lattice timing

[AntonioLao]

The reality of local infinitesimal motion (LIM) allows the definition of a quantum of time independent of the quantum of space-time. If the quantum of space-time is represented by two linked circles then the quantum of time is represented by one of these circles. The other represents one dimensional quantum of space. To represent 3 dimensions of space would require 3 spatial circles. However, three space-time quanta give three quanta of time and three quanta of space. All linked together.

Lattice timing can occur if and only if groups of temporal circles of the space-time continuum are oriented in the same arbitrary directions. If all directions are pointed inward to a particular point then a contracting singularity will eventually occurs at time zero. If all directions are pointed outward from a particular point then an expanding volume will continuously increase toward time infinity (in a certain sense this also points to time zero). If all directions are randomly oriented then they form many states of quantum vacuum fluctuations where and when no special direction is preferred giving a new form of sub quantum uncertainty as the square of DE×Dt³h or (DE)²×(Dt)²³h² where DE is the measureable energy uncertainty and Dt is the corresponding measureable time uncertainty. Equivalently, (Dr)²×(Dp)²³h² is also true in position-momentum configuration space. Both imply h²=4p²L(c)²/G² where L is Planck length, c is light speed, and G is the universal constant of gravity. This extremely small value suggests that square of energy is truly a sub sub-quantum phenomenon and for all practical purposes is zero.

[mkirkpatrick]

How "local" is LIM? Is not motion ubiquitous?



regards michael.

[AntonioLao]

Infinitesimally local near the region of Planck length.

[SteveA]

Here's an interesting correlation. You mentioned the relativistic measure of energy, including a momentum term as:

E^2=p^2c^2+m^2+c^4

And you've also mention 3 Planck scale loops at an intersection.

Let me add in Rule 110 http://en.wikipedia.org/wiki/Rule_110

I won't bother to go in to great detail unless you'd like me to clarify, but Rule 110 is a 1 dimensional automaton that's capable of universal computation (with the correct I/O mapping it could emulate a program on any other computer).

Each element in this space is identical, except for an internal binary value stored at each location. The computation each element performs is a function of its internal state as well as it's 2 neighbors, so we could see each element as performing a computation in 3 dimensions - itself and two neighbors, though it's all connected into a whole over time.

The rule can be written in terms of a truth table:

000->0
001->1
010->1
011->1
100->0
101->1
110->1
111->0

We can write this in a sum of products form as:

Q(t+1)=~A(t)*~Q(t)*C(t)+~A(t)*Q(t)*~C(t)+~A(t)*Q(t )*C(t)+A(t)*~Q(t)*C(t)+A(t)*Q(t)*~C(t)

I'll remove the subscripts to shorten the representation:

Q'=~A~QC+~AQ~C+~AQC+A~QC+AQ~C

We can rewrite this in complimentary terms as:

~Q'=~A~Q~C+A~Q~C+AQC
~Q'=(1-A)(1-Q)(1-C)+A(1-Q)(1-C)+AQC
~Q'=(A+(1-A))(1-Q)(1-C)+AQC
~Q'=(1)(1-Q)(1-C)+AQC
~Q'=1-Q-C+QC+AQC
~Q'=1+(-Q-C+QC+AQC)
~Q'=1-(Q+C-QC-AQC)
~Q'=~(Q+C-QC-AQC)
Q'=Q+C-QC-AQC
Q'=Q+C-QC-AQC
Q'-Q=C-QC-AQC
dQ=C(1-Q-AQ)
dQ=C(~(Q+AQ))

So this gives the equivalent of a probabilistic force applied in opposition to the current state of a cell in space, Q, dependent upon the state of its neighbors A and C.

Now let's take your E^2=p^2c^2+m^2c^4 and rewrite this as:

E^2=c^2(p^2+m^2c^2)

Notice we could rewrite this as f(x)=x^2 and have:

f(E)=f(c)(f(p)+f(m)f(c))

And then correlating this against the equivalent probabilistic force, velocity or acceleration (it's a quantum unit of change) on a cell in Rule 110:

dQ=C(~(Q+AQ))

Notice that if the direction along this 1-D axis is indeterminant, a superposition of A and C can appear to occur. We could create the appearance of superimposed dimensions by by "XORing" A and C together or using sum and difference terms for A and C. This could allow for a 1 to 1 mapping between components of this relativistic energy and a Rule 110 automaton using superimposed quantum states as the terms.

In that case the 3 loops would end up being chain links (fractally unfolded from potentially a single process applied to a single dimension of space - parallel processor or single processor?).

[SteveA]

Look at how much physical phenomenon such a 1-D string can be mapped to (especially if we assume there's a superposition between both directions along this line that makes it difficult to determine from which direction information has arrived).

1) Computations occur at an intersection of 3 units of information each in a dimension. So we have the potential for the perception of a 3 dimensional space.

2) If one of these elements is considered to be a representation of ones own state, then this leaves 2 dimensions observable regarding external objects (and this could agree with a model of onesself interacting with 2-D surfaces of interaction).

