Registered: Dec 2003
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Mark Suppes © 2003

I propose that gravity is the macroscopic expression of the tendency for particles with mass to be net consumers of nodes, and empty space to be a net producer of nodes. This theory is an extension of the model of physics presented by Stephan Wolfram in A New Kind of Science.

According to Wolfram’s view of fundamental physics, the universe is made of a trivalent network of nodes and connections between nodes. These nodes correspond with the smallest possible unit of spatial measurement – the Planck length, about 10^-33 centimeter. In this model, distance is measured as the count of nodes along the shortest path between two objects. An object’s volume corresponds to the number of nodes that make up the object.

The evolution of the network is based on a set of simple replacement rules that have yet to be discovered. Each time the rules are applied, time has passed. It is important to note that the passage of time is discrete, corresponding to the Planck time of 10^-43 seconds.

In this model, a particle is a collection of nodes with features that persist as the network evolves. This persistence is why an electron remains an electron as time passes. Empty space refers to areas of the network that do not contain persistent structures identifiable as particles.

It is interesting to note that there is some ambiguity as to which nodes belong to a particle and which nodes belong to the empty space around the particle. As the network evolves, nodes that begin as part of empty space can find themselves as part of an elementary particle later on. The converse is also true, nodes that begin as part of a particle can become part of empty space.

Certain rules reduce the total number of nodes in the network when they are applied.

(see image attached at bottom of post)

When this rule is applied, exactly two nodes cease to exist.

Now imagine that this reducing rule tends to be applied more in massive particles than in empty space. This means that massive particles absorb more nodes from free space than they return back to free space. Thus the particle is essentially sucking in and consuming the space around it.

A particle’s consumption of nodes reduces the amount of empty space around the particle, producing the macroscopic force of attraction we perceive as gravity. As a massive particle pulls the fabric of space into itself, objects that exist in the fabric become closer to the massive particle. An object falling toward a mass does not "feel" acceleration because the object is not accelerating relative to its surrounding space. Instead, space itself is moving toward the particle.

There is a direct relationship between a particle’s likelihood to reduce node count and the particle’s mass.

This formulation of gravity does not require the existence of a force-carrying particle such as the graviton, which has so far eluded discovery.

The Expanding Universe

I predict that space is an overall producer of nodes. As nodes are added throughout empty space, the volume of the universe expands, and all particles are pushed apart from one another. This predicted expansion is consistent with the experimental observation that the universe is expanding.

By building expansion into the mechanism of space itself, there is no need to explain the expansion of the universe in terms of dark energy. Empty space produces more empty space, so as the amount of empty space increases, the rate of expansion increases as well. This matches the experimental observation that the expansion of the universe is accelerating.

General Relativity

This theory can be made to explain the experimental outcomes predicted by General Relativity, such as the slowing of time near gravity sources. However, it requires rethinking the notion of time dilation accepted since the 1930s.

I propose that time is a constant, and that distance dilation produces the effects we have perceived as time dilation. At a point of high gravity, time is not slower, distance is longer. This misunderstanding of time dilation comes from the way we perceive the passage of time.

Let’s begin by reviewing the process of perceiving the passage of time. Broadly speaking, for us to perceive the passage of time, we depend on witnessing some perceptible change in our environment. This could be the everyday process of watching a clock’s second hand move forward, or a particle accelerator’s detection of a particle. Even the most fundamental observation of the passage of time is preceded by a large number of particle and virtual particle interactions. Consider the cesium atomic clock: this device requires a myriad of sub-atomic particles interacting to produce its macroscopic representation of time.

Now imagine that the average distance each particle had to travel before it interacted with the next particle in the system is increased. Assuming the particles are traveling at the same average rate, this increase in distance will cause the subatomic process to happen at a slower rate. According to Newtonian mechanics, this makes perfect sense –if you have further to travel at a constant rate, it takes longer to get there.

Why would particles at a point of high gravity have a greater distance to travel? Because gravity curves space-time, which in turn curves a particle’s trajectory. This means that a particle must take a more curvy and convoluted path between interactions. A place of high gravity has many obstacles that must be navigated before an interaction takes place.

The most extreme case of distance dilation is orbit. If all particles are locked in binary orbit, time has effectively stopped as far as we can perceive it. To some degree, this is the picture you would see at the center of a black hole, where it is predicted that time essentially stops due to the extremely high gravity.

