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| Tags: dead, final, proof, relativity, special |
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#1
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In 1971 the Hafele-Keating experiment was conducted. It is a well-known
and well documented experiment with two planes, carrying two atomic clocks. One clock flew in western direction around the earth, and one flew in eastern direction around the earth. The purpose was to prove "time delation" as predicted by Einstein's theories of Relativity. The results of the experiments were presented as a big success, proving the theory of Special Relativity. The atomic clocks onboard the planes did walk at a different rate than a stationary atomic clock that was used for reference. However, the results did not PROVE Einsteins Special Relativity but DISPROVED it. One clock walked indeed slower than the reference clock, but the other clock walked FASTER than the reference clock. This phenomenon was explained by noting that one of the clocks flew counter to the rotation of earth, and so was moving even slower than the reference clock. Hm... peculiar! I thought that central to SR was the fact that each inertial frame is equivalent, and there is no "zero" inertial frame AKA "aether". However, the Hafele-Keating experiment showed that the faster one moves with regard to an inertial frame against which also earth moves (through its rotation), the slower your clock goes. So there is a "zero" inertial frame (aether), and experiments conducted in this "zero" frame have results that differ from experiments conducted in inertial frames that move with regard to the "zero" frame. The main difference is that in the zero-frame, clocks walk fastest. The experiment showed that there IS NO RELATIVITY. There might be time delation, but it is a phenomenon that is based on movement with regard to an ABSOLUTE zero-frame. I have recently presented four proofs against Relativity on this forum. A summary of the status of the various discussions. #1 (communication faster than light). The possibility of communication faster than light is denied. I cannot check the claims of certain researchers that they have conducted experiments with information transmission faster than c. What I do know is that if something is not practically realizable, it might be CONCEIVABLE. Immediate communication is theoretically conceivable, and therefore the denial of the existence of absolute time is silly. #2 (stationary and traveling clock experiment). No one has presented a calculation or even a reasoning why my conclusions based on this experiment are wrong. Someone wants to present a calculation, but first I have to prove that I am capable of appreciating the math, by doing some exercises. Ridiculous of course. I think I know why the calculation is "tricky" and why it is not presented. It is so convoluted that it is (in practice) impossible to prove it wrong. Calculations of this kind need to be big and complex. It requires major effort to present such a calculation. Therefore its presentation is delayed with childish conditions. The only real result: objections against Relativity are not disproved. #3 (two clocks in orbit experiment). No one has presented a convincing argument why this experiment doesn't work the way I want. It's a simple application of the rules of mister Einstein. The outcome is devastating for Relativity. #4 (Hafele-Keating). I am curious what convoluted reasoning will be presented to counter the inevitable message from this experiment: RELATIVITY DOES NOT EXIST. I have seen a lot hostile reactions. Calling names, and even the change of the title of one of my postings, by someone who has apparently moderating privileges on this forum. There is a simple psychological explanation for this. Someone who knows for certain that his ideas are right does not behave in a hostile manner. Only if you cling to ideas for other reasons than love for the truth, you will react hostile if your illusions are in danger. |
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No data, no calculation, proof by "Jan says so".
