Register to reply 
The case for True Length = Rest Length 
Share this thread: 
#343
Apr811, 04:50 PM

P: 432

I do have a disagreement with Mike on one particular matter (ie instantaneous Avelocity 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 Amotion arises per the noninertial 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. 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 chronicsalespitchinflavor", 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. Did buying Mike's paper help you in any respect? GrayGhost 


#344
Apr911, 12:29 AM

P: 432

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 ½tv^{2}/c^{2} seconds slow.In a theory devoid of gravity, it seems to me that a clock moving in a continuously curved line is noninertial. 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 allinertial 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 allinertial scenario. That point was made way back yonder, and it's not as though anyone didn't already know it. 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 coordinates, 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. 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 


#345
Apr911, 06:51 AM

Mentor
P: 17,505




#346
Apr1011, 02:38 AM

PF Gold
P: 4,776




#347
Apr1011, 04:34 AM

PF Gold
P: 4,776

Your comments show that you don't understand the difference between a noninertial object/observer and a noninertial 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 noninertial. But he doesn't assign a noninertial 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 allinertial 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 spacetime coordinates of different events in the first frame, you can use the Lorentz Transform to see what the spacetime coordinates are in the second inertial frame. That's what SR is all about. 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 noninertial 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. We might, of course, content ourselves with time values determined by an observer stationed together with the watch at the origin of the coordinates, and coordinating 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 coordination 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. 


#348
Apr1011, 06:57 PM

P: 432

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 noninertial, 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 Aclock readout and the associated Brange 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 Brange at that instant based on (what Mike says) his own observations, measurements, and calculations. Twin A's calculated Brange at said Atime must precisely match the twin B LT spacetransform 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 noninertial 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). GrayGhost 


#349
Apr1111, 12:50 AM

P: 432

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 alwaysinertial 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 noninertial POV, although the process of their application is not so easy. 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. GrayGhost 


#350
Apr1111, 06:26 AM

Mentor
P: 17,505




#351
Apr1111, 11:01 AM

PF Gold
P: 4,776

This, by the way, is the source of many socalled 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 noninertial, 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". 


#352
Apr1111, 12:47 PM

P: 432

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)tv^{2}/c^{2} 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 


#353
Apr1111, 04:17 PM

Sci Advisor
PF Gold
P: 5,078




#354
Apr1111, 04:56 PM

P: 432

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)tv^{2}/c^{2} sec slow on arrival. Yes? I do realize that one cannot say anything about what the accelerated clock might record of the alwaysinertial clock while noninertial "as he goes", from a standpoint of using the LTs as designed as they are applied in allinertial scenarios. All anyone can say is that B cannot dispute his clock aged (1/2)tv^{2}/c^{2} less than the alwaysinertial clock over the entire interval in collective. However ... However ... can the alwaysinertial clock say the accelerated clock (which moves at constant v curvilinearly) always ticks slower by (1/2)v^{2}/c^{2} as it goes? It seems to me he can declare such, however I will need to verify that first. 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 frameofreference. 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. GrayGhost 


#355
Apr1111, 05:41 PM

P: 432

GrayGhost 


#356
Apr1111, 06:09 PM

P: 250

(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 "pointofview") what the current distance is to some particular remote person, and what the current dateandtime 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 (perpetuallyunaccelerated) 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 "pointofview"... 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 dateandtime 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 dateandtime 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 "pointofview"), 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 dateandtime, 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 "counterfactual" 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 perpetuallyinertial observer who is (temporarily) colocated 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) colocated perpetuallyinertial observer, about the home twin's distance and dateandtime. 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 "fullfledged" 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 


#357
Apr1211, 12:15 AM

P: 432

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


#358
Apr1211, 06:56 AM

Mentor
P: 17,505




#359
Apr1211, 08:12 AM

PF Gold
P: 4,776

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



#360
Apr1211, 09:59 AM

P: 250

Mike Fontenot 


Register to reply 
Related Discussions  
Rest Length, Coordinate Length, and an argument for True Length  Special & General Relativity  242  
Length in the rest frame  Advanced Physics Homework  0  
Basic Calculus III Arc Length Parameter and Length Getting a negative length  Calculus & Beyond Homework  6  
More physics behind the concepts of length and rest length  Special & General Relativity  0  
Rest length in general relativity  Special & General Relativity  124 