The case for True Length = Rest Length

[ghwellsjr]

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Now now. You should consider that you may be reading something into my statements that are not there.
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If it does indicate to you as such, then you're mis interpreting what I said. There is no requirement to assign coordinate systems to anything including oneself, however one may also always imagine it is done so even if it was not. There's no harm in it.
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Of course. I just can't figure out why you feel the need to tell me? I could tell you the same thing, but what good does it do?
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I hear you saying you understand that it is not necessary to assign multiple coordinate systems to each observer/object, but we'll see what you really believe when I address one of your answers down below.

Indeed, he did not assign any coordinate system to the accelerating clock. This doesn't mean that one cannot imagine an observer carrying the clock, who assigns himself the origin of a coordinate system he calls his own. Bottom line, it was an extrapolation of the LTs by Einstein to the accelerational case. Here's what he did ...

Yes, he did assign a coordinate system to the accelerating clock, it was the stationary system as he called it.

As you pointed out, said OEMB scenario presented an accelerating clock from the POV of an inertial clock. Of course, because the LTs are based upon the POV of a stationary observer.

No, he didn't say it was from the POV of an inertial clock. He said both clocks are "viewed in the stationary system". He didn't say or imply and it's not true that what he described about what the traveling clock experiences is what the stationary clock sees. We, as super observers, can "see" both clocks simultaneously according to our arbitrarily assigned coordinate system, but there is no implication that we have determined what either of them sees of the other one (until they are colocated again).

However, the LTs were also designed for moving inertial bodies of constant v. Einstein tactically specified that his accelerating clock move at a constant velocity v, while it moved in curvilinear motion. As you know, gamma does not depend upon the direction of motion, but rather only the relative speed. Therefore, since his accelerating clock is always the same specific v in any instant, the value of gamma must remain constant as well, since it depends on v (ie speed) and not x or t. So per the stationary POV, the accelerating clock must tick slower by the same rate an always inertial clock of the same velocity would.

Equally tactical, Einstein begins and ends the interval with the 2 clocks colocated, and so no observer in the cosmos may disagree on the outcome. The accelerating clock must tick slower per the stationary clock, and thus must age less over the common interval. However, although the accelerating clock must agree that it ages less, Einstein makes no conjecture as to the relative rate of that always-inertial clock per the accelerating clock. However, just the fact that the accelerating clock must age less over the defined interval, was an extrapolation of the special case to the more general case. My opinion is that the LTs also apply from the non-inertial POV, although the process of their application is not so easy.

Einstein didn't use any LT in his analysis of the traveling clock because he only used one frame of reference. LT are for the purpose of seeing what coordinates are assigned to the same even in two frames of reference.

Well, amonst other things, it does explain why the muon decays (as it does) as it transcends the atmosphere to earth. If folks could fly at luminal speeds from here to there, it would be nice to know in advance how much you'll age relative to others over the interval. Another way of looking at it, let's say you have intel that Darth Vader will emit a particle beam that destroys Earth at 11:24pm by his own clock. You can predict the last moment you can destroy him before he destroys the earth, assuming he flies inertially over the interval and you knew his clock readout at some prior point :)



The point would be for the same reasons I mentioned above for the all-inertial case.

What you would learn is how mother nature really works. The LTs show how the dimensions are related by velocity under an invariant c. That's a great advancement in physics, and cosmology as well. The LTs explain the nature of spacetime in the special case. If our understanding of the nature of spacetime can be extended to the more general case (devoid of gravity), I see it as no less important than the advancement under the special case.

Add, folks are generally very interested in answering the questions that remain unanswered. Often, there are many different opinions as to how to answer a yet unanswered question. That usually suggests that all those competing theories are wrong. Usually, when the correct theory arises, everyone knows it and agrees, although it may take some time to be accepted. Beyond SR, if there is a correct transformation between any 2 frames in flat spacetime, then I for one want to know what it is.



I'll give you an A for persistence :) I hope you feel like you helped me get whatever it is that you believed I need.

GrayGhost

As long as you have assigned coordinates to all significant events according to one inertial frame of reference, you cannot learn anything by using the LT to see what those coordinates look like in another frame of reference. LTs will not help you in your Darth Vader scenario unless you have previously answered the question in one FOR.