Very convincing, noise generator. Oh well, at least that's over. Androcles wrote in message oups.com... | In 1971 the Hafele-Keating experiment was conducted. It is a well-known | and well documented experiment with two planes, carrying two atomic | clocks. One clock flew in western direction around the earth, and one | flew in eastern direction around the earth. The purpose was to prove | "time delation" as predicted by Einstein's theories of Relativity. | | The results of the experiments were presented as a big success, proving | the theory of Special Relativity. The atomic clocks onboard the planes | did walk at a different rate than a stationary atomic clock that was | used for reference. | | However, the results did not PROVE Einsteins Special Relativity but | DISPROVED it. One clock walked indeed slower than the reference clock, | but the other clock walked FASTER than the reference clock. This | phenomenon was explained by noting that one of the clocks flew counter | to the rotation of earth, and so was moving even slower than the | reference clock. | | Hm... peculiar! I thought that central to SR was the fact that each | inertial frame is equivalent, and there is no "zero" inertial frame AKA | "aether". However, the Hafele-Keating experiment showed that the faster | one moves with regard to an inertial frame against which also earth | moves (through its rotation), the slower your clock goes. | | So there is a "zero" inertial frame (aether), and experiments conducted | in this "zero" frame have results that differ from experiments | conducted in inertial frames that move with regard to the "zero" frame. | The main difference is that in the zero-frame, clocks walk fastest. | | The experiment showed that there IS NO RELATIVITY. There might be time | delation, but it is a phenomenon that is based on movement with regard | to an ABSOLUTE zero-frame. | | I have recently presented four proofs against Relativity on this forum. | A summary of the status of the various discussions. | | #1 (communication faster than light). The possibility of communication | faster than light is denied. I cannot check the claims of certain | researchers that they have conducted experiments with information | transmission faster than c. What I do know is that if something is not | practically realizable, it might be CONCEIVABLE. Immediate | communication is theoretically conceivable, and therefore the denial of | the existence of absolute time is silly. | | #2 (stationary and traveling clock experiment). No one has presented a | calculation or even a reasoning why my conclusions based on this | experiment are wrong. Someone wants to present a calculation, but first | I have to prove that I am capable of appreciating the math, by doing | some exercises. Ridiculous of course. I think I know why the | calculation is "tricky" and why it is not presented. It is so | convoluted that it is (in practice) impossible to prove it wrong. | Calculations of this kind need to be big and complex. It requires major | effort to present such a calculation. Therefore its presentation is | delayed with childish conditions. The only real result: objections | against Relativity are not disproved. | | #3 (two clocks in orbit experiment). No one has presented a convincing | argument why this experiment doesn't work the way I want. It's a simple | application of the rules of mister Einstein. The outcome is devastating | for Relativity. | | #4 (Hafele-Keating). I am curious what convoluted reasoning will be | presented to counter the inevitable message from this experiment: | RELATIVITY DOES NOT EXIST. | | I have seen a lot hostile reactions. Calling names, and even the change | of the title of one of my postings, by someone who has apparently | moderating privileges on this forum. There is a simple psychological | explanation for this. Someone who knows for certain that his ideas are | right does not behave in a hostile manner. Only if you cling to ideas | for other reasons than love for the truth, you will react hostile if | your illusions are in danger. | |
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wrote:
In 1971 the Hafele-Keating experiment was conducted. It is a well-known and well documented experiment with two planes, carrying two atomic clocks. One clock flew in western direction around the earth, and one flew in eastern direction around the earth. The purpose was to prove "time delation" as predicted by Einstein's theories of Relativity. The results of the experiments were presented as a big success, proving the theory of Special Relativity. The atomic clocks onboard the planes did walk at a different rate than a stationary atomic clock that was used for reference. However, the results did not PROVE Einsteins Special Relativity but DISPROVED it. One clock walked indeed slower than the reference clock, but the other clock walked FASTER than the reference clock. This phenomenon was explained by noting that one of the clocks flew counter to the rotation of earth, and so was moving even slower than the reference clock. Ahh... No. The experiment didn't include a light path so it couldn't prove or disprove anything about SR (1920) It's been re-analysed to reflect the change in nuclear-resonance with change in altitude. The reinterpretation continues to obscure rather clarify the fact that *time-dilation* is a corruption of canonical terms for retarded-potential, nuclear resonance, Sagnac, Doppler imaginary-time and anything else that might demand a tweak a tweak on the 't' in an equation. You are justified to smell a rat but your skills in obfuscation, far exceed those of H&K. You make the sale for H.G. Wells interpretations far more effectivly