A question has been bothering me for some time about the use of reference frames in SRT.

I do realise that there is always a good answer to questions regarding SRT and I guess this will be no exception to the rule. I am not interested in challenging SRT as I only wish to understand it.

When working with SRT a Reference frame is selected and this selection can be quite arbitary.

Say we have two objects that are separating at a v = 0.5 'c'

Normally we would choose a RF be it object A or Object B. I wanted to know how this selection of either Frame can be justified when a global two frame perspective would be more intuitive.?

How can a RF determine itself at rest when it is unable to determine anything except it's relationship with the other frame.
Why woudln't a RF autromatically assume that both he and teh other are moving equally?

What is tha SRT reasoning that requires a frame be deemed "arbitarilly " at rest when this is obviously not the case as SRT states quite clearly that there is no absolute rest frame?

Why deem a RF at rest when "at rest" is an illusion?

A question has been bothering me for some time about the use of reference frames in SRT.

I do realise that there is always a good answer to questions regarding SRT and I guess this will be no exception to the rule. I am not interested in challenging SRT as I only wish to understand it.

When working with SRT a Reference frame is selected and this selection can be quite arbitary.

Say we have two objects that are separating at a v = 0.5 'c'

Normally we would choose a RF be it object A or Object B. I wanted to know how this selection of either Frame can be justified when a global two frame perspective would be more intuitive.?

How can a RF determine itself at rest when it is unable to determine anything except it's relationship with the other frame.
Why woudln't a RF autromatically assume that both he and teh other are moving equally?

What is tha SRT reasoning that requires a frame be deemed "arbitarilly " at rest when this is obviously not the case as SRT states quite clearly that there is no absolute rest frame?

Why deem a RF at rest when "at rest" is an illusion?


Excellent point QQ. SRT is based on the very thing it prohibits. :D

Remember, QQ: if MacM says “Excellent point!” it signals that you have asked something indeed … stupid.
Let’s see what you have asked.
1. When working with SRT a Reference frame is selected and this selection can be quite arbitary
Not quite right: When working with any physical theory a Reference frame is selected and this selection can be quite arbitrary!
2. Normally we would choose a RF be it object A or Object B. I wanted to know how this selection of either Frame can be justified when a global two frame perspective would be more intuitive.?
Nobody needs to justify his choice of RF – it is his free will: nothing will be wrong in any RF. The unlucky choice will lead to the more tough calculations and description, but if you will not make errors at calculations everything will be OK. Wont to make economy at calculations – make a optimal choice of RF!
And what the hell is “a global two frame perspective”?
3. How can a RF determine itself at rest when it is unable to determine anything except it's relationship with the other frame.
Any inertial observer (not RF!) can determine himself at rest exactly because inertial motion is a relative notion! No matter what constant velocity inertial observer will determine for himself (and respectively – for his RF!) nothing will change in his description of events of Nature – this is the sense of the Principle of Relativity, which expresses the entire experience of Science!
4. What the hell is that:
Why woudln't a RF autromatically assume that both he and teh other are moving equally?
5. What is tha SRT reasoning that requires a frame be deemed "arbitarilly " at rest when this is obviously not the case as SRT states quite clearly that there is no absolute rest frame?
Absolutely contrary! SRT is a theory about description of Nature at any choice of the inertial RF! SRT never “required” any special inertial RF!
6. Why deem a RF at rest when "at rest" is an illusion?
Because in many cases it is convenient (takes a little of calculations) to assume that your RF is “in rest”: Principle of Relativity provides reliability of your research at any choice of speed of your inertial RF.

And this salad of ignorance MacM calls “excellent point”!

QQ wrote:

Why woudln't a RF autromatically assume that both he and teh other are moving equally?

You live on a planet. You all communicate with each other and see nothing unusual with your radio transmissions. There is an approaching spacecraft hailing you on a strange frequency. You realize it is the standard frequency, blue shifted slightly. You deduce that he is approaching you at an easily calculated speed, based on the frequency shift. Would you assume you are moving toward the spacecraft? You might be, after all! The question is meaningless though unless there is a preferred frame of reference, a "frame 0". All of science indicates that there is not.

MacM,

I really wish we had a couple of spacecraft that could move near c. We could all take a ride together and play SRT games. It would be fun.

Say we have two objects that are separating at a v = 0.5 'c'

Normally we would choose a RF be it object A or Object B. I wanted to know how this selection of either Frame can be justified when a global two frame perspective would be more intuitive?
You can choose any reference frame you like. It's arbitrary.

