature is that low. Otherwise, electrons are always on the move and repel each other.

Philip Mintz
http://philmintz.tripod.com


Posted by: Gunnar Tomasson

Thanks, Philip!

Let me explain why I find it problematic to fit the concept of ever-increasing entropy with Newton's Third Law of Motion, taking as my point of departure your comment "The subject is matter in motion."

Since "matter in motion" = kinetic energy, I construe Newton's Third Law of Motion to imply that the NET kinetic energy of all matter in the Cosmos is ZERO.

If the NET kinetic energy of the Cosmos is ZERO, then the NET rate of transformation of kinetic energy into heat energy must be ZERO.

Whence if follows that the NET Entropy of the Cosmos is CONSTANT.

As it happens, this very proposition has long been known within the community of theoretical physicists, albeit in somewhat different form as explained by Paul Davies in his book 'About Time - Einstein's Unfinished Revolution':

"A particular slicing of spacetime into spatial sections will show how the geometry of space evolves with the time coordinate. In the simple case of a uniform universe, space just expands at a certain rate. But if we take a different method of slicing, we get a different description - e.g., a different size and expansion rate - at the same particular value of the time coordinate. The point about Einstein's time is that all such descriptions must be equivalent; the value of the time coordinate itself is arbitrary.

"If you nevertheless go ahead and use an arbitrary time coordinate anyway, and treat the motion of [within?] the universe just like that of any other mechanical system, then you can use Einstein's gravitational field equations to write down equations of motions for the universe, and identify familiar quantities such as the total energy. But here lies the rub. For the equations to remain valid whatever flexitime (i.e., slicing) you opt for, it turns out that the total energy of the universe is constrained to be exactly ZERO."

Of course!

"So Einstein's view of time forces us to conclude that, if the universe as a whole is naively [?] treated like a mundane mechanical system, the energy is obliged to vanish. This remarkable result, known to physicists for many years [since Newton's statement of the Third Law of Motion! - insert] has profound consequences for a quantum description. In quantum physics, energy always goes hand in hand with time. In a sense, the amount of energy determines the rate at which time passes - the beat of the quantum clock, if you like. No energy means the quantum clock ceases to tick: time bafflingly [?] drops out of the physical description altogether [See Parmenides et al. - insert]. So quantum cosmology, treated in this manner, makes no reference at all to time: in effect, time has totally vanished too! Spacetime, the very entity on which Einstein's theory of relativity was founded, has been substituted for a motley collection of spaces of different geometry, but with no time left to stitch them together. Like the dog that failed to bark in the Sherlock Holmes story, the cosmic clock that failed to tick seems to be a crucial clue that may help us to solve the riddle of time, but we lack the sleuth's fabled powers of reasoning to crack the problem." (Penguin Books, 1995, p. 180)

And why didn't the dog bark?

Here is Pascal's answer as applied to modern mathematical physicists:

"...the reason why mathematicians are not intuitive is that they cannot see what is in front of them: for, being accustomed to the clearcut, obvious principles of mathematics and to draw no conclusions until they have clearly seen and handled their principles, they become lost in matters requiring intuition, whose principles cannot be handled in this way. These principles can hardly be seen, they are perceived instinctively rather than seen, and it is with endless difficulty that they can be communicated to those who do not perceive them for themselves. These things are so delicate and numerous," Pascal continued, "that it takes a sense of great delicacy and precision to perceive them and judge correctly and accurately from this perception: most often it is not possible to set it out logically as in mathematics, because the necessary principles are not ready to hand, and it would be an endless task to undertake. The thing must be seen all at once, at a glance, and not as a result of progressive resaoning, at least up to a point." ('Pensées', Penguin Classics, 1975, p. 211)

In the context, Quantum Comology IS the end product of "progressive reasoning" which lays bare - but uncomprehended - Time as ILLUSION.