than H&K ever dreamed possible. ;-) Learn some physics: http://farside.ph.utexas.edu/teaching.html http://web.mit.edu/8.02t/www/802TEAL...ight/index.htm http://en.wikipedia.org/wiki/Multiple_integral Time-independent Maxwell equations Time-dependent Maxwell's equations http://farside.ph.utexas.edu/teachin.../lectures.html Sue... Hm... peculiar! I thought that central to SR was the fact that each inertial frame is equivalent, and there is no "zero" inertial frame AKA "aether". However, the Hafele-Keating experiment showed that the faster one moves with regard to an inertial frame against which also earth moves (through its rotation), the slower your clock goes. So there is a "zero" inertial frame (aether), and experiments conducted in this "zero" frame have results that differ from experiments conducted in inertial frames that move with regard to the "zero" frame. The main difference is that in the zero-frame, clocks walk fastest. The experiment showed that there IS NO RELATIVITY. There might be time delation, but it is a phenomenon that is based on movement with regard to an ABSOLUTE zero-frame. I have recently presented four proofs against Relativity on this forum. A summary of the status of the various discussions. #1 (communication faster than light). The possibility of communication faster than light is denied. I cannot check the claims of certain researchers that they have conducted experiments with information transmission faster than c. What I do know is that if something is not practically realizable, it might be CONCEIVABLE. Immediate communication is theoretically conceivable, and therefore the denial of the existence of absolute time is silly. #2 (stationary and traveling clock experiment). No one has presented a calculation or even a reasoning why my conclusions based on this experiment are wrong. Someone wants to present a calculation, but first I have to prove that I am capable of appreciating the math, by doing some exercises. Ridiculous of course. I think I know why the calculation is "tricky" and why it is not presented. It is so convoluted that it is (in practice) impossible to prove it wrong. Calculations of this kind need to be big and complex. It requires major effort to present such a calculation. Therefore its presentation is delayed with childish conditions. The only real result: objections against Relativity are not disproved. #3 (two clocks in orbit experiment). No one has presented a convincing argument why this experiment doesn't work the way I want. It's a simple application of the rules of mister Einstein. The outcome is devastating for Relativity. #4 (Hafele-Keating). I am curious what convoluted reasoning will be presented to counter the inevitable message from this experiment: RELATIVITY DOES NOT EXIST. I have seen a lot hostile reactions. Calling names, and even the change of the title of one of my postings, by someone who has apparently moderating privileges on this forum. There is a simple psychological explanation for this. Someone who knows for certain that his ideas are right does not behave in a hostile manner. Only if you cling to ideas for other reasons than love for the truth, you will react hostile if your illusions are in danger. |
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#4
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wrote in message oups.com... In 1971 the Hafele-Keating experiment was conducted. It is a well-known and well documented experiment with two planes, carrying two atomic clocks. One clock flew in western direction around the earth, and one flew in eastern direction around the earth. The purpose was to prove "time delation" as predicted by Einstein's theories of Relativity. The results of the experiments were presented as a big success, proving the theory of Special Relativity. The atomic clocks onboard the planes did walk at a different rate than a stationary atomic clock that was used for reference. However, the results did not PROVE Einsteins Special Relativity but DISPROVED it. One clock walked indeed slower than the reference clock, but the other clock walked FASTER than the reference clock. This phenomenon was explained by noting that one of the clocks flew counter to the rotation of earth, and so was moving even slower than the reference clock. The Hafele-Keating experiment was riddled with controversy. Hafele and Keating didn't give the actual test results in their paper; they gave figures that were radically altered. It is also shown that the clocks used were not of sufficient stability to prove anything. "The magnitude of the random alterations in performance during air transport were such as to make any such result useless". "Also, Louis Essen, the inventor of the atomic clock, published an article in which he discussed the (in his opinion) inadequate accuracy of the experiment." See http://en.wikipedia.org/wiki/Hafele-Keating_experiment Hm... peculiar! I thought that central to SR was the fact that each inertial frame is equivalent, and there is no "zero" inertial frame AKA "aether". However, the Hafele-Keating experiment showed that the faster one moves with regard to an inertial frame against which also earth moves (through its rotation), the slower your clock goes. So there is a "zero" inertial frame (aether), and experiments conducted in this "zero" frame have results that differ from experiments conducted in inertial frames that move with regard to the "zero" frame. The main difference is that in the zero-frame, clocks walk fastest. You mistakenly conclude that the inertial frame had to the so called "aether", but their analysis clearly describes how their inertial frame was the centre of the earth and they even adjusted their data to prove SR in terms of the centre of the earth as the at inertial frame. So if you even read the paper wouldn't be talking so much crap. Please spare us any further "proof". [snip] |
