I don't think that I EVER agreed with the nonsense you have been posting in this forum. My answer clearly shows that you are wrong in your assumption that deceleration has an opposite effect to acceleration in the calculation of elapsed time. The coefficient \(\sqrt{1-(v/c)^2}=\sqrt{1-(at/c)^2}\) is dependent on the square of acceleration, so its sign has no effect. What does this word salad have to do with the question that I answered earlier?
Tach, If the rocket has a velocity v, relative to the planet and the planet has a velocity x, relative to a third frame, iow it is itself moving, then wouldn't the actual velocity of the rocket, on the outward and inward legs of its trip (assuming the planet's velocity is in the direction of the outward bound rocket) be, \(v+x\) and \(v-x\) respectively. This leading to \(\sqrt{1-((v+x)/c)^2}\) for the outbound trip, and \(\sqrt{1-((v-x)/c)^2}\) for the in bound trip?
This is yet a DIFFERENT question, which contains a few more mistakes. The bottom line is that the ONLY thing that counts in the calculation is the relative speed \(v\) of the rocket wrt the planet. BTW, the speed of the rocket wrt to the third frame you introduced gratuitously is NOT \(v+x\) and \(v-x\) . But this is a smaller mistake.
If you understood the physics you wouldn't have to guess. You still don't get that the speed of the rocket is only considered relative to the planet and thus so is the time dilation. The local observer NEVER "experience time dilation" in their own frame. All observers perceive their own local time the same as always, regardless of any change in their motion. Yes, to that third frame, which the planet is in motion relative to, the rocket's relative velocity on both legs is likely to be unequal, and this includes the rocket's time dilation compared to this third frame. BUT THIS DOES ABSOLUTELY NOTHING TO AFFECT THE SPEED/TIME DILATION BETWEEN THE PLANET AND ROCKET. Time dilation is not absolute, so what dilation may exist between the planet and your third frame has NO EFFECT on that between the planet and the rocket. NONE AT ALL. You must assume absolute motion to even entertain such a notion. The basic TE assumes the rocket's time dilation on both legs of its journey is equal BECAUSE IT IS ONLY RELATIVE TO THE PLANET. Doesn't matter one wit what the motion of the planet may be. You're assuming an absolute rest frame because you are assuming absolute motion. Same scientific illiteracy as RealityCheck.
Tach, I know this is long and overly wordy. There is no help for that. Please take the time to try and understand the underlying intent. I don't believe they are different issues. And yes I did express the velocity of the rocket in a classical way rather than relativistic. That is just an issue of simplicity of intent. My intent is and was..., If the planet has a constant velocity, relative to say a galaxy, such that it is leaving that galaxy and a rocket takes off from that planet in the direction of its velocity relative to the galaxy, with a constant velocity relative to the planet, turns aground at some point and returns to the planet, with a constant velocity relative to the planet, equal to its out bound velocity, relative to the planet...., its velocity on each leg of that trip relative to the galaxy will not be equivalent. While the planet will experience time dilation which is constant relative to the galaxy's frame of refrence. The rocket will experience time dilation relative to the galaxy that is not equivalent, on both legs of its trip.... And the difference between the time dilation on its out bound leg and inbound leg, will not be equal to the time dilation experienced by the planet. In this situation the time dilation experienced by the planet cannot simply be subtracted from the total time dilation experienced by the rocket and be found to be equal to the conclusions drawn where the planet is assumed to be at rest. It could be even more complicated than this, but more complicated does not always lead to an easier resolution, of the general issue. IOW it is not necessary to present an exact solution in agreement with reality, to highlight the issue.
I already explained this to RealityCheck: "If the planet is moving at P_speed and a rocket launches from it, that rocket's speed would be R_speed relative to the planet and R_speed + P_speed relative to whatever you are measuring P_speed with respect to. This doesn't change R_speed in the least, as it is the relative difference in the speeds of the planet and the rocket. This is so basic it hardly bears saying, although you two seem to need such elementary education."
What in the "ONLY the relative speed \(v\) between rocket and planet intervenes in the calculation of differential aging" did you fail to understand? What in "the sign of acceleration does not intervene in the calculation of differential aging" did you..... Once again, irrelevant since only the relative speed between rocket and planet counts. "Time dilation" is not what is going on here. I already explained earlier how you calculate total elapsed proper time. Since the twins want to compare their total elapsed proper time, you need to learn how to calculate it. When (and IF) you will ever learn how to do that, you will realize that you only need to consider their relative speed. The speed of the planet wrt the galaxy is irrelevant. It does not affect the final result. Standard word salad.