Gunnar


Posted by: Philip Mintz

Very interesting: Deep thought succeeds in disclosing the folly of relativity and quantum. I reached the same conclusion by a different path. I made two lists. 1, real things ... 2, abstractions . The result was only one thing is real, matter, and everything else is abstract.

In the spirit of NKS, long before there was NKS, I started with the simplest rules and found the two bits interacting with an endless supply of the same, with the result of exceedingly complicated arrangements of bits.

In my system, the number of bits in a body of matter is its mass or its energy. These are mere numbers. Matter is real, mass and energy are abstract. Instead of worrying about the quantity of energy or entropy or space or time, just remember that the number of bits in the universe is constant.

Philip Mintz
http://philmintz.tripod.com


Posted by: Gunnar Tomasson

Thanks again, Philip!

I looked at your website a few days ago and am still digesting the 'bit' approach - hope to do so soon.

But I do agree that "matter" is the stuff of the Cosmos viewed as the "permanent possibility of perception" alias the non-observed sub-stratum or generator of mass/energy dependent observations of empirical phenomena.

While reflecting on related issues in 1977, it occurred to me that these twin aspects of the Cosmos MUST be mechanically related in a fashion which, at the time, I summarized as follows:

MATTER BECOMES ENERGY WHEN IT LEAVES A STABLE ORBIT.

I should add that the concept of "stable orbit" is one which accords more nearly with Kepler's view of solar system orbital mechanics than with that of Newton.

It is predicated on a non-Newtonian view of solar system structure as indicated in my comments on Stellar Aberration at the end of my earlier post on "Einstein's 'Scientific Testament'" - one where the Planets are viewed as spherical field structures at INERTIAL REST within a Solar spherical field structure, whose rotation around its axis imparts orbital motion to the planetary structures.

This view of solar system structure has implications for Newton's reflections below from Book Three of 'Opticks', including his 'very certain' conclusion that "MOTION may be got or lost":

"And thus Nature will be very conformable to herself and very simple, performing all the great motions of the heavenly bodies by the attraction of gravity which intercedes those bodies, and almost all the small ones of their particles by some other attractive and repelling powers which intercede the particles. The vis inertiae is a passive principle by which bodies persist in their motion or rest, receive motion in proportion to the force impressing it, and resist as much as they are resisted. By this principle alone there never could have been any motion in the world. Some other principle was necessary for putting bodies into motion; and now they are in motion, some other principle is necessary for conserving the motion. For from the various composition of two motions, 'tis very certain that there is not always the same quantity of motion in the world. For if two globes, joined by a slender rod, revolve about their common centre of gravity with a uniform motion, while that centre moves on uniformly in a right line drawn in the plane of their circular motion, the sum of the motions of the two globes, as often as the globes are in the right line described by their common centre of gravity, will be bigger than the sum of their motions when they are in a line perpendicular to that right line. By this instance it appears that motion may be got or lost."

Also, if the field strength of solar system structures decreases discontinuously between their centers and the region of planetary orbits, then a plausible alternative to the orthodox vast-distance-energy explanation of Quasar red-shift comes into sight.

For if Quasars have far less radiating mass relative to that of the Sun, then much greater Quasar field strength at the mass surface would be signaled by "anomalous" red-shift.

Gunnar


Posted by: Karl Smith

QUOTE
Instead of worrying about the quantity of energy or entropy or space or time, just remember that the number of bits in the universe is constant.
ENDQUOTE


I think that enthropy is useful in squaring things that seem real on one level to things that seem real on perhaps a slightly deeper level.

It seems like certain things "want" to do something. Gases want to difuse. Vaccums want to be destroyed. Heat wants to flow from hot matter to cold matter. Salinity wants to be equalized through osmosis. Glasses want to break and plans want to fail.

People say that trying to stop these things from happening is hard, and they mean something by it.

Enthropy tries to solidify what it is that they mean. In that way I think it is a profoundly important concept linking physics, mathematics and statistics to real world experiences.