Or, you can not choose a reference frame at all... unless you want to do some analysis of the situation. In that case, then you need a reference frame.

A 'two frame perspective' might be more intuitive, but it doesn't lend itself to analysis of the situation with the tools that I have. There might be tools out there, or you could design your own... but why bother, when there's a perfectly good set in simple SR? Do you expect that you'll get different answers working from a different perspective?

The point of reference frames being arbitrary is that when you analyse the situation, you always get the same answers for the important questions, regardless of the frame you work from (frame dependent quantities aren't important).

How can a RF determine itself at rest when it is unable to determine anything except it's relationship with the other frame.
Why woudln't a RF autromatically assume that both he and teh other are moving equally?
You can pick a frame in which both craft have opposite velocities. You'll get the same results as for any other frame.

What is tha SRT reasoning that requires a frame be deemed "arbitarilly " at rest when this is obviously not the case as SRT states quite clearly that there is no absolute rest frame?
The fact that no frame is absolute doesn't imply that no frame exists.
The fact that no frame is absolute does imply that all frames are arbitrary.

Why deem a RF at rest when "at rest" is an illusion?
'absolutely at rest' is an illusion.
'at rest in this specified frame' is not an illusion.




Further reading:

The question 'how fast?' is like the question 'how far?' Neither make sense without a reference to something else.
'How far am I from my chair' has any easy answer: zero. Zero isn't an absolute answer to 'how fast', of course... that would imply that my chair is the centre of the universe. But zero isn't a wrong answer either... it's perfectly correct given the arbitrary reference of 'my chair'.

Same for 'how fast'.
'How fast am I moving compared to my chair?' zero, of course. I'm not implying that I am absolutely at rest, of course, but my speed is truly zero in the specified reference frame.

Do you see?

Thanks Pete, Yuiry, you have answered my question.

The reason I asked it, was to clarify the use of rest frames so that it may help me with another little question floating around in abstract land waiting to mature into a full question.

Abstraction:
I get the impression that the transforms work well [as described here at sci forums] with the use of rest frames and yet they fail in the final wash up, simply because the net result should be global and not frame specific......yet we use rest frames to get there......
Just a little question waiting to mature, But I thought I'd mention it any way to explain why I am asking such a simple question about frames.
It [the question] is not mature enough to be posed here though.

Excellent point QQ. SRT is based on the very thing it prohibits. :D

Ditto on the post QQ. Excellent.

I was on the brink of introducing a similar thread differing primarily only from the inclusive generality of your thread to a focused example - an 'ant-SRT point of singularity. AE described a famous and familiar embankment/moving train gedanken currently used fequently for educational and practical purposes.

This gedanken all though brief, effectively varied, and contiues to affect the public perception (and conception) of simultaneity. T is the moving observer on reference frame T (a passenger train). The gedanken designed to describe how a stationary observer E on the embankment, perceives events dfferently than a moving observer wrt E (what a concept).

T at the midpoint of the T frame arrives at the midpoint of two photon sources F and R stationary wrt E just as photons are emitted simultaneously from F and R. T is moving toward the oncoming F photon and detects F before R catches up to him later from the rear.

SRT allows T to assume the RF T is at rest wrt E, which is moving and when T detects F before detecting R he assumes that the F photon was emmited before the R photon was emitted (T thinking he is not moving thinks the disance between himslef and the photon surces is identical). The only way T can make any conclusions here is if T was informed that he was at the midpoint of F and R when the photons were emitted. Otherwise just being motionless somewhere and detecting two light pulses says nothing about when the lights were emitted or their relative respective spatial arrangement. Only with the information that T was colocated with the midpoint of F and R when the photons were emitted can the observer now make some rational conclusion.

Now, T having moved from he midpoint of F and R must see the photons arrive at the T observer sequentially. T says:"If I was at the midpoint of F and R wrt E, and at rest wrt E when photons were emitted from F and R then the F photon must have been emitted before the R photon. was emitted. What is simultaneous for the staionary oberver is not simulaneous for the moving observer".

"So you use the assumption you are a rest wrt E, yet you say the stationaary and moving obsevers do not share simultaneous observations. But you just said you were at rest. Isn't this a contrad,,,", he was interrupted by T shrugging off the statement and signalling him continue.

"The observer E on the embankment says the photons were emitted when you were colcated with the midpoint of F and R. The reason you detected the F before R arriving is that you were moving toward F which was emitted incoming to your direction of motion. R was emitted to you going away from the R photon. Your conclusion that F was emitted before R is erroneous,"

"But", replied T, "I couldn't detect my motion, therefore, I can choose either the T or the E frame to be at rest wrt the other, it's basic SRT "., now barely stiffling a yawn.