Let's put that to the test shall we. Assume the velocity of the rocket is 0.866c relative to the planet. First we work out the answer assuming the that the planet is "at rest". This is fairly straight forward. The time dilation factor is 0.5, so assuming that a clock on the planet goes from 0 to 2 yrs during the round trip, the clock on the ship goes from 0 to 1 yr, with the rocket making its turn around when its clock reads 0.5 yr. So basically, we have the rocket leave the planet when both its and the planet's clocks read 0 and returns when its clock reads 1 yr and the planet clock reads 2 yrs. This also means that the length of each leg is 0.886 ly in length (as measured by the planet). Now let's assume that the planet is "moving" at 0.6c, which gives it a time dilation factor of 0.8. Okay, first the outbound leg: The rocket will be moving at \(\frac{0.6c+.866c}{1+\frac{(0.6c)(0.866c)}{c^2}}\) or 0.9647c, which gives a time dilation factor of 0.26325 So this means that as the Rocket clock's goes from 0 to 0.5 yrs, "our" clock ticks off 1.9 yrs. At 0.9647c, this means that the rocket will travel 1.832 ly on the first leg. During this time, the planet will move 1.1394 ly and its clock will have ticked off 1.52 yr. it will also be 0.6926 ly from the rocket. Second leg: After the rocket turns around, it will be moving at \(\frac{0.866c-.6c}{1-\frac{(0.866c)(0.6c)}{c^2}}\) or 0.5537c with a time dilation factor of 0.8327 With the Planet and Rocket moving towards each other at 0.6 and 0.5537c respectively, we get a closing speed of 1.1537c with a starting separation distance of 0.6926 ly apart, it will take .6 yr for them to meet and with the given time dilation factor, 0.5 yrs will pass on the rocket clock in this time for a total of 1 yr. With its time dilation factor of 0.8, 0.48 yr will pass on the Planet clock in this same period. Adding this to the 1.52 yr that passed during the first leg, we get a total of 2 yr passing on the planet's clock. In conclusion, we have the planet and Rocket clocks reading 0 when the Rocket leaves, with the Rocket clock reading 1 yr and the planet clock reading 2 yr, just like we got when we assumed when the planet was "at rest". So it does not matter to the end results if we consider the planet as moving or not, but considering it as moving does complicate the calculation. This is why the planet is considered "at rest" in the classical example; it simplifies the problem without changing the end result.
Janus58, that was a good explanation of the situation from the planet/rocket frames. Thanks for adding the relativistic effects of added velocities. It has been over forty years since I dealt with the math involved and it is a lot of work for me to "work" through it, especially on an iPad. Your post is a better argument for why the planet is consider to be at rest than, the argument I was presenting. If you plug those same numbers into the frame of the galaxy, planet and rocket, there should be disagreement. Is this something that you would agree with? It seems from my now antiquated achedemic exposure, to be a simutaneity of relativity issue, which from that perspective does not require agreement. How that disagreement is reconciled has some further ramifications, but I believe that it moves outside of the confines of SR. The underlying question came up in another thread some time back and more recently in this thread by another party. That question was and is, (re-phrasing) is there any absolute relationship between the Lorentz contraction and time dilation, which is velocity dependent in an absolute manner. Some attempts to explain the length contraction of an object, do suggest some absolute connection, which does not include a knowledge or the existence of any absolute frame of reference. Basically the suggestion is that length contraction and inertia are emergent from the motion of matter through the ZPF. I am not an expert in this area, I have been doing some reading on the issue over the last few years and believe I have a basic understanding where inertia in accelerated frames is concerned. I cannot say the same when the discussion tends toward quantum gravity, but it seems at least for now there is no successful model. Work is still ongoing. In either case both are yet in the very early stages of exploration and are not completely consistent with experience, as we understand it today. A question that I personally was attempting to drive the discussion toward (and granted this was not my initial intent), is while we can say that SR is locally accurate, how is locally really defined in the terms of a thought experiment where velocities relative to a galaxy are involved. If any of these effects.., length contraction, time dilation, even inertia, are in fact emergent (from an interaction between matter and the ZPF), where does locally end. There is even some reference which seems to suggest that the ZPF must be conceived of as itself dynamic, even to the point of an occasional reference to its local density. I don't know if any of the above even clearly describes the question, as i understand it in my own mind. Or that there is any real merit, in the question, at all. The classical twin paradox and even the relativistic solution in your post are not new. They were being discussed 40 years ago when I was in college and some portions as much as 100 years ago.., before I was born... I do not know the answer to the questions, I was attempting to raise. I am not sure anyone really does.
No, there shouldn't. Proper time is frame invariant. It is time for you to take a class in physics. There is no "absolute connection". Actually, there is nothing "absolute" in SR. Could you please stop using this forum for pushing your fringe theories?