Posted by: Philip Mintz

to Karl Smith et al

I have no argument against your statements. However, I am concentrating on the attempt to understand the world we find ourselves in. NKS traces back from a resulting complexity to a starting simplicity. It occurs to us that whatever we observe has a cause or several causes. Having worked back to electrons and protons, we need to continue to the
fundamental particle that is the building block of all matter. It turns out that the electron has an internal structure, a core surrounded by an aggregate of pairs of bits, a negative bit and a positive bit.

Neg and pos attract each other until they reach a point where the force between them is zero. Thus they exist as bit pairs. In the electron, the pairs are oriented with the pos facing the core of the electron.

This becomes interesting when an electron encounters a positron and the negative core of one combines with the positive core of the other, and the bits that they are made of form pairs. Then the pairs line up, the first pair with one orientation, followed by the next pair with opposite orientation. The resulting photon is a procession of bit pairs.

If I weren't pressed for time with other obligations, I would type out a long story.

Philip Mintz
http://philmintz.tripod.com


Posted by: Gunnar Tomasson

Let me second Philip's comments and add the following with respect to Karl's points.

The question of Entropy has important implications for our modern world-view as reflected, inter alia, in the following comments by Stephen W. Hawking in 'A Brief History of Time':

"To summarize, the laws of science do not distinguish between the forward and backward directions of time. However, there are at least three arrows of time that do distinguish the past from the future. They are the thermodynamic arrow, the direction of time in which disorder increases; the psychological arrow, the direction of time in which we remember the past and not the future; and the cosmological arrow, the direction of time in which the universe expands rather than contracts. I have shown that the psychological arrow is essentially the same as the thermodynamic arrow, so that the two always point in the same direction. The no boundary proposal for the universe predicts the existence of a well-defined thermodynamic arrow of time because the universe must start off in a smooth and ordered state. And the reason we observe this thermodynamic arrow to agree with the cosmological arrow is that intelligent beings can exist only in the expanding phase. The contracting phase will be unsuitable because it has no strong thermodynamic arrow of time.

"The progress of the human race in understanding the universe has established a small corner of order in an increasingly disordered universe. If you remember every word in this book, your memory will have recorded about two million pieces of information: the order in your brain will have increased by about two million units. However, while you have been reading the book, you will have converted at least a thousand calories of ordered energy, in the form of food, into disordered energy, in the form of heat that you lose to the air around you by convection and sweat. This will increase the disorder of the universe by about twenty million million million million units - or about ten million million million times the increase in order in your brain - and that's if you remember everything in this book." (Bantam Books, 1988, pp. 152-153)

IF the NET entropy of the Cosmos is CONSTANT, as concluded in my second post in this thread, THEN Hawking's "boundary proposal for the universe" which "PREDICTS the existence of a well-defined thermodynamic arrow of time" is FALSIFIED.

Gunnar


Posted by: Philip Mintz

With emphasis on the "New", we are not compelled to view the universe as the big bangers do. We undrstand more if we see a universe that was always there. The graph of the growth of entropy stops rising at very high temperatures. Energy that arrives at a star increases the temperature of the star until pieces of the star come flying out with escape velocity. So we may agree that the entropy of the universe is constant.

Our New point of view uncovers the behavior of the building blocks of all matter. Bit is just a name. The bit has characteristics, without which it would be nothing. There is no explaining the why and how of characteristics. So that is where we begin.

Two neg bits repel each other, except when they are pushed closer together past a point of zero net force. Closer than that they attract. When neg bits continue to arrive, they aggregate until the size of the pile is at the outer limit of the force of attraction. The aggregate of neg bits is the core of an electron.

Other bits combine when a neg meets a pos. They become a bit pair. When a bit pair gets close to an electron, the pos end of the pair is attracted to the electron, so the pair becomes attached to the electron. This interaction causes the electron to move. Every time another pair attaches itself it adds motion to the electron.

