Celeritas

Michel123456, In my prior, I said the above. Better wording (edits are in red highlight) as follows ... For purely inertial spacetime systems, all events move downward at the steady rate of proper-time. However our animated GIF presents the POV of a properly accelerating observer, represented by a sequence of momentarily co-located and co-moving inertial reference frames (MCCIRF). For our non-inertial POV here (presented as stationary), there is a super-positional effect that occurs only within his spacetime system, that causes the downward rate of events to change from the steady rate (governed by the rate of proper time) to a faster downward rate, a slower downward rate, or even cause events to move upwards. This super-positional effect is greater with greater event-range, and with greater relative velocity. But in general ... Best regards, Celeritas

michel123456, All events move downward at the steady rate of proper-time in the animated GIF. However, there is a super-positional effect that occurs only within the spacetime system of the properly accelerated POV, that causes the downward rate to change from its steady rate (governed by the rate of proper time) to a faster downward rate, a slower downward rate, or even cause events to move upwards. But in general ... An event that moves upward, means that the proper acceleration caused the event to become "a lot less in his past" than the normal downward rate of proper-time would place it (within only the spacetime system of he who properly accelerated). An event that moves downward slower than the normal rate of proper-time, means that the proper acceleration caused the event to become "less in his past" than the normal downward rate of proper-time would place it (within only the spacetime system of he who properly accelerated). An event that moves downward faster than the normal rate of proper-time, means that the proper acceleration caused the event to become "more in his past" than the normal downward rate of proper-time would place it (within only the spacetime system of he who properly accelerated). With a change in one's own state of motion comes a change in one's own sense-of-now. Sense-of-now (across the all-of-space) being depicted by a line-of-simultaneity. In this GIF, the line-of-simultaneity was removed, however it sits there always horizontal thru the origin. A proper acceleration causes a change in the angular orientation of his line-of-simultaneity (relative to others), but since it is fixed in this animation its rotation is instead manifested as a relocation of events (in space and time) accordingly. Best regards, Celeritas

Hi bvr, I addressed the B experience per B, and the A experience per A. Intentionally, I omitted the A experience per B and the B experience per A. I just wanted to ensure the first case was understood first, before addressing the other ... However yes, you are of course correct ... the B experience per B does match the B experience per A. But the A experience per A does not match the A experience per B, given the 2 specific events identified. EDIT: I made an edit in red highlight on my prior post. Best regards, Celeritas

Yes, both Tim88 and VandD said it right. Again ... the car observer makes a simultaneous measurement of the separation between the dropped balls (that are dropped simultaneously), which is a proper-length (LP). The measurement is made by a ruler at rest with the car, of proper-length LP, and fits precisely between the balls. The ground observer, makes a simultaneous measurement of the length of the moving length-contracted car-ruler, and measures it at L = LP/γ. The balls impact the ground simultaneously, per the car. The LTs require they cannot impact the ground simultaneously per ground, if they were simultaneous per the car, as differing POVs must disagree as to what are simultaneous events. The ground observer therefore records those impact-events as asynchronous. Per ground observers ... the length-contracted car-ruler MOVES between those 2 asynchronous impact-events, and so the separation between those impact-events includes BOTH the moving car-ruler's contracted-length (LP/γ) PLUS its traversal distance (vt) between the events. By the LTs, the spatial separation between those asynchronous events as measured by the ground is dilated ... and to the precise tune of ... γ*LP. So, the moving car-ruler is length-contracted by 1/γ, while yet the spatial separation between the impacts events upon the ground is dilated by γ (per ground). No paradox. Best regards, Celeritas

