vuquta Posted February 6, 2010 Posted February 6, 2010 Alternative Twins Paradox The traditional twins paradox is solved such that all agree the traveling twin is younger because of non-symmetric acceleration. However, the uniform acceleration equations and Lorentzian transformations of special relativity are all that are needed. So, this twins paradox will produce symmetric acceleration and force SR to exclusively explain reciprocal time dilation. O and O' are physicists testing special relativity. These physicists are going to test the aging of two twins. O, O', twin1 and twin2 are in the same frame and sync their clocks with Einstein's clock synchronization method. They all agree to burn for BT and agree on the number. Next, all set their clocks to 0 and reside at the same origin for a common start point. Then, twin1 take off from the frame in a spaceship at proper acceleration a and for burn time BT in the proper time of the accelerating frame such that they attain a relative motion v compared to the prior frame. Then, for a long period of time, they remain in relative motion to O' and twin2. So, O and twin1 see O' and twin2 moving away at relative motion v and O' and twin2 see O and twin1 moving away at relative motion v. After some long period of t, O' and twin2 take off in an identical spaceship in exactly the same direction as O and twin1 did at the same acceleration a and for the same burn time BT. After the burn is complete, all are back in the same frame but at a distance between them and O' immediately sends out a light pulse. O records the time it receives the light pulse. Then, O performs the round trip speed of light calculation to decide the distance between the two ships. Once the distance D between the two ships is known, O subtracts D/c from the time it received the light pulse from O'. This gives O the exact time in its own proper time when O' stopped accelerating and entered the frame of O. In addition, this gives a correct endpoint to the experiment that matches the endpoint of O'. Thus, O and O' share a common start point and end point to the experiment. Let BT be the burn time in the accelerating frame. Let a = acceleration and v = the relative speed attained by the acceleration. O and O' calculate the proper time of the twins as follows. Calculations of O for the twins Elapsed proper time calculation for twin 1 twin1's acceleration phase BT twin1's relative motion phase t' twin2's acceleration phase c/a sinh(aBT/c) Total elapsed proper time calculation of O for twin1 BT + t' + c/a sinh(aBT/c) Please note above, O marked an endpoint to the experiment after receiving a light pulse from O', call that time, Te. Then, Te = BT + t' + c/a sinh(aBT/c) + D/c where D is the distance between the two ships in the resulting frame as derived above. Thus, t' = Te - BT - c/a sinh(aBT/c) - D/c. Elapsed proper time calculation for twin 2 twin1's acceleration phase c/a sinh(aBT/c) twin2's relative motion phase t'/ λ twin2's acceleration phase BT Total elapsed proper time calculation of O for twin2 c/a sinh(aBT/c) + t'/λ + BT Conclusion of O, twin1 is older. Calculations of O' for the twins Elapsed proper time calculation for twin 1 twin1's acceleration phase BT twin1's relative motion phase t/λ twin2's acceleration phase c/a sinh(aBT/c) Total elapsed proper time calculation of O' for twin1 BT + t/λ + c/a sinh(aBT/c) Elapsed proper time calculation for twin 2 twin1's acceleration phase c/a sinh(aBT/c) twin2's relative motion phase t twin2's acceleration phase BT Total elapsed proper time calculation of O' for twin2 c/a sinh(aBT/c) + t + BT Conclusion of O', twin1 is younger. Since all are now in the same frame, they again use Einstein's clock synchronization method for the actual hard data of the experiment to test the clocks of the twins for age ordinality. This answer of the clock sync is to be accepted by all those in the frame because as Einstein said, "We assume that this definition of synchronism is free from contradictions". This clock sync can also establish the time ordinality of the clocks. This is how it is done. Twin1 sends its time ttwin1 to twin2. Twin2 immediately sends its time ttwin2 back to the clock of twin1. Twin1 receives this light at t'twin1*** Einstein concludes the two clocks are in sync if ttwin2 = ½ ( t'twin1 - ttwin1). Thus, the age ordinality is established as ttwin2 - ½ ( t'twin1 - ttwin1) http://www.fourmilab.ch/etexts/einstein/specrel/www/ SR is supposed to be a reliable tool for the calculation of the proper time of one frame to another frame. However, both O' and O cannot be correct with their SR conclusions when presented with the factual data of the clock sync. References http://arxiv.org/PS_cache/physics/pdf/0411/0411233v1.pdf http://www.ejournal.unam.mx/rmf/no521/RMF52110.pdf http://users.telenet.be/vdmoortel/dirk/Physics/Acceleration.html http://en.wikipedia.org/wiki/Twins_paradox
swansont Posted February 6, 2010 Posted February 6, 2010 Thus, O and O' share a common start point and end point to the experiment. I'm missing how the twins are co-located if there is a delay between their rocket burns.
