It is really, really simple. They will agree on the astronomical positions but will disagree on the time it took for the bodies to attain the positions. Get it?
A 'dilated' clock is only dilated when measured from another reference frame. In it's own frame, it still takes on second to tick one second.
Great question! In actual fact, each twin sees the other twin as aging more slowly then him/herself...The equivalence principle governs that. What actually defines one twin from the other is that the travelling twin needs to decellerate to turn around and come back, and accelerate up to speed again. In reality, the "Twin Paradox" is not really a paradox at all.
Good you have it. The traveling twin witnessed 12 earth years while away. So, he knows he is 12 earth years older based on scientific observation. Yet, SR claims his clock reads 10 earth years have elapsed. Being a good scientist, the twin accepts he lived 12 earths years and that his clock malfunctioned. See, you are saying he lived both 12 earth years and 10 earth years, which is a contradiction.
You still do not have it. His clock shows 10 earth years. His astronomical observations show 12 earth years. He must say he lived 12 years based on observations. He then checks his clock and it claims only 10 years years have elapsed. He knows his clock malfunctioned because it does not tell the truth.
No that is not the case. The traveling twin witnessed 12 earth years by observations. Yet, his clock claims the earth orbited the sun only 10 times. His clock is inconsistent with scientific observation. It is therefore defective.
Hi Lakon! Please Register or Log in to view the hidden image! Sorry I am really rushed again today so can't stay long. Rushed answer... Unless they both srated from a co-moving starting 'state of motion' (ie, like from a common sun-centric orbital location (Earth); or started from a co-moving inertial situation in the same instantaneous motional state, then you don't have a comparison 'standard' from which to set up or run the experimental scenario. So if they start out in different motional states and that is the first one twin knows about the other twin, then any comparisons made between them would be purely ABSTRACT/relative (pure SR without any external information from which to deduce anything else), and so neither can say anything compared to the other except that they are moving at a certain closing/separation speed (whatever the case may be). HOWEVER, in the thread scenario involving Earth-sun system orbit motions/cycles, the twins started out from a co-moving and co-timing state. One twin then accelerated to higher speed and eventually fell behind his stay-put twin's clock/aging TICK/RATE. As I said earlier, the traveling twin counts the same Earth orbits NUMBER, but his 'seconds' of clock/aging TICK/RATE 'value' DIFFER from the 'value' of that for the stay-put twin clock/aging, even though his 'year count' of twelve is of the same 'absolute count number of orbit cycles of Earth. Chinglu seems to be conflating the concept/word "LIVED" with the concept/word "AGED" and arriving at a 'paradox' that is not a paradox when the difference between those two is recognized. He seems to think that 'living' for 12 Earth orbits is the same as 'aging' the same amount as the Earth twin does. Obviously the traveling twin does NOT 'age' the same number of Earth years as the stay-put twin, hence the same 12 Earth orbits mean two different things in this context. Namely: The Earth twin who is still aging (and living) at the initial agreed starting co-located/co-moving STANDARD tick/rate is the BASE REFERENCE for all comparisons thereafter. SO...when the traveling twin compares after traveling faster for 12 Earth orbits number count, the traveling twin may have "LIVED" for twelve Earth orbits BUT has "AGED" for 10/12 of the 'value' of those 12 orbits according to HIS TIME DILATED 'value' for his traveling clock/biological process RATE which differes from the STANDARD which his stay-put twin is STILL under the influence of. So, 'lived' for 12 orbits is not the same as 'aged' for 12 orbits unless both twins remain under the influence of the same 'starting standard' (which they don't if the traveling twin accelerates away to greater speed from co-located/co-moving 'states. I hope this rushed clarification helps, mate! PS: I'll just make a quick reply to Chinglu referring to this post and then I'm off again. Cheers!
I have bolded the part which is causing you to arrive at a paradox when no paradox exists. See? It's subtle but important aspect/difference: You are obviously conflating "lived" with "aged", and so mixing concepts/logics which produce the confusion (ie, imagined paradox). "Lived" means "existed" without reference to anything other than duration per se without any specifics as to 'value' of particular "existence period units" etc.; whereas "aged" immediately involves particular "existence period units" (in this case each twin has different such "units" because their rate/count of accumulation of such INHERENT CLOCK/BIOLOGICAL TIMING/PROCESSING "units" differs, and hence the value of inherent "aging" differs even though both twins are "living through" the same 'absolute number' of commonly observable external things as the number of Earth orbit cycles. See? PS: Please see my previous post to Lakon above for further clarification of where the problem/confusion arises. Sorry but I have to rush off again, Chinglu! Bye and good luck and good thinking and good discussing to you, and everyone! Cheers! Please Register or Log in to view the hidden image!
You have still not dealt with the issue. You are now using terms like lived and aged to justify a failed theory. Now, you must reconcile how the traveling twin witnessed 12 earth orbits and yet his SR clock claimed 10 earth orbits. Which is correct? You are claiming both, which is a contradiction.