Michel123456, The thread is presumedly about "interpretation of correct relativity statements". You have registered a complaint, that forum members are trying to explain relativity instead. Yet, the only reason folks interpret the traditional statements of relativity incorrectly, is because they do not really understand SR yet. That alone, makes it impossible to ever understand the much more complex twins scenario. Here's another example. robinpike has been trying to build a proof that relativity is not self contradictory. He's doing this, by collecting all the relativity related buzz-phrases that many relativists make, and that most relativists agree about. If he attains all the required buzz phrases, he believes his collection will stand on its own, and in a way such that anyone (who does not yet understand relativity) will easily "see the light". However, this is about the worst way in which one can come to understand the theory, to always interpret proper statements of relativity correctly. One must first learn the math, that is, the LTs. Run some calculations for the basic scenarios. Best, would be to derive the LTs. A good understanding of relativity is expedited immensely, with a good understanding of spacetime diagrams. The relativistic effects are reciprocal. The only time that time-dilation is not reciprocal, is when one transitions inertial frames of reference (ie properly accelerates). He who does so, undergoes a change that impacts his predictions of others. I could make a simple statement ... twin B 's POV dynamically changes while properly accelerating, and this causes others to shift in his spacetime system in a way that inertial POVs never experience. But, that will help little to none, for one who does not yet understand SR well enough. In post 266 I provided a very simple description wrt the classic twins scenario as to why B ages less than A, and all agree. There, it was all about the A experience without consideration of B, and the B experience without consideration of A. However, to understand how B can predict the A experience, and vice versa, there is much more to that story. One cannot possibly understand that, without first understanding SR. For example ... Let's say twin B is also always inertial, and he executes a flyby of twin A on earth. B coasts to a flyby of planet X (at rest with earth) a proper distance LP away. One must understand that BOTH record the other moving, and his moving clock ticking slower. Yet A records more time between those 2 events (A/B flyby → B/X flyby) than does B (both events on the B worldline). Here, we consider the A experience per A and the B experience per B . ← And, this is an all-inertial scenario, and it does not violate reciprocal time-dilation. This is the first thing that needs understood. Then, one considers A per B and B per A. Then one considers 2 events on the A worldline to 2 events on the B worldline, in which case reciprocal time dilation is made clear. Only after doing that, does one have the tools to tackle the twins scenario of acceleration. (of course, all clocks of the earth frame are always synchronized in their own frame). EDIT: The red highlight was added to the original post. Best regards, Celeritas

michel123456, 1) Yes, only events are shown in the animated GIF, other than the curvy worldline representing the properly accelerating observer's path thru spacetime. 2) Yes, although the term "wild" does not apply, as this is the case for all-inertial scenarios as well. WILD only applies to the rapid repositioning of events in spacetime due to the wild changes in the accelerated observer's own POV caused by his own wild proper-accelerations. 3) Yes, if an event does not occur AT the origin (where the observer is), he cannot yet know it has happened. He must await light to traverse the space between himself and the event. 4) Yes. 5) The event entered the observer's past back when it progressed below the horizontal line-of-simultaneity thru the origin (not shown). So what you really mean here, is that once the event crosses the lower 45 deg lightpath, the flash event has then been seen by the observer ... and no change in his own proper acceleration hence forward can possibly change that. What happened, happened. 6) The block universe is considered static in the 4-space perspective we are not privied to. However, we directly experience 3-space, a NOW, and the seemingly steady passage of time, and so things happen all the time. So the block universe, and "change as we experience it", are not incompatible. 7) Well, I would not personally express spacetime as soft, let alone as a marshmellow. Different POVs simply measure space and time differently. And so the POV of he who properly accelerates dynamically changes as he transitions inertial frames of reference, ie as he transitions thru each sequential MCCIRF. That's it. Best regards, Celeritas

I agree, this is a good case to study first. After subsequently addressing the full twins scenario, its also good to compare the all-inertial time-handoff scenario to the other 2 cases. Best regards, Celeritas

This post, and my prior post, have been edited (after a good night's sleep ... case 1 ... In all inertial diagrams, time passes by imagining the steady upward advancement of time on a static figure, all lines and points on the figure static. The 45 deg lightpaths and lines-of-simultaneity "may be envisioned to" travel upward with the origin as it advances thru time. case 2 ... In the animated gif whereby proper acceleration always active, the origin and (omitted) horizontal line-of-simultaneity and lightpaths are all static, and the all of spacetime (with all event-locations within it) moves steadily downward as time progresses, a new MCCIRF observer always at the origin with the accelerated observer. In either case, events will eventually cross the 45 deg line (of the past). In the animated case, the big difference is that the location of flash events shift wildly as time progresses as the result of the proper acceleration. Best regards, Celeritas

OK, so ... Wrt green highlight ... Yes, where "directly observable" means "currently observable" at the depicted origin. Q1) It means only that ... for the current given range to the prior event, enough time has passed since its occurrence, that the light from it has reached the observer at the depicted origin. This is true even for all inertial diagrams. Q2) Sounds about right. The animated spacetime diagram is a mapping of (what you may assume as) flash events. Flash events in the future have not flashed yet, those locations residing above the horizontal line-of-simultaneity drawn thru the origin. Once an event location intersects the horizontal line-of-simultaneity, it flashes. That event's location then enters into the observer's past, and yet you remain unaware of its existence. It is not until said event's location reaches a point in the past upon the 45 deg light-path, that the light has reach your eyes (then currently visible at the origin), and so you actively see the flash event (an image of a flash that occurred in the past). Any event that resides between the diagonals represents an event that has already been see by the observer. In this paragraph, the "observer" and "system" or "system" are taken as the momentarily co-located and co-moving inertial frame (MCCIRF) observer or MCCIRF system. There is always one MCCIRF observer at the origin with the properly accelerated observer. Best regards, Celeritas