"What makes you think you are justifird in choosing youself at rest?" asked E.

"The equivalency of inertial frames postulate" answered T now glancing at his wach.

"Did you know that a passenger on T was colocated with the midpoint of Fand R when th ephotons arrived there simultaneously?" enquired E. "This occured after you detected the photons emitted from F and after you had moved from the midpoint of F and R", E informed T hopefully.

"So what?: asked T. "I concluded F was emitted before R because I saw F first at my location on T."

"So what?" asked E. "Did you feel an acceleration when you left the station earlier?"

"So what?" answered T, as he avoided a direct eply.

"There was no indication of a corresponding acceleration of the embankment" answered E. "What if you had assumed that you were moving instead of assuming you were at rest wrt E? Does SRT allow you to assume you were moving wrt E?" asked E.

"Yes", answered T,"but as I will always measure the velocity of light as c with respect to my motion what ever it may be wrt to any other inertial frame, I am justified in assuming my relative velocity wrt E is zero, wrt E and this is what I did." said T with finality.

"Can your velocity ever be less than the speed of light?" asked E.

"Of course my speed is always less than the speed of light" scoffed T incredulously, shaking his head in disbelief.

"Well, how much faster is light from the speed of the train?" asked E.

"A lot" rplied T with forced patience while removing a pen from his coat pocket, "The train is moving at 200 km/hr so C is larger than V by the amount C - V or 3x10^5km/sec - 200/3600 km/sec, or (300000 - 1/18) km/sec.", while showing E is calculations.

"Then you could have made the calculation (C -V) before you assumed you were a rest couldn't you?" asked E innocently.

"I could have assumed I was moving and the embankment was at rest I suppose," answered T, "but, so what? I assumed I was at rest. I have a right to make this assumprion."

"Everybody in the universe was watching you on the train when only you were colocated with the midpoint of F and R when the photons were emitted." said E. "A co-passenger on T was colocated with the midpoint of F and R when the photons arrived their simultaneously. You had moved toward the oncoming F photon by then", exclaimed E. "The co-passenger had smuggled a fourth clock on board T and he measured the simultaneous arrival time of F and R. After this event, you measured the arrival of the R photon coming from the rear of T".

"So what?", asked T sarcastically.,

"Well your clocks on the train measured the simultaneous emission of the photons. You felt an acceleration of the train that provided motion from and wrt the previous station, and there is no data indcating that you decelerated to a zero velocity later. The previous station felt no acceleration, ever. You are using some postulate of light to negate the observed events because some men, all dead now, wrote books and papers telling you that you can never add the velociy of light C and velocity V of an object as nothing can go faster than the speed of light. Therefore, C + V is a physically insignificant statement. And as C is a constant of nature it can never diminish. Therefore, C - V is also a physically meaningless statement. You were justified in assuming the contrary to the unambiguois observation, you say which requires you to ignore verified events and results?" gasped E rhetorically. "What does the phrase, 'light moving in vacua' mean any anyway?" asked E.

"It means you creep", said T, "that SRT is so ingrained in the mentality of the members of the scientific community, and the public, that all your protestations, your logic, your rational thought processes and analyses and especially your precious observations mean nothing. Sure, the GPS does not have SRT embedded in the system software. If this were the case GPS wouldn't work and NASA isn't staffed by stupid engineers. Don't you realize that the weight of belief of the mainstream scentific community officially defines the described physical realty? In the case of SRT, well everyone", he paused making certain the intended warning was communicated, "must get used to the fact that the weight of belief has overcome the weight of rational and objective observation. SRT is just ambiguous enough that it is unlikely the general public will ever discover inconsistencies and then voice eheir objections. The public follows along. Do you see how this is done?

"I understand " said E, "Please continue."

