The Painted Pony

THE PAINTED PONY
by du gabriel

In a 1950 letter to Shroedinger Einstein said,
"You are the only contemporary physicists, besides Laue, who sees that one cannot get around the assumption of reality - if only one is honest. Most of them simply do not see what sort of risky game they are playing with reality - reality as something independent of what is experimentally established."
Present relativists have abandoned Einstein's mature judgement in favor of the Minkowskian doctrine that reality "whateverthatmeans" (mantra 1) is nothing but the measurements themselves. This posting will now prove that Einstein was right {this time}.
We will here discuss a device, "the painted pony" (tpp), designed to internally measure the absolute velocity of a single system - a spacious chest - existing all by itself in Newton's hypothetical metrical "empty space" (which is accepted herein purely for heuristic purposes). There has been an ongoing argument as to whether this device would work. I will here describe the original device and Brian Jone's "Kiss-tpp" version, and then review the arguments. Then I will present the device (tpp 2) that accommodates and refutes the relativists' arguments.
Although Maxwell's laws were based on a universally stationary ether as as referent for the actions and speed of light, we will here employ Einstein's hypothesis that "the velocity of light is a definite constant c in empty space". (The mathematics is the same either way.) By the galilean principle of relativity, a ray will therefore pass a system moving at v in empty space at c-v in the direction of v and at c+v in the opposite direction. As measured by such a system the relative velocity of such rays, c', should differ from c.
When experiments failed to detect such a variable value, the goal of physics was to show how Maxwell's laws, in which c = 1 in a universally stationary aether, would hold good in all systems regardless of their states of motion. The answer of the moment is based on the physics embedded in the Lorentz Transformation Equations (LTE) that resulted: Clocks of a moving system run slow by q and lengths in the direction of motion shrink by
q = sqrt(1-v²/c²).
Minkowski, thus his followers, denied that such physical deformations occur, "except as viewed by a differently moving observer" (mantra 2). Their denials will herein be proved false.
Whereas such physically real length and rate deformations will allow a moving system to measure the round-trip relative velocity of light as c, they will not by themselves let c' = c in a one-way trip. We will therefore accept Poincare's pre-1903 method of setting clocks as another step required to reach his LTE thus satisfy his 1903 "Principle of Relativity" that the laws of nature (our equations) are to remain valid in all systems regardless of their variable velocities in empty space. Poincare' pointed out that if a ray is sent from clock A to clock B of a moving system (Earth) and back again, and if clock B is turned back by vx/c² seconds, the speed of light will be the same in both directions as measured by such clocks. He stipulated that clocks "so adjusted" would not, of course, remain synchronous.
Einstein used Poincare's light-signal method to set clocks; but changed the definition of "synchronous" to mean that ONLY such clocks are thereupon synchronous. Because they aren't really synchronous, for semantic veracity I will call clocks set that way "esynched".
The painted pony takes advantage of the fact that esynched clocks have identical simultaneous settings on lines perpendicular to the system's absolute motion and maximum -vx/c² offset "local times" compared to one another in the direction of v, where x is the distance between two such clocks as measured by the moving system itself and v is the unknown absolute velocity ("abv") of that system in the X direction.
The device lets a rod, with contact buttons at ends A and B, spin on an axle mounted perpendicularly through the center of a stationary circular plate. Clocks mounted around the plate's perimeter are repetitively esynched. Each time end A or B touches one such clock, the "time" of that clock is reported to a CPU; which then plots the "times" of diametrically opposite clocks when A and B are there. The directions of greatest and zero differences (the "offsets") in settings of such paired clocks is then calculated by the computer, which prints them out via perpendicular lines on a monitor screen attached to the stationary plate.
Relativists argue that as viewed by a differently moving outside system taken as "at rest", the net velocity of elements of the spinning rod would differ, wherefore so would the amounts of viewed Lorentz contractions; wherefore the rod would appear curved. Hence, their argument asserts, due to this curvature the two ends will not touch diametrically opposite clocks simultaneously; hence would not accurately plot the directions of greatest and least offsets. The relativistic argument continues: Since the spinning rod's origin is "at rest" in the chest - taken as the "rest frame" of the device - the observers in the chest would not see nor be able to plot any such curvature, thus could not use it to calculate their own abv.
In his "KISS-tpp" postings Brian Jones (BJ) suggested that prongs attached to the ends of the spinning rod (or at the ends of a diameter line line drawn upon a spinning disk) could be used to START the perimeter perimeter clocks of the stationary plate. This would start corresponding clocks at the instant the ends of the straight rod touched them; wherefore such clocks would be truly synchronous rather than esynched. BJ suggested that the observers in the chest could then send one-way light signals from the first of two oppositely located synchronous clocks to the other, and time the initial and arrival "times" - which would show that the rays travel at variable velocities in different directions relative to the inertially moving chest. From the discrepancies between c=1 "in empty space" and the values of c' so plotted, the observers could instantly calculate their own absolute velocity.