Hi michel123456, No, its not that events come from nowhere. It means only that the light from those events have had time to reach you. Wrt the bottom triangular region you specified (time-like interval wrt the past) ... you'll see that once an event's location (ie a dot) reaches the 45 degree lightpath, then the light from that event is currently being received by the observer at the origin. For events between the lightpaths, light has already reached the observer. You can see that once any event crosses the lightpath into the bottom triangular region, it never leaves that region no matter what the acceleration thereafter. Ie. he has already received the light from those events and nothing can ever change that. As they said alot in the TV series LOST, "what happened, happened". And, all must agree. Spacetime systems map the point-location of event occurrences. An event occurs, and then it's only a matter of waiting until the light from that event reaches you, whereby you then have first knowledge (or evidence) that it ever existed. Causality. An event occurs when and where it does, no matter if you have received EM proof of it yet, or not. Best regards, Celeritas

Thanx. That wiki animation was better before someone went and removed the twin B horizontal line of simultaneity from it. Best Regards, Celeritas

Tim88, Then we disagree. Best regards, Celeritas

Tim88, As VandD had already pointed out, the time dilation and length contraction of SR are not optical effects. They exist in the spacetime system, and are not the result of visual effects caused by light-transit time after departing distant events. Your statement here, as written, suggests that you are comparing optical geometric effects wrt relativistic effects. However, the LTs define how things exist within the system (at any time), not what they appear to look like later after light's transit (although that is of course always calculable). Navigation systems do not care what things might look like per the pilot. They only care about where things exist right now within the coordinate system, and any predictions as to where they will be later or in the future, also cares only about "where they then exist within the system". The pilot knows that the optical effects he witnesses during flight, do not change "how things actually exist within his navigation system's coordinate system" (his own system). He can just "enjoy the show", while basing his flight decisions on his navigation system readouts. Which brings us back to my prior post here. The MCCIRF method, which is just one method, constructs a map of how things "exist in the system". Twin B cannot apply SR's convention-of-simultaneity directly to his track data while non-inertial, because light's speed is not invariant c across the-all-of-B-space while non-inertial. Preferably, one would desire that twin B (of relativistic rate) use a convention-of-simultaneity of his own (while non-inertial), applied directly to his track data ... that produces spacetime solns "that are always in complete agreement with the predictions of all inertial observers". One then asks, what convention-of-simultaneity would that be? Best regards, Celeritas Tim88, I already addressed this post as well, wrt the twin B. I'll briefly restate it here more generally ... There is no harm whatever, that one models the heavens circling himself as the result of earthly proper-rotation. That, is kinematics. One would have to be a masochist to want to do that, but it is not improper. However, if one is to address energy-considerations, well then energy is absolute. And so if the earth bound observer chooses to make himself the zero reference for all relative motion, he cannot also say that "all of the heavens expended energy to cause the relative motion". He must assign the energy expenditure (that caused the relative motion) to that which in fact experienced the applied force. This is more important in relativity than in classical mechanics, for otherwise the twin B could never accurately predict twin A's clock wrt return. Navigation systems always assign itself the zero reference for motion. For a period of proper-acceleration, a spaceship nav system computes the final location and speed wrt the initial parameters as reference. However, for relativistic rates ... Just before B's virtually-instant turnabout, an inertial phase (v=0.866c so gamma=2) is coming to an end. The location of twin A just before B's proper acceleration is (say) 1 light hr. At the moment halfway thru his turnabout, he is momentarily at rest with earth and twin A, and so twin A "must then be" 2 light hr distant. That happens "in virtually no time at all", because of B's virtually instant turnabout. 2 lt-hr being the proper separation between earth and the turnabout point. Not only that, but with A's wild shift in B-space, comes a wild shift in A-time (in only the B system). Twin A's worldline rapidly rotates in its angular orientation wrt the B worldline, because B's line-of-simultaneity remains always-fixed (since he assumes himself the zero-ref for motion). That rotation also requires twin A to advance wildly along his own worldline (not something that A experiences), but only in the B system, and so (per B) the twin A clock ticks wildly fast during his turnabout. Given such, twin B may accurately predict the twin A clock on return, without any consideration of how A himself experiences it all. Again, this is what the MCCIRF method does. It allows twin B to assign himself the zero reference for all motion, but dynamically adjusts worldlines within B's spacetime system knowing that it was "B himself" who underwent the applied force (causing the change in relative motion). In this way, his spacetime predictions always match that of any inertial observer, who we know all concur with each other using an accepted theory. Twin B's nav system accounts for its own proper acceleration, and adjusts all worldlines in B's own system accordingly. B does not ignore "the consideration of energy-expenditure", but rather accounts for it as necessary. So I"ve already addressed this. If you have a different point that I did not address, maybe just say it, cut to the chase. My point here is that energy considerations are not ignored by twin B using the MCCIRF method. He accounts for it. Twin A knows it was twin B who changed in his own state of motion, because twin A is always inertial and never feels his own inertia. However, the spacetime predictions made by twin A are indifferent wrt who properly accelerated". It matters not, to twin A, because he's always inertial. Twin A knows that for higher relative velocity, the B clock slows down, and that's all A needs. Twin B knows that for higher relative velocity, the A clock slows down, and that's all B needs during his inertial phases of his roundtrip. However during non-inertial phases, twin B "cannot and does not" ignore energy considerations, for otherwise his spacetime predictions of twin A fail. Best regards, Celeritas