The immediacy of your response indicates you haven't read and properly considered fully the distinction between "lived" and aged" which seems to be at the centre of your confusion. Also you have already forgotten what I posted to you about the effectively "causal disconnectedness" or INHERENCY of the clock information/rates; or the 'value' difference between the INHERENT TICKS/RATES of the two twins when one is traveling faster. That inattention and confusion is what leads you to STILL make illogical/incorrect statements like that above (my bolding). The traveling twin's clock only 'claims' an INHERENT cumulative count of its particular value SECONDS. And nothing else. See? It is YOU who is illogically 'connecting' the traveling twin's clock count with the orbital number and ABSTRACTLY and SUBJECTIVELY 'seeing/judging' it 'same/different' or whatever...exacerbated by your other illogical conflation of "lived" with "aged" concept. Until you DISCONNECT the INHERENT information (your clock counts) from the EXTERNAL REFERENTS (the Earth orbit cycle number), you will be connecting and conflating your way to an imaginary paradox. Take time to re-read everything I explained to you (including my response to Lakon), and then think about what IMPLICATIONS the SUBTLETIES I explained have for your 'analysis' and assumptions/assertions. Only after you properly understand those subtleties/implications will you understand that what you stated (my bolding) in your above post is NOT valid, since it is your own imagined connection and not the reality of what the clock is or is not 'claiming'. PS: Lucky I was still checking for typos when you posted so immediately! But really have to go now, so the typos will have to look after themselves because I haven't time to check for them now. Good luck! Please Register or Log in to view the hidden image!
What you mean is, the traveling twin saw the earth orbit the sun 12 times. No, he knows 12 years have elapsed on the earth. That's because time isn't flowing at a constant rate everywhere, it depends on how fast you're moving relative to other objects, like the earth. That's what an ignorant twin might accept, but a twin who knows about relativistic effects doesn't think his clock malfunctioned. Rubbish, his clock tells him the earth is moving 1.2 times faster relative to him than for people on the earth. What if he checks the clock and finds no defect? What kind of irrational explanation would he need then? It looks like you still haven't got it. Maybe you never will.
He experienced 10 Earth years, but witnessed[observed] 12 Earth years in the other frame of reference. No, he knows he is 10 years older both by on board system clocks and his own biological systems. Right: No, his clock did not malfunction, and nor did his own biological system go haywire...He has aged 10 years. No you are saying that because you [1] Ignore FoRs, Ignore experiments validating time dilation and length contraction, and have not yet had the intestinal fortitude to check the explanatory video I supplied. Either that, or like I suggested before, you are playing silly buggers.
I just scrolled quickly through the last 3 pages since my last post and given I don't see any algebra from chinglu I'll conclude he continues to be unable to actually show the GR contradiction, only assert it. Chinglu, it is obvious to everyone you cannot do any relativity, special or general, which is explains why you can only resort to assertions without justification. Until such time as you can attempt to justify your claim using actual mathematical formalisations, without resorting to lies, misrepresentations and deceptions no further discussion is needed. You cannot even formalise the problem, much less work through the GR description to show the conclusion you claim. As I said previously, you really should feel embarrassed and ashamed for the profound level of wilful ignorance you show. I really hope you're a troll, doing this deliberately, as the alternative is you're a disgraceful human being.
I think this is the essence of what puzzles me, and what I've tried to talk about in my recent exchanges with Undefined on this thread. So I address this post to anyone on this thread. Keeping in mind the above, what defines which twin is actually travelling, decellerating, etc. Stripping it down to bare facts, and assuming an otherwise empty space, how can it be said that, say, twin A is accellerating as opposed to twin B ? Would not the equivalence principle mean that either could say that the other accellerated / decellerated and is therefore younger ?
I notice the anti-relativity club tends to rely on incongruent observations like this to try to build their fallacies. No one on Earth observes the annual rotation of the Earth in its orbit. They're looking at the sky, which is rotating on several different axes. The astronaut in some ill-defined observation plane - presumably well above the plane of Earth's orbit, anchored somehow to the position of the Sun--but of abitrary range, pitch, roll and yaw from anything that could actually be called a reference frame--is so vaguely established we can't very well argue the math one way or the other. If the argument is to try to redefine units of time measurement to 1 solar year on Earth then obviously the fallacy is exposed as soon as we point out that this has no bearing on the astronaut who apparently isn't doing any such orbit. Of course the navigation math of the hypothetical astronaut hasn't been offered (although since I have the worst offenders on ignore I might have missed any attempts to do that). Similarly, any astronaut has necessarily moved away from the gravitational potential of Earth. He may or may not be in an apparent state of time dilation. The other possibility is that he is on Jupiter or a giant ball of lead and his clock is running faster, and he returns a little older than his twin. There's no need to go through this convoluted geometric hand waving anyway. All the nuts need to do is to tell us that the experts are lying, which I presume is the main thrust of this thread. There's no need to go to Jupiter or Andromeda or even waste money on rocket fuel. I would just go to NIST and explore what's observable right under our noses: http://www.nist.gov/public_affairs/releases/aluminum-atomic-clock_092310.cfm This has been covered in some other threads so apologies in advance if I'm repeating myself. But the denialists can read it and weep. Please Register or Log in to view the hidden image!
Not real easy to explain [at least for an amateur such as myself] but it is simply the act of the travelling twin slowing to turn back [decelerating] and accelerating again back up to speed that defines them. The stay at home twin is not accelerating nor decelerating with respect to the Earth. The principle of Inertia assures that deceleration and acceleration are felt and distinguished from constant motion....You are pushed back in the seat if you accelerate, and are forced forward if you decelerate. I'll leave it to Undefined or Aqueous to define it more accurately then that... Please Register or Log in to view the hidden image!
In special relativity, the one who leaves the reference frame (esp. at very high speed) is the one who experiences the time dilation relative to that frame. In general relativity, it's a question of who moved toward or away from the gravity of the original reference frame, and the effect is reversed (the clock ticks faster as it leaves the gravity well).
