Discussion concerning the first major re-evaluation of Dewey B. Larson's Reciprocal System of theory, updated to include counterspace (Etheric spaces), projective geometry, and the non-local aspects of time/space.
according to E = mc^2, energy is inversely related to time. Is Larson at odds with Einstein's equation or am I just misunderstanding? ...mass being inversely related to space
Energy (t/s) is inversely related to speed (s/t), not time or space independently, since neither can exist indepenently. Einstein's equation just says that mass is analogous to 3-dimensional energy, since 'c' is a speed: t/s = t3/s3 (s/t)2.
after motion is initiated, all that is required is gravity and not the spring?
Even if there is no friction, there is still a constant deceleration being provided by gravity, so it will come to a stop without a force to counterbalance the deceleration.
So if t/s = t^3/s^3 * (s/t)^2 and s/t=Unity, then the equation is 1 = 1^3 * 1^2 since t/s must also be equal to Unity. So everything identifies with unity? I'm now really confused. Where am I going wrong? Is not t/s also Unity. If space is expanding, then entropy is increasing, mass is decreasing and energy must be increasing by E = mc^2 ( assuming light speed is constant). Can you clarify this for me?
With respect to the pendulum; you are absolutely right. So, what we can conclude here, if we may extrapolate, is that gravity controls the motion and the spring upholds the motion. Would you agree with that? This suggest that current scientific thinking is wrong from Newton down, and that creation is , in fact, continuous and not just a product of a 'push of the hand' at some time in the past. What does Larson say regarding this?
If s/t = Unity, would that not mean that E = m * (s/t)^n where n can be any integer? One to any power is one, but, then this could not be. Can you see my confusion? Maybe I am overlooking something. The unity datum is troubling for me because I have concluded that space must be 4 dimensional. An expanding cubic space is by definition 4 dimensional, not 3, so I do not see a one to one correspondence with 3 dimensional time. I agree that they are inseparable and reciprocal, but it is like apple and oranges. I referred peviously to time as a measure of space but the reverse cannot hold. Space could not contain 3 dimensional objects unless it was 4 dimensional. So I think that the universe requires 7 dimensions to exist, not 6. I don't agree with Einstein about many things but E = mc^2, I think, can be written in stone even if one would not agree on light speed being constant ( remember that I do not think that c is a constant). Whether c is constant or not is not the point here, however. The point here is that Larson's version of the energy equation would allow c to be raised to any power. Please tell me where I'm going wrong.
Your conclusion that space is 4-dimensional is an Ad Hoc assumption. Most likely it is the result of thinking of "objects" suspended in 3-dimensional space. There is another explanation that you are overlooking, namely that the objects themselves are composed of knots of space and time. This is known as background-independent theory - a prerequisite to getting out of the rut of the legacy theories.
When you call time and space as "apples" and 'oranges", you seem to imply that they are completely unrelated. If they were so, then the univese would be 6-dimensional, indeed.
Namely: 3 dimensions of apples + 3 dimensions of oranges.
In other words, if the 3 space dimensions were indeed purely independent of the 3 time dimesions, then the universe would be 6-dimensional. But it is not so, because by definition, dimensions must describe TOTALLY INDEPENDENT magnitudes. In RST and RS2 time and space are codependent as aspects of one motion and that simple relation destroys their independence and consequently prevents them from qualifying as separate dimensions.
You should also beware of the difference between "dimensions" and "directions". In geometry each dimension is totally independent from the others and each dimension has two directions.
Obviously my comments require additional explanations. First, 4 d space is not an ad hoc assumption, it is a deduction. The postulates of projective geometry used in RS2 require a toriodal topological universe, a deduction. Inverse relationships abound in nature. Larson's very own theory is based on this and this we can agree on. The graph of the inverse function is a familiar geometry form called a hyperbola. A hyperboloid is the 3 d representation. I refer you to hyperbolic geometry web sites for visuals of this figure. The geometry of this space bounded by this hyperboloid is x^2, y^2. Imagine two mirrors intersecting at right angles. The mirrors in Plato's Timaeus. This geometry is not yet explored. We can find a suitable equivalent to study by representing the intersecting mirrors in a cube. The cube is 3 dimensional. An expanding cube, as in expanding space, is a hyper cube and is 4 dimensional. Imagine a tesseract with expansion of its 8 corner points radially from its center. There is my 4 dimensional expanding space. Objects are not suspended in space, they are mass created in space by the inversion of space at points which become centers of rotational motion. This motion is inertial by definition and, therefore, are accelerated motions. If these are the 'knots' you are referring to, well then ok. This rotational motion is toroidal and I see where you could describe the spiral motion in a vortex as knot-like. I agree, legacy theorys must go, but they must be replaced with sound ones.
