Space Lattice, Brownian Time, Gravity, Relativity, Stochastic Light Speed, Euclidean Space

Ok, I'm going to combine together a lot of ideas here and see what the universe might look like:

1) Let's assume there's a higher level "checkboard" or multidimensional lattice in which objects move. The motions in this lattice do not correlate directly to space and time as we perceive, but our measurements reconstruct approximations by detection some forms of interactions within this.

2) Only exchanges of information and not forces contain information for our space. Motion and force alone do not create spacetime as we see it. It's information passed via. electromagnetic forces that allows our space to exist.

3) A single process goes through space randomly swapping (or other local "computations") pieces of information in this higher dimensional lattice. This could be seen as causing individual quantum collapses, one at a time. I'll call this process "time energy" and a unit of it, a "time energy quanta" or 'teq'. NOTE: This process occurs effectively infinitely fast. It's speed can't be measured directly is only used in our space in relative measurements.

4) Most (if not all) electromagnetic interactions create events we use to determine time. They may also (if not always) contain an accompanying force.

5) Gravity, spacial motion and inertia in themselves do not contain events that define time in our space.

6) Physical measurements must be made in relative terms, from within the system with a point of detection or relative measurement. The state of the universe is not directly detectable without electromagnetic information being transferred to detect it. (In other words, an observer has to be in the "loop" to see the flow of information)

Ok, let's start:

Brownian Time

Though time could still be seen as flowing forward in this higher dimensional lattice, we can't see this flow directly. Instead we use various calculations and approximations to determine how long "time has been messing with" something, since we last looked, and we interprete this as a difference in time, or rate of change.

Time can only be physically measured in terms of a system with more than one "particle". Each particle within this system will tend to be displaced in a bidirectional fashion in space (or what we might also interprete sometimes as time). This bidirectional motion generally cancels and the overall displacement (or standard deviation) grows proportional to the square root of the time energy quanta it's been exposed to.

d' refers to physical displacement over some time interval. p refers to a specific particle and teq' refers to the true number of time energy quanta (events) it's participated in.

d'(p)~=(teq'(p))^0.5

or

d'(p)^2~=teq'(p)

For a system, composed of particles p0, p1, ... you can sum up the total teq' exposure estimates during an interval to estimate the total time of the system.

teq'(system)=d'(p0)^2+d'(p1)^2+d'(p2)^2 ...

(Does anyone see a Euclidean space here or energy calculations? Wait until we add relativity!)

We'll also create the idea of a mass for these systems as the number of particles they contain and the idea of a time constant (tc) to space and set this to be a quantity of time energy in a system that creates an average displacement of 1 for each particle within it.

At least on large scales, for working with concepts of mass, distances and times, I believe this gives approximately:

teq(system)/tc=mass(system)

Stochastic Light Speed

Let's start off by measuring the velocity of a couple "photons".

...A.......d......B.....

This is suppose to represent two photons A and B separated by distance, d, in a one dimensional space.

As time energy goes by and randomly rearranges adjacent cells in this line, A and B do not interact until they're "swapped" in position. The average displacement over time for each "photon" for such Brownian motion grows proportional to sqrt(teq(A)+teq(), or the number of time energy quanta each has been exposed to.

Now we can't truly see A or B until they interact, but let's look at where each might appear if we tried to estimate the "light speed" of each.

When either A or B is exposed to a teq, d becomes either d+1 or d-1.

Using our distance estimate above, d^2=t, we can interprete what the time would appear like in this system between these two particles. We'll calculate the average "light speed", c, by average the two possible motions, calculating the new distance and comparing it to the old.

((d+1)^2+(d-1)^2)/2 = (d^2 + 2d + 1 + d^2 -2d + 1)/2 = (2d^2 + 2)/2
= d^2 + 1

The change in distance per teq would be d^2 + 1 - d^2 = 1

So this distance estimate would increase, per teq for either A or B, at what appeared to be a constant velocity away from both. Photons would always appear to be moving away (or easily interpreted as moving toward things also, as you can only detect individual events, as these are wave collapses on single particles that have no real spacial direction - they either interact or they don't).

For each teq encountered by either A or B an apparent increase in distance of 1 would be perceived (not directly though, but theory might easily misinterprete light speed as being constant on large scales especially ).

NOTE: The above is an inaccurate oversimplification as the only "realspace" event detected by both A and B would be an encounter with the other particle. Without anything else in the universe, these particles would only see each other and nothing else, constantly and forever because the only events that create a subjective change in time for either A or B are in their interactions.