This, by the way, is the source of many so-called SR confusions and paradoxes; assigning half the coordinates for one observer/object according to one FOR and assigning the other half for another observer/object according to another FOR and trying to answer questions about how to reconcile them. It can't be done. If you do it completely in one FOR for all observers/objects (like you're supposed to), then you'll have all your answers, but if you want, you can also see how those coordinates look for the same events according to any other FOR. By the way, I'm always talking about inertial FORs, if you want to talk about non-inertial, you're on your own.

Let me repeat, nobody in our scenarios owns any FOR. All observers/objects are equal in terms of the information they have independent of any FOR. We, as super observers can talk about what all the observers and objects in our scenario experience if we do extra work in analyzing that POV for each of them. Their individual POVs are not helped by our assigning a FOR in which they are stationary and they can't do it themselves without us, as super observers telling them things that we know that they cannot know.

I'll be persistent with you as long as you continue to not get it, but I'd rather you see the light and say "oh, now I get it".

 

[GrayGhost]

OK then, I can see you are dedicated to this mission here, so let's bang it around for awhile.

I was thinking that the accelerated clock was always in motion, that it happened to possesses the same time readout of the other clock on the initial flyby, and that it was never accelerated. However, I just went back and reread it. Einstein did state the 2 clocks begin in system K, and so he is assuming an instant (or virtually instant) acceleration upon one clock at point A. He does not state whether the clock ever decelerates upon return to point A, not that it matters I suppose. That said ...

Yes, Einstein did indeed define a stationary system K, whereby each clock exists at a different point in the K system, neither necessarily located at the origin of K.

Here's what is stated ...

From this there ensues the following peculiar consequence. If at the points A and B of K there are stationary clocks which, viewed in the stationary system, are synchronous; and if the clock at A is moved with the velocity v along the line AB to B, then on its arrival at B the two clocks no longer synchronize, but the clock moved from A to B lags behind the other which has remained at B by (1/2)tv²/c² (up to magnitudes of fourth and higher order), t being the time occupied in the journey from A to B.

It is at once apparent that this result still holds good if the clock moves from A to B in any polygonal line, and also when the points A and B coincide.

If we assume that the result proved for a polygonal line is also valid for a continuously curved line, we arrive at this result: If one of two synchronous clocks at A is moved in a closed curve with constant velocity until it returns to A, the journey lasting t seconds, then by the clock which has remained at rest the traveled clock on its arrival at A will be (1/2)tv²/c² second slow. Thence we conclude that a balance-clock at the equator must go more slowly, by a very small amount, than a precisely similar clock situated at one of the poles under otherwise identical conditions.

OK. So we know the 2 clocks begin as stationary in some inertial system K. One clock is never put into motion wrt K, and so that clock always remains stationary in the system K. The other clock is put into motion wrt K, so it accelerates and moves thru system K. The interval considered is that defined by the clocks possessing relative motion, both beginning at rest at a point A in K, and both ending at the same point A in K.

So all the observations and deductions stated by Einstein here are made wrt any arbitrary observer stationary in the K system.

Einstein says the accelerated clock must tick slow by (1/2)tv²/c² sec per any frame K observer over the defined interval. IMO, he stated such because gamma (of the LTs) is dependent upon v, and not x or t. His requirement was that the accelerated clock move at constant v over the defined interval from point A back to point A.

OK, so what would you like to say next on this matter?

GrayGhost

 

[PAllen]

OK then, I can see you are dedicated to this mission here, so let's bang it around for awhile.

I was thinking that the accelerated clock was always in motion, that it happened to possesses the same time readout of the other clock on the initial flyby, and that it was never accelerated. However, I just went back and reread it. Einstein did state the 2 clocks begin in system K, and so he is assuming an instant (or virtually instant) acceleration upon one clock at point A. He does not state whether the clock ever decelerates upon return to point A, not that it matters I suppose. That said ...

Yes, Einstein did indeed define a stationary system K, whereby each clock exists at a different point in the K system, neither necessarily located at the origin of K.

Here's what is stated ...

​

OK. So we know the 2 clocks begin as stationary in some inertial system K. One clock is never put into motion wrt K, and so that clock always remains stationary in the system K. The other clock is put into motion wrt K, so it accelerates and moves thru system K. The interval considered is that defined by the clocks possessing relative motion, both beginning at rest at a point A in K, and both ending at the same point A in K.

So all the observations and deductions stated by Einstein here are made wrt any arbitrary observer stationary in the K system.