Tim88, OK, would it be fair to reduce your point to ... the B system does not measure light speed invariant "throughout his own space" in any duration during his own thruster burns. As such, Einstein's convention-for-simultaneity (used in SR) is an invalid convention for non-inertial POVs. The Einstein convention assumes both the 1-way and 2-way light speed is invariant, isotropic at c, and independent of the motion of the light's source. However, that's why I chose to use the collection of MCCIRF POVs, ie to map all entities within the B system over his proper acceleration in a way completely consistent with inertial POVs (who always concur). I realize that asking michel123456 to explain how the A & C clocks exist in the B system during turnabout, is indeed far over his head at this venture. There are different ways to approach that. And wrt the MCCIRF method i mentioned, one cannot consider that method unless they have first mastered the all-inertial scenarios. However, the MCCIRF method (I used as an example) is a preferred method IMO, because if at anytime B drops into coast-mode, there is no disjunct in his spacetime coordinate predictions for other observers, and no matter where they are or how far their range. It's seamless, and completely consistent with all inertial POVs (who all always concur with each other). The MCCIRF method does not use B's own POV, but rather builds his POV from the collections of MCCIRF infitesimals. Twin B, using Einstein's convention-for-simultaneity (of SR), cannot (while non-inertial) map the heavens in concurrence with all inertial observers. Yet, twin B receives the very same light the MCCIRF observers do. So star maps must be built from inertial POVs, and while properly accelerating, twin B's navigation system would have to dynamically adjust the worldlines of all inertial stars (or bodies), and all steadily accelerating bodies. Then, his own navigation system's current map, could always be completely consistent with maps of all inertial observers. That said, the twin POV is invalid in so far as upholding all the laws of physics, if he uses the convention-for-simultaneity used in SR for all inertial observers, which was ... τ1 = ½ (τ0 + τ2) because the above synchronicity eqn requires that the speed of light be invariant at c, not just locally, but across the all of space in any instant. This fails for non-inertial POVs of relativistic rate, because light's speed is no longer c (per measurement) across an expanse of space in the instant. Best regards, Celeritas

Tim88, I had already addressed those posts, so I'll have to go back and see where the breakdown is, if any. I'll have another look-see. Thanx Best regards, Celeritas