In other words, a universe could not operate solely on the principles above and this was just a beginning example ... though with a third particle and a truly randomized time energy, you can work magic But you need at least 3 particles (if not more), a source of randomness or "chaos" for time energy, in a system for it to possibly be considered a potentially real universe. At least that's how I see it.

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A more accurate value for c, if variable "densities" of time energy in space occur would be:

c=1/tc

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Gravity, Mass and Time Dialation in a "gravity well"

Now it's more difficult to interprete clusters of data, but let's assume two identical systems, not individual particles, are "viewing" each other, each as they "diffuse" into space.

I'll draw systems A and B as collections of particles.

....AAAAAAAA.................d...............BBBBBBBB....

Now over time, both A and B diffuse, or are spread out slowly by time energy.

But neither A, nor B can measure their own diffusion, because they themselves are their own rulers.

On average, if A and B begin with the same density and width, they'll grow and diffuse at approximately the same rate and neither will witness an expansion of the other ....

But, they will experience something that would appear as a contraction in space over time, as their larger sizes tend to shrink distance estimates over time. Also time, for each particle, would appear to slow as they grow larger and interactions between each sub particle in their system would take longer and longer to communicate within each system (slowed time in a gravity well).

Also, on the edges of A or B more diffusion outward occurs than inward and the perception of a compressive force along the edges could be interpreted as existing.

Now let's calculate what the distances over time would appear between A and B above.

We'll assume for simplicity, both systems evolves from a point of infinite density (unlikely in reality). We'll call the total number of particles in each, the mass 'm'.

Each time step, the variance, in the width of each particles grows by 1 - they're expanding at light speed! Yet, stationary and don't perceive this expansion or the expansion of each other, but instead they see a continual rescaling of space dependent upon thier own "width". This distance perceived between the two would be:

relative distance and time(t) = d/width(A or

or

dr(t) = d/(t^0.5)

or

dr^2(t) = d^2/t

Reciprocal Space!

So from this view, "realspace" would appear to be continually contracting by a factor 1/t. Remember, "realspace" estimates use d^2, not d itself.

Ultimately A and B diffuse and contact each other to where they begin using the whole AB system to determine distances. So the two particles eventually merge into one, via an unfelt force - gravity and warped spacetime.

(Continuing below with more goodies .... BTW, Should I post this under the TOE section?)

This post has been edited by StevenA on Aug 5 2006, 08:17 PM

(Oops, I see the smilies "rewrote" my post above)

Quarks and Spacetime

Now I'm going to alter the picture some (and this will likely result in some changes, but it's necessary for a good understanding of what we see as "spacetime").

Let's first make an incorrect assumption and assume each location of this lattice contains only a single binary value (matter/antimatter, particle/space, 0/1 etc.).

We need to include a reference for observations for I'll use parenthesis to select an observation point:

0001110000000(1)10010000011...

Now the 1 doing the "observing" could encouter a teq and be swapped with either the 0 to the left or the 1 to the right. So one of these two observations is possible, but there's a problem.

Imagine this:

00000000(0)0000000...

or

11111111(0)1111111...

In neither of the last two examples would the observation point ever experience anything other than a constant "input" (though in the bottom example, the universe might be interpreted as being able to instead see the observer).

But even for 00110011(1)00110... the observer can only see a binary string with no other independent reference for time.

An observer must be able to create its own reference for time. If you say a string of 1s or 0s, it wuoldn't matter whether they were 1 long or 10,000 long, they would individually encompass ALL observations for the observer and no change would be detectable from unit to unit, as long as they remained the same.

So you could compress a sequential observation of:

111000001000011...

into an indentically perceived sequence of:

10101... (it simple repeats this "wave" forever and no subjective perception of spacetime is available ... such a view could be similar to seeing coherent light)

Now let's add a third symbol and see what an observation would look like over time:

112011100022001...

Again, we compress out the duplicates and get:

12010201...

Now because for subjective time to be present a continual differentiation is made. Each time a symbol other than the last one observed must be found. So in this case you could reduce the compressed trinary string into a subjective binary, at a lower dimension, by realizing you can't observe the same symbol twice, so only two possibilities exist for the next observation.