"This is not a trivial matter", said T, now beginng to roll with his own momentus flow, "Why do you suppose the catholic (universal) church burned Giadorno Bruno at the stake? The answer you nut case, is." T's volume now rising acutely framed by a bright crimson near blood-red face, " that Bruno challenged the authority of the state to arbirate the defined reality. If the confidence of the public in their instututions to provide the truth is diminshed, chaos and confusion result. [Controlled] Institutions defne the realty that generates direction to 'official policy'. Besides this", concluded T, his voice suddenly barely audible, whispered, "if I talked about SRT like you dissidents do I and thousands like me wouldn't have a regular pay check, thousands of scientists and their respective institutions would suffer unbearable personal, professional, economic and governmental embarrassment - recognizable and sufferable pain - the SRTist have a functional duty to preserve the public perception of the vitality of SRT as the right and power of the institution to arbitrarily define and mediate peceptions of reality is too consequentially significant -'too big to change' - and this is just how it is. The 'inalienable rights of the single person and he public' to collectively and singularly define their own reality, based on their unique perceptions and observation would erode the power of instututional governing and is therefore an extremely radical and admistratively untenable condition. Such radicalism cannot be allowed serious consideration and dialogue in space and time. The dissidents charcterization of SRT as flawed and scientifcally useless is unquestionably and unconditionally accurate as anyone with half a mind knows to the nth degree of resolution. Such a characterization is also laughably naive."



"Ah yes" mused E slowly and silently, his personal mantra now perfectly exposing his mind to a state of rested and attentive alertness, void in time and activity consraints. As E started to drift from the balanced alertness he carefully and silently reintroduced his mantra into the meditation ...., "Ah yes... Chaos and confusion? . . . what a crok of shit!"

Geistkiesel.

MacM,

I really wish we had a couple of spacecraft that could move near c. We could all take a ride together and play SRT games. It would be fun.

And I just wish you would recognize that GPS says YOU and SRT are in error. The earth's pole is not an absolute rest referance but it is a local preferred rest frame and mathematics shows that to calculate time dilation using differential velocity between a clock at the equator and an orbiting GPS clock yields the incorrect value of time dilation. It is only correct when both clocks referance the preferred rest frame and take the differential of their respecticive gammas.

That is it is not proper regardless of Yuriy's stupidity and that of SRT to claim either observer may assume to be at rest. The Lorentz gamma function only works when you referance a common third point between to observers such that the absolute "relative" velocity between them can be ascertained. That is which one has the higher velocity.

.

Remember, QQ: if MacM says “Excellent point!” it signals that you have asked something indeed … stupid.

And this salad of ignorance MacM calls “excellent point”!

For anybody interested in facts instead of sour grapes from a twit that another Phd Physicist has said repeatedly that Yuriy doesn't even know Highschool physics - See Thread

You live on a planet. You all communicate with each other and see nothing unusual with your radio transmissions. There is an approaching spacecraft hailing you on a strange frequency. You realize it is the standard frequency, blue shifted slightly. You deduce that he is approaching you at an easily calculated speed, based on the frequency shift. Would you assume you are moving toward the spacecraft? You might be, after all! The question is meaningless though unless there is a preferred frame of reference, a "frame 0". All of science indicates that there is not.
Your example assumes the craft is moving toward and an absolute refeence frame. The equvalence postulate denies the possibility of detecting motion yet you offer the contrivance of "visitng aliens" "as a distraction when a returning earth vehicle would do just as well) as an argument supporting SRT.

geistkiesel

When working with SRT a Reference frame is selected and this selection can be quite arbitary.By definition it must be arbitrary.

I wanted to know how this selection of either Frame can be justifiedNeither frame is allowed preference, to be more important than the other. The laws of physics must work the same for both. This is the lynch-pin for special relativity. Everything else depends on it.

How can a RF determine itself at restIt does not determine itself to be at rest. It defines itself as being at rest.

Why woudln't a RF autromatically assume that both he and teh other are moving equally?They are.

What is tha SRT reasoning that requires a frame be deemed "arbitarilly " at rest when this is obviously not the case as SRT states quite clearly that there is no absolute rest frame?Special relativity does not require any frame to be at rest, but rather allows any frame to be at rest.

And what the hell is “a global two frame perspective”?Sounds like something Kerry invented twice so it could work both ways.

A 'two frame perspective' might be more intuitive, but it doesn't lend itself to analysis of the situation with the tools that I have. There might be tools out there, or you could design your own... but why bother, when there's a perfectly good set in simple SR? Do you expect that you'll get different answers working from a different perspective?He must get the same answer or he's using the wrong perspective.

Your example assumes the craft is moving toward and an absolute refeence frame. The equvalence postulate denies the possibility of detecting motion yet you offer the contrivance of "visitng aliens" "as a distraction when a returning earth vehicle would do just as well) as an argument supporting SRT.

geistkiesel

Read my post you lunatic. All I state is a ship approaching a planet. Standard frequency, blue shifted. It is an earth vehicle. Can you really be as dumb as your writing suggests?

Read quickly before it gets edited.