Indeed, that was quite the blunder on my behalf. I had started with improper convention, with primes on the right and unprimed on the left. Had just started to make the changes, got sidetracked, forgot to complete it and posted. Thanx for pointing that out. It's such a mess, I'll repost it for michel123456 below ... Best regards, Celeritas EDIT: Below is a re-post of my Post 14 for michel123456, with corrections as per Tim88 Primed variables should only have existed on the left side of the LTs shown (S' system). ****************************************************************************************************** [ 45 ] ... The spatial distance of two events that are simultaneous for a certain group of observers, is shorter for them than for all other observers in arbitrary motion relative to them. This statement contains, as a particular case, what is called the Lorentz contraction, that is to say, the fact that the same ruler considered by different groups of observers, some resting, others in motion relative to it, is shorter for those who see it passing by as for those who are attached to it. Hi michel123456, I understand your question. It is a standard obstacle along the path to a better SR understanding. wrt body length ... the length of a body (eg ruler) is obtained by measuring the spatial location of its endpoints within one's own system. The measurement of each endpoint marks an EVENT, the measurement occurring at a specific location in both space and time. As such, 2 simultaneous events define the length of a body, whether moving or not. While the length determination may be made from 2 non-simultaneous events, maybe with more rigor, the measurements are generally taken simultaneously, simply because its easy. For measurements taken simultaneously, one can simply subtract one event's spatial coordinate from the other event's spatial coordinate to attain the body's length in the measurer's own frame (moving or not). Consider the 2 cases ... If the body is in motion ... and its endpoints measured at 2 different moments in time, the body moves between the 2 moments of measurement ... and one must then subtract the ruler's distance-traversed from the total-spatial-separation between those 2 events to determine the moving ruler's simultaneous contracted-length. But if one prefers doing things the simply way, one takes their endpoint measurements simultaneously, if possible. If the body is stationary ... the measurer need NOT bother to take the measurements simultaneously (although usually one does). The reason, because no point of the ruler moves over any duration, ie all points of the ruler are INDEPENDENT OF TIME (in the rest system). As such, one may measure one endpoint of the ruler at any time, and the other endpoint at any (or any other) time, subtract the two x coordinates, and one attains the very same length every time. This length being the PROPER LENGTH of the ruler, an invariant length, and it's longest recordable length. wrt the LTs ... Events are occurrences that exist in any and all frames, whose locations are defined in both space and time, ie by 0 dimensional points in 4 dimensional spacetime. Here's the important part ... The LT's of Relativity require observers to disagree as to what are simultaneous events if in relative motion. The moving contracted-length is a simultaneous consideration, and so those same 2 events CANNOT exist AS SIMULTANEOUS in the rest frame. Does that hurt anything? The LTs relate the 2 simultaneous events of the moving ruler (say separation 0.5), to 2 asynchronous events in the ruler's rest frame (say separation of 1, given v=0.866c). Since the location of any point of the stationary ruler is independent of time, they never change in their location irregardless of when said endpoints are considered in the rest frame. And so a simultaneous measurement of its endpoints always produces the very same length as any non-simultaneous consideration of its endpoints. As such, one may say that a proper-length (Lp) of a stationary ruler corresponds to a contracted-length (Lp/γ) of that same ruler viewed in relative motion at v, without bothering to mention all the details of how the LTs make that happen. Yet, to understand relativity, one must know all the details, whether its mentioned or not. Anyone who does not understand all the details, will forever be confused to some extent when discussing relativistic scenarios. You may be wondering why I bother to mention all the above ... wrt your error ... What you believe to be a contradiction (2 different measures of the same length), is instead 2 entirely different considerations. Realize that, then there is no conflict ... EDIT: If you start from the rest frame (S) and take 2 simultaneous measurements of the stationary ruler's endpoints, those same 2 events cannot be simultaneous in the other frame (S') that holds the ruler in motion. The LTs, can only transform those 2 simultaneous points in S to a set of asynchronous points in S'. Since those points occur sequentially in S', the moving contracted length (L' = Lp/γ) must traverse a distance (x’sep = vt') between the occurrence of those events (t' = t'2-t'1). So the length between those 2 events in S', includes a traversal-distance of the moving ruler PLUS the contracted-length of the moving ruler ... x'sep = v(t’2-t’1) + (Lp/γ). And it is always the case that x'sep > Lp for v > 0 , as follows ... x’ = γ(x-vt) x’sep = γ(Lp-v(t2-t1)) for endpoint measurements taken simultaneously (t2 = t1, and so t2 -t1 = 0) in the ruler's rest frame (S), then the separation between those events in the frame that moves relatively (S') is then ... x’sep = γ(Lp-v*0) x’sep = γLp and so it is always true for v>0 (hence γ>1) that ... x’sep > Lp Lp ... the spatial separation between the 2 events in the rest frame (S), ie the rest length or proper length. x’sep ... the spatial separation between the same 2 events in the frame that moves relatively (S'). That's the reason the S' observer records a greater spatial-length between the 2 events, than does the observer at rest with ruler. Best regards, Celeritas

Hi VandD, Good point. We cannot predict the future, agreed. Also, we only ever experience the NOW. However, the required time-desynchronization of moving bodies cannot be explained unless all moments in time co-exist. To suggest such a continuum is not a part of reality, is IMO to suggest that relativistic effects are not a part of reality. The moving length-contracted train is comprised of different eras of the train's own proper-time, yet they must exist in the stationary observer's NOW per the theory. As you know, it is not optical effect. I do understand the desire to define reality based upon what is directly measurable in the current ever changing moment, because we only ever perceive an ever changing moment. However, the time-desynchronization of moving bodies suggests that NOW is not all that exists in the continuum, but rather that all NOWs co-exist. The fact that one never lives in anything but the present, does not negate the required existence of time-desynchronization of moving bodies ... Consider a tree in your backyard. It was there for (say) 30 years, but yesterday it was cut down. Is that tree part of reality? You may say "not today it isn't", at least in the form it existed yesterday. Yet if I move in such a way and fast enough, your tree (just before) being cut down exists AND you yourself pondering its existence the next day in your own living room also exists, all in my own NOW. Does your tree in reality exist? I'm only suggesting that reality may be more than we might casually tend to figure. We cannot measure the Planck length directly, yet its use in physics has been with astounding success. One may say that time-desynchronization of moving bodies is to relativity, as the Planck length is to quantum mechanics. Each are deducible and validated from repeatable test results that prove other aspects of the theory (or physics). Prove length-contraction and time dilation by consistent measurements of various repeatable experiments, then logical deduction leads that time-desynchronization of moving bodies "exists in nature". I agree these things are best left to philosophical discussions. It comes down to what we accept as true. We define truth per consistent repeatable measurement and consistently predictable outcome. However if the math requires something to exist that is not directly measurable, then if the physics (or accepted theory) that involves that math is otherwise proven by repeatable measurements, then I would personally vote that that something be considered real and a part of single shared reality per many POVs of it. Tomorrow, I may change my vote Best regards, Celeritas