The apples and oranges metaphors was perhaps unfortunate because I did not mean to imply that space and time were not related, just not related as Larson proposed. Incidentally, apples and oranges are both fruits and they are both toroidal structures.
I propose that time and space are related, inseparable, as I have said in previous post, and related inversely. No disagreement there. BUT , there relation is inverse square. Instead of s/t, they are related by s/t^2. This is what I was referring to in my metaphor. My objection is the unity datum. This is why. Take Einstein's equation E = mc^2. This is in reality a partial differential equation and only properly written as
dE/dt = dm/dt * c^2.
This partial differential equation relates to motion because of the time element. Try and substitute Larsons units in this equation and see what you get. Remember, this is an equation of motion and if Larson's motion units are valid they should make sense in this equation. Larson plugged them in many times and Bruce did that for us in the previous posts.
d/(t/s)/dt = d(t^3/s^3)/dt * (s/t)^2.
s/t=unity
t/s=unity
substituting,
1/dt = 1^3/dt * 1^2 or
1 = 1 * 1
This is what is called 'identity'. There is no motion here. Space expansion can be scalar but time has direction, and that direction if FORWARD. That is why your statement cannot be so. Time is a measure of space but space cannot be a measure of time! Space can expand, Space can contract, your lungs and heart do this all the time. Time, one the other hand, can only accelerate and decelerate, but it can only move FORWARD. Which one is the apple and which one is the orange, I dont know. If they could be measured by each other, we would have unity, and unity by definition, is NO MOTION!
Bruce says that the 'fulcrum' between force and acceleration is mass. This is not true. The fulcrum is the center the inertial mass. The center is motionless and therefore is the only candidate that qualifies as one would define fulcrum. You may also say that time is not a vector, and that is correct , but I did not say that. I said it has direction whereas space does not, only expansion/contraction. Time can be described as 3 dimensional but circular. Time is NOT an arrow , but a curve. That curve can better be visualized as a spiral. The spiral always moves forward in three dimensions, like a corkscrew. The special feature of this spiral is that it can get larger (same as deceleration or dilation) or its curvature can get more acute ( same as acceleration ). This it does coordinatly with space in an inverse fashion. And that is how you relate time and space. As space expands, time decelerates by progressing in ever larger corkscrew-like. Conversly, as space contracts time will NOT reverse, BUT it will accelerate by ever tighting the radius of its corkscrew. It is a curious thing that while time does not reverse its forward direction it can turn to the opposite 'inward' direction from an 'outward' direction to follow space in contraction without reversing. Imagine drawing spirals on a sheet of paper. You can start at the bottomed the sheet and spiral up the page then spiral down without ever lifting your pen off the paper or reversing the forward direction of the pen. Because in this way time can be the coordinate associate of space, be inseparable, inversely related and participate in expansion and contraction of space. This eliminates the need for Larson's ad hoc 'cosmic sector'.
Essentially what I'm saying is that one can look at space as a cube with a sphere inside where the sides of the cube are tangential to the cube. The sphere is curved time and the cube is rectilinear space. They share a center; the cube can expand and contract; the sphere can coordintely rotate and expand and contract, keeping touch with with cube tangentially. This is how I see tome and space relating. No need to see time in a coordinate system just like space. Time can more properly be seen as circular and space cubed (coordinate) yet retain all of Larson's relationship, avoiding the unity datum which does not allow for motion. Not really apples and oranges but cubes and spheres in motion, rotational and respirational.
Motion squares the circle. Likewise, motion cubes the sphere. Here I will refer you to Mathis's paper on Pi is equal to 4. He will show how kinematically, pi is 4 and an orbit ( dynamic circle) of radius 1 has a distance to time ratio ( velocity) equal to 8. Exactly the perimeter of the square that lies tangential to it. Very good presentation by Mathis.
