## The case for True Length = Rest Length

 Quote by DaleSpam The Lorentz transform transforms between different inertial frames where v
Indeed. I do not disagree, assuming one assumes the LTs cannot be used by non-inertial observers, because v must be v < c in the LTs. IMO, there exists a luminal A-velocity that relates to the super-luminal A-velocity noted by twin B, and the luminal v allows twin B to use the LTs to correctly transform between the A and B systems at any B-instant. I just need to prove it :)

 Quote by DaleSpam Again, you can re-define velocity, but you need to be clear that you are doing so. Alternatively, you can leave velocity unchanged and define some other parameter that allows you to select the correct Lorentz transform.
Wrt your 1st sentence here ... Yes.

Wrt your 2nd sentence here ... Not sure what you mean there. If v>c, no LT transform can be adequately selected for use, because the results will not be correct.

 Quote by DaleSpam I think that is a good idea. You will learn alot in the process regardless of the eventual outcome.
It was your idea. The only reason I hadn't persued a math-model in the past, is because I felt certain it had already been done by many others since 1905. So, we'll see :)

GrayGhost

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 Quote by GrayGhost The only reason I hadn't persued a math-model in the past, is because I felt certain it had already been done by many others since 1905.
This shows that you lack a basic understanding of Einstein's theory presented in his 1905 paper. He didn't talk about non-inertial frames and he didn't talk about each observer in a scenario being stationary in their own frame or having their own rest frame. His original version of the Twin Paradox had the traveler going in a big circle with the inertial observer located at one point on the circle, not at its center. The traveler is never inertial and yet Einstein analyzes him using a frame in which the inertial observer is stationary. Get it? One inertial frame to analyze all observers. That was Einstein's theory.

 Quote by ghwellsjr Do you realize that Mike believes his approach is the only valid way? And that is the argument that we all have with him? Not that his approach is wrong, it's just not preferred, but he thinks it is in some fundamental way.
Yes and yes, I realize that.

 Quote by ghwellsjr I doubt that you are going to understand his approach unless you get a copy of his paper because he never explains it fully on this forum. He leaves important definitions out of his explanations because he wants everyone to buy his paper for $15. If he explained what is contained in his paper on this forum, why would anyone want to buy his paper? I think I understand Mike's approach, since it's similar to what I myself have long envisioned, if not the very same thing. Although ... I do have a disagreement with Mike on one particular matter (ie instantaneous A-velocity per B), however I'm not sure it matters far as his spacetime solutions are concerned. The way I see it, he's making correct assumptions w/o knowing WHY they are correct. I believe I have the soln to that matter, and it not only validates his assumptions but also explains WHY superluminal A-motion arises per the non-inertial B POV ... and also how a superluminal motion equates to an equivalent LT luminal velocity. So, I kill 2 (or 3) birds with 1 stone there, and possible w/o changing Mike's model's solns at all.  Quote by ghwellsjr I have a copy of his paper but it is copywrited. I'd like to discuss his ideas but if I give away all his secrets or quote from his paper, am I violating his copywrite? Is if fair for me to be discussing his ideas on this forum when only he and I (and anyone else with his paper) will know what we are talking about? The last person that was promoting a book he wrote for$8 got instantly banned. Why is Mike still able to promote his \$15 paper and not get banned? Huh?
If I cannot discuss his work after having bought it, then I see no reason to buy it in the first place.

I wouldn't ban any fellow for periodically mentioning his published paper is available for purchase, if it relates to the discussion at hand. If the posts become "too often, or chronic-sales-pitch-in-flavor", then maybe so. I don't think Mike falls into that category from what I've seen here, personally.

What sounds promissing is that you and DaleSpam seem to agree his paper is valid. I've read many papers that weren't worth a penny, and in fact I should have been paid for the time I wasted reading it. Some journals will publish almost anything, and I'll never know why they keep their reviewers.

GrayGhost

 Quote by ghwellsjr This shows that you lack a basic understanding of Einstein's theory presented in his 1905 paper.
I understand the special theory as well as you do, probably better.

 Quote by ghwellsjr He didn't talk about non-inertial frames ...
OEMB section 3: 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 travelled clock on its arrival at A will be ½tv2/c2 seconds slow.
In a theory devoid of gravity, it seems to me that a clock moving in a continuously curved line is non-inertial. Therefore, even though Einstein's SR was a theory of uniform translatory motion, he extrapolated what the effect of acceleration would be based upon the all-inertial theory.

All I've been doing here in this thread ghwells, is hypothesizing by extrapolation (of the special theory) how twin B might apply the LTs to accurately transform his spacetime coordinates into the twin A system. Clearly, twin B cannot apply the LTs as easily as one would in the all-inertial scenario. That point was made way back yonder, and it's not as though anyone didn't already know it.