If we reinterprete the above string, subtracting the prior symbol and taking it modulo 3, we get:

1
(2-1) mod 3 = 1
(0-2) mod 3 = 1
(1-0) mod 3 = 1
(0-1) mod 3 = 2
(2-0) mod 3 = 2
...

We can rewrite the string in binary by subtracting 1, but now it has a realspace clock attached to it and is waiting to be interpreted as a first person view of spacetime!:

00001100..

(Is anyone else thinking of quarks at this moment? Photons are envisioned as being composed of two indivisible quarks with periodic wavelengths and other matter being composed of 3. The 3 colors of these quarks is meaningless except in terms related to other quarks and it's the combinations that define the subatomic particles)

This the information stream we perceive to construct spacial dimensions from and motion and time. I'll work on some more example of how to use this later.

So we came from a specific sequence of observation made by a single observer being swapped within a lattice of trinary values, to extracting a string of binary differentials over time and with an associated realtime clock for measurements. The above binary string could be laid out and rather directly interpreted as a string of 2 ones at a light speed distance of 4 from the origin etc.

NOTE: Because an observer only makes one observer per teq exposure, after extracting time, no more than one subjective time event per teq is possible and generally this will be much lower, depending especially on the local distributions of information within the lattice (areas where much of the information is the same will generate a lower rate of time in spacetime, though this needs to be viewed relativistically as no observer themself can determine this except by comparisons).

Further comments:

In a period of time, tc, we have an average motion on the lattice of one step.

If we first assume a system is composed of a random and uniform distribution of trinary values, then the probability for an individual particle to encounter one of the 2 other trinary values is proportional to the sum of the densities of the other two values divided by the total.

We should work with times, though and calculate the overall ratios of period of times for various combinations to occur. The average time to wait for a specific symbol is:

tc(symbol) = volume(system)/mass(symbol)

I'm going to call these three values A, B and C.

For time references based upon a stochastic cycles passing equally through all of these symbols, and I'll include the term g(system) as a reminder that this is made under the assumption of a uniform distribution in densities. So we have:

tc(A,B,C) = g(system,A,B,C)*volume(system)^3/(mass(A)*mass(*mass©).

g(system,A,B,C)=1 for a uniform distribution.

I'm going to assume this time constant is associated with mass and is likely 3 dimensional (just thinking out loud ...).

If we look at time constants between all combinations of two of these symbols we have three values for time, depending on which rates of interactions we're looking at:

tc(A, = g(system,A, * volume(system)^2/(mass(A)*mass()
tc(B,C) = g(system,B,C) * volume(system)^2/(mass(*mass©)
tc(A,C) = g(system,A,C) * volume(system)^2/(mass(A)*mass©)

Anyway, that's enough details, but there you have some references for time on larger scales in various dimensions.

We'll go back to simpler approximations to analyze Mass, Energy, Euclidean Space and Newtonian concepts next.

(Anyone think I can do it?)

To be continued ...

This post has been edited by StevenA on Aug 5 2006, 11:24 PM

Gravity and Galactic Orbits

Let's consider for a moment what we actually sense, related to gravity. We imagine a force downward but the pressure we feel is from mass pushing (and accelerating upward).

Gravity is assumed to be a counteracting force.

If you're Newton watching an apple fall from a tree, did the apple fall, or did the Earth rush up and hit it from below?!

If matter expands at the same relative rates (and relativity needs to focus strongly on scales of relative sizes and not just relative distances as distances define sizes), then no relative scales change for measurements and the sizes appear the same - the Earth, the apple and you, all increase in size proportionally, yet each is expanding at a rate proportional to its mass.

For brownian motion in a Hamiltonian space, all motions appear to have an average constant velocity away from a reference.

Each time step, a distance d becomes either d+1 or d-1. When we attempt to use a Euclidean metrics, we see this:

((d+1)^2+(d-1)^2)/2 - d = 1

We can get a larger scale of view of gravity by looking at distant galactic orbitals.

http://en.wikipedia.org/wiki/Galaxy_rotation_problem

So there's no more need to worry about trying to measure the speed of gravity or fnid gravity waves or explain dark matter etc. because gravity is not a real force, but instead an illusion created by expanding matter (and space).

This post has been edited by StevenA on Aug 8 2006, 12:06 AM

Galactic Arms and the Golden Spiral

With space and masses expanding over time, our relative observations of distances adjust as well.

As I stated earlier, our view of spacetime requires at least three fundamental particles (yes, likely similar to quarks). This allows a single reference to witness a division between the other 2 forms and truly acquire information.