The relativists raise the same objection as above: When the rod (or if so chosen, the disk) spins, it will distort because elements of its body have different overall velocities as viewed by an outside observer. That would cause a curvature of the line and thus a displacement of end B compared to end A, wherefore they would not touch oppositely placed clocks simultaneously to thereby true synch them. Taking the spinning disk-line as curved_{mantra
2}, they insist that because of that curvature the spinning disk would actually esynch the clocks, whereupon the mechanism would fail.
BJ and I agree that in terms of empty space as referent, this would physically happen. However, they argue, the observer in the chest frame will see his spinning line as "straight", so will think he synchronized rather than esynched his clocks. [To the relativists, the esynched clocks ARE synchronous and so are those of other esynched systems; they only appear to be offset "as viewed by a differently moving system".]
Faced with the counter-argument that if the rod only "appeared" to curve but really remained physically straight, the clocks would be truly synchronous rather than Einstein-"synchronous", the relativists resort to their time-honored semantic reply: It will be really_mantra1 curved as viewed by the outside observer and "physically" straight as plotted by the co-moving observer, because the only meaning of "really" and "physically" is whatever either system's measurements happen to be. "'Reality' in one system need not be the same as 'reality' in another", they say, "because reality is relative to the observer" and "there's no such thing as absolute motion".
{In his 1905 paper Einstein said, "Examples of this sort ... suggest that the phenomena of electrodynamics as well as mechanics possess no properties corresponding to the idea of absolute REST." One might wonder why the relativists don't therefore accept the implicit consequence that everything is in a state of absolute motion. But that's a different issue .}
Here is the gist of the argument:
In article <R.843294827@sheol.org> Wayne Throop wrote:
< glird@gnn.com (glird)
<> Since the objection seems to be that a straight line drawn on the
<>disk, with a prong at each end that can start two clocks beating, will
<>become curved as a result of the spin, why can't the "stationary"
<>observers in the chest see and measure that curvature itself?
<Because, as I pointed out, in the "chest frame", it isn't curved. It is
<only curved in the alleged "absolute frame". It is straight when
<measured from one frame curved when measured from the other,
<just like the analogous example I gave in ordinary, everyday, simple
<euclidean geometry.
In article <843583093@sheol.org> Wayne Throop wrote:
<But of course, the outcome can be CAUSED by purely relative
<effects, such as ...
<> The warpage must be real to really E-set the lab clocks,
<Sure. Forces really are lorentz-invariant. It's just that space and
<time measures from some "fixed frame" need not be what's real to
<get a real result.
<>This real result c could not have happened unless its causes were also real.
<Sure. It's just that these real causes need not involve "empty space"
<or a "fixed frame" or an "absolute velocity" or any such superfluous stuff.
< The bottom line is the result that KISS-TPP will "truly" set the
<clocks (that is, set them to equal times in the "fixed" frame) is purely
<derived from assuming that spun disks remain straight in that frame
<instead of in the co-moving frame. But since spun disks are held
<together with lorentz-invariant forces, that seems unlikely to be the case.
< ... As for me, I really don't care whether you want to call the
<distortions "real" or "apparent". ...
< The only problem is, bjon insists that there must be some space and
<time measures that behave as if they were objective, when this
<doesn't need to be, or seem now to be, the case. ...
< The problem is, bjon says that "real" effects aren't observer
<relative. Then he turns around [as did Einstein: 1950!] and says that
<there must exist some specific frame WRT to which space and time
<are "real"; that is, some frame in which space and time measures are
<special in some way.
And THAT is what TPP 2 will prove. Having begun and lived via imaginary experiments, Einstein-Minkowski STR is about to die via the same device.
TPP 2
In tpp 2 a prong is attached to end A and another to end B of a diameter line scribed on a circular disk while it is locally at rest. This disk is then spun counter-clockwise on an axle mounted through the center of a similar circular plate to which it remains parallel. Instead of clocks around the perimeter of the plate sensor buttons are so mounted. A cpu is connected directly to button one at zero degrees of the stationary plate, with that button on the origin of a coordinate system K (x',y',z';t') attached to the chest as referent. Each time prong B of the spinning disk touches a button on the plate a light-signal is sent to the CPU. When prong A touches the zero button the cpu begins to count the number of signals thereafter arriving from buttons touched by prong B. (The number of signals thus counted will therefore include signals still in transit when the count begins.) When B touches the zero button the count is stopped and recorded.