3) If both ends of this line are superimposed upon each other, then the central point of a computation could appear as an endpoint and as the interior of an object with a surface of interaction that can be in one of 4 states.

Notice also that every position in space connected to this "self" endpoint could appear to contain 1 of 4 elements because at any distance from the origin there are 2 values superimposed upon each other (consider the correlation here with DNA as a 1-D strand of objects in one of 4 states connected to a physically unmeasurable "self" - DNA could be the equivalent of a conscious nervous system)

4) If the movement of information in both directions is superimposed, then we do not have coherent motions in a single direction, but a spread of possible distances or times that can be interpreted similar to the Uncertainty Principle in terms of discrete Planck units of time.

5) The uncertainty of the position of this superimposed distant information could be seen in terms of 2 components - the Poisson bias as a coherent light speed component and the remaining Gaussian as a material expansion (gravity).

6) If this thread/string was seen as curled or bent in some context, we could project this as independent components of a field by computing a correlation coefficient - a simple projection would be to map changes in state of neighboring elements as electrical or magnetic fields.

Due to the superposition of these directions, a cyclic interaction between these two components would appear to exist - information moving "away" from an origin can also appear to reside in space that has information moving back toward the origin, hence resonant properties can appear to exist on larger scales with increasing wavelengths.

There are more correlations that could be made between this model and physics but that's enough for a good start.

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Consider this as well - let's assume that a multiverse interpretation of quantum mechanics is correct - well which universe would you happen to be in? It would appear that if there exists free will, then the universe you happen to be interacting with is the one that describes the rules you happen to be using at any moment - how's that for Karma?

Rule 30 is in many ways even better, though it's more complex: http://en.wikipedia.org/wiki/Rule_30

[AntonioLao]

Are we really just 1 dimensional simulations of 1's and 0's? However, I would like to replace the 0's with -1's since both 1 and -1 are exclusively found in all orders of symmetric Hadamard matrices. See http://en.wikipedia.org/wiki/Hadamard_matrix and http://mathworld.wolfram.com/HadamardMatrix.html

[SteveA]

Are we really just 1 dimensional simulations of 1's and 0's?

I don't think so. These properties are just the concrete kernels that to not change, or the figurative landscape upon which the rest moves relative to, but it appears impossible to embed time within a logical structure. It's often imagined that we can have logic equations that describe an evolution over time, but there's actually nothing in the logic that allows for anything to change without it becoming untrue or indeterminant.

Also, the binary properties do not very well characterize the properties that arise over quantities of space along this dimension (in which case we have various physical and geometric forms with various properties similar to resonance within a space).

I see this structure more as an infinite fractal tree of all possible laws and rules that could be constructed, yet nothing experienced in time ever precisely describes it, nor does this logic describe the qualities and sensations of perceptions. So it's just a universe language describing all possible relationships that could exist stably over time, but ironically it can't represent a single language because, even after reading an entire book, there would be no certainty as to what it meant because it would still have a potentially unlimited number of contexts for languages in which it could have been written - something that can do everything cannot even do a single thing because there are an infinite number of contexts for what has been done and so it did an infinite number of things (even if that infinite is relatively infinitesimal to itself - just like human fingers cannot pick up a specific electron, though they can pick up many).

Also, the qualities of conscious perceptions, though potentially conveying discrete information, are not themselves describable in terms of discrete quantities - for example, we might be able to describe an intensity and color red as specific ratios of specific wavelengths of light, the conscious perception is not of x number of photons of a wavelength y, but of a quality that appears to possess arbitrary and inexplicable characteristics - someone could show a flashcard of some color or play some music to thousands of people and it may be that none of them perceive the experience the same, despite the fact that they're all sharing some of the same information content.

The human body and/or the universe may ultimately be much like a massive internet, but it doesn't appear capable of doing anything without "something else" beyond it, nor does its structure appear capable of describing anything beyond itself.

However, I would like to replace the 0's with -1's since both 1 and -1 are exclusively found in all orders of symmetric Hadamard matrices. See http://en.wikipedia.org/wiki/Hadamard_matrix and http://mathworld.wolfram.com/HadamardMatrix.html

The 1 and -1 work fine as well.

I've wondered if there might be some efficient convolution type techniques using Hadamard matrices. I've noticed that for parity computations we can do a matrix multiplication for basically "free", though this technique doesn't extend beyond binary values ... if we could at least use 3 symbols, there would be very simple and extremely fast ways of doing matrix multiplication (which would be a technological revolution with countless applications, and these quite likely do exist but there are lots of difficulties in either generalizing upon them to arbitrarily large sizes or getting a general form to be efficient on realistic scales of data).

A couple links if you're curious http://surj.stanford.edu/2004/pdfs/kakaradov.pdf and here's a more theoretical pursuit http://arxiv.org/PS_cache/math/pdf/0307/0307321v2.pdf

[AntonioLao]

But if all the symmetric Hadamard matrices of any arbitrary order are all singular their products or nth powers provide extractable integer factors making a multiplication algorithm unneccessary.