The mass of the electron (including pairs) is the count of the number of bits. The unit of mass is 1 bit. Likewise, the energy of the electron is the count of the number of bits . the unit of energy is 1 bit.

The kinetic energy of the electron is the number of bit pairs x 2. While the potential energy is the number of bits in the core.

It is important to note that, although mass and energy are interchangeable, matter and energy are not interchangeable.
Mass and energy are abstract. Matter is real.


Posted by: Franck Binard

Don't remember much physics, question might be stupid


I could understand how matter could "grow" out of
matter that already exists, and how it could go from one form to
another, but a CA that has an initial configuration of nothing can
also grow complex patterns if the 0 subrule is included in the set
of rule by which it evolves.

What are the implications of any rule based system that includes
the first basic rule? Doesn't it somewhat implies that matter
could be created out of nothing ?




[LATER---------------------------This is a post edit]

Got to thinking about it some more, and took a look at it using
that rule i've been falling in love with (mod 7, described in another
thread) when the initial configuration is 0 across the board.
It includes a 9 bit version of the 0-rule, so it
would be a creation rule (assuming that means something).




  1. Tried it first on a 100x100 grid, on cells (matter) green, black
    cells (emptiness) black. Can't see anything
    interesting, just a lot of very regular lines
    flashing rapidly across the screen.

  2. 500x500: Its slower that way (working on a P650)
    It takes a while, but there is definitively
    cool stuff happening. Because the board is finite, the
    lines are coming from both size of the end grid
    (which is set to be 0). It's very regular, but it
    eventually grows in complexity. Never close to 30.


  3. Maybe the complexity is somewhere else, like in
    the length of adjacent matter.
    [idea: matter that seems to behave like waves]
    Try to change the coloring scheme, so i can see something like wavelengths (except in this case it's wavewidth). Ties it up to the length of adjacent on cells. Even there, it stays regular (0.966 color intensity on RGB (from the VC debugger)which i subtract from 1). Maybe i've got a bug.

    i think i might see something like randomness on the tip of some
    of the "waves", but i don't know how to make it come
    out. This is




    what i'm looking at

    (z/x zoom, arrows translate, 'A' stop/start).
    (falling asleep/getting hypnotized (all that regularity :)))







Posted by: Philip Mintz

fbinard finds it hard to accept the idea of matter building matter.

Matter as a fundamental particle is attracted to another fundamental particle. The result is a bit pair.

If the fundamental particles are of like charge, they repel unless they are pushed together hard enough to come together within a tiny sphere which can accommodate 4.918 x 10^11 bits. The result is an electron core if the charge is negative, or a positron or proton if the charge is positive. The difference between a positron and a proton is the number of bit pairs that surround the core. The number of bit pairs in the proton is nearly 2000 times as many as their number in a positron.

Let an electron be close to a proton, and they attract each other. The electron rushes toward the proton until it enters a sphere in which the force is repulsive. The electron oscillates toward and away from the proton. During each half cycle of oscillation, the electron emits a bit pair, causing a procession of bit pairs with alternating orientation, called a photon. A photon is matter, being built of bits. The proton plus the electron are an atom of hydrogen.

Should an electron be pushed through the barrier of repulsive force between the proton and electron , the pos end of each bit pair that is on that side of the proton will be attracted to the electron. The electron will combine with the proton
without coming in actual contact. There is an aggregate of bit pairs between them. The combined proton-neg-pos-electron unit is called a neutron.

To cause a neutron to be formed, the electron has to get sufficient speed. In some nuclear reactions that speed is attained. The usual place to find such electron speed is in a star, like the sun. In that instance it is evident that nothing and nobody is needed to bring about the grouth of complexity from simplicity.

Philip Mintz
http://philmintz.tripod.com


Posted by: Franck Binard

it's not matter building matter that i have problems with. I'm even comfortable with matter building more matter than itself (using nothing else but itself as raw material).

What i have a problem with (but i'm getting over it) is matter getting built out of nothing. is that possible ?