NO!. Did you even bother to read my post? It shows that there is No disagreement when it comes which frame you use. First I solved it assuming the planet was at rest, and then solved it assuming the planet was moving and got the same answer in both cases[i/]. The only reason to assume that the planet is at rest is to simplify the math, not because you get any disagreement if you don't. You can solve this problem from any frame you want and always get the same answer.
I think you misunderstood what my intent was. I extended the conditions to reconciling elapsed time from all three frames, the planet, the rocket and the galaxy. From the galaxy's frame the planet's time dilation works the same as you demonstrated between the planet and rocket. Except there is not added velocity between the two. However, times as measured from the galaxy frame should not agree with times as measured from the planet's frame when both are measureing the rocket's time dilation. The relationship between the rocket's velocity relative to the galaxy is not an equivalent situation, as that between the planet and rocket. The rocket does not maintain and equivalent velocity relative to the galaxy comming and going. And as the rest of my post suggests, the question remains, though SR is locally accurate, how locally is defined may be and likely is questionable in practice.
Hi Syne. Please Register or Log in to view the hidden image! No worries, mate. I am perfectly well aware of SR theory treating motion as 'relative to something else'. No sweat. What if there WERE NO 'something else'? Would SR 'explanations' and 'asumptions/perspectives' be 'applicable' in a 'domain' where universal "space" is empty escept for the planet complete with rocket on launching pad? And since you have confirmed my reading of your earlier post that you do not claim motion 'relative' to 'space', then what is SR 'relative' explanation/perspective on PLANET'S INITIAL MOTION/STATIC STATE based on if there is no other object in that "space" except the planet and rocket on launch pad? That is why I mentioned where SR says "no absolute motion" and "no absolute rest" and ask clarification on what you explain to OnlyMe in that context. The clarification I need is because IF we removed all else but the planet and the rocket ready to go, then we are left with the apparent "Catch 22" I mentioned. Do you see it? IF there is no "absolute rest" in a universe empty of all but the planet, then how do you measure whether the planet is "moving" or "stationary"? And "relative to" what? That is the reason I am asking further clarification about what your textbook explanation actually means when the scenario is simplified as I just did and see the irreducible essentials. The stripped-down essentials are: - The planet in an otherwise empty universal "space" is EITHER 'stationary' OR it is 'moving'; - BUT just because WE cannot tell which it is because WE cannot "measure relative to" something other than the planet, it is STILL a "having it both ways' argument to claim that the planet has BOTH "no absolute motion" AND "no absolute rest". Do you see that? So, as I observed before, in such a simplified scenario where extraneous aspects have been removed, if one claims that the planet IS "moving", then one effectively is saying that the planet is moving with respect to "space" (for that is all there is other than the planet, see?). Then again, in that same simplified scenario, if one claims the planet is NOT "moving", then one effectively is claiming that it is at 'stationary' with respect to "space" (again, for that is all there is other than the planet). Now I KNOW (and you have confirmed) that you are not claiming motion or rest of the planet with resect to "space". Fine. No sweat. But then we have the situation that SR cannot say anything for sure about what the planet is INITIALLY (for the experiment) doing one way or the other. Which is why we are left with BOTH the 'Catch22' situation I observed to you, AND ALSO with your 'having it both ways' explanation from SR which you posted to OnlyMe and which I asked clarification of for the reasons I just gave. Please Register or Log in to view the hidden image! See? I was NEITHER claiming absolute motion' NOR was I claiming 'absolute rest'; I simply pointed out where (in the case of an empty universe except for the planet and the surrounding "space") it is SR explanations that effectively try to 'have it both ways' when there is NO OTHER thing to measure "relative to' in order to judge either 'motion' or 'rest'. So, if the rocket leaves the planet in an otherwise empty universe with nothing but "space" all around, then SR CANNOT BE IN ITS DOMAIN OF APPLICABILITY IN THAT CASE UNLESS SR can say something about the planet's INITIAL 'motion or stationary' state. BUT we can see that SR in that stripped-down scenario CANNOT SAY anything of the planet INITIAL 'motion/stationary' state. That is the 'domain of applicability' Catch 22' that effectively makes 'having it both ways' SR explanations about it 'unapplicable'. See? And that is why I asked for further clarification of your textbook SR reply to OnlyMe. Please Register or Log in to view the hidden image! For your answer there effectively tried to invoke SR even when, IF we simplified the scenario as I just did, that same SR cannot BE used to 'explain' the situation about planet 'moving' or 'at rest', since UNLESS you DO claim that motion/stationary is with respect to "space" (which is all there is other than planet, remember), then you effectively cannot say anything about OnlyM's planet state before the rocket lifts off that planet in any direction. So NO-ONE (including SR) can say anything about whether that planet is moving or at rest UNTIL that rocket takes off and returns and takes off again ON A DIFFERENT RADIAL EACH TIME for sufficient number of times that any differences in the rocket clock between radials shows up or not. See? Only then can we say (in a universe empty except for that planet and rocket on it and the "space" around) whether that planet had any motion or not (we can tell because any difference in the time dilation values for each radial trip of the rocket would show that one radial direction is more dilating than another at the same speed regime with resect to the planet). That is why I needed clarification. If in my simplified 'empty except for planet and space universe' DOMAIN, then SR cannot say anything about the planet's initial (moving or stationary) state, then any SR explanations are do NOT APPLY in that 'domain'. That was all I wanted to have clarified in context with your reply to ONlyMe that prompted my requst for clarification. And contrary to your insinuation, I made NO claim there either way about motion or rest. I merely pointed to SR and observed the 'catch 22' and 'both ways' implications of your textbook SR 'explanations' to OnlyMe in the post I wanted clarified in this context of SR 'domain of applicability' etc. Thanks. Cheers! .