robinpike, I provided an alternate description in my prior post, which you requested. wrt your scenario, you mistakenly presume it reveals an inherent contraction in SR. The contradiction you presume, is only the result of a lack of understand of SR in the very first place, and SR is a kinematic model that does not directly address proper accelerations. Someone could try and answer your questions in brief layman's terms, however this can never satisfy you. You would then need to ask WHY the description explains it. Then, the math would need presented, and possibly some geometric figures in support thereof. That could not possibly satisfy you either, because you are still trying to learn the basic concepts of SR. For example, you are presently trying to learn how POVs properly keep track of the relation between proper lengths and its corresponding contracted-length the length between 2 events per POVs in relative motion. Add, the twins case is very complex, the all inertial case far simpler. You need to focus on the easy challenge first, master it, and then you will possess the tools to understand WHY the twins scenario is no paradox when someone properly explains it. I'll just say this though, wrt the red highlight: during B deceleration at turnabout (thru midpoint of turnabout) ... in the C spacetime system ... the B tick rate slows down, until it matches the A tick rate. The A tick rate remains steady and slower, since inertial. in the A spacetime system ... the B tick rate speeds up, until it matches the A tick rate. The C tick rate remains steady and slower, since inertial. in the B spacetime system ... this is too difficult for you understand at this venture. Since you have declared an inherent contradiction in SR, please explain how your A & C tick rates exist in the B spacetime system during B's deceleration (not just when v=0 wrt A). That should reveal a great deal regarding the source of your belief of a contradiction inherent in SR. Best regards, Celeritas

Per SR ... in A's spacetime system ... moving clocks must tick slower per any inertial POV, and twin A (on Earth) is always inertial. As such, it matters not that twin B changes in his own state of motion, ie he moves relatively during both thruster burns and coasting. Only at one instant at turnabout (say at planet X) does twin B momentarily arrive back into the twin-A frame, but even then B's clock ticks at the same rate as A's at that instant, not faster. So the B clock always ticks slower, except for an instant. Over the roundtrip, B clock MUST age less. in B's spacetime system ... B properly accelerates to depart from A, and so the relative velocity builds. Twin B then records the separation between Earth and planet X in motion, and any moving-length contracts from its proper length. The greater the v, the closer planet X gets. We can assume virtually instant B accelerations, for simplicity. The shorter the distance to planet X (ie x'), the shorter the time to get there at v (since t' = x'/v). The same applies for the return leg of B's trip. Over the roundtrip, B must age less than A. As such, both twins agree that B ages less than A. Best regards, Celeritas

You must also compare your, your brother's, and his coach's rulers for a relative length comparison, before and after each jog. Best regards, Celeritas

micehl123456, Nothing in SR or Langevin's work suggests a different reality. I think you might be good here, but one must be careful with their choice of words. Here, you are considering the car per the ground observers ... the car is moving relatively, and hence length contracted. But do the car passengers live in a contracted reality? Per themselves, they never notice any change in their own length or their own clock rate over duration, accelerating or not. The reason ... nothing within their car moves (relativistically) relative to themselves. Given v=0, then no relativistic effects exist. Same holds for ground frame observers considering things that essentially co-move with them. Only things observed in relative motion (at relativistic rate) undergo measurable relativistic effects. This is only to say that differing POVs (of a single shared reality) exist, not that different realities exist. That may be what you meant? On the other hand, Lorentz's LTs (which are the same as Einstein's) mean something much different. Lorentz built his LTs upon a foundation of an absolute ether frame, where light only moves at c in that frame. Lorentz's LTs require that moving observers physically contract in a stationary ether as they move thru it, and as such they would actually be length-contracted in-and-of-themselves even though their measuring apparatus are incapable of ever measuring it (contracted rulers measure equally contracted lengths as uncontracted). However per SR, we all live in a PROPER CONFIGURATION where oneself (and all that co-move with oneself) undergoes zero relativistic effects, ie they are not contracted in-and-of-themselves ever. In that particular respect, SR follows Galileo and Newton (no change). This is just one of many reasons SR was accepted over Lorentz's version. So, relativistic effects only exist between PROPER CONFIGURATIONs, ie between POVs in relative motion (v>0) who each hold themselves stationary and the other in motion. Of course, it requires a relativistic rate (non everyday speeds) to measure the relativistic effects. Best regards, Celeritas