For simplicity, let the chest-measured diameter of the circular plate and pre-spun disk be
D = 9549.9266 km = .1/pi = .0318311 light-units, where one light-unit equals 3x10^5 km. The circumference is thus piD = 30,000 km long. Let the buttons be mounted 1 km apart, wherefore there are 30,000 of them. Let the disk be spun at a peripheral rotary velocity of
vR = .1c = 30,000 km per second as measured by its own system. (The disk thus rotates once
per second.) The time it takes a prong to move from one button to the next is thus
t'_p = 1/30,000 = .0000333 seconds per button, as measured in its own system.
The Gedanken Experiments.
Let a coordinate system S (x,y,z;t) ["cs S"] happen to be at rest in empty space, thus have units of length that are identical in all directions and truly synchronous clocks even when esynched. Let the chest [cs K (x',y',z';t')] be moving up Z of this (unknown) stationary system at abv = v = .6c. Let a system k (x",y",z";t") be moving on Z at abv = v" = .882353c and a system K' at v = -.6c as measured by system S. Let each system have its own similar tpp2 apparatus, similarly aligned, with the plate's zero degree button on the origin of the given system. Let the corresponding axes of such systems remain parallel at all times and let
their origins, thus zero-degree buttons, coincide at t = 0, when all origin clocks also read "0". Let each system then predict the count that the cpu per system, including its own, will obtain.
We will first calculate the prediction each system would predict for itself, using the chest as our example:
Prong B is at 180 degrees at say t' = 0 when prong A starts the cpu count. It takes
t'_s = D/c = .03183 seconds for a light-signal from B to reach the cpu. Allowing for the fact that nearby buttons not on Z are a mite closer than D to the cpu, there will be t's/t'p = 955 such light-signals still in transit when the count begins. Since each system will use these same numbers in predicting its own count, each system will thus predict a count of 15,955 for itself.
Each system's prediction for a different system will obviously be based on the degree of curvature each plots. How much will line AB of the chest, etc, curve and in what directions and why, as plotted by the differently moving systems? {Well, after a week or so of punching my hand calculator around, i discovered that the problem is harder than i'd thought! If we
allow Lorentz deformations to exist in advance, then system S will predict such and such a count. If we adhere to the notion that such deformations are ONLY as plotted by differently moving systems and proceed to let S plot K, no such deformations would be found by synchronous system S; so a different prediction would result. Accordingly, in order to do the math "right" we first have to know what the *physical problem* actually is!}
Independently of anyone measuring things, do moving systems deform or don't they? We will now try the case both ways.
First, we will allow that NO length or rate deformations occur and that esynched clocks per moving system really are synchronous. Then we will hold lengths and rates per system constant (except mantra 2) but will allow that the operation of esynching clocks of a moving system does insert the -vx'/c² local-time offsets, in which v is the unknown but operative absolute velocity of the given system. Then we will add rate changes but no real length changes. Finally, we will allow the real and physical length and rate deformations plus the local-time offsets built into the relativistic equations and transformations themselves. Along the way you will see why the LTE are inapplicable UNLESS the Lorentzian deformations really do occur; whereupon all mantras are deleted. (For brevity herein, I will round off some of the numbers even though I used the full numbers in calculating results via my hand calculator.)
Scenario One: No physical deformations. Rates of clocks of system S are arbitrarily appointed however we choose. Clocks of all systems are adjusted to run at that same rate. Clocks are synchronous in each system.
S treating K: At t=t'=z=z'=0, with prong A of K at button one at degree zero of the plate, prong B is at the 180 degree button on Z' and Z. Plotting prongs A and B via its synchronous clocks, S marks A at z=0 and B at z=D at t = 0 in both places. (No curvature would be plotted!) S then calculates that it would take ts = D/(c+v) = .0199 seconds for a light-signal from B to arrive at the cpu. Since the origin clock of K running at the same rate as clocks of S) marked the period of its disk's rotation as one second, so will the clocks of cs S. Accordingly, t_p=.00003 seconds in S terms too. Therefore, the number of signals still in transit when the count begins will be ts/tp = 597; each of which will also be counted. S will thus predict a count of 15,597; while K predicts a count of 15,995.
{Since there can be only one actual count by the cpu, only one such prediction can be right! Which will it be, "it's only relative"ists?}
K treating S: At t=t'=z=z'=0, with prong A of S at button one at degree zero of the plate, prong B is at the 180 degree button on Z' and Z at z' = z = D. Plotting A and B via its synchronous clocks, K marks them at z' = 0 and z' = D at t' = 0. If, then, there are no physically real offsets in esynched clocks of a moving system, S and K will agree that A and B were marked simultaneously IN BOTH SYSTEMS.