Einstein says the accelerated clock must tick slow by (1/2)tv²/c² sec per any frame K observer over the defined interval. IMO, he stated such because gamma (of the LTs) is dependent upon v, and not x or t. His requirement was that the accelerated clock move at constant v over the defined interval from point A back to point A.

OK, so what would you like to say next on this matter?

GrayGhost

Did you ever answer my post form long ago on this thread, that despite Mike's category of "elementary observations and calculations", none of the conclusions you draw from applying LTs from instantaneously comoving frames, match what you actually observe and measure, with light delays factored in (or even without). In short, you have to interpret your actual observations in excruciatingly tortured ways to make them consistent with LT of instantaneously comoving inertial observer's LTs. The reason boils down to the co-moving observer has completely different history than you, and pretending that history doesn't count is ludicrous.

 

[GrayGhost]

Yes, he did assign a coordinate system to the accelerating clock, it was the stationary system as he called it.

He designated a coordinate system K. And you are right, he did begin with both clocks stationary (somewhere) in the K system. The K system is an arbitrary inertial system from which observations may be made and LTs applied.

No, he didn't say it was from the POV of an inertial clock.

He said it was wrt the system K, and the always inertial clock is at rest in the K system. So I may state that the accelrated clock runs slow from the POV of the always inertial clock if I wish. Because I do, does not lead that others stationary in the system K will disagree.

He said both clocks are "viewed in the stationary system". He didn't say or imply and it's not true that what he described about what the traveling clock experiences is what the stationary clock sees. We, as super observers, can "see" both clocks simultaneously according to our arbitrarily assigned coordinate system, but there is no implication that we have determined what either of them sees of the other one (until they are colocated again).

Well, I'm not sure what you mean by "super observers". An observer is an observer is an observer. None are more super than the next.

OK, so wrt your comment here ... you are saying that neither observer can say anything about the current readout or rate of the other clock unless colocated, and that on 2nd relocation, the accelerated clock is (1/2)tv²/c² sec slow on arrival. Yes?

I do realize that one cannot say anything about what the accelerated clock might record of the always-inertial clock while non-inertial "as he goes", from a standpoint of using the LTs as designed as they are applied in all-inertial scenarios. All anyone can say is that B cannot dispute his clock aged (1/2)tv²/c² less than the always-inertial clock over the entire interval in collective. However ...

However ... can the always-inertial clock say the accelerated clock (which moves at constant v curvilinearly) always ticks slower by (1/2)v²/c² as it goes? It seems to me he can declare such, however I will need to verify that first.

Einstein didn't use any LT in his analysis of the traveling clock because he only used one frame of reference. LT are for the purpose of seeing what coordinates are assigned to the same even in two frames of reference.

Well, he did state that upon return to point A, the accelerated clock will have ticked (1/2)tv²/c² slow compared to the always-inertial clock, over the interval in collective. To state this, he must assume that that the accelerated clock will tick slow per system K by the 1/gamma, and gamma is inherent in the LTs.

As long as you have assigned coordinates to all significant events according to one inertial frame of reference, you cannot learn anything by using the LT to see what those coordinates look like in another frame of reference.

I disagree. What you will learn, is how to properly map spacetime cooridnates between an inertial and non-inertial system. Also, whether the non-inertial POV records relativistic effects that always-inertial POVs do not. That's the goal here, to determine what a non-inetial POV really looks like. I do concur that observers of both the inertial and non-inertial systems must agree on the readout of clocks at all spacetime events, even if the events are imagined in a way consistent with nature.

LTs will not help you in your Darth Vader scenario unless you have previously answered the question in one FOR.

Well, I never said that any other inertial frame could not make the prediction, given the required variables are known. Maybe I am the very first inertial observer to determine the last opportune moment to stop Darth Vader dead in his tracks, and save mother earth. Maybe not.

This, by the way, is the source of many so-called SR confusions and paradoxes; assigning half the coordinates for one observer/object according to one FOR and assigning the other half for another observer/object according to another FOR and trying to answer questions about how to reconcile them. It can't be done.

I never said anything of the sort. You should not suggest to others that I did.

If you do it completely in one FOR for all observers/objects (like you're supposed to), then you'll have all your answers, but if you want, you can also see how those coordinates look for the same events according to any other FOR.

Of course. Everyone knows that. I could repeat this statement to you, but to what gain?

Let me repeat, nobody in our scenarios owns any FOR. All observers/objects are equal in terms of the information they have independent of any FOR.