Conclusion

I imagine that for Mechanical Gravity to be fully tested it first requires the discovery of Wolfram’s rule for the universe. Until then, smaller steps can be taken, such as looking for network update rules which produce convections toward non-accelerating vectors. Looking for the cosmological constant in a system’s growth rate could provide a good litmus test for a candidate rule for the universe.

Gravity may prove to be the ultimate strange attractor.

PDF Version:
http://www.twistet.com/ticktock/pdf...vity_theory.pdf

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Mark Suppes

Last edited by Mark Suppes on 08-23-2006 at 09:10 PM

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Registered: Oct 2003
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You suggested:

(...) particles absorb more nodes from free space than they return back to free space.

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Registered: Jan 2004
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Mark, this is Zubair. let me start by saying that I am not familiar with Wolfram's Theories, so I'll have to take a look at them before I can make a judgment on the larger thrust of your ideas. Let me offer some casual observations.

Your theory seems to be that massive objects "absorb" space between them, that this is what draws them together. Is this a continuous process? If a single massive body was placed in an otherwise empty universe (excluding of course zero point fuzziness), would it eventually absorb the entire universe?

Interestingly, some of your ideas a similar to concepts present in "loop quantum gravity," a theory based on a quantization of spacetime itself. It creates minimal volumes and areas on the plank scale. The theory is not very old but it has already had some success duplicating the thermodynamics of black holes and accounting for Hawking radiation. Again, though, I'll review the theories your work is based on.

One important point I want to make however, is that your understanding of relativistic concepts is a little flawed. The hardest thing to wrap your mind around in General Relativity (and indeed in the special case) is that what you see is what you get. First, distance is indeed longer, but the measure of time is light, which moves at the speed of information. That is to say, the universe communicates with itself through particles that move at a set speed c and always at this speed. If I perceive your time as dilating, it MUST be dilating, otherwise about fifty other important ideas, such as conservation of momentum and energy go flying out the window. and I don't think you're quite ready to get rid of conservation of momentum.

I apologize for that last paragraph not being as clear as I'd like. I can try again if you tell me what is confusing about it.

Last edited by Schroedinger on 01-28-2004 at 05:55 PM

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To be honest, this idea popped into my head while reading an article on Loop Quantum Gravity in the Jan 2004 issue of Scientific American. I was shocked at the similarities between Loop Quantum Gravity and Wolfram's framework for physics. In fact, the illustration attached to this post is included in both publications.

As far as i can tell, Loop Quantum Gravity never actually identifies gravity's mechanism of action as the application of a rule that reduces node-count. Although is does the heavy lifting of providing a framework for such a notion.

If this idea holds up, it would be pretty exciting, as it would rather concretely identify the mechanism of gravity's action.

Regarding the question of continuity - The process would be discrete, as almost everything is in both Wolfram's model, and Loop Quantum Gravity. Each time the update rule is applied, patterns near the perimeter of massive particles would be replaced by patterns with fewer nodes. Since there is a relationship between node count and distance, there is also a relationship between node count and volume. Thus if node count is reduced, volume is also reduced.

Would a single massive body eventually consume the universe? Perhaps. But I am guessing that empty space tends to increase the number of nodes over time (corresponding to the expanding universe) - So in some sense, space makes more space, and gravity consumes space.

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Mark Suppes

Last edited by Mark Suppes on 02-16-2004 at 09:32 PM

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explain what you mean by nodes

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Okay, can you derive basic Newtonian Gravitation from this? Forget Relativity, can you match predictions in classical situations?

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I think this theory matches the observations of classical Newtonian gravity quite well.

I am saying that particles with mass consumes the space around them, thus pulling in the surrounding space and any other particle that space contains.

This matches the observation that objects with mass get closer over time.

An object that is freely falling towards a source of gravity has the subjective experience of zero - gravity (assuming the object is a point). Mechanical Gravity Theory says that gravity pulls in space itself. Any object that exists within this fabric of empty space goes along for the ride, but does not feel it because it is not accelerating relative to it's surrounding space.

Gravity follow the inverse square law. The force of gravity is inversely proportional to the square of the separation between the two objects.

If you think of a particle consuming the space around it, the disturbance will be felt maximally close to the particle. The disturbance would be attenuated as you move further away from the particle. On average, I think you would see the familiar inverse square law emerge.

Nodes are pretty clearly defined by Wolfram in Chapter 9 of A New Kind of Science. Basically they can be thought of as nodes in graph theory.