[This simple arithmetic proves that without the local-time offsets, relative simultaneity doesn't exist. Hence we see that "the relativity of simultaneity" is exclusively due to the local-time offsets physically inserted into absolutely moving systems by esynchronizing them as per Einstein's defined method. Though nobody knows its value, the absolute v is put into the local clocks by esynchronization itself!]
Since S marks vR = .1c so will K. Hence, K will agree that t'_p = .00003 seconds. As before, no curvature would be plotted. With v = -.6c, K says the light-signals from near Z' approach the S cpu at c - |v|, thus that t_s = D/(c-v) = .0796 seconds, wherefore t'_s/t'_p = 2389 signals will still be in transit when the count begins. K therefore predicts an S count of 17,389. {This, of course, will be experimentally wrong.}
[If K now plotted the relative velocity of cs K' (moving at v = -.6c on Z' of K) it would obtain a result that v = -1.2c! Accordingly, if we adhere to the scenario believed by SR - that NO deformations or local offsets physically exist in differently moving esynched systems (except mantra 2); not even the speed limit of c would hold up. Hence we see that the real reason for c being a "maximum possible speed" is a combination of the sqrt(1-v²/c²) deformation factors (which become mathematically meaningless if v > c) plus the local-time offsets; both of which relativists insist aren't really_{mantra 1} there except mantra 2.]
Let prong A continue on. At t=.25 it is at z = .5D = .0159, x=y= 0; and will be at
z' = z-vt = -.134, x'=y'=0, and t = t' = .25 as plotted by K. Hence we see that these galilean and only the galilean transformations hold good between systems whose unit-lengths are equal in all directions per system and in all systems and whose clocks all beat at identical rates and are truly synchronous. {It is utterly incredible to me that so many otherwise expert mathematicians and physicists seem unable to see this. They seem to think that their mantras are superior to pure mathematics itself.}
We imagine further that at the two ends A and B of the diameter line rAB = D of the circular plate of the absolutely moving system K clocks are placed, which synchronize with the clocks of the stationary system, that is to say that their indications correspond at any instant to the time of the stationary system at the places where they happen to be. These clocks are therefore synchronous. We imagine further that with each clock there is a co-moving observer, and that these observers apply to both clocks the criterion established by Einstein's defined method for esynching clocks.
Let a ray of light depart from A at the time t'A = 0, let it be reflected at B at the time t'B, and reach A again at the time t'A'. Taking into consideration the principle of the constancy of the velocity of light in empty space we find that
t'B - t'A = rAB/(c-v) and t'A' - t'B = rAB/(c+v)
where rAB denotes the length of the moving diameter - as measured in both physically undeformed systems. Observers in the moving chest could instantly calculate their own abv directly from that discrepancy in one way "times" of the ray.
Instead, they now obey Einstein's definition of "synchronism". They esynch all clocks B in the direction of abv, which in this case is Z'. To accomplish that, they turn all clocks B back by the needed "offset". Via Voigt's local-time equation, the time of the K clock at B will thereupon read t'B = t'A - vz'/c² = 0 - .6D = -.0191 at the instant clock A reads zero.
[In that equation, v = abv is the only operative agent that governs the "time" placed into clocks B when a moving system esynchs its own clocks independently of its variable relative velocity as marked by myriad other differently moving systems. Mantra 2 plays no role in the esynchronization of a given system's clocks. It comes into play only AFTER each system has done that all by itself. It is itself merely a consequence of the offsets the relativists, trapped into logic-circles by their own mantras, insist aren't really there.]
Having been thus esynched, clock B now reads t' = -.6D = -.0191 when clock A reads t' = 0. At tA=tB=t'A=0 prong A of the spinning disk of K is at z = z' = 0. Prong B is at z=z'=D at tB = 0 and t'B = -.019. Accordingly, tA = t'A = tB =/= t'B.
Hence we see that "the relativity of simultaneity" has nothing whatever to do with how God made the world, it's merely a consequence of Einstein's operationally useful but semantically false definition of "synchronism". Nothing happens to rates or unit lengths when K esynchs its clocks. We have therefore now reached the next scenario.

Scenario Two: No physical deformations. Clocks esynched in each system. Any deformations are only as plotted by differently moving systems.
S treating K: It is at once evident that stationary system S, whose esynched clocks remain synchronous, will plot no length, rate or shape deformations at all and will still predict a K count of 15,597. System K, however, now faces an internal problem. What count will it predict for itself?
K treating itself: At t'A = 0 prong A of its own disk is at z' = 0 and prong B is at z' = D at
t' = -.019! K waits for its prong B to be at a local clock at "t'B=0". In .019 seconds, moving at tp = t'p = .00003, prong B will have moved about 573 buttons past Z to reach a clock that has beat off its own offset and marks t' = 0. Line AB of its own disk will thus appear curved to the left as plotted by K.