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Again, simply because I imagine an observer (or body) at the origin of a system, does not lead that he must be. If at the origin, does he own it? One can call it his if they wish, including he himself. It's simply more convenient to imagine oneself at the origin. You should not assume he owns anything, simply because I refer to it as his frame-of-reference. Anyone may call any system their own. If it cause you great discomfort, I can try to avoid referring to it as "his frame of reference". Or, you can just assume that when I say that, he is not only stationary in said system but also the origin. Others may call it their own if they wish.

We, as super observers can talk about what all the observers and objects in our scenario experience if we do extra work in analyzing that POV for each of them. Their individual POVs are not helped by our assigning a FOR in which they are stationary and they can't do it themselves without us, as super observers telling them things that we know that they cannot know.

Hmmm. What would be an example of what a super observer would know that said individual POVs would not know?

I'll be persistent with you as long as you continue to not get it, but I'd rather you see the light and say "oh, now I get it".

OK then. The problem is, I'm not precisely sure what it is that you believe I do not git? Most things you suggest regarding what you believe I do not understand are simply untrue, no doubt because you make unwarranted assumptions about what I say. The only thing I've seen thus far is this ... you do not like it when I refer to a cooridnate system or frame of reference as "his or hers". As I said, I can try to refrain from that if you are uncomfortable with that.

GrayGhost

 

[GrayGhost]

Did you ever answer my post form long ago on this thread, that despite Mike's category of "elementary observations and calculations", none of the conclusions you draw from applying LTs from instantaneously comoving frames, match what you actually observe and measure, with light delays factored in (or even without). In short, you have to interpret your actual observations in excruciatingly tortured ways to make them consistent with LT of instantaneously comoving inertial observer's LTs. The reason boils down to the co-moving observer has completely different history than you, and pretending that history doesn't count is ludicrous.

I do not disagree in that the process is rather laborious, from the non-inertial POV. However, I submit that it is possible. The inertial frame must be the reference for all spacetime transformations, which does not suggest inertial frames are preferred. Indeed, their histories differ. The fact that they differ should be reeconcilable. The LTs cannot be applied by twin B while non-inertial, unless applied in the infinitesimal of B-time.

GrayGhost

 

[Mike_Fontenot]

[...]
First ... to correctly map spacetime coordinates between systems, one must first determine where the other fellow is in your own system, and the method you use must match mother nature. [...] Twin B must keep track of his proper acceleration every inch the way, and incorporate that into the estimated location of twin A.
[...]

Just FYI:

(You may already know this ... I've tried to get the point across it before ... but just to be sure you've got it, here it is again, perhaps stated slightly differently):

Suppose the accelerating traveler wants to determine (from his own personal "point-of-view") what the current distance is to some particular remote person, and what the current date-and-time reading currently is on that particular person's wristwatch, at any given instant in the traveler's life.

And take the more difficult case where the traveler is ALWAYS accelerating (perhaps sometimes toward, and sometimes away from, the (perpetually-unaccelerated) home twin, with only isolated instants in his life where his acceleration is momentarily zero).

It MAY be possible for the traveler to make those determinations purely from his own measurements and elementary calculations, and purely from his own "point-of-view"... i.e., starting with his own DIRECT determination of remote distance, velocity, and remote time. I don't KNOW for sure if that's possible, because I've never spent any time trying to figure out how to do it ... I didn't NEED to do that, because I figured out how to get the answers he wants in (what is almost certainly) a MUCH simpler and easier way.

The easy way (the way that is used in the CADO methodology), is for the traveler to figure out, at each instant "t" of his life, the distance to the home twin, and the date-and-time on her wristwatch, ACCORDING TO THE HOME TWIN. All he needs to do that, is to know how his acceleration (on his own accelerometer) has varied, for all times in his life up to (and including) the current instant "t". (He also needs to know what her distance and date-and-time were at some instant "t0" of his past, and he doesn't actually need to know what his acceleration profile was before t0, or what it will be after the instant "t").

So the amount of work he needs to do, so far, is exactly the same work that his home twin needs to do (from her own "point-of-view"), in order to determine that same information ... it's the SAME information, and the SAME calculations. It's a relatively simple process, since she is perpetually inertial. (For instantaneous velocity changes, with coasting segments in between, the process is trivial. For constant acceleration segments, it is harder, but still analytically possible, in closed form. For completely general acceleration profiles, numerical integrations are necessary.)