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Last edited by Mark Suppes on 01-28-2004 at 08:21 PM

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Actually, I was thinking of getting a mathematical (or whatever)derivation that gets us to the idea that the attractive force is proportional to the masses and inversely proportional to the square of the distance.

The little I've picked up about Wolfram's ideas suggest he's not so big into the equations, but there must be some kind of predictive apparatus. My question is simply, given two masses at a known distance, based on your ideas can you calculate how long it should take for them to come into contact? Can you tell me their velocities at various times?

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If I understand your node eating hypothesis correctly, it seems to predict that on a macroscopic scale the velocity will be proportional to the inverse square distance between masses instead of the acceleration being proportional to the inverse square distance, as predicted by Newton's law of gravitation.

Here is my oversimplification.

Assume we have constant masses and that in a quantum of time, dt, that we have a total of M * dt nodes consumed by a large mass. In addition I assume that the total number of nodes in a volume (say a sphere) is proportional to r^3 , say K*r^3. Thus our conservation of nodes equation is

K * (r + dr)^3 = K * r^3 - M * dt ,

where dr is the change in the radius of our volume after the nodes have been 'eaten' by the mass.

Ignoring terms like dr^2 and dr^3 we arrive at the equation

dr/dt = -M/(3*K*r^2) .

The solution to the classical Newton's equation is quite different (and more complex).

If we throw in your space expansion term, including the creation of nodes, one gets

K * (r + dr)^3 = K * r^3 + dt * (- M + E * r^3 ),

where I assume the number of nodes created is proportional (on average) to the volume of the region with proportionality constant E. This adds a linear term to the velocity which presumably would dominate once you were far enough away from the mass, yet it is still very different from the classical case.

dr/dt = -M/(3*K*r^2) + E * r / (3 * K)

I think you will be led to propose some kind of time variation in your node eating schedule to make it match, or perhaps even worse, you will have to propose a space time dimensionality that is different from 3, although I do not believe a constant dimensionality will suffice to match the solution to Newtons gravitational law.

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Okay, I actually had to translate the equations onto a piece of paper, at which point it started looking pretty bad.

The most fundamental flaw in your thinking is that you have volume as a function of radius, which is normally true, but in a scenario where volume (and therefore radius) is being consumed, radius becomes a function of another variable, perhaps time. [instead of V(r), you have V(R(t)) ]

Even assuming you could use "dr", you're negative sign is in the wrong place.

I don't mean at all to bash. You took a shot at answering the question I asked and I appreciate that. I'm curious though, as to the level of mathematical education you have. Your casual disregard for dr^2 and dr^3 scares me.

Last edited by Schroedinger on 02-04-2004 at 08:13 PM

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While Mark's idea is tempting, MattBro's conclusion is correct. Let me simplify MattBro's analysis for the scenario of central mass acting by deleting nodes.

Note first of all that the dimension is irrelevant. One can restrict to the path of a hypothetical particle, and thus to one dimension. This makes exact analysis easier, and meaningful experiments possible.

Imagine the discrete points of space are all evenly spaced on the real line. Each point is given a coordinate value on the real line. Distance is measured using the real line, which is roughly proportional to how many points lie between. Velocity and acceleration is measured using the distance of the real line.

Consider the central mass to be at x=0, and are test particle at the 100th node at x=1. At each step the central mass eats a node, so our test particle becomes the 99th after the first step, at x=.99, and so on: Length[#]/100&/@NestList[Rest, Array[pt,100],50] gives a constant speed.

Basically, here we are thinking of the nodes as sitting inside traditional space-time, which might not turn out to be the right thing. As one can see from the graphic, it seems that disappearing nodes only where there is mass is not realistic, no matter what choice is made to give the geometry. The main feature missing from Mark's idea is that gravity, in Newtonian physics, acts at a distance. Action in a discrete causal network picture has to be essentially local, and presumably gravity would have its long range effect by causing a chain of coincidences from the central mass to its target. Besides, one would expect a rewrite which caused node disappearance to play a role in many other things as well as gravity and motion.

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I would not be too quick to give up on the general thrust of Mark's idea. It makes sense at too many levels.

Firstly we should not imagine that the dynamics of any underlying structure of nodes/vertices and links/edges is going to be selected for our ability to get our heads around it or to simulate it easily on our computers. (I can live with assuming that such as structure is a reasonable best guess as to the fundamental fabric of existence.)