[Item of interest: Line AB of the spinning disk of K will remain undeformed as plotted by the stationary system but {despite the relativists' claims} will now appear curved AS PLOTTED BY ITS OWN SYSTEM.]
Now K calculates that the time in transit of light signals from buttons near z'=D will be
t's = D/c = .0318 seconds. It still finds vR = .1c thus t'p = .00003. K therefore figures that t's/t'p = 955 signals will still be in transit when the count began. It will thus predict that its own count will be 15,000 - 572 + 955 = 15,383; instead of the 15,955 predicted in Scenario one. S, of course, will still predict a count of 15,597.
[Note then, It's Only Relativists, the count of its cpu doesn't change just because K "synchronized" its clocks. THEY play NO ROLE in the actual experiment! (If, instead of plotting it with their offset esynched clocks, cs K merely assumes (as do the relativists) that its own disk's line AB would remain straight as measured by observers in the chest, then K would again predict a count of 15,955. In the case here treated, this would still differ from its cpu count, and K could calculate its own abv from that difference.)]
K treating S: At t'A=z'=0 prong B is at z' = D at t' = -.019, and so is end B of the plate of S. K wants to plot them at t'B = 0. Where will that be? An equation for that seems to be,
(D - nD)/.6 = .6nD; so D - nD = .36nD; so 1 - n = .36n;
so n=1/1.36 =.735294. At t'A = 0 the time of a local K clock at z' = nD reads t' = -.014. It will take B of the plate .014 seconds (of both systems!) to reach a K clock at z'=.7353D at t'B=t'o-vz'/c²=.014-.6nD = 0. (We will assume that since prong B was moving sideways on the plate for that moment, it will be close enough to z'B of the plate, at t'B = 0, to ignore the very slight difference due to the circular path.)
Since all K clocks on a line parallel to X have the same "time" as each other, prong B will have moved .014/.00003 = 421 buttons past Z' and will be marked as being approximately to the left of z' = .7353D at t'B = 0. (Hence line AB of S would appear curved to the left as plotted by esynched K.)
Now K plots vR of the spinning disk of S. At t=0 prong A is at z'=t'=0. One second later it is at z' = -.6. The time of the local K clock at that point reads t'A'=t'o-vz'/c²=1.36, so K decides that vR = .1c/1.36 = .07353c wherefore t'p=1.36/30,000=.0000453. Noting that the top of the stationary plate of S is at z' = .7353D at "the same time" (t'=0) that the bottom is at z' = 0, cs K decides that lengths in S in the direction of motion have contracted by
n = .7353, thus that D of the S plate is nD long. Noting that light signals from B are moving in the same direction as the cpu of S, thus approach it at c-|v|, K would figure that t's=nD/.4=.058513 seconds --*IF* K plotted v of S as being -.6c. (We will get to that in a moment.)
Meanwhile, K calculates that t's/t'p = 1291 signals will be in transit when the count began, thus predicts a count of 15,000 - 421 + 1291 = 15,870. {That, of course, will be wrong.}
[We saw above, "... why can't the "stationary" observers in the chest see and measure that curvature itself?" "Because, as I pointed out, in the 'chest frame', it isn't curved. It is only curved in the alleged 'absolute frame'." (In the present case "the 'stationary' system" is K). "It is straight when measured from one frame, curved when measured from the other ... But of course, the outcome can be CAUSED by purely relative effects".
Contrary to this relativistic argument, the "outcome" (i.e. the actual cpu count per system) is NOT caused by purely relative effects; nor predictable by esynched moving systems if we adhere to Minkowski's notion that nothing happens to lengths or rates except mantra 2.]
To illuminate this magnificent detail a bit deeper we will now let S, k and K predict the count of k.
S treating k: Since its esynched clocks remain synchronous, S will plot no deformations in line AB of the spinning k disk and no deformations of k (which is undeformed in this case). S therefore calculates that ts = D/(c+v) = .017 seconds. Finding that vR" = .1c thus
tp = .00003, cs S calculates that ts/tp = 507 signals will still be in transit when the cpu count began, thus that the count will be 15,507.
k treating itself: Finding its own disk-line curved to the left even more than K found its own, k will plot it about 850 buttons to the left of Z" at t"B = 0 "when the count began at t"A = 0." Figuring that about 955 signals will still be in transit from there when the count begins, k will predict its own cpu count as 15,105 which, of course, will be wrong.
K treating k: To discover t'p, K first plots vR" of the k disk. At t' = 0 prong A is at z' = 0. One everyone's second later it is at z' = t(v" - v) = 1(.88235-.6) = .28235. The K clock there reads t'z' = t'o-vz'/c = 1-.1694 = .83. K thus figures that it took that many seconds per period, so vR" = .1c/.83 = .12c, wherefore t'p = .0000277.
