Questions about interactions of motion

[cdannemi]

I have been studing RS and RS2 theory for some time, I would also post this question on the RS site, however it forums are down. It would be nice if I could get these questions answered both in terms of the RS theory, and the RS2 theory. The basic questions I have is, when do motions interact, and how do they interact, and I am really looking for the matematical answer to this question, because what I would like to do since I am an adept computer programmer is test my understanding of the RS & RS2 theories in computer simulations. Here is what I have been able to find in my reasearch form Larsons book "Nothing But Motion", Chapter 8:

In the two-photon case considered in Chapter 7, the value of 1/n is 1/1 for both photons. A unit of the motion of photon X involves one unit of space and one unit of time. The time involved in this unit of motion (the time OX) can be measured by means of the registration on a clock, which is merely the temporal equivalent of a yardstick. The same clock can also be used to measure the time magnitude involved in the motion of photon Y (the time OY), but this use of the same temporal “yardstick” does not mean that the time interval OY through which Y moves is the same interval through which X moves, the interval OX, any more than using the same yardstick to measure the space traversed by Y would make it the same space that is traversed by X. The truth is that at the end of one unit of the time involved in the progression of the natural reference system (also measured by a clock), X and Y are separated by two units of total time (the time OX and the time OY), as well as by two units of space (distance). The relative speed is the increase in spatial separation, two units, divided by the increase in temporal separation, two units, or 2/2 = 1.

If an object with a lower speed v is substituted for one of the photons, so that the separation in space at the end of one unit of clock time is 1 + v instead of 2, the separation in time is also 1 + v and the relative speed is (1+ v)/(1 + v) = 1. Any process that measures the true speed rather than the space traversed during a given interval of standard clock time (the time of the progression of the natural reference system) thus arrives at unity for the speed of light irrespective of the system of reference.

I understand here the two-photon case, but to a degree I don't understand the 1 photon + lower velocity case, or the case where there are to motions m₁, and m₂, that are moving at slower than 1/1. For the sake of argument lets say I have to motions m1, and m2, that are both traveling at the same speed, 1/2 c, or one unit of space per two units of time, as Larson would put it. Using Einsteins Equation, vnet = (v1 + v2)/(1 + (v1v2/c^2)), we get the net motion being 4/5 c. However using the arguments from NTB (RS theory), or what I know of complex number theory in various combinations (RS2 Theory), I cannot arrive at 4/5 c. There are many differnt thoughts I have about what the ressolutoin might be, but I feel that someone on this forum might be able to just point me in the right direction.



The second question I have is when does the interaction of motion occur, in a 1D Land Line it is very easy to see in princable, at least one possible answer, when to motions intersect the collsion occurs, the quesiton however is what about in true s^3/t^1? If the motion doesn't have some sort of "fatness" it would appear that collsions are unlikey.

[cdannemi]

I have continued researching this issue.... I found the answer to part (1) of my question here: http://www.reciprocalsystem.com/rs/satz/lorentz.htm, with regards to RS, I will work tonight on the math to seek a similar deviation for RS2.

That leaves the second fundamental question, notably that question is: when does a collision occur, especially in higher dimensions. Regardless the interactions of the motions can give me something to work with in so far as the basic building blocks that are needed for a computer simulation of these fundamental forces.

[bperet]

The second question I have is when does the interaction of motion occur, in a 1D Land Line it is very easy to see in princable, at least one possible answer, when to motions intersect the collsion occurs, the quesiton however is what about in true s^3/t^1? If the motion doesn't have some sort of "fatness" it would appear that collsions are unlikey.

From the RS viewpoint, "motion" cannot collide, simply because it is pure speed... think of it like stepping on to a moving sidewalk. You are walking 4 mph, the sidewalk is moving at 6 mph. When you step off the floor and on to the moving walkway, you are now moving 10 mph relative to the fixed floor, but still moving 4 mph relative to the walkway. If you happened to be orthogonal to the walkway, you would move in two dimensions, forward at 4 mph and sideways at 6 mph--until you took the next step and stepped off it.