I see. I went thru thread thread more closely from the OP. Semantics. Indeed, that's always a problem when folks are trying to learn the theory. I was there Got it, thanx. I'm assuming that you are referring to the wild shifts in the A-clock location and time-readout in only the twin B spacetime system during B's proper-turnabout? Said effects are logically deduced, but not directly measured. I do understand that on the grounds of "not measurable", one might argue it is not real. I disagree on that particular matter, however I do understand the complaint I've looked thru the 2 threads, and did not notice your 2 illustrations you mention here. Could you please give me a hyperlink to those, and I'll take a look. Thanx Best regards, Celeritas

[ 45 ] ... The spatial distance of two events that are simultaneous for a certain group of observers, is shorter for them than for all other observers in arbitrary motion relative to them. This statement contains, as a particular case, what is called the Lorentz contraction, that is to say, the fact that the same ruler considered by different groups of observers, some resting, others in motion relative to it, is shorter for those who see it passing by as for those who are attached to it. Hi michel123456, I understand your question. It is a standard obstacle along the path to a better SR understanding. wrt body length ... the length of a body (eg ruler) is obtained by measuring the spatial location of its endpoints within one's own system. The measurement of each endpoint marks an EVENT, the measurement occurring at a specific location in both space and time. As such, 2 simultaneous events define the length of a body, whether moving or not. While the length determination may be made from 2 non-simultaneous events, maybe with more rigor, the measurements are generally taken simultaneously, simply because its easy. For measurements taken simultaneously, one can simply subtract one event's spatial coordinate from the other event's spatial coordinate to attain the body's length in the measurer's own frame (moving or not). Consider the 2 cases ... If the body is in motion ... and its endpoints measured at 2 different moments in time, the body moves between the 2 moments of measurement ... and one must then subtract the ruler's distance-traversed from the total-spatial-separation between those 2 events to determine the moving ruler's simultaneous contracted-length. But if one prefers doing things the simply way, one takes their endpoint measurements simultaneously, if possible. If the body is stationary ... the measurer need NOT bother to take the measurements simultaneously (although usually one does). The reason, because no point of the ruler moves over any duration, ie all points of the ruler are INDEPENDENT OF TIME (in the rest system). As such, one may measure one endpoint of the ruler at any time, and the other endpoint at any (or any other) time, subtract the two x coordinates, and one attains the very same length every time. This length being the PROPER LENGTH of the ruler, an invariant length, and it's longest recordable length. wrt the LTs ... Events are occurrences that exist in any and all frames, whose locations are defined in both space and time, ie by 0 dimensional points in 4 dimensional spacetime. Here's the important part ... The LT's of Relativity require observers to disagree as to what are simultaneous events if in relative motion. The moving contracted-length is a simultaneous consideration, and so those same 2 events CANNOT exist AS SIMULTANEOUS in the rest frame. Does that hurt anything? The LTs relate the 2 simultaneous events of the moving ruler (say separation 0.5), to 2 asynchronous events in the ruler's rest frame (say separation of 1, given v=0.866c). Since the location of any point of the stationary ruler is independent of time, they never change in their location irregardless of when said endpoints are considered in the rest frame. And so a simultaneous measurement of its endpoints always produces the very same length as any non-simultaneous consideration of its endpoints. As such, one may say that a proper-length (Lp) of a stationary ruler corresponds to a contracted-length (Lp/γ) of that same ruler viewed in relative motion at v, without bothering to mention all the details of how the LTs make that happen. Yet, to understand relativity, one must know all the details, whether its mentioned or not. Anyone who does not understand all the details, will forever be confused to some extent when discussing relativistic scenarios. You may be wondering why I bother to mention all the above ... wrt your error ... What you believe to be a contradiction (2 different measures of the same length), is instead 2 entirely different considerations. Realize that, then there is no conflict ... EDIT: If you start from the rest frame (S) and take 2 simultaneous measurements of the stationary ruler's endpoints, those same 2 events cannot be simultaneous in the other frame (S') that holds the ruler in motion. The LTs, can only transform those 2 simultaneous points in S to a set of asynchronous points in S'. Since those points occur sequentially in S', the moving contracted length (L' = Lp/γ) must traverse a distance (xsep' = vt') between the occurrence of those events (t' = t'2-t'1). So the length between those 2 events in S', includes a traversal-distance of the moving ruler PLUS the contracted-length of the moving ruler ... x'sep = v(t'2-t'1) + (Lp/γ). And it is always the case that x'sep > Lp for v > 0 , as follows ... x’ = γ(x-vt) x’sep = γ(Lp-v(t'2-t'1)) for endpoint measurements taken simultaneously (t'2 = t'1, and so t'2 -t'1 = 0) in the ruler's rest frame (S), then the separation between those events in the frame that moves relatively (S') is then ... x’sep = γ(Lp-v*0) x’sep = γLp and so it is always true for v>0 (hence γ>1) that ... x’sep > Lp Lp ... the spatial separation between the 2 events in the rest frame (S), ie the rest length or proper length. x’sep ... the spatial separation between the same 2 events in the frame that moves relatively (S'). That's the reason the S' observer records a greater spatial-length between the 2 events, than does the observer at rest with the ruler. Best regards, Celeritas