vuquta Posted February 6, 2010 Author Posted February 6, 2010 I'm missing how the twins are co-located if there is a delay between their rocket burns. I do not co-locate them at the termination. I use the SR clock simultaneity convention which is logically equivalent to co-location. If they are co-located, then you can look at their clocks. If they are in the same frame at the endpoint, then you use the SR clock sync method to look at the clocks and establish ordinality. The ordinality can be established same as with the eyeballs.
swansont Posted February 6, 2010 Posted February 6, 2010 I do not co-locate them at the termination.I use the SR clock simultaneity convention which is logically equivalent to co-location. Don't say they have the same endpoint, then. They can compare clocks, and their clocks will disagree. The burn time is a distraction; it's a common term in all of your expressions, so set it to zero. The only relevant term is the time twin1 is in the O' frame. Do the measurement as soon as twin2 gets there. In O, a time t will have elapsed. The clock for twin1 will read t/λ, the clock for twin2 will read t, according to an observer in O. In O', the situation is reversed. Twin1's clock will read t', and twin2's clock will read t'/λ So what? We know that two different frames will disagree. In the classical twin paradox, each twin *and anyone in that frame) thinks the other is younger until acceleration breaks the symmetry.
vuquta Posted February 6, 2010 Author Posted February 6, 2010 (edited) Don't say they have the same endpoint, then. They can compare clocks, and their clocks will disagree. The burn time is a distraction; it's a common term in all of your expressions, so set it to zero. The only relevant term is the time twin1 is in the O' frame. Do the measurement as soon as twin2 gets there. In O, a time t will have elapsed. The clock for twin1 will read t/λ, the clock for twin2 will read t, according to an observer in O. In O', the situation is reversed. Twin1's clock will read t', and twin2's clock will read t'/λ So what? We know that two different frames will disagree. In the classical twin paradox, each twin *and anyone in that frame) thinks the other is younger until acceleration breaks the symmetry. 1) Technically, I have to say endpoint because it is a piecewise integral. 2) The reason burntime is used rather than instant acceleration instead is to keep the experiment a posteriori. 3) It needs to be a posteriori is to compare the results at the end because that is needed to produce the contradiction. The purpose of the above is to show LT cannot possibly calculate the proper time of a moving frame correctly since it provably calculates two different answers. The significance is not that they disagree as much as it indicates one or both are wrong. In particular, the above experiment gives physical evidence by the final clock sync so we are no longer in the realm of different points of view since this sync gives verificable evidence on whether LT correctly models reality. The above shows LT does not model reality because the physical evidence proves both cannot be younger. Edited February 6, 2010 by vuquta
swansont Posted February 6, 2010 Posted February 6, 2010 (edited) The purpose of the above is to show LT cannot possibly calculate the proper time of a moving frame correctly since it provably calculates two different answers. You get different answers for different frames of reference. This is relativity. To anyone with a basic grasp of the concept, this is not surprising. The significance is not that they disagree as much as it indicates one or both are wrong. Non-sequitur. In particular, the above experiment gives physical evidence by the final clock sync so we are no longer in the realm of different points of view since this sync gives verificable evidence on whether LT correctly models reality. There is no physical evidence — this is a thought experiment. There is no clock synch because the clocks will not be in synch. The above shows LT does not model reality because the physical evidence proves both cannot be younger. You have not done a physical experiment, so you have no physical evidence. You can draw no conclusions about whether relativity models reality without one. What you have shown is that relativity does not model your intuition about reality. You intuition is wrong. You are a member of a very large club in this regard. Edited February 6, 2010 by swansont
vuquta Posted February 6, 2010 Author Posted February 6, 2010 (edited) You get different answers for different frames of reference. This is relativity. To anyone with a basic grasp of the concept, this is not surprising. Non-sequitur. Uhhh, no. Each step of this experment can be performed in physical reality. In other words, it is algorithmic. So, LT is supposed to calculate the proper time of a moving frame. It is supposed to model physical reality. Now, if you have a theory that provably decides one twin will be older while at the same time the other twin will be older in the same set of circumstances, then you have a theory that cannot correctly model physical reality because from experience we know this cannot happen. There is no physical evidence — this is a thought experiment. There is no clock synch because the clocks will not be in synch. You have not done a physical