It has the appearance of collision only because the two motions exist at the same, physical location. They are still independent motions because they are in two, different time regions. There are conditions when the speeds can cancel each other out--that is called "chemical bonding." It is like walking up the "down" escalator at the Mall. Each step up you take is countered by each step on the escalator moving down at the same rate.



If you want a computer analogy, look at virtual reality or ray tracing and the use of homogeneous coordinates. It describes the RS perfectly... to draw and orient an object, the [x,y,z,1] points describing the shape are multiplied by a 4x4 transformation matrix that contains rotation, translation and scaling variables to give a new points as to where the object is, in 3D space. The "points" are the "absolute locations" of the RS, and the transformation matrix is the "scalar motion."



The difficult part of the RS/RS2 is to think in terms of speeds, rather than "things." Larson ultimately ended up describing "motion" as "nothing but CHANGE in three dimensions", which IS the computer transformation matrix. Try thinking in terms of CHANGE, rather than WHERE.

[cdannemi]

Interactions as "two counter motions" is an interesting way of looking at it. I liked the way you described how simple harmonic motion could be the result of two polar motions in complex form, using Euler's formula. My background in Digital Signal Processing and Fourier Anaylis, made that part of the theory very palatable.

This does raise a lot of questions, but to keep our conversation focused, and on the hope that as I understand the basics, many of the questions will be answered, I will keep it to the most fundamental questions for now.

Due to the fact that my day job is programming Real Time Computer Simulations using modern hardware I am going to take the statements you have made about Homogenous transforms and run with them, as a result of I simply went from hitting intellectual wall to another please forgive me. For now lets simplify the argument and assume a universe that follows RS2 theory, but has one and only one motion.

I found this forum post this morning that you wrote (http://rs2theory.org/node/325). There are several things here that could be the input and the output. I assume that the 4x4 motion matrix M is constant, at least in this simplified universe, since there is no "outside force" to interact with. The only way I can see to get this to work is to plug in either the vector T and Cs, or S and Ct, and arrive at the "other" identity. If this is the case I will whip up this first program using WebGL and JavaScript so that I can refine my understanding of this simple universe.

[bperet]

I found this forum post this morning that you wrote (http://rs2theory.org/node/325). There are several things here that could be the input and the output. I assume that the 4x4 motion matrix M is constant, at least in this simplified universe, since there is no "outside force" to interact with.

I've been a programmer since the days of punched cards and I have played around a lot with this approach. Homogeneous transforms make a good model of how scalar motion interacts with coordinate space. It is a bit tougher to comprehend with coordinate time; rather than having points referenced from zero you have planes referenced from infinity. Computers just don't like numbers going to infinity, which is why HC does do a reasonable representation (though expect those "divide by zero" errors). But you need to be clear on what transforms represent.

Start with a basic understanding of "force," which only exists in physics because they do not have coordinate time. Force is not needed in RS2, at least as conventionally understood. Take a read of this topic: Force and Force Fields.

The only way I can see to get this to work is to plug in either the vector T and Cs, or S and Ct, and arrive at the "other" identity. If this is the case I will whip up this first program using WebGL and JavaScript so that I can refine my understanding of this simple universe.

The transformation matrix represents speed. The identity matrix represents unit speed, the progression of the natural reference system. What the transform does is convert "absolute locations" into "relative locations"--conceptually the same as hopping in your car and hitting the gas pedal, and ending up at the end of the driveway. EACH location has a identity matrix to represent the speed of motion at that location. When a non-uniform motion is introduced, then you're going to end up with overlapping relative locations, and it is at those points where you multiply the transforms together to get the net motion at that location. Remember the RS is a discrete system... locations are integer coordinates.

Good luck! I'll be very interested to see what you come up with.

[cdannemi]

Looking at the post, http://rs2theory.org/node/325, I see that you have real numbers, and four complex components, i, j, k, and w. I am not familiar with this hyper complex number system, as it has one additional term from a quaternion. What are the identities for multiplying various combinations of the hyper complex system together. Eg in quaternion the identities are.


Quaternion multiplication

×	1	i	j	k
1	1	i	j	k
i	i	−1	k	−j
j	j	−k	−1	i
k	k	j	−i	−1

[bperet]

Looking at the post, http://rs2theory.org/node/325,...