Special relativity does not require any frame to be at rest, but rather allows any frame to be at rest.

True and that is unfortunante since GPS shows that to make that assumption doesn't compute the correct time dilation actually observed. The correct dilation requires that each clock i.e and orbiting clock and one for example on the surface of the earth, requires that they each referance a locally preferred rest frame and to then take the differance in their respective gammas. The frame that is used is the earth's pole (axis).

If you merely assume SRT is valid and take the differential velocity between the clocks you get an incorrect answer, regardless of which clock you assume to be at rest.

Using the GPS system infact prohibits the reciprocity advocated by SRT. That is the orbiting clock will always have the higher velocity. It is not reversable and the physical reality is that is does not reverse.

Abstraction:
I get the impression that the transforms work well [as described here at sci forums] with the use of rest frames and yet they fail in the final wash up, simply because the net result should be global and not frame specific......yet we use rest frames to get there......
What net results do we get that are frame-specific, but that should be global?

Pete as i said my question is immature at this juncture. The first thing I need to do before getting into the answer is learn all the SRT math and correct language. Until then the question stays as an abstraction, as I am not equipped to explain it correctly.

It does however premise it self on the fact that lights events are universally simultaneous and it's position only is relative. Which means that v=c is actually v= c^2
as 'c' is an inherant velocity of all matter.

But as I said it is all too much of a bother IMO maybe when I learn the lingo a bit I can post it properly.
Thanks for asking though all the same...

True and that is unfortunante since GPS shows that to make that assumption doesn't compute the correct time dilation actually observed.Huh? I guess that means my GPS can't tell me where I'm standing.

The correct dilation requires that each clock i.e and orbiting clock and one for example on the surface of the earth, requires that they each referance a locally preferred rest frame and to then take the differance in their respective gammas.Huh? I'm sure you meant to mean something there.

If you merely assume SRT is valid and take the differential velocity between the clocks you get an incorrect answer, regardless of which clock you assume to be at rest.Uh, no. GPS systems work, which they wouldn't if you were correct.

Using the GPS system infact prohibits the reciprocity advocated by SRT.Uh, no.

Huh? I guess that means my GPS can't tell me where I'm standing.

Huh? I'm sure you meant to mean something there.

Uh, no. GPS systems work, which they wouldn't if you were correct.

Uh, no.

I'll not comment step by step but merely summarize. You seem to be under the misconception that Special Relativity is used in the GPS system.

The simple fact is at no time do they compute the relative velocity between clocks. They use the earth's axis (pole) as a local preferred REST referance frame.

A simple calculation will show that to compute the relative velocity between surface clocks and the orbiting clock will give you an incorrect answer.

Further GPS does work but only because they abandoned Special Relativity and use a form of Lorentz Relativity by having the common rest frame to judge respective velocities. They DO NOT compute time dilation by (Orbit Velocity - Surface Velocity) = V3 and then gamma of V3. That gives the WRONG answer. GET IT. SRT doesn't work.

Abstraction:
I get the impression that the transforms work well [as described here at sci forums] with the use of rest frames and yet they fail in the final wash up, simply because the net result should be global and not frame specific......yet we use rest frames to get there......
Is your impression that the net results should be global but they aren't?

Or are you worried that we use a non-global model to discover global results?

MacM is, of course, completely wrong about the GPS system. There is an old thread on this.

MacM is, of course, completely wrong about the GPS system. There is an old thread on this.

You have got to be kidding. Yes indeed there is a thread on this I started it. I also ended it.
************************************************** ***
GPS satellites have a velocity (V1) of 3,874.5 m/s. A surface clock (at the equator) has an absolute velocity (V2) of 463.8 m/s and "0" m/s at the poles.

The "Relative Velocity" between the orbiting clock and a clock at the equator is V3 = (V1 - V2) = (3,874.5m/s - 463.8m/s) = 3,410.7m/s.

Using Special Relativity in GPS one gets: 3,410.7/c = 1.1369E-5, squared = 1.2925E-10. Divided by 2 = 6.4627E-11.

Time loss would be 6.4627E-11 * 24 * 3,600 = 5.58378E-6 or - 5.58 micro-seconds per day.

HOWEVER: Using the absolute velocity of orbit of 3,874.5 m/s and NOT "Relative Velocity" per SRT one gets 1.2915E-5c, squared = 1.66797E-10. Divided by 2 = 8.33986E-11.

8.33986E-11 * 24 * 3,600 = 7.205E-6 or 7.2 micro-seconds per day due to orbit velocity.