Syne, actually I was attempting to arrive at point in the SR discussion where someone might have some input about what appears to be another issue, when exploring similar conditions as emergent quantum phenomena. I have not been doing a good job of that. It has often been a clumsy attempt. I have admitted that I have a limited basic understanding of the inertia and length/time dilations issues, as emergent phenomena raised in a number of published papers. None of which I am qualified to evaluate personally. I believe that as far as this discussion is concerned, all the way along I have been.., trying to push in that direction, or to a point where it might become relevant. Though I presented the expansion of the hypothetical with intent, I was in this case not playing devil's advocate. I really do not know the answer, when the environment extends beyond a locally defined space and SR and really am interested in understanding to what extent even abscent GR and curved space, SR can be considered locally defined. I don't really have any trouble with the classical twin paradox, in most of its incarnations. They were being discussed long ago. In fact there was a time when I was younger, I did not look beyond the limits, as defined in any of those thought experiments. I have the leisure today to look under rocks and behind the trees.
Why do you keep repeating the same false statement after you have been corrected three times? Proper time is frame invariant.
There is no "IF" . There is no absolute rest, this issue was resolved more than 100 years ago. Can u please stop spamming this forum with your fringe ideas?
Tach. Please Register or Log in to view the hidden image! That was not a claim in any way shape or form or intent. You obviously just pick on 'contextually removed snippets and run your strawmen with them. Please Register or Log in to view the hidden image! Why do you keep doing that? Is your attention/reading so narrow that you cannot read in context? Or is it just distraction tactics again to avoid addressing/discussing the actual points made IN CONTEXT? That "IF" statement was part of a post made in context of an "IF, THEN" logical option for the arguments presented in the relevant posts exchange. You are obviously misrepresenting again! It had NO SEPARATE or UNCONDITIONAL claims or connotations attached to that "IF" in context of the post/exchange where it appeared. Tach, please stop cluttering up the thread/discussion with your own misconstrued strawmen. The admin/mods are watching you and noting your persistent distraction tactics and obvious out-of-context shenanigans! Please Register or Log in to view the hidden image! Careful! .
The only "catch-22" is in your imagination. Nope. You first assertion there cannot be entertained without assuming some absolute frame of reference. You also seem to miss the very simple fact that rest is only one extreme of a gradient of motion. Asserting that having both is somehow inconsistent is equivalent to saying that no gradient requires a minimum value. That which applies to one part of a gradient necessarily applies to the whole gradient. So logically, if any state of motion is only relative, so is a state of rest. You seem to be trapped in the logical inconsistency of assuming a counter-factual absolute frame. Nothing can be compared "with respect to space" as space doesn't offer any landmarks. Really? How can you judge the motion of a planet simply by a succession of rocket launches? As you vary their speed relative to the planet you also vary their time rate accordingly. Time dilation only occurs relative to the observation frame, not relative to that observation frame and some completely different third frame. Whatever happened to simplification? You're adding superfluous frames again, and this time counter to your claimed intent. You just seem confused. Only with respect to a third frame, which you've denied in your simplification. Even in your planet-rocket-only universe, you still must introduce yet another frame of reference to know anything about any possible motion of the planet other than relative to the rocket. You can't honestly require something of SR that your scenario is specifically designed to preclude. That is intellectually dishonest. "Pointed out", "claimed", what's the difference? You've consistently opined from a perspective of an absolute frame of reference. Whether you are confident enough to admit it or not, doesn't change a thing. In SR, the local frame includes everything which is co-moving and at rest relative to a given observer.
Here is your complete statement, fully outlining your frine misconceptions: Your exact quote says that you are lying, trying to cover once your fringe notion has been exposed. RC, You have been denying length contraction, relativity of motion, mostly basic SR concepts for quite a while.