I never did get that to work the way I wanted it to. The problem I ran into was that homogeneous coordinates contained 4 real components, whereas the quaternion had 1 real + 3 imaginary--which worked better. The 'w' was an attempt to introduce an imaginary component into the homogeneous vector as the scale, to make it operate as the opposite of a quaternion. That way, there would be a linkage between the homogeneous vector and quaternion--the vector containing an imaginary scale component; the quaternion containing a real scale component (1 in your matrix).

What I did was make each element of the transformation matrix a complex number, so that the homogeneous vector and quaternion could be represented in a single transform. (I had to build my own vector and matrix classes to handle the complex functions.)

The idea worked well, because the atomic rotations could be represented by the quaternion (based on one of Nehru's papers), and it could be positioned and moved about in space by the homogeneous coordinates. Ran into problems when I had to model the electric rotation of atoms and particles, because it was a rotation in space--not in time--and I could not use the 3rd element of the quaternion since it was on the wrong side of the fence--would have to impose a rotation matrix using the homogeneous coordinate side (real components) to get that electric rotation, which was not correct. That goes back to introducing the 'w' with an imaginary component--as a rotational operator in the 'real' side of the homogeneous coordinates, it could be used to represent the electric speed.

But as I mentioned, I never got it to work the way I wanted it to. Since then, we have found that:

• The column vector represents a location in space.
• The quaternion vector (row vector in node/325) represents a location in time.
• The transformation matrix IS the "motion" of Larson's system.
• The atomic rotation is the "scale" diagonal of the transformation matrix, and when set to an identity, is uniform motion.

The problems I ran into were:

• Particles only need two magnetic rotations, i and j. "k" is never used because you can only have two magnetic rotations in a double-rotating system.
• Atoms need two, double-rotating systems, which means 4 rotational operators in one transform, or two, separate transforms at each location. Of course, that begged the question of "why stop at 2?"
• No way to easily model the spatial rotation or vibration, since the Euler relations only work in time.
• Since transforms are not commutative, and many transforms can be present at any given coordinates in space or time, what order to you use to assemble them into a net motion? Outside of the two, double-rotating systems you can also capture photons, electrons and neutrinos--a lot of transforms at a single location in space.

We did find that rotation in time, being based on planes, tends to form geometric structure--faces of Platonic solids, wrapped in shells around each other as complexity increases. That shell ordering may give a clue as to how to sequence the transformations.

The only identities I used were the basic, complex number ones--but placed in array elements. All the matrix operations had to operate on complex quantities. A complex number can also be represented as a 2x2 matrix--was going to look into that to see if it would make the system more effective, but never got around to coding it.

[cdannemi]

At this point I am just going to put something together. Once I have some javascript code ready to go, I will put a link up here so that you can help steer me in the right direction. I will definitly split up the code into parts Matrix Math vs. Actual Simulation code. I just feel like I am at the point where I can't bang my head against the wall much more, it time to just code.

[cdannemi]

So I have coded up the first module, its an abstract implementation of Hypercomplex Algebra's. Bperet based on your experience it appears flexibility over speed is critical you need something that you can just adapt and change rapidly is key. This class reflects that, you can see the code on a temporary website I have for this... http://dannemiller.routesoft.net/rs/hypercomplex.js.

The question is looking back to old post we where talking about where you had a Time Vector T, a motion Matrix M, and a Space Vector S in the form of TMS = 1. The problem I have is how do I solve for S or T, since M is locked up? My understanding of Linear Algebra seems to prevent doing anything here due to the fact I would need to invert T or S, but you cannot because vectors are not "square matrices" and therefore don't have an inverse, or am I just missing something simple?

[bperet]

Ah, yes. That brings back some coding problem memories when I was attempting it--division does weird things, since you can end up with multiple answers and have to resort to probability.

A vector can be expressed as a square matrix, by creating an identity matrix of appropriate dimension, then filling in the vector components in the "translation" row or column. Coordinates are just translations (offsets) from the zero datum, so it remains valid. Just remember to normalize back to unit scale, as the coordinate system is Euclidean--all dimensions must have an absolute scale of 1.0.