To obtain the value of t's K now plots the relative velocity of k. As just shown, via use of its esynched clocks K notes that the origin of k (which is where prong A was at t'=0 and is at t'=.83) moved z'=.28 units in this .83 seconds. It thus plots the velocity of k as
v" = dz'/dt' = .34c. To obtain the value of D" in order to calculate t's, K now plots the length of a k unit rod lying on the axis of motion, Z'. At t=0 let an (undeformed) k rod extend from z" = 0 to z" = -1, thus from z' = 0 to z' = -1. End A (the lower end) will be plotted at z'=-1 at t'A = .01909 and end B at z' = 0 at t'B = 0. K therefore waits for B to proximate a clock marking "the same time", t'B = .01909, that A was marked. It will take
t'o = .00649/(v" - v) = .0229854 seconds
for end B to get to z'=.00649. At that instant the local clock at this point reads
t'B = t'o-vz'/c² = .01909.
Cs K thus marks A at z' = -1 and B at z' = .00649 "at the same time", t' = .01909. (Units of k, thus D" as well, will appear 1.0065 *EXPANDED* in the axis of motion, as measured by the esynched but otherwise undeformed moving system K!) Cs K then figures that
t's = 1.0065D/(c+v")=#/1.34 =.024 seconds.
[*Instructive detail: This demonstrates that the LTE are inapplicable to the Minkowski case in which units of length and rate of a moving system remain constant except mantra 2. By employing the LTE in their verbal arguments, the relativists have unconsciously switched to the physical realities upon which the LTE are based: Real and physical length and rate deformations, independently of the spurious relative values plotted by the offset esynched clocks of each differently deformed differently moving system. And THAT is the very blindfold itself: The relativists are blocked by their own mantras from comprehending the underlying physics imposed by their own relativistic equations.]
K plots prong B of k as being at z' = D at t'B = -.01909 when prong A starts the cpu count at t'A=0. It therefore waits for B to reach a k button at "t'B = 0". In .023seconds the top of D" of the k plate will have moved .00649 units up Z', thus will be at z' = D + .0065 = .038. The "time" of K clocks at this z' level will then be t'B = t'o-vz'/c² = .023 - .023 = 0. Prong B will have moved about .023/.00003 = 690 buttons past Z' when plotted there at t'B = 0.
[Instructive detail: Though line AB of the k disk will appear less curved to K than it appeared to k, it will still be curved TO THE LEFT. As plotted by K, then, prong B of k will have reached the 180 degree button BEFORE prong A reached the zero button. Given that, then instead of esynching tpp's clocks by -vz"/c², exactly the opposite offsets would appear: Clock B would be offset by PLUS instead of minus.
Also, K plots both lines, AB of k and AB of S, as curved to the left, even though k and S are moving in opposite directions relative to K. {So much for the relativistic argument which - instead of actually doing the physics by the numbers, merely assumes that the curvature "as viewed by a differently moving system" would (somehow) always esynch the viewed system's tpp-clocks.}]
K now calculates that t's/t'p = 863 signals will still be in transit when the k count began. Accordingly, cs K will predict a k count of 15,000 - 690 + 863 = 15173. So we see that S predicts a count of 15,507, K predicts a count of 15,173, and k predicts a count of 15,105; all for the very same cpu.
[Relativists insist that "reality" is whatever a given system's measurements reveal, that one system's reality is different than another's. Will the actual cpu count of k therefore "really be different" when viewed by the three systems? Of course not.]
K now decides to plot the velocity of system S. At t'=0 end A of the circular plate was at z'=0. At t=t'o=1, A is at z' = -.6. Via Voigt's local-time equation, the time of the K clock at
z' = -.6 registers t'A' = t'o-v(-z')/c² = 1.36 at that universal instant. System K thus concludes that S moved -.6 units in 1.36 seconds, thus has a velocity of of v = -.6/1.36 = -.44c; and reciprocity has just collapsed! We will therefore abandon scenario two because the PR of special relativity DOESN'T FIT THIS PHYSICS!
System K now decides to determine its own absolute velocity by measuring the roundtrip time of a ray of light in the Z' axis, which happens to be the direction in which K is now moving. It takes the ray
(rAB/(c-v) = .0795833)+(rAB/(c+v)=.0198958)=2D/(c²-v²) = .0994791 seconds.
Had the chest been stationary, it would have taken 2D/c = .064 seconds.