 Quote by ghwellsjr ... and he didn't talk about each observer in a scenario being stationary in their own frame ...
OEMB section 1: We might, of course, content ourselves with time values determined by an observer stationed together with the watch at the origin of the co-ordinates, and ...
and that statement allows us to imagine the same anywhere else in the OEMB paper, including section 3 where the LTs are derived. Although it does not have to be, said coordinate system may well be assigned by the observer to himself, as his own frame of reference.

 Quote by ghwellsjr His original version of the Twin Paradox had the traveler going in a big circle with the inertial observer located at one point on the circle, not at its center. The traveler is never inertial and yet Einstein analyzes him using a frame in which the inertial observer is stationary. Get it? One inertial frame to analyze all observers. That was Einstein's theory.
Get it? You're kidding, yes?

So now I must ask you, why did you feel the need to tell me all this in the first place? What's your motive here?

GrayGhost

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 Quote by GrayGhost It was your idea.
Hehe, yes, I do tend to think my own ideas are good ideas

 Quote by GrayGhost What sounds promissing is that you and DaleSpam seem to agree his paper is valid.
I have not read his paper, since I am unwilling to pay for it. However, I have no objection to what he has described of his CADO equation on this forum. My objection is limited to his occasional incorrect claims that his CADO convention is the only correct simultaneity convention for a non-inertial observer and all other conventions are wrong. He has avoided making that claim in this thread, so I am OK with what he has said here.

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 Quote by GrayGhost I think I understand Mike's approach, since it's similar to what I myself have long envisioned, if not the very same thing.
Good, here is a post that Mike linked to in his first post on this thread (page 11, post #167)
 Quote by Mike_Fontenot I would say that there IS a valid frame for an accelerating observer. That frame consists of the (infinite) collection of inertial frames (the MSIRFs), one for each instant of the accelerating observer's life, each of which being momentarily stationary wrt the accelerating observer at that given instant in his life. This frame is a well-defined...there is no ambiguity or inconsistency at all. And it is NOT a "convention": there are no other reasonable alternatives, because it is the ONLY possible frame for the accelerating observer which doesn't contradict his own elementary measurements and elementary calculations.
Maybe you could tell us what he means by "elementary measurements and elementary calculations", because he won't tell us:
 Quote by Mike_Fontenot Those elementary observations and elementary calculations are given, in detail, in my paper. I'm not willing to reproduce them here.
Oh, now he calls them "elementary observations and elementary calculations". I guess "observations" is the same as "measurements". In any case, since you think you understand his approach, and it is similar, if not identical to what you have long envisioned, what exactly does he and would you mean by these terms?
 Quote by GrayGhost What sounds promissing is that you and DaleSpam seem to agree his paper is valid.
I wonder why you think that. Can you provide the link that gave you this idea?
Help me? You mean help me understand his position? Yes, I believe I understand exactly what his fatal mistake is.

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Quote by GrayGhost
 Quote by ghwellsjr This shows that you lack a basic understanding of Einstein's theory presented in his 1905 paper.
I understand the special theory as well as you do, probably better.
I'm sure you do, but I was talking about Einstein's theory presented in his 1905 paper which you alluded to in a previous post. Special Relativity has evolved since then in all kinds of directions which I have never seen the need to investigate and I don't claim to understand these additions to what Einstein first presented.
Quote by GrayGhost
 Quote by ghwellsjr He didn't talk about non-inertial frames ...
OEMB section 3: 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 travelled clock on its arrival at A will be ½tv2/c2 seconds slow.
In a theory devoid of gravity, it seems to me that a clock moving in a continuously curved line is non-inertial. Therefore, even though Einstein's SR was a theory of uniform translatory motion, he extrapolated what the effect of acceleration would be based upon the all-inertial theory.
(Please note, you are quoting from the end of section 4, not 3.)

Your comments show that you don't understand the difference between a non-inertial object/observer and a non-inertial frame of reference. This indicates to me that you have this erroneous concept that Special Relativity requires you to assign each object/observer to its own frame. This is completely wrong.