Just for a very weak analogy, I'm going to call these

0 = vacuum
1 = space
2 = matter

And say interactions between 0 and 2 create matter, between 0 and 1 create space and between 1 and 2 create photons. (In this case our reality would likely be the interactions between 1 and 2 only)

Now if there's a slight local differential in these densities, we can imagine seeing a preponderance of on versus another. So you might say that again, for a relative measurements, vacuum could be much more dense than either space or matter locally, and space and matter can both diffuse into this vacuum over time. (Anti particles would exist as a complimentary lesser density)

If we're going to look at orbitting bodies, we need to determine what properties this expansion has.

To keep this simple, I'm going to limit things to observations for two bodies in circular orbit.

Because each body, A and B, is diffusing into space, let's define a time period, x, in which the expansion increases by a factor of e (natural exponent). So the widths grow proportionally to this.

width(A)=width(B)~=e^x

Then the distance must increase by this factor as well:

d(x)=d*e^x

The rate of change is the same (an exponent is it's own derivative):

d'(x)=d*e^x

At any point in time, the rate of this expansion in distance is proportional to itself, so the additional distance gained by perpendicular motion, per unit time, must be proportional to the distance out.

It's a golden spiral, and when we look at galaxies we see spiral arms.

This post has been edited by StevenA on Aug 8 2006, 01:54 AM

The Big Bang, Inflationary Period

I'll just toss out a coule ideas here for observations of the Big Bang.

If we assume the Big Bang represents a location in lattice space that receives an "impulse" of mass at a location, this mass diffuses over time.

We already know this expansion can occur faster than the average speed of light through space. Relative to light speed, each tc would create and approximate linear increase in diameter in realspace, though some improbable actions could potentially expand parabolically in terms of realspace distances.

But, the actual growth on average would be proportional to t^0.5, and these general characteristics match observations of the Big Bang

This would give a very rapid rate of change in the size in latticespace early on and slowly decay though appear to have linear growth, in terms of c, later one.

Now the additional term for relative measurements of time (depending upon the local density of time defining spacial interactions) needs to be considered here as well for what the current perceived velocities would be so as to actually correlate the rates to spacetime.

As densities decrease, local rates of time slow also (though not locally detectable), and follow a 1/t ratio for t^0.5 spreading. So this could give a t^1.5 characteristic to current observations as a t^0.5 spread is observed by a rate of time slowing at 1/t. Though if we're only seeing small fluctuations in a large background sea of particles, then this might not be the case as the overall level of interactions remains rather constant ... it depends on exactly what we're using to measure rates of time.

Hi Steven, I don't know if this is true, but how could one ever get out of the 'box' to see it expanding? It would all look the same to us here inside the box. We could eventually individually get larger than the present universe and never have a sensory/temporal idea of it.

But is it really an illusion? When I think of source, I think of a center that emanates. Einstein definitely saw gravity as not a primary source but as a resulting force, but one nonetheless, so shouldn't it have it's own defining mathematics that have relation to the mathematics of the forces/events that created this result? Einstein thought so even though he said it wasn't a 'real' force. I guess what you're saying is that gravity really is the transmission of a force caused by an inequality that rectifies, not the force itself. Are we looking in the wrong place to find a math that's friendly to the other three forces? Don't get too equational with me; I'm not a physicist.

Yes, that's correct if everything expands at the same rate, but if not everything does, or you can witness delayed and unexpanded events, then this isn't necessarily the case.

Now with diffusion, things actually don't expand at the same rate, and this seems the key. Smaller systems expand faster and this is why you can have an appear of lightspeed (or faster) motion on small scales yet have larger systems appear stationary and slower in their expansion.

If you look inside a solid diffusing, there are actually large numbers of interactions internally and the surface only expands much slower. Though there's still an overall expansion rate for the system as a whole, smaller units of it can expand faster and collide with neighbors constantly during this process. It's only the overall scaling component that disappears once you use relative measurements, so your rulers always appear to stay about the same size though it's diffusing and things internally are colliding.

Well gravity could be equated to a general differential in pressure in an area.

I wish I had some good graphics online, like Zephir, but if you imagine a a gaussian density in space, it's a hump that decays on either side. If you considered this like gas diffusing, there's a pressure differential on edge but not in the center or far from the edges. The differential pushes one direction on one side and in the other direction on the other side. If you expand this to a cloud of gas, you can find an area inside, similar to an expanding wavefront in 3 dimensions that's the pressure differential as this expands. The interesting part is that the inside is the same as the outside if you can only make local measurements - you only detect the edges and not the center - we see mass with similar characteristics - lots of waves but no "hard candy" center .