Posted by: Philip Mintz

It is not possible to get something from nothing. A mathematician can do many things with zero. In nature there is no zero. Even the big bangers don't start with zero. They have a singularity. What they say is that energy can turn into matter. They fail to realize that matter is real and energy is abstract and not a thing in itself.

If one wonders how the matter got there, the only possible answer is that it was always there. If one tries to get around it by postulating a creator, one must be ready to explain how the creator was created.

The quantity of matter in the universe is constant.

Philip Mintz
http://philmintz.tripod.com


Posted by: Franck Binard

I've thought along the same lines all my life. CA's are changing my certitudes.


If the universe is built along the lines of a CA, if it uses all the possible rules, then it might be possible to get something for nothing. Look at the 255 simple automatas. The beginning configuration is usually chosen to be a center bit 'on'. However, there are some of those that do not need an initial configuration at all to produce patterns.

How do we know that the quantity of matter in the universe is constant ?


Posted by: Mike Lin

No cellular automaton can produce behavior that is interesting (in ways that matter to Wolfram) from a completely blank initial condition, simply because no cell is distinguishable from any other to the underlying rule. The behavior is always going to be repetitive in an especially boring way.

The existence of CA rules that are not conservative does not imply that any rule that might underlie the universe is not conservative. The chapter on fundamental physics in the NKS book shows that cellular automata that do conserve certain quantities can still show the kinds of behavior important to Wolfram (although apparently none of the 256 elementary rules do).

I should say that it is no longer the prevailing view of the physics establishment that matter is conserved. By adopting theories that abandon conservation of matter we have managed to learn some other interesting things. But really, one can give some arguments and "evidence" for either position, and philosophically you can never really decide. Currently, the physics establishment does hold that certain other quantities like momentum and electric charge seem to be conserved.


Posted by: Franck Binard

From Mike Lin: No cellular automaton can produce behavior that is interesting (in ways that matter to Wolfram) from a completely blank initial condition, ...

What if the grid is finite ? Depending on how the borders are handled, patterns can grow from the edges.

For example, i handle some of my grids with an extra row of cell/columns on the edges that stays unlit no matter what. So a rule that fills up all the space because it lights when the previous tiles it depends on are all unlit, will start evolving on the second iteration because the edge cells will have varied configurations.

I have a pic of an example attached (doesn't produce complexity though).

Wouldn't that count as getting something for nothing or is it cheating ?

What if you flip the issue, and consider that the initial configuration is that all the cells are lit ? Does that mean that you can never get interesting patterns from the unlit cells ?


Posted by: Philip Mintz

In nature, the starting material is matter and the product is matter. In the search for rules, the starting matter is a brain, human or mechanical, but material nevertheless. However, the activity is all nonphysical and the result is abstract, regardles of how much motion of particles is involved. If one likes rules, rule number one is "distinguish between real things and abstractions.

Looking for evidence, count the bits of starting material and count the bits in the product.

Philip Mintz
http://philmintz.tripod.com


Posted by: Franck Binard

Philip,

Using your 'bit' vocabulary to matter in the universe.

I really don't understand why we must assume that we need
n bits of input to get n bits of output given a computation performed over time (talking real world material, not abstraction).

Has it been proven by anyone that matter remains constant in the universe or is it just intuition ? Because intuition is often wrong. Are there experimental results anywhere that makes this out into a fact ?

Is there any better argument that "you need n apples to get n apples after you mix them", because that is an intuitive argument.

If in fact, the amount of matter in the universe wasn't a constant, how would we know ?

One thing about NKS, it observing the real world through simple programs, assuming that it does behave like one.

I think Mike Lin's point (just because there are rules that creates stuff from nothing and expand or contract the amount of material that their universe is made from does not mean our universe is built from one of these rules) is valid. But i also think that just as our universe might not be built using such a "creation" rule, the fact that such rules do exist raises the possibility that it might be.