Einstein's SR is a theory about a single inertial frame of reference in which all objects/observers are described and analyzed, and each object/observer can have its own velocities and/or accelerations but still described by that one single frame. In this example, he talks about two clocks, one at rest at location A and the other traveling in a circle starting at A, moving away from A, and then returning to A, accelerating all the time. In other words, this clock is non-inertial. But he doesn't assign a non-inertial frame of reference to it in which it is continuously at rest nor does he assign a series of inertial frames to it in which the clock is at rest in all of them. He wasn't extrapolating SR from an all-inertial theory to include accleration. In fact, if you read the paragraph immediately before the one you quoted, you will see:
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 ½tv²/c²(up to magnitudes of fourth and higher order), t being the time occupied in the journey from A to B.
Now, after you describe and analyze all the stationary, moving, and accelerating objects and observers in a scenario according to one inertial frame of reference, you can switch to a different inertial frame of reference which is described as having a motion with respect to the first frame of reference. And then by looking at the space-time coordinates of different events in the first frame, you can use the Lorentz Transform to see what the space-time coordinates are in the second inertial frame. That's what SR is all about.
 Quote by GrayGhost All I've been doing here in this thread ghwells, is hypothesizing by extrapolation (of the special theory) how twin B might apply the LTs to accurately transform his spacetime coordinates into the twin A system. Clearly, twin B cannot apply the LTs as easily as one would in the all-inertial scenario. That point was made way back yonder, and it's not as though anyone didn't already know it.
I always wonder why anyone would want to go from one inertial frame to another inertial frame, I can't image why you would want to try to go from an inertial frame to a non-inertial frame. What's the point? Suppose you can find someone who has done this somewhere during the last century or suppose you figure out how to do it on your own. What do you learn by doing this?

Take for example the Twin Paradox. It is most easily described and analyzed using a frame of reference in which both twins start out at rest. You get your answer, the traveling twin has aged less upon his return. You know that any other frame will yield the same answer, so why do it? Even if you knew how to use a non-inertial frame (or a series of inertial frames) in which the traveler was always at rest to describe the scenario, why do it? You're going to get the same answer.
Quote by GrayGhost
 Quote by ghwellsjr ... and he didn't talk about each observer in a scenario being stationary in their own frame ...
OEMB section 1: We might, of course, content ourselves with time values determined by an observer stationed together with the watch at the origin of the co-ordinates, and ...
and that statement allows us to imagine the same anywhere else in the OEMB paper, including section 3 where the LTs are derived. Although it does not have to be, said coordinate system may well be assigned by the observer to himself, as his own frame of reference.
Here's the whole quote:
We might, of course, content ourselves with time values determined by an observer stationed together with the watch at the origin of the co-ordinates, and co-ordinating the corresponding positions of the hands with light signals, given out by every event to be timed, and reaching him through empty space. But this co-ordination has the disadvantage that it is not independent of the standpoint of the observer with the watch or clock, as we know from experience. We arrive at a much more practical determination along the following line of thought.
Einstein was rejecting this idea because it doesn't work and he proceeded to describe a method that does work. And he wasn't describing a frame of reference here. He was describing what happens when you separate time from space and treat them as independent absolutes.
Quote by GrayGhost
 Quote by ghwellsjr His original version of the Twin Paradox had the traveler going in a big circle with the inertial observer located at one point on the circle, not at its center. The traveler is never inertial and yet Einstein analyzes him using a frame in which the inertial observer is stationary. Get it? One inertial frame to analyze all observers. That was Einstein's theory.
Get it? You're kidding, yes?

So now I must ask you, why did you feel the need to tell me all this in the first place? What's your motive here?

GrayGhost
My motive is to help you learn, and I hope you get it this time.

 Quote by ghwellsjr Good, here is a post that Mike linked to in his first post on this thread (page 11, post #167) Maybe you could tell us what he means by "elementary measurements and elementary calculations", because he won't tell us: Oh, now he calls them "elementary observations and elementary calculations". I guess "observations" is the same as "measurements". In any case, since you think you understand his approach, and it is similar, if not identical to what you have long envisioned, what exactly does he and would you mean by these terms?
Observations = measurements, per most folks.

Wrt Mike Fontenot's "elementary observations and elementary calculations", I can only guess what he means. There are 2 issues at hand here ...

First ... to correctly map spacetime cooridnates between systems, one must first determine where the other fellow is in your own system, and the method you use must match mother nature. One thing's for certain, while non-inertial, B cannot assume A sits at half the EM's roundtrip length. Twin B must keep track of his proper acceleration every inch the way, and incorporate that into the estimated location of twin A. Or, B may also use the receipt of light signals "of known proper frequency upon transmission" to determine (via doppler shift) the relative range to A, although that may be more difficult and less accurate. In either case, the latest known location of A corresponds to the prior reflection event contained in the latest received EM signal, not anytime thereafter (which would be a guess). In any case, once B knows where A was at the reflection event, then ...

Second ... if the LT calculation (that B runs for A) is correct, then the results must precisely match what twin A then observes (measures) and calculates ... Twin B has his LT calculated A-clock readout and the associated B-range per A at that time. When twin A "observes" his current clock readout at that B estimated time value, twin A then possesses a calculated B-range at that instant based on (what Mike says) his own observations, measurements, and calculations. Twin A's calculated B-range at said A-time must precisely match the twin B LT space-transform result, or someone screwed up somewhere.