So yes, gravity could could be partly due to local pressures. We do see gravity lensing for example, but again, this could very well be from a distorted perspective of space and not from an actual force "pulling" on light.

Something to also consider is that local densities in space can affect the local rate of time. So you could see light as being slowed in a higher density instead. I admit I still would need to really do a lot more work getting a more detailed theory but overall I believe this Hamiltonian to Euclidean mismatch is the missing link in a ToE.

This post has been edited by StevenA on Aug 8 2006, 06:27 AM

Gravity - A seething field of gravitons or invisible forces or point to point, visible local interactions?

If you look at gravitational forces inside the Earth, they're seen as many invisible 1/d^2 interactions all passing invisibly through space. But what really happens inside the Earth? Do we need all these invisible interactions as dense gravitons etc. flying through space or should we simply look at it as expansion?

If you analyze the gravitational force going into the Earth, the equivalent force toward the center is the same (assuming a uniform distribution of mass) as removing all the mass further away from you - just like peeling off the layers of an onion.

So if you're 1 mile from the center of the Earth, the "gravitational force" you feel is the same as if you were standing on material, 1 mile in radius that was expanding outward - the material further out than that has effectively already passed you by (in reality these forces from further out diffuse and cancel except for a likely remaining compressional force).

Now if you take the view of gravity as an invisible force, then you're suppose to imagine every particle in the Earth is transmitting invisible forces (that still haven't been unified with EMF yet), and we're being attracted to all these simultaneously, or alternately you can see gravity as a network of visible, local, one to one EMF interactions.

Now the interface isn't unidirectional and there's a complimentary aspect of space diffusing into mass, so truly both views are legitimate, but I think keeping the perspective oriented as observations made from mass is best when possible.

This post has been edited by StevenA on Aug 9 2006, 11:26 PM

I've got to bump this thread again.

Look at how gravity operates and the ideas of a curved spacetime - the event horizon of a black hole is actually seen as what? It's a boundary racing out at light speed, though you could also view this as a bidirectional diffusion of mass outward at light speed, and a complimentary diffusion space into a mass at light speed - it's not a static boundary.

So let's say mass grows exponentially in size over time period of time - what happened during this period of time? It diffused over a volume of space proportional to its mass or gravitational force and you could see this as a flow of space into a mass with a rate proportional to it's mass.

Now if that flow is also diffused into a 3-D space, then this flow is dispered and would follow a gradient 1/d^2 (imagine sucking air out of some point in space - the flow of the remaining air is inward with the highest differential pressure being in the middle whether the acceleration is greatest).

But space itself is diffusing into the vaccum (and you need a minimum of 3 different components anyway to create the appearance of spacetime), so it also is encompassing more volume (imagine adding air to this space equally everywhere, while it's flowing into the "hole" where mass sucks the air out). So you have an expansion of space as well as mass.

If you look at the gravitational force (ignoring the scaling), it's:

g=m/d^2

So the mass creates a flow of space inward (or complimentarily mass expands outward as it's bidirectional) proportional to itself with a rate of flow that's diffused along any distance proportional to the surface area of a spherical shell through which it passes (the area of this spherical shell would be d^2 so 1/d^2 would be the flow).

There you go, gravity and it doesn't require a bunch of invisible particles but a much simpler point to point diffusion of space and mass by forces that are inherently largely chaotic for macroscale levels from a quantized and latticelike quantum space.

(P.S. Truly it should be the equivalent of a pressure differential diffusing through space at a density of the gradient of 1/d^2 so as to have a 1/d^2 force and not 1/d^2 flow and for air flows, there's resistance encountered so you have the equivalent of a drag that doesn't necessarily need to exist for space)

This post has been edited by StevenA on Aug 18 2006, 03:06 AM

steven
Though time could still be seen as flowing forward in this higher dimensional lattice, we can't see this flow directly. Instead we use various calculations and approximations to determine how long "time has been messing with" something, since we last looked, and we interprete this as a difference in time, or rate of change.

amrit
time is running into a-temporal space
not forward not backward, it is just running

as you experience time running through the mind "past-present-future" you see it runs forward
but that is a human illusion