Tim88, Very sorry, circumstances have me moving very slowly as late ... Wrt Langevin … I was talking about what exists IN only the B spacetime system, not an analysis based upon received light after the delay in its transit (eg Langevin's analysis), although that is no problem. Wrt fictitious force … You’ve suggested that the superluminal relocation of twin A in the B system (at turnabout) is caused by a fictitious force. The only force "there is", is B’s proper acceleration(s). Twin A is always inertial. If the wild shifts of twin A (wrt location and time-readout) within only the B spacetime system are properly related to B’s transitioning of inertial frames, then A’s wild shifts are explained. If it can be shown that that force accounts for the wild shifts of A, then there is no fictitious force causing A’s superluminal shift (or rapid advancement of time-readout). B’s own thruster burn produces a change in relative motion, and hence a change in relativistic effects, wrt A. The force is real, and it is B’s measurable inertia. Wrt valid physical description … While other analyses exist, I used the analysis of momentarily co-located and co-moving inertial reference frames (MCCIRF) wrt twin B. You pointed out that the sequential concatonation of an infinite collection-of-infitesimals of MCCIRFs (wrt B) is not any single real POV. I would say this … My scenario used a single B clock always at the B origin, and assumed twin B proper accelerations were instant. As such, my position is that the collective of MCCIRF infitesimals constitute how twin A exists in the twin B spacetime system. I mean, at any momentary co-location, twin B and the corresponding MCCIRF POV are at relative rest, and also receiving essentially the same EM from twin A. As such, the relativistic effects required within the B system during turnabout (that do not occur in the twin A system), must be the direct result of twin B’s own frame-transitioning, the related force being B’s own inertia at turnabout. I consider the analysis a valid representation of the B spacetime system (far as the A-clock within it), and therefore a valid representation of reality in that respect. The stars seem to fly superluminally across the night sky, if one does not account for earthly rotation. A consideration that appropriately considers forces, reveals the earth rotating and the stars essentially fixed. Certainly, twin B rotates in spacetime when properly accelerating. Twin B may use the twin A system as the reference for all motion, if he so chooses, or he may use his own. However, using his own not-always-inertial system without consideration of force, is to consider kinematics alone, and so spacetime predictions could not be correct, nor consistent with the predictions of all inertial POVs (who do all agree). The MCCIRF method builds a twin B POV from inertial POVs, and thus must be consistent with all inertial observers. As such, it explains how B's frame-transitioning at turnabout relates to the always-inertial POVs. That is, the mapping of twin A in the B spacetime system is a function of B's proper acceleration during turnabout. It's built-in, using the MCCIRF method. This is not to say that the MCCIRF is the only method. Wrt violations of physics … Twin A is always inertial, and so there is no violation of c there. Twin B is always at v<c wrt A, and so no violation of c there. The only real question, is … does the superluminal shift (or wildly fast time readout advancement) of twin A in only twin B’s spacetime system violate the cosmic speed limit? I say no … The superluminal shifting of A within the B system, is caused only by a rapid shift in B’s own POV, and the theory requires it. Otherwise, B could not successfully predict that A ages more than he (for say a pre-planned scenario), upon return. To suggest such wild shifts cannot be real, is to say that relativistic effects as per SR cannot be real, and no worthy relativist believes that. All that’s required to understand how twin A can move superluminally in the B system without being a violation of physics, is to understand that all moments in time co-exist as inches on a ruler do. Ie it’s a continuum of BOTH space and time, not just space. Twin A essentially fast-forwards along his own dynamically rotating worldline in ONLY the B spacetime system during B’s own transitioning-of-frames at turnabout, and his own inertia (a measurable force, hence real) is the source of that. Yet, in A's own spacetime system, the rate of proper-time is always steady as usual. The wild shifts of A in B's system are due to a change in the way B measures space and time, ie a twin B POV change, as the direct result of a change in B's own state of motion. VandD's twin's related spacetime figure (in the prior post) presents this rather elegantly. Best regards, Celeritas

Tim88, OK. Thanx for your review comments. I'll digest it carefully, before responding. Best regards, Celeritas