AFTER he has that information, the ONLY remaining thing he needs to do is use that data in the basic CADO equation, which is always a trivial undertaking: it's just one multiplication and one addition (or subtraction).

Above, I said that I don't know (and don't much care) how (and even if) the traveler can determine his "point of view" of her distance and date-and-time, DIRECTLY from his own measurements and calculations. So WHAT do I mean when I say "that any OTHER reference frame (besides the CADO frame), in which the traveler is permanently at the spatial origin, is unsatisfactory, because they will all contradict the traveler's own measurements and elementary calculations"?

The answer is that the traveler makes those measurements and calculations ONLY during segments of his life when he is NOT accelerating. So the argument is basically a "counter-factual" argument: at any instant of his life, the traveler CAN, if he so chooses, decide to stop accelerating for more than a single momentary instant ... for some segment of his life ... before resuming accelerating again. He may not choose to ever do that, but he CAN if he wants. IF he does, he can make the SAME kind of observations and calculations that a perpetually-inertial observer who is (temporarily) co-located with him during that segment can make.

What I prove in my paper is that if the traveler does that, he will always agree with that (temporarily) co-located perpetually-inertial observer, about the home twin's distance and date-and-time. And they will agree no matter how short that segment of the traveler's life is. It is even possible to show, with a careful limiting argument, that they will agree EVEN when the acceleration is zero only at a single instant (although in this case, they don't agree about velocities, they only agree about remote distances and remote times at that instant). This is the proof that basically allows me to say that the traveler is a "full-fledged" inertial observer during any segment of his life in which he is unaccelerated, no matter how short. And this is the characteristic which is NOT found in any of the alternatives to the CADO frame.

Mike Fontenot

 

[GrayGhost]

Mike Fontenot,

OK, thanks for that post. I need to process a few things first before responding.

GrayGhost

 

[Dale]

So WHAT do I mean when I say "that any OTHER reference frame (besides the CADO frame), in which the traveler is permanently at the spatial origin, is unsatisfactory, because they will all contradict the traveler's own measurements and elementary calculations"?

Mike, as we have discussed many times in many threads this is simply a lie and repeating it does not make it true. Due to diffeomorphism invariance all coordinate systems, inertial or non-inertial, using any arbitrary synchronization convention or even not using a timelike coordinate, all possible coordinate systems will agree on the result of any experimental measurement. Despite numerous challenges you have yet to substantiate this claim with even a single supporting example. In your paper you may have defined "elementary calculations" in such a way as to make it tautologically true, but your assertion that other coordinate systems contradict the traveler's measurements is a bald-faced lie.

 

[ghwellsjr]

Mike, do I have your permission to quote from any part of your paper to critique your position?

 

[Mike_Fontenot]

Mike, do I have your permission to quote from any part of your paper to critique your position?

Sure, at least as far as I'm concerned ... that's what publications are all about. I suspect the publisher might not like to see LARGE portions of any paper, on which they hold the copyright, reproduced anywhere, and the law would probably be on their side, but I doubt they'd care about fairly limited quotes. At any rate, any decision you make to quote from that paper doesn't really have anything to do with me, since I had to sign the copyright over to them ... they own it ... it's just between you and the publisher.

Mike Fontenot

 

[ghwellsjr]

At any rate, any decision you make to quote from that paper doesn't really have anything to do with me, since I had to sign the copyright over to them ... they own it ... it's just between you and the publisher.

Mike Fontenot

Is that the reason you would make this statement?

"Those elementary observations and elementary calculations are given, in detail, in my paper. I'm not willing to reproduce them here."

 

[Mike_Fontenot]

Is that the reason you would make this statement?

"Those elementary observations and elementary calculations are given, in detail, in my paper. I'm not willing to reproduce them here."

Well, I wouldn't do a long quote for several reasons: for one thing, because of the copyright agreement I signed, but also because I was only willing to do that much work ONCE, when I wrote the paper. ONCE is enough.

Mike Fontenot

 

[ghwellsjr]

Well, I wouldn't do a long quote for several reasons: for one thing, because of the copyright agreement I signed, but also because I was only willing to do that much work ONCE, when I wrote the paper. ONCE is enough.

Mike Fontenot

Are you suggesting that I could not adequately state your definition of "elementary observations and elementary calculations" without a long quote and much work?