Knowing that the average relative velocity of light is c' = 1-v²/c² on the axis of motion, the chest's people could easily calculate that since c' = .063.../.099 ... = 1-abv²/c² = .64, its own abv equals .6c. {The MMX says that won't happen, thus that THIS Minkowski scenario won't work either. We will therefore abandon Minkowski.}
A severe complication has now crept in. If lengths in the direction of motion do NOT contract (except mantra 2), and rates remain unchanged (except etc), then there is no way for K to plot the velocity of light as c even with its esynched clocks. For that physics (no physical length changes in the abv direction) a Q = q² = 1-v²/c² rate slowdown is needed. The demonstration follows:
At t'A= 0 a ray is send from A at z' = 0 to B at z' = 1, with AB on the line of that system's velocity v in "the empty space" in which Einstein postulated that light has the definite velocity c. The ray will take t'B =1/(c-v) = 2.5 seconds to get to B. It will take 1/(c+v) = 5/8 seconds for the return trip; a total time of 3.125 seconds. In relativistic terms, it is supposed to take 2AB/c = 2 seconds. Turning clock B back by .6 seconds does NOT let the "stationary" system K determine that it took either one second each way nor two seconds for the roundtrip! For that to happen, rates of K have to slow by Q = .64. Given THAT, then the time out is .
64 x 2.5 = 1.6 seconds and the return time is .625 x .64 = .4 and the total time = 2. Turn clock B back by .6 seconds and the "time" each way then becomes 1 second, whereupon the
velocity of light will remain c as "DETERMINED" by this esynched "stationary" coordinate system just as Einstein said in the second of his several light postulates. {But if we insist on holding lengths constant in the direction of motion, NOT unless the "stationary" system's clocks run Q slow as a consequence of that system's absolute ("definite") velocity in Einstein's hypothetical empty space.}
After setting its clock rates Q slower than before, K decides to measure the velocity of light in directions perpendicular to Z. It sends a ray from x'=0 to x'=1 and back. Travelling at
c' = q relative to K in that axis, the ray takes 1/.8 = 1.25 seconds each way, thus 2.5 seconds for the roundtrip. Running Q slow, the K origin clock has beat off 1.6 seconds. STR requires
that it MUST take 2 K seconds.
Hence we see that if we hold lengths constant (except etc), then c' =/= c in the perpendicular directions even if we slow the esynched clocks by Q to hold c' = c in the axis of motion. (If we slow them by q, so 2.5q = 2 in X' and Y', then c' becomes unequal to c in the Z' directions!)
Accordingly, if we wish to hold lengths constant in Z' we must let rates slow by Q AND we must let lengths expand by 1/q in the perpendicular axes, a deformation which may be represented by 1, 1/q, 1/q, Q; in Z', X', Y' and t'. It may be noted that this deformation sets unit-lengths in the axis of motion q-shorter than in the perpendicular directions, even though members of this system will continue to measure its own unit lengths as equal to unity and equal to each other in all directions.
(If we allow this deformation to happen, though, then S would no longer agree that it takes 1 second per revolution of the K disk, nor, therefore, that vR' = .1c. Instead, it would take 1.5625 seconds per rotation, wherefore vR' = .15625c and tp = .000052 seconds. Accordingly, ts/tp = 382 signals would be in transit when the K count began, wherefore S would predict a K count of 15,382. Hence we see that the actual count is a function of the degree of length and rate changes per system, independently of the settings of anyone's asynchronous clocks.)
And THAT is the beauty of this tpp 2 gedanken experiment: The actual cpu count is totally independent of clock settings, but the predictions per system are not!!
The real deformations per system are a function of abv. The metrical values found by another system are a function of which system is plotting them. The amount of such deformation per given system really is different AS PLOTTED BY differently moving thus differently deformed esynched systems, which is where and why mantra 2 was born. {To be accurate, it should have been, "as PLOTTED by a differently moving relativistic system".}
Noting Einstein's rather anthropomorphic 1905 assertion that, "In agreement with experience we further assume the quantity 2AB/(t'A'-t'A) = c to be a universal constant - the velocity of light in empty space", system K now obeys Einstein's assumption. From above, we get t'B - t'A = rAB/(c-v) = D/.4 = .0796 and t'A'-t'B = rAB /(c+v) = .0199, wherefore
t'A = 0 and t'A' = .0994791. Hence 2AB/(t'A'-t'A) = .0995.
Since it has to take 2D/c = .063662 seconds (assumes Einstein), this requires either that clocks of K spontaneously slow down as a consequence of increased internal density of the system as a function of the increased resistance by the displaced medium thru which the system travels; or that the chest people themselves slow the rates of their clocks. We will assume the latter. They therefore slow their clock rates by
dt'_after/dt'_before = .063662/.0994791 = .64 = Q.
[Hence we see that if lengths of a moving system remain constant in the direction of motion, clocks must run slower by Q, not the LTE's q, in order to hold the roundtrip speed of light a determined constant, c = 1, in that system. If we let t denote the time of a stationary system in which light-speed really is c in all directions, then in this case dt'/dt = Q; in which dt'/dt symbolizes the ratio of rates of the two systems. Indeed, that IS what it denotes in Einstein's 1905 derivational equations.]