Posted by: Gunnar Tomasson

Re. the following:

I really don't understand why we must assume that we need n bits of input to get n bits of output given a computation performed over time (talking real world material, not abstraction).

Has it been proven by anyone that matter remains constant in the universe or is it just intuition ? Because intuition is often wrong. Are there experimental results anywhere that makes this out into a fact ?

Is there any better argument that "you need n apples to get n apples after you mix them", because that is an intuitive argument.

If in fact, the amount of matter in the universe wasn't a constant, how would we know ?

Comment:

The proposition that the amount of "matter" in the Universe is constant rather than variable implies that the Universe is a Closed rather than an Open System.

As such, the proposition has served as point of departure for theoretical work in the field of modern physical science since its inception four centuries ago.

This includes Quantum Mechanics, which models QM phenomena with precision which, effectively, would seem to falsify the contrary proposition that matter is NOT constant.

Gunnar


Posted by: Franck Binard

I do seem to remember something about physics:

How the universe was assumed for hundreds of year to be euclidian geometrically, and how Newtonian physics could (and still does) accuratly predict a whole bunch of stuff on a euclidian based universe.

Then i seem to remember that the N in NKS stands for new. Are there things that we have been wrong about ? Should NKS force us to look at previous assumptions in a different light ?


Posted by: Gunnar Tomasson

Re. the following:

I do seem to remember something about physics:

How the universe was assumed for hundreds of year to be euclidian geometrically, and how Newtonian physics could (and still does) accuratly predict a whole bunch of stuff on a euclidian based universe.

Comment:

The non-Euclidean view of the universe is predicated on certain pre-suppositions of which Einstein wrote to Michel Besso, his long-time friend and early collaborator in August 1954 as follows:

"I concede, however, that it is quite possible that physics cannot be founded on the concept of field - that is to say, on continuous elements. But then, out of my whole castle in the air - including the theory of gravitation, but also most of current physics - there would remain almost nothing."

Re. the following:

Then i seem to remember that the N in NKS stands for new. Are there things that we have been wrong about ? Should NKS force us to look at previous assumptions in a different light ?

Comment:

I have seen nothing to suggest that the NKS approach is suitable for resolving foundational issues with respect to the geometry of universal space.

Gunnar


Posted by: Franck Binard

Sorry, the stuff about euclidian geometry was just to demonstrate that just because an assumption is intuitive AND yields correct predictions on a subset of states does not make it true. (BTW, I also seem to remember that there are others who saw the possibility of non-euclidian universe before Einstein.)

Suppose the universe is made up of K bits of matter (K REALLY large).

Suppose the universe behaves as a CA in which K bits at step i always produces K bits at step i+1 (i know there is another possibility, ie only one bit gets updated at every stage, but for the sake of ...) .

Suppose the 'grid' is infinite. Doesn't that mean that the universe's configuration must eventually repeat (bijectively with the distances separating the bits of matter)? If it doesn't, doesn't it mean that every (or at least some) bits must eventually move further and further apart from every other bit ?


Posted by: Gunnar Tomasson

Re. the following:

Suppose the 'grid' is infinite.

Comment:

In my view, this supposition opens up a whole set of issues which theoretical physicists of first rank, both past and present, have yet to address in coherent fashion.

For IF the proposition that Matter in the Universe is Constant is properly held to IMPLY a Closed-System Universe, THEN the idea of an Infinite Universe embraced by Newton is on par with that of a Square Circle insofar as intelligibility is concerned.

Ditto for Stephen Hawking's idea which he outlined in 'A Brief History of Time' as follows:

"It was at [a] conference at the Vatican...that I first put forward the suggestion that maybe time and space together formed a surface that was finite in size but did not have any boundary or edge. My paper was rather mathematical, however, so its implications for the role of God in the creation of the universe were not generally recognized at the time (just as well for me). At the time of the Vatican conference, I did not know how to use the "no boundary" idea to make predictions about the universe. However I spent the following summer at the University of California, Santa Barbara. There a friend and colleague of mine, Jim Hartle, worked out with me what conditions the universe must satisfy if space-time had no boundary. When I returned to Cambridge, I continued this work with two of my research students, Julian Luttrel and Jonathan Halliwell.