experiment, so you have no physical evidence. You can draw no conclusions about whether relativity models reality without one. What you have shown is that relativity does not model your intuition about reality. You intuition is wrong. You are a member of a very large club in this regard. There is no physical evidence — this is a thought experiment. There is no clock synch because the clocks will not be in synch. I am sure you are aware that the experiment can be performed in reality. Now, if I needed infinite sets or something that are not available in the real world, the above comments would hold as valid. Further, you cannot prove the clocks will be in sync or not in sync. That is a failure of LT. But, since they are in the same frame, we can establish the ordinality of the clocks by using the clock sync method. Can we trust this method when they are in the same frame? Einstein wrote: We assume that this definition of synchronism is free from contradictions, http://www.fourmilab.ch/etexts/einstein/specrel/www/ Yes, so we use the method to see if they are in sync and if not, we can determine the ordinality. Now, once this answer is provided, we find LT supplying two different answers for the same problem. Thus, in SR, we have one answer that is free from contradictions and two answers from LT that contradict each other. Edited February 6, 2010 by vuquta
swansont Posted February 6, 2010 Posted February 6, 2010 Uhhh, no. Each step of this experment can be performed in physical reality. In other words, it is algorithmic. How does that change the fact that relativity predicts that you will get different answers in different reference frames? I am sure you are aware that the experiment can be performed in reality. Now, if I needed infinite sets or something that are not available in the real world, the above comments would hold as valid. So do it. Further, you cannot prove the clocks will be in sync or not in sync. That is a failure of LT. I can use relativity to predict if the clocks will be in synch or not. Experiments have shown that the moving clocks run slow. But, since they are in the same frame, we can establish the ordinality of the clocks by using the clock sync method. Can we trust this method when they are in the same frame? What are you meaning by "ordinality of the clocks?" Which is running slow? Einstein wrote: We assume that this definition of synchronism is free from contradictions, http://www.fourmilab.ch/etexts/einstein/specrel/www/ Yes, so we use the method to see if they are in sync and if not, we can determine the ordinality. Now, once this answer is provided, we find LT supplying two different answers for the same problem. You are mixing frames. Within each frame you get one answer. Thus, in SR, we have one answer that is free from contradictions and two answers from LT that contradict each other. Careful here, this seems like the fallacy of equivocation. Einstein is using "contradiction" in a specific way, and in the context of synchronizing clocks. That in no way implies that clocks/timing in different frames will agree with each other. The theory never says that the answers from different frames will agree. Issues of timing and simultaneity are RELATIVE to the frame you are in.
vuquta Posted February 6, 2010 Author Posted February 6, 2010 How does that change the fact that relativity predicts that you will get different answers in different reference frames? It does not. The thought experiment is a step by step procedure which terminates at the clock sync. Each step is well defined. The clock sync produces one answer. Therefore, this is a recursive procedure. As such, the problem is logically decidable. Other the other hand, LT produces two different answers. Therefore, the problem is not logically decidable. This is a contradiction. I can use relativity to predict if the clocks will be in synch or not. Experiments have shown that the moving clocks run slow. Assume GPS and the satellite frame as stationary. The earth clocks do not run slower as they should since that would be the moving frame. Hence there is comething absolute about time dilation and not relative. What are you meaning by "ordinality of the clocks?" Which is running slow? Sort of. It means the order in terms of time. a < b, a > b or a = b. It would establish which one of these is true. You are mixing frames. Within each frame you get one answer. Agreed, but that is not frame mixing. I call one frame stationary and do the calculations. Then, I call one the other frame stationary and do the calculations. Careful here, this seems like the fallacy of equivocation. Einstein is using "contradiction" in a specific way, and in the context of synchronizing clocks. That in no way implies that clocks/timing in different frames will agree with each other. The theory never says that the answers from different frames will agree. Issues of timing and simultaneity are RELATIVE to the frame you are in. Well, not exactly about relative. Free from contradiction means there is only one answer. It means they are in sync or not in sync and not both. The clock sync is more fundamental than LT also. In fact, it is the basis of LT construction. So, since the clock sync can be performed and the answer is trusted, this proves this experiment concludes with one viable answer only and not two as suggested by LT.