The idea is this ... we already have a special theory that maps spacetime cooridnates between inertial systems. The goal is to apply the LTs in the non-inertial case, and in a way that is completely consistent with the special theory, even if the process is not identical. If it is inconsistent with the special theory, then it's no good. Also, all observers must concur on all results, including their expected disagreements due to relative simultaneity (as in the special theory).

 Quote by ghwellsjr I wonder why you think that. Can you provide the link that gave you this idea?
Well, DaleSpam had just stated here that he's had no problem with Mike's approach. He and you both have stated that you are not arguing about his model, but rather only that he believes it's the only correct approach. I'm pretty sure you had just stated that recently here.

 Quote by ghwellsjr Help me? You mean help me understand his position? Yes, I believe I understand exactly what his fatal mistake is.
Pray tell :) I'd like to hear this !

GrayGhost

 Quote by ghwellsjr I'm sure you do, but I was talking about Einstein's theory presented in his 1905 paper which you alluded to in a previous post. Special Relativity has evolved since then in all kinds of directions which I have never seen the need to investigate and I don't claim to understand these additions to what Einstein first presented.
Well, I too learned SR straight from the 1905 paper as well. IMO, it's by far the best way. Minkowski evolved Einstein's SR graphically w/o changing it, and added much to its meaning. Others did as well, eg (say) Terrell, Penrose, and Loedel. Others, extended the SR to the case of acceleration, eg Rindler for example. I do not see that anyone has since altered the original 1905 OEMB. It's still correct as written under the scope for which it was considered.

 Quote by ghwellsjr Please note, you are quoting from the end of section 4, not 3.
Indeed, good eye. Section 4 it was.

 Quote by ghwellsjr Your comments show that you don't understand the difference between a non-inertial object/observer and a non-inertial frame of reference...
Now now. You should consider that you may be reading something into my statements that are not there.

 Quote by ghwellsjr This indicates to me that you have this erroneous concept that Special Relativity requires you to assign each object/observer to its own frame. This is completely wrong...
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.

 Quote by ghwellsjr Einstein's SR is a theory about a single inertial frame of reference in which all objects/observers are described and analyzed, and each object/observer can have its own velocities and/or accelerations but still described by that one single frame.
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?

 Quote by ghwellsjr In this example, he (Einstein) talks about two clocks, one at rest at location A and the other traveling in a circle starting at A, moving away from A, and then returning to A, accelerating all the time. In other words, this clock is non-inertial. But he doesn't assign a non-inertial frame of reference to it in which it is continuously at rest nor does he assign a series of inertial frames to it in which the clock is at rest in all of them. He wasn't extrapolating SR from an all-inertial theory to include accleration.
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 ...

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. 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.

 Quote by ghwellsjr 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 ½tv²/c²(up to magnitudes of fourth and higher order), t being the time occupied in the journey from A to B.Now, after you describe and analyze all the stationary, moving, and accelerating objects and observers in a scenario according to one inertial frame of reference, you can switch to a different inertial frame of reference which is described as having a motion with respect to the first frame of reference. And then by looking at the space-time coordinates of different events in the first frame, you can use the Lorentz Transform to see what the space-time coordinates are in the second inertial frame. That's what SR is all about.
Indeed. Again, I have no idea why you are telling me this as though I do not know?

 Quote by ghwellsjr I always wonder why anyone would want to go from one inertial frame to another inertial frame, ...
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 :)

 Quote by ghwellsjr ... I can't image why you would want to try to go from an inertial frame to a non-inertial frame. What's the point? Suppose you can find someone who has done this somewhere during the last century or suppose you figure out how to do it on your own. What do you learn by doing this?
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.

 Quote by ghwellsjr ... My motive is to help you learn, and I hope you get it this time.
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

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 Quote by GrayGhost One thing's for certain, while non-inertial, B cannot assume A sits at half the EM's roundtrip length.
Sure he can. See the Dolby and Gull figure 9 that I pointed out earlier.

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 Quote by GrayGhost ... Now now. You should consider that you may be reading something into my statements that are not there. ... 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. ... 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? ...
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.
 Quote by GrayGhost 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.
 Quote by GrayGhost 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).
 Quote by GrayGhost 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.
 Quote by GrayGhost 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".

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 possess 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 ...
 Quote by 1905 OEMB 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 travelled 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

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 Quote by 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 possess 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.

 Quote by ghwellsjr 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.

 Quote by ghwellsjr 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.

 Quote by ghwellsjr 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.

 Quote by ghwellsjr 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.

 Quote by ghwellsjr 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.

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.

 Quote by ghwellsjr 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.

 Quote by ghwellsjr 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?

 Quote by ghwellsjr 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.
.

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.

 Quote by ghwellsjr 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?

 Quote by ghwellsjr 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

 Quote by PAllen 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

 Quote by GrayGhost [...] 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

 Mike Fontenot, OK, thanx for that post. I need to process a few things first before responding. GrayGhost