 

[GrayGhost]

Mike_Fontenot,

Interesting subject it is.

There are a few issues here ...

1. what does twin B see as he goes?
2. does B see the heavens precisely as the co-located MSIRF observer does, at that instant?
3. why can the A-velocity per B go superluminal, while the co-located MSIRF observer disagrees (which is never superluminal)?
4. can the LTs be applied by twin B while non-inertial, and if so, how?
5. is there a way that twin B may make correct spacetime transformations using only his own measurements alone?

I've got answers of my own on these matters, however I'm not sure where to start.

BTW ... wrt 4) EDIT: I'm rethinking this for now :)

GrayGhost

 

[GrayGhost]

Just FYI:

... at any instant of his life, the traveler CAN, if he so chooses, decide to stop accelerating for more than a single momentary instant ... for some segment of his life ... before resuming accelerating again. He may not choose to ever do that, but he CAN if he wants. IF he does, he can make the SAME kind of observations and calculations that a perpetually-inertial observer who is (temporarily) co-located with him during that segment can make.

EDITs have been made in this post, and they are highlighted ...

Mike, let me ask you ...

What's the difference between going inertial for 1 quintillionth of a microsecond, versus considering the velocity at a point on the x vs t position plot while still non-inertial? I mean, from a standpoint of what twin B can do in that time, what's the diff?

On the one hand, I realize that while inertial, one is not dynamically changing in POV. On the other hand, there's not enough time for twin B to bounce any radar signals out and back off twin A, either way. Now, the LTs were designed for the all-inertial case, yes, however it seems to me that all heavenly bodies exist precisely where the co-located MSIRF observer says they do, including twin B. Why not? Twin B and the MSIRF observer are "at that instant" colocated and of zero relative v. They are both then receiving the same light signals from their surroundings, including from twin A, so they should then see the heavens the same at that instant. If the MSIRF observer says twin A is currently right there, then although twin B may not know such from his own classical calculations, there's no good reason that twin B should disagree, because the special theory is rock solid. If they were of differing v when colocated, I'd contend differently, however they are not.

If twin B's calculations based upon his own measurements tell him something differently, then something is amiss. What's amiss IMO, is the fact that the non-inertial twin B deduces the twin A velocity differently from observations and "calculations made in the classical way". Let's face it, he can't plug superluminal velocities into the LTs, nor should he try. His POV dynamically changes, which causes light's speed to appear variable across spatial expanse (but never at his own location). The reason he measures the A-velocity differently is because he (rather accidentally) accounts for length-contraction while ignoring dilation (and doppler effects). If he does not ignore said effects, and accounts for all of them, then he should obtain the relative A-velocity representing the current slope of the A-worldline. Events move in spacetime while non-inertial, and this cannot be ignored whether B is trying to determine the A-velocity from bounced radar signals, or determining the A-velocity from a space vs time plot after the fact, IMO.

Now I realize that you use the twin-A system as the reference for all future calculations as they go, so you do not have the superluminal problem. I'm just trying to nail down the reasoning as to why twin B should disagree with the MSIRF observer at their moiment of colocation, and how to justify a resolution of that matter in a way that all observers agree (as consistent with SR).

GrayGhost

 

[Mike_Fontenot]

[...]
What's the difference between going inertial for 1 quintillionth of a microsecond, versus considering the velocity at a point on the x vs t position plot while still non-inertial?

It turns out to be true that the traveler DOES agree with his MSIRF (about distances to, and ages of, remote people) at each and every instant of his life, even when he is stationary with that particular MSIRF at only that single instant. But to PROVE that, I needed to FIRST prove that it is true for an arbitrarily long segment of the traveler's life, and then prove it for a finite, but arbitrarily short segment, and then finally (by using a limiting argument) to prove that it is true even when the "segment" consists of only a single instant of time.

It's not possible to understand those proofs by trading "sound bites" on a web forum. If you really want to understand them, you're just going to have to spend a lot of "quiet-time" with my paper ... there's no other way.

(Most university libraries will either have the volumes of that journal, or can get them through inter-library loan. At least that's the case in the USA. I don't know about in other parts of the world, though ... in those cases, you may just have to "bite-the-bullet" and give the publisher his due. Otherwise, you'll just have to answer your questions on your own, or from sources other than me.)

[...]
I'm just trying to nail down the reasoning as to why twin B should disagree with the MSIRF observer at their moment of co-location [...]
[...]