It is clear that the number of nodes is increasing, currently at a rate proportional to something greater than t**2. While space is expanding, empty space is clearly not becoming significantly thinner with age. Whatever the "simple" mechanism is that supports that nett increase in "empty" space nodes could easily be masking localised elimination of nodes close to now very rarified matter.

Every time I look at the kind of node substitution diagram that Mark attached and which adorn NKS as well as other respectable publications, I am forced to wonder about our instinctive guess that any nodes and links might persist for more than microscopic time. Might not everything get simpler, except for our feeble brains, if the actual zero state process involves the continuous creation of all nodes and links. Certainly it seems ambitious to imagine that some propagation of node colour alone will manage to transport photons of all wavelengths at C in all directions, let alone a few of the other taken for granted features of the world in which we find ourselves.

It is also well known that Newtonian/relativistic gravity has only been validated to planetary scales and that there are sufficient discrepancies at larger scales to have generated the whole dark matter/energy industry. Something important is missing, but we cannot yet be confident that that something is just massive particles.

The good thing about being an unapologetic generalist is that you can speculate. Right now, the idea that mass is a measure of nett local consumption of nodes is starting to have some appeal. Yes, we also have to think how it might play out for other forces which keep giving broad hints that they might be more directly understood in terms of network topology.

Given that distance is likely to be a measure of nodal separation, as suggested in NKS, might not the local ongoing nett consumption of nodes produce just the observed curvature in the distance metric near massive objects? There is something inherently attractive in the idea that particles continuously consume empty space nodes at the same time as vastly more empty space nodes are created in the voids.

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The conjecture that dark matter and dark energy somehow point to faults in relativity on a cosmological scale is an interesting interpretation.

The basic idea, as I am understanding it, is that space moves towards massive bodies. Other bodies get dragged(?) by moving space and so appear to be attracted to the massive body? What about acceleration then? If I drop an apple from the top of a tall building, why does it continue to accelerate (until terminal velocity)? Wouldn't every falling object be dragged at a constant rate? Otherwise, doesn't that suggest that the absorption of space nodes is increasing per unit time? Wouldn't this acceleration of absorption very quickly lead to silly infinities?

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Consider spherical shells around the massive object at radius r1 and r2, r2 >> r1, with n nodes absorbed by massive object in time t.

If we are in a local region where the expansion of space can be neglected, that means that a nett n other nodes need to pass inwards through each shell in the same time, but the area of each shell is proportional to r**2, thus the rate of acceleration is proportional to r**-2.

This argument relies on conservation of linear momentum to ensure that it is the acceleration rather than the velocity which is proportional to r**-2, and explaining conservation of linear momentum in such a space of nodes and links might be a lot tougher than explaining gravitational acceleration given conservation of linear momentum.

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I'm not sure I follow your reasoning Tony. Can you explain more explicitly how momentum constrains the nodes?

In my analysis all I was trying to do was to equate the shrinkage of space with the proposed consumption of nodes. If we assume that the number of nodes consumed per unit time is a constant, proportional to the mass, and if we assume that the number of nodes in space for any given volume is proportional to the cube of the radius, then my velocity equation should hold to first order.

I made the assumption here that the motion induced by gravity is the result of the fabric of space being pulled into the mass as it consumes nodes.

I am not trying to throw cold water on this theory per se, because I also find it intriguing. I just believe that to make it work it needs to be able to agree with the macroscopic Newtons law on planetary scales, since experimental evidence seems to verify this.

I do not propose abandoning the theory, I just want to fix it so that it matches the macroscopic case, and then see what the implications are. I think there are probably several approaches we can take to get this theory to match classical physics.

To make the math come out right, what has to happen is that mass has to consume momentum, or velocity, not spatial nodes (or distance). There are probably several frameworks we could propose to make this happen.

Here is just one idea, which is probably a bit closer to classical physics. If we allow each node to have some kind of discrete state variable (perhaps momentum or mass and velocity etc.), then the effect of nearby mass is to consume momentum / velocity quanta from neighboring nodes. The velocity quanta consumed would be any that point away from the neighboring mass.

The current state of a node would determine a particle's motion if a particle were currently occupying the node. This idea could be made quite precise if we used Feynman's least action formulation of Quantum mechanics. A particle in one node would transition to a neighboring node based on a density that is determined by a least action principle, computed in theory from the state variable of neighboring nodes. Perhaps all that is required is a simple deterministic rule for the state transition in these models I don't know.

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