The postulate of RST and RS2 is that motion comes in three scalar dimensions and three speed classifications: unit speed(1, 1/1), below lightspeed (V,s/t) or above lightspeed (E,t/s).
The overview of possible speed combinations can be ordered as a triangle in the shape of a tetraktys:
(111)
/ \
(V11) -- (E11)
/ \ / \
(VV1) -- (VE1) -- (EE1)
/ \ / \ / \
(VVV) -- (VVE) -- (VEE) -- (EEE)
The right side of the triangle can be identified as going from unit motion(111), to "Energy"(E11), to "Momentum"(EE1) and to "Mass"(EEE). I'm not so sure about labeling the other combinations, though (V11) is obviously "speed" and Larson identified (VVE) as "intermediate speed" motion and (VEE) as the "ultra high speed" motion.
Anybody having suggestions?
Motion tetraktys
Not a tetraktys, but a pyramid
The right side of the triangle can be identified as going from unit motion(111), to "Energy"(E11), to "Momentum"(EE1) and to "Mass"(EEE). I'm not so sure about labeling the other combinations, though (V11) is obviously "speed" and Larson identified (VVE) as "intermediate speed" motion and (VEE) as the "ultra high speed" motion.
You've kind of mixed apples and elephants here, interpreting E as t/s (mass) and again as s/t (speed range).
It is a quadration, not a dichotomy, since you have these conditions for non-unit motion (V=s/t, E=t/s):
If you stick V's and E's at the corners of a square base (16 possibilities), then you can work out the combinations, which will form a pyramid in 3 dimensions, 1 at the top, 4 at the next level, 9 at level 3 and 16 at level 4. You might recognize the pattern... n2--same pattern the elements use, but with the restriction of s=1 (material) or t=1 (cosmic).
You've kind of mixed apples and elephants here, interpreting E as t/s (mass) and again as s/t (speed range).
It is a quadration, not a dichotomy, since you have these conditions for non-unit motion (V=s/t, E=t/s):
- V > 1 (cosmic speed)
- V 1 (material energy)
- E 1 = 2-x (intermediate speed)
- V1 V>1 = 3-x (ultra-high speed)
- V>1 V>1 V>1 = cosmic speed (inverse low speed--unobservable since no dimensions are <1)
If you stick V's and E's at the corners of a square base (16 possibilities), then you can work out the combinations, which will form a pyramid in 3 dimensions, 1 at the top, 4 at the next level, 9 at level 3 and 16 at level 4. You might recognize the pattern... n2--same pattern the elements use, but with the restriction of s=1 (material) or t=1 (cosmic).
Every dogma has its day...
Are speeds above unity different from Energy?
I had taken this text and picture from Larson as the starting point:
The two-unit maximum range in one dimension involves one unit of speed, s/t, extending from zero speed to unit speed, and one unit of inverse speed, t/s, extending from unit speed to zero inverse speed. Unit speed and unit energy (inverse speed) are equivalent, as the space-time ratio is 1/1 in both cases, and the natural direction is the same; that is, both are directed toward unity, the datum level of scalar motion. But they are oppositely directed when either zero speed or zero energy is taken as the reference level. Zero speed and zero energy in one dimension are separated by the equivalent of two full units of speed (or energy) as indicated in Figure 8.
So that is apparently a wrong impression, but I interpreted that as both Energy being the reciprocal of Speed and Speeds above unity being equivalent to Energy from our material perspective. But that last statement is not true then?
The two-unit maximum range in one dimension involves one unit of speed, s/t, extending from zero speed to unit speed, and one unit of inverse speed, t/s, extending from unit speed to zero inverse speed. Unit speed and unit energy (inverse speed) are equivalent, as the space-time ratio is 1/1 in both cases, and the natural direction is the same; that is, both are directed toward unity, the datum level of scalar motion. But they are oppositely directed when either zero speed or zero energy is taken as the reference level. Zero speed and zero energy in one dimension are separated by the equivalent of two full units of speed (or energy) as indicated in Figure 8.
So that is apparently a wrong impression, but I interpreted that as both Energy being the reciprocal of Speed and Speeds above unity being equivalent to Energy from our material perspective. But that last statement is not true then?
Energy and Cosmic Speed
So that is apparently a wrong impression, but I interpreted that as both Energy being the reciprocal of Speed and Speeds above unity being equivalent to Energy from our material perspective. But that last statement is not true then?
The statement is basically true, but incomplete, because there are TWO sectors to consider, and therefore two speeds and two energies, depending on if you define speed as s/t (material) or t/s (cosmic).
Energy (t/s) and cosmic speed (t/s) have the SAME units of t/s, but they differ in the fact that energy is localized in space (for example, the electric and magnetic fields are spatially adjacent to their source), whereas cosmic speeds are non-local in space (widely distributed, as in cosmic background radiation and cannot be connected to their source.)
Cosmic speed is not normally involved in the atomic and chemical relations, so in Larson's early books, he tends to just analyze the material side of things and ignores the cosmic. But when you get to the astronomical realm, the cosmic speeds start to play a significant role because stars and galaxies operate in the intermediate and ultra-high speed ranges, and therefore produce non-local effects in space, such as the CBR.
When you get to life units (Beyond Space and Time), being an aggregate of m-atoms and c-atoms, the distinction between material energy and cosmic is substantial.
The conclusions you reached are perfectly logical, given the way Larson presents his material. But understand, they will change as you get further into the RS as the picture gets larger to include the cosmic. I'm hoping you can see the difference early on, as I didn't, and it took Nehru quite a while to clear it up for me!
In the RS2 world, the difference is that "energy = inverse" and "cosmic speed = conjugate".
The statement is basically true, but incomplete, because there are TWO sectors to consider, and therefore two speeds and two energies, depending on if you define speed as s/t (material) or t/s (cosmic).
Energy (t/s) and cosmic speed (t/s) have the SAME units of t/s, but they differ in the fact that energy is localized in space (for example, the electric and magnetic fields are spatially adjacent to their source), whereas cosmic speeds are non-local in space (widely distributed, as in cosmic background radiation and cannot be connected to their source.)
Cosmic speed is not normally involved in the atomic and chemical relations, so in Larson's early books, he tends to just analyze the material side of things and ignores the cosmic. But when you get to the astronomical realm, the cosmic speeds start to play a significant role because stars and galaxies operate in the intermediate and ultra-high speed ranges, and therefore produce non-local effects in space, such as the CBR.
When you get to life units (Beyond Space and Time), being an aggregate of m-atoms and c-atoms, the distinction between material energy and cosmic is substantial.
The conclusions you reached are perfectly logical, given the way Larson presents his material. But understand, they will change as you get further into the RS as the picture gets larger to include the cosmic. I'm hoping you can see the difference early on, as I didn't, and it took Nehru quite a while to clear it up for me!
In the RS2 world, the difference is that "energy = inverse" and "cosmic speed = conjugate".
Every dogma has its day...