I think you need to spend some more time with this posting:

https://www.physicsforums.com/showpost.php?p=3231195&postcount=328 .

If that's not enough to answer your question (about WHY the traveler, whenever his acceleration is non-zero, doesn't agree with his MSIRF about their respective relative velocities wrt the home-twin), then I think it's possible that you might need some additional experience working with derivatives: exactly how they are defined, what they mean, and how they are used.

Mike Fontenot

 

[Dale]

GrayGhost, this is Mike's pattern. Whenever he is asked for details he simply refers to his paper, and whenever challenged to justify a false assertion he simply avoids responding entirely. He is very passive-aggressive.

 

[GrayGhost]

Mike Fontenot,

Derivatives are not a problem for me.

It sounds like we are in agreement far as twin A existing precisely where the co-located MSIRF observer says he does. Twin B will disagree based upon his own measurements and calculations assuming he makes them in the typical classical way, however twin B will be wrong in his assessment. My position is that twin B is incorrect because of 2 reasons ...

(1) because he (w/o knowing) accounts for contractions while (w/o realizing) ignoring dilations. IOWs, twin B fails to account for the fact that events move in spacetime while non-inertial, and such an event would be the B-departure-from-A. So, B's assessment is incomplete IMO.

(2) because while non-inertial, light's speed must appear to travel variantly because of one's own dynamically changing POV. This is analagous to measuring light's speed across an expanse of space which includes a very large and very strong gravity well, from the vantage of one far removed from the region. Yet, light's speed is always c when measured at the non-inertial observer, and it is always measured at c in any small locale of the gravity well.

In my mind, I see why twin B calculates things differently, and inconsistently with any co-located MSIRF observer. Instead of just saying they "should" disagree (given the special theory requires it), and reverse engineering the B side from the A side, my opinion is that the reasoning of their disagreement needs articulated, and then a transformation from B's assessment to the co-located MSIRF observer's assessment may be obtained (with fuller meaning). The hope would be that twin B does not have to consider everything from the A-side first to determine the state of the union from his own measurements and calculations.

As to whether there already exists any other methods (and conventions) that differ, while getting the job done (properly, and considtent with SR), I am not sure.

GrayGhost

 

[GrayGhost]

GrayGhost, this is Mike's pattern. Whenever he is asked for details he simply refers to his paper, and whenever challenged to justify a false assertion he simply avoids responding entirely. He is very passive-aggressive.

Well, it seems to me that in discussing a paper, it would promote folks to want to buy it. Imagine the 1905 OEMB paper was posted today for the first time in an online physics journal. No matter how much relativity is discussed online regarding OEMB, countless folks will always debate it ... mainly because they don't grasp it all. I'm quite confident that I'd buy that paper today, to obtain the story straight from the horse's mouth ... especially given all the debates about the details of the theory. That said, I would figure that detailed discussions of the key points of the paper would encourage increased sales.

GrayGhost

 

[Dale]

Me too, which is partly why I believe it is simply a debate tactic when he knows he has an indefensible claim.

 

[ghwellsjr]

Did buying Mike's paper help you in any respect?

Help me? You mean help me understand his position? Yes, I believe I understand exactly what his fatal mistake is.

I have posted my critique of Mike's scheme here:

https://www.physicsforums.com/showthread.php?p=3245978#post3245978

Please respond there, rather than here.

 

[GrayGhost]

OK, so wrt your comment here ... you are saying that neither observer can say anything about the current readout or rate of the other clock unless colocated, and that on 2nd relocation, the accelerated clock is (1/2)tv²/c² sec slow on arrival. Yes?

I do realize that one cannot say anything about what the accelerated clock might record of the always-inertial clock while non-inertial "as he goes", from a standpoint of using the LTs as designed as they are applied in all-inertial scenarios. All anyone can say is that B cannot dispute his clock aged (1/2)tv²/c² less than the always-inertial clock over the entire interval in collective. However ...

However ... can the always-inertial clock say the accelerated clock (which moves at constant v curvilinearly) always ticks slower by (1/2)v²/c² as it goes? It seems to me he can declare such, however I will need to verify that first.

ghwellsjr,

I finally got to looking at this. I'm just curious ... Do you agree that-by-extrapolation-of-SR the accelerating clock will tick slower by the factor of 1/gamma over the entire interval, and at any point during its transit, per the inertial clock?

GrayGhost