Scenario Three: Lengths remain physically constant in Z and expand by 1/q in the perpendicular axes. Rates at which clocks beat in moving systems run slow by
Q = q² = 1-v²/c². This deformation can be represented by 1, 1/q, 1/q, Q in which, since Z is here the direction of motion, these changes are in Z, X, Y and t. Clocks per system are esynched.
We now let rates of all moving systems run Q slower than before, and let the spin rate of their disks be set to peripheral vR = .1c as measured by them. Taking themselves as "stationary" and plotting their own curved lines AB as "straight", they each predict that their own count will be 15,955.
S treating K: S will measure AB of the K plate as D long. As shown above for this case, S will predict that 382 signals will be in transit from near z = D when prong A of K starts its cpu's count. Hence S predicts a count of 15,382. (This assumes that any discrepancies in the width of the spinning disk due to unequal velocities of its opposite moving sides may unequally bulge the disk laterally, creating a curve to the left in the middle of line AB, leaves prongs A and B on Z at the same time anyway, when line AB of the disk is "parallel" to Z.)
K treating S: K now plots vR of S. In 1 S second prong A is at the origin of S again, thus on the Z' axis at t=1. This origin is now at z'=-.6. The K clocks will have beat off .64 seconds. At t=t'o=0 (and ever after) the local clock at z' = -.6 is offset by -vz'/c² = +.36 seconds compared to its own origin clock. Hence the K clock at z'=-.6 reads t'= .64+.36 = 1.
Cs K thus finds that rates of S clocks remain identical to those of K! In this scene, moreover, the origin of S reached z' = -.6 in 1 K second, thus S travels at v = -.6c as plotted by K. (Reciprocity has been restored.)
At t=t'=z=z'=0, prong A of S is at button one of the plate. At that instant the 180 degree button (and prong B) are on Z and (undeformed) Z' at t=0, z'=z=D, where the esynched local clock of K registers vz'/c²=-.0191. In order to plot the value of D of S, K must wait for that button to reach a K clock on Z' at t'B = 0. At t=0 the time of the K clock at z' = .64D registers t' = -.01223. It takes .01916 seconds for this clock to register t' = 0, during which cs K will have moved .0115 units up Z; so the top of the S plate would be at z' = QD at t'B = 0. Hence, K will find that system S is Q contracted in the direction of motion.
Allowing that prong B of S will be on a line approximately perpendicular to z'=.64D, it will therefore be marked there at t'B = 0. In S terms it will thus have moved ts/tp = 573 buttons to the left of Z before being plotted there at t'B = 0 "when the count began", according to K.
Finding S rates identical to its own, cs K agrees that vR = .1c, so t'p = .00003 seconds. Finding unit-rods of S Q-contracted in the direction of motion, K figures that
t's = QD/(c-|v|) = .05 seconds for signals from buttons near 573 to reach the cpu of S, so t's/t'p = 1529 signals would still be in transit "when the count begins". K would thus predict an S count of 15,000 - 573 + 1529 = 16,956, which (given that buttons on the perimeter of the elliptical plate are a bit closer than QD to the cpu) is close enough to 15,955 as to be correct. [But ONLY if we permit K rates to *physically* run Q-slow. If not, then D of S remains nD-contracted as measured by the esynched clocks of K; v, vR, t'p and t's change, and so does the predicted count.]

So you see, what the various systems will predict is a function of our choice of what the underlying physics actually is. Which is calamitously ambiguous, in relativistic terms!
[Illustrative point: In relativistic transformations where X is the direction of motion, the degree of rate change, dt'/dt, as plotted by system A for system B, becomes an equivalent length change, dx/dx' of system A as plotted by system B; and the degree of length change, dx'/dx, plotted by A for B, becomes the degree of rate change, dt/dt', of A as plotted by B. Since dx'/dx = dt'/dt = q in the LTE, these internal mathematical exchanges became invisible {tho still there!}.]
The real message of TPP is given in its five Appendices. The first sets forth the force equations by which both Lorentz and Einstein provided physical reasons for the actual deformations that Lorentz claimed but Einstein - via Minkowski - denied. The second mathematically explains the physical and mathematical meanings of every symbol in the LTE, as well as the steps by which the transforms have the same form for both systems, thus are "reciprocal". The rest of the appendices demonstrate what Einstein's initial paper had been doing before he radically revised it in order to fit and include Poincare's LTE ; what's wrong with Minkowski's claims, and a revision of Einstein's entire published paper to set forth both the physics and mathematics on which it was initially based, which was far better than the published version. Collectively they show that although Einstein didn't understand the physical meanings of his own equations, neither did anyone else until now.