For the earth surface clock I calculate V2 = 463.8 m/s = 1.546E-6c. Squared = 3.29E-12. Divided by 2 = 1.195058E-12 * 24 * 3,600 = 1.0325E-7 or -0.10325 Micro-seconds per day being only about 1% in the daily time loss may be disregarded.
************************************************** *****

Now make a specific claim of error or back off. GPS does not directly use the differential velocity between clocks.

Where did you get your velocity data, both for ground clocks and for GPS clocks, MacM? Also, which formulae are you using to calculate "time loss"?

Where did you get your velocity data, both for ground clocks and for GPS clocks, MacM? Also, which formulae are you using to calculate "time loss"?


Like you said James R., there is a thread dedicated to this and the data came from Ashby, Hatch, Hewlett Packard and other GPS experts. It seems assinine to ask what formula is used considering I get the correct answer.

Not trying to be difficult here but fail to see the necessity of re-argueing this issue. It has been resolved in detail.

Fair enough, MacM. I am satisfied that you are wrong, so we'll leave it at that.

Fair enough, MacM. I am satisfied that you are wrong, so we'll leave it at that.

Yuriy has indicated to you in another thread that my calculations are correct. So your being convienced I am wrong really doesn't say much, other than you simply refuse to recognize the truth when laid out in clear mathematical form.

Yuriy has indicated to you in another thread that my calculations are correct.

Please link me to the relevant post.

Please link me to the relevant post.

As usual Yuriy would likes to take credit but that is to be expected. I had ran part of a calculation on my Casio fx-7400G Plus, but it ran out of decimal places and I merely made a general approximation stating my calculator wouldn't go that far. Yuriy used taylor to produce the result.

Since he in typical fashion tried to insult me and cast innuendo, I then used Taylor to compute the GPS data.

Yuriy's Post

Fair enough, MacM. I am satisfied that you are wrong, so we'll leave it at that.
James R I am looking to have someone, anyone, find a fault with my post measuring the absolute velocity of two inertial frames moving uniformly wrt each other. I do not know if you were aware of the thread, or post, but I would like your input to find any specific fault with the model.
A and B are moving with respect to each other a 10000 units. I assume first (without loss of generality, see below) that the A and B RF are moving toward each other. The expression for the relative velocity of the system is Va + Vb = Vab = 10000. Now I claim that I am able to determine the individual velocities of each frame, A and B with respect to each other. That is, measure the Va and the Vb such that Va + Vb = 10000..
There are three significant time segments. t < 0, when a third frome of reference is moving directly beside the A frame with zero relative velocity of the C and A frame, Therefore, at the beginning Vab = Vcb. As Vc = Va.
At t = 0, the second time segment begins. Here C begins to accelerate in the direction of the B velocity. We will asssume here that as C accelerates C makes a continuous set of measurements. C has one goal: to increase velocity until C is moving at the exact speed and direction of the B frame.

Here is a schematic with every thing described in simple figures, (http://www.sciforums.com/attachment.php?attachmentid=3959&stc=1)

C begins this quest starting at Vcb = Vab. As C accelerates (in spurts) in the B velocity direction Vcb dimiinshes until that instant that Vcb = 0 and Vac = Vb. Vc = Vb. Remember this is a measured relative velocity.
When Vac = Vb the data collection is over this is at t = 1.
C has been measuring the relative velocity A wrt C assuming the A frame at rest wrt C. As Vc = Vb, Vac is the increase in realtive velocity of the C frame wrt A. A being at rest wrt C, therefore we may write, Vac = Vc = Vb
From the expression Va + Vb = Vab and Va = Vab - Vb = Vab - Vc.
Every thing is complete. Do you see any errors?
Don't let me down James R you must find something specific beside concluding the post is SR heresy, OK?
If B had been moving in the opposite direction then the forst measuremtn by C woykld have shiown an increase in realtive velocity of C wrt B and C would have decelerated until reacxhing the condition Vc = Vb. If the relative velocity of Vcb ind=creased whether CD accerated or deceerated then B smust be at absolute zero velocity wrt to A, All generality questions should be answered to your satisfaction OK?
I am anticipating some kind of skewer of the model , but caveat James R if there is a flaw you will find it . If there is no flaw then the absolute motion of inertial reference frames haves been measured and detected,
Correct?
To make it interesting A was measured at 4000 units after acceleration was completed. B was measured at 6000 unitss wrt Ve. Neither the A nor B observer is aware of these measured velocity figures, wrt Ve the embanment. Only you and I.

Geistkiesel