swansont Posted February 6, 2010 Posted February 6, 2010 It does not. The thought experiment is a step by step procedure which terminates at the clock sync. Each step is well defined. The clock sync produces one answer. Therefore, this is a recursive procedure. As such, the problem is logically decidable. Other the other hand, LT produces two different answers. Therefore, the problem is not logically decidable. This is a contradiction. Correction — the clock comparison produces one answer, in the O' frame, since that's where the clocks are. They do not and cannot give an answer in the O frame. Only an observer in the O frame can get that answer. Assume GPS and the satellite frame as stationary. The earth clocks do not run slower as they should since that would be the moving frame. Hence there is comething absolute about time dilation and not relative. GPS satellites are in a rotating reference frame, and as such are not in an inertial frame. Which means the symmetry of SR is not present. Sort of. It means the order in terms of time. a < b, a > b or a = b. It would establish which one of these is true. Agreed, but that is not frame mixing. I call one frame stationary and do the calculations. Then, I call one the other frame stationary and do the calculations. So? Labels ultimately do not matter. You get a different answer for each frame. That is not in contradiction with any part of relativity. Well, not exactly about relative. Free from contradiction means there is only one answer. It means they are in sync or not in sync and not both. The clock sync is more fundamental than LT also. In fact, it is the basis of LT construction. So, since the clock sync can be performed and the answer is trusted, this proves this experiment concludes with one viable answer only and not two as suggested by LT. Clock synchronization is only valid in one frame of reference. Once you bring another frame into it, all bets are off, since simultaneity is relative. Clocks that are synchronized in one frame will not be in another, as was shown in the last thread (unless you erroneously assume the answer, of course) You are making the same error of assuming simultaneity here.
vuquta Posted February 6, 2010 Author Posted February 6, 2010 Correction — the clock comparison produces one answer, in the O' frame, since that's where the clocks are. They do not and cannot give an answer in the O frame. Only an observer in the O frame can get that answer. The end of the experiment brings both twins back into the same frame. Each can perform clock synching to decide the age ordinality or one can transmit the answer to the other. It doesn't matter, each will know one answer. And, if the clock sync method is not realiable, meaning produces incorrect results or multiple results, then LT is immediately false since it is based on the clock sync method. GPS satellites are in a rotating reference frame, and as such are not in an inertial frame. Which means the symmetry of SR is not present. This is not a basis for ruling out reciprocal*time dilation. Further, to support this claim, one would need to prove a rotating referencing frame proves absolute time dilation, meaning one way. There is no such proof. So? Labels ultimately do not matter. You get a different answer for each frame. That is not in contradiction with any part of relativity. I suppose labels matter, but what I am doing is not connected to labels. I am assuming one frame as stationary and calulating the results. This is normal. Therefore, the frame will have a view of its proper time and also a view of the proper time of the other frame. This is all I did. Clock synchronization is only valid in one frame of reference. Once you bring another frame into it, all bets are off, since simultaneity is relative. Clocks that are synchronized in one frame will not be in another, as was shown in the last thread (unless you erroneously assume the answer, of course) You are making the same error of assuming simultaneity here. I am not assuming anything. I bring clocks together in one frame. I check their clock values and report the results while they are in the same frame. There can only be only answer. Specifically, what do you find wrong or assumed here? I do not really know if they will have the same clock values (simultaneity). What I do know is there is one and only one answer. Do you dispute this?
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