"I'd like to emphasize that this idea that time and space should be finite without boundary is just a _proposal_; it cannot be deduced from some other principle. Like any other scientific theory, it may initially be put forward for aesthetic or metaphysical reasons, but the real test is whether it makes predictions that agree with observations. This, however, is difficult to determine in the case of quantum gravity, for two reasons. First, as will be explained in the next chapter, we are not yet sure exactly which theory successfully combines general relativity and quantum mechanics, though we know quite a lot about the form such a theory must have. Second, any model that described the whole universe in detail would be much too complicated mathematically for us to be able to calculate exact predictions. One therefore has to make simplifying assumptions and approximations - and even then, the problem of extracting predictions remains a formidable one." (Bantam Books, 1988, pp. 136-137)

While Hawking's "proposal ... cannot be deduced from some other principle," it can be tested for logical coherence.

In this respect, the supposition that a "finite" - or Closed-System - Universe may "have no boundary", as Hawking summarized his "proposal", is another way of representing the mathematical attributes of an Infinite - "no boundary" - Universe.

And where does all this leave us?

Briefly,

(1) A Closed-System Universe is necessarily a Finite Universe;

(2) Newtonian gravitational interaction would cause a Finite STATIC Universe to collapse on its center of gravity;

(3) Hence Hawking's remark (pp. 5-6) that "It is an interesting reflection on the general climate of thought before the twentieth century that no one had suggested that the universe was EXPANDING" - therefore had NOT collapsed on its center of gravity; OR, going back to square one,

(4) Einstein was right on target when he "concede[d] that it is quite possible that physics cannot be founded on the concept of field - that is to say, on continuous elements. [In which case, of his] whole castle in the air - including the theory of gravitation, but also most of current physics - there would remain almost nothing."

Gunnar


Posted by: Philip Mintz

Re. fbinard, has it been proven?

Nothing has been proven. That is why a new kind of science is possible. In the practice of science, after the step of "observation" the next step is interpretation. There is practically no limit to the number of different interpretations that can be offered for a single observation.

When a proton that is driven by an accelerator is received we observe a proton plus several particles. One interpretation finds that, in the process of acceleration, energy is added to the proton, which energy turns into matter in the form of particles. Another interpretation finds that the accelerator transfers bit pairs from the power source to the proton, and the increase of the number of bits in the proton provides the material for the particles that are observed.

If we want to conduct experiments to establish a fact, we spend much time and money and end up with results that can be interpreted variously, anyway. There is a library overflowing with reports that are crying for new interpretation. There is ample evidence for all the theories we want to develop.

Philip Mintz
http://philmintz.tripod.com


Posted by: Franck Binard

Gunnar,

Suppose the universe is finite in space. Suppose the amount of matter in it is constant. That means that there is only a finite number of configurations for that matter in the universe.

If time is infinite, doesn't this then implies that the universe must eventually repeat itself ?

But the CAs we are interested in (30, 110) do not repeat (at least we hope). These are also the CAs whose class we look at as being prime candidates for the building of something as complex as the universe.

What happens in a universe whose mass is not constant but that is finite ?

I like the idea of a finite universe that grows and/or shrinks.


Posted by: Franck Binard

Attached are pictures of a 2D moore neigh. CA of range 1 which develops complicated behavior when the initial configuration is empty.

The rule is for the 512 9 bit cell neighs. arranged as 000000000 to 111111111

The 512 bit rule is based on the function:
ith bit = (i mod 3 == 2) OR (i mod 7 == 0)
it is a modification of the mod7==0 rule, which produces very regular wave like patterns with a nil initial configuration, but rapidly becomes complex with very simple initial configuration.


I implemented a binary that illustrates the evolution of the rule. It can be opened here




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