If you understand what I'm getting at then we can discuss further what I think Larson has really discovered. He is actually describing the SOURCE of motion, not motion itself. He even called it by its name, UNITY. He was pointing to the fulcrum itself, which is motionless but without which there cannot be motion. Larson was defining a center where space and time are unified. This is just one derivative away from actual phenomenal motion; we call it acceleration. But don't call it unit acceleration. This motion is motion by virtue of its disunity. s/t is unity but not motion. s/t^2 is motion. Unity is the ONE, the source, the fulcrum, the unchanging stillness. Larson even equated s/t with light speed, but unified space-time is 'still' light. Speed is a scalar quantity and velocity a vector, but neither should be in our vocabulary when addressing the physical world. They are merely useful ideas and should remain in the realm of ideas. Therefore, light that we see is moving light, accelerated light. It is divided light because space and time had to be divided for motion, and thus the universe, to exist. That is why there is no speed or velocity in the physical world. It exist only in the ideal, the realm of concepts which is prephysical. Manifestations of motion proceed from these ideas into the world we can perceive. THIS has been the source of all the confusion in legacy physics. Velocity has been given a phenomenal reality. Newton was the instigator of this error and all others followed. Newton treated light as infinite in velocity, Einstein said it was a constant. Neither is correct. We must not allow Larson's theory to follow the same primrose path when a simple correction at the foundational level will avoid those pesky ad hocs that he was so critical of. Look at how the theory was improved with projective geometry. Larson had no excuse on this one either because PG had been around for centuries and as an engineer he must have encountered it in his formal studies. He just did not employ it, being satisfied with Euclidian plane geometry. As an engineering student in the mid seventies I spent many a tedious hours in engineering graphics with my t-square and triangles rotating objects in space on my two dimensional board using the techniques of projective geometry. This of course was before computers, which is what brought about a revival of this once forgotten technique. But engineers never forgot it and used it all the time before computers made the old graphics obsolete. In my humble opinion I think the theory deserves another tweaking and RS2 is a great platform to stand on. You guys know it best and I wish you well.
I wanted to correct something about the pendulum in my conversation with Bruce as to why the pendulum winds down, even if friction is discounted. I can' t believe I missed seeing this one even after endless annoying hours solving heat transfer and thermodynamic problems as an undergrad. The answer is ENTROPY. In expanding space, entropy is increasing and this means that mass is decreasing in the system. Time is decelerating as light is accelerating. Energy must be added to the equation to balance it out since light carries a greater weight in the equation because it value is squared. Another advantage that engineers have in their education is a grounding in applied math. Generally speaking, partial differentials are stressed more in engineering curriculums than in physics or math departments at universities. Good luck on your progress. Time is of the essence because I get get the feeling that the old paradigm is fast crumbling. Larson's theory is first in line to take up the mantle, pick up the dropped baton and run with it.
So if t/s = t^3/s^3 * (s/t)^2 and s/t=Unity, then the equation is 1 = 1^3 * 1^2 since t/s must also be equal to Unity.
You have your superscripts wrong. If you are considering t/s to be a positive power, then s/t would be negative:
11 = 13 * 1-2
If space is expanding, then entropy is increasing, mass is decreasing and energy must be increasing by E = mc^2 ( assuming light speed is constant). Can you clarify this for me?
Time is also expanding, so speed does not go from 1/1 to 2/1, but from 1/1 to 2/2. Entropy, mass and energy remain constant when both numerator and denominator of the equation are considered.
is that gravity controls the motion and the spring upholds the motion
That is a matter of perspective. It could be just as easily said that the spring controls the motion, and gravity upholds the motion. Observer principles must be accounted for. How do you know that the pendulum isn't STILL, and it is the Earth that is swinging in SHM along with the observer?
The unity datum is troubling for me because I have concluded that space must be 4 dimensional.
Based on my recent update using Mathis' information, I would conclude that projected motion is 4-dimensional (the underlying, scalar motion is still 3D) and that tetrahedral geometry is a better representation of this structure. Unlike the cube and the sphere, the tetrahedron is self-dual; the geometry is the same even if you yank it inside-out, so it's applicability to either space/time (Material) or time/space (Cosmic) is uniform. The illusion of cube and sphere would be an artifact of our consciousness normalizing the tetrahedral system (outsides = linear, insides = polar).
So I think that the universe requires 7 dimensions to exist, not 6.
That is only true for atomic structure, not the vacuum of space between atoms. Larson states that atoms are comprised of two "double-rotating system." Each double-rotating system has 3, independent dimensions of motion associated with it. Therefore, the atom is a 6-dimensional rotating system (Nehru discusses this in one of his quantum articles). When that atomic motion is scaled by the clock function during projection, the atom (any mass) requires 7 dimensions to accurately represent it.