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#6
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wrote in message oups.com... In 1971 the Hafele-Keating experiment was conducted. It is a well-known and well documented experiment with two planes, carrying two atomic clocks. One clock flew in western direction around the earth, and one flew in eastern direction around the earth. The purpose was to prove "time delation" as predicted by Einstein's theories of Relativity. The results of the experiments were presented as a big success, proving the theory of Special Relativity. The atomic clocks onboard the planes did walk at a different rate than a stationary atomic clock that was used for reference. In reality the results were hardly conclusive. However, the results did not PROVE Einsteins Special Relativity but DISPROVED it. One clock walked indeed slower than the reference clock, but the other clock walked FASTER than the reference clock. This phenomenon was explained by noting that one of the clocks flew counter to the rotation of earth, and so was moving even slower than the reference clock. Hm... peculiar! I thought that central to SR was the fact that each inertial frame is equivalent, and there is no "zero" inertial frame AKA "aether". However, the Hafele-Keating experiment showed that the faster one moves with regard to an inertial frame against which also earth moves (through its rotation), the slower your clock goes. Then ask your school money back. ;-) SRT is based on inertial frames, just like classical mechanics. The rotating earth surface is not a valid inertial frame for such a global experiment. Similarly for GPS the earth centered inertial frame is used. So there is a "zero" inertial frame (aether), and experiments conducted in this "zero" frame have results that differ from experiments conducted in inertial frames that move with regard to the "zero" frame. The main difference is that in the zero-frame, clocks walk fastest. Wrong (but an often seen mistake). Any inertial frame can be chosen, but there are preferred frames for simplest calculations - again just as in classical mechanics. The experiment showed that there IS NO RELATIVITY. There might be time delation, but it is a phenomenon that is based on movement with regard to an ABSOLUTE zero-frame. That interpretation is perfectly compatible with "relativity" theory. According to SRT, no such zero frame can be determined. That's all there is to it; just ignore bunkum. Cheers, Harald |
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"jem" wrote in message ... wrote: In 1971 the Hafele-Keating experiment was conducted. It is a well-known and well documented experiment with two planes, carrying two atomic clocks. One clock flew in western direction around the earth, and one flew in eastern direction around the earth. The purpose was to prove "time delation" as predicted by Einstein's theories of Relativity. The results of the experiments were presented as a big success, proving the theory of Special Relativity. The atomic clocks onboard the planes did walk at a different rate than a stationary atomic clock that was used for reference. However, the results did not PROVE Einsteins Special Relativity but DISPROVED it. One clock walked indeed slower than the reference clock, but the other clock walked FASTER than the reference clock. This phenomenon was explained by noting that one of the clocks flew counter to the rotation of earth, and so was moving even slower than the reference clock. Hm... peculiar! I thought that central to SR was the fact that each inertial frame is equivalent, and there is no "zero" inertial frame AKA "aether". However, the Hafele-Keating experiment showed that the faster one moves with regard to an inertial frame against which also earth moves (through its rotation), the slower your clock goes. So there is a "zero" inertial frame (aether), and experiments conducted in this "zero" frame have results that differ from experiments conducted in inertial frames that move with regard to the "zero" frame. The main difference is that in the zero-frame, clocks walk fastest. The experiment showed that there IS NO RELATIVITY. There might be time delation, but it is a phenomenon that is based on movement with regard to an ABSOLUTE zero-frame. I have recently presented four proofs against Relativity on this forum. A summary of the status of the various discussions. #1 (communication faster than light). The possibility of communication faster than light is denied. I cannot check the claims of certain researchers that they have conducted experiments with information transmission faster than c. What I do know is that if something is not practically realizable, it might be CONCEIVABLE. Immediate communication is theoretically conceivable, and therefore the denial of the existence of absolute time is silly. #2 (stationary and traveling clock experiment). No one has presented a calculation or even a reasoning why my conclusions based on this experiment are wrong. Someone wants to present a calculation, but first I have to prove that I am capable of appreciating the math, by doing some exercises. Ridiculous of course. I think I know why the calculation is "tricky" and why it is not presented. It is so convoluted that it is (in practice) impossible to prove it wrong. Calculations of this kind need to be big and complex. It requires major effort to present such a calculation. Therefore its presentation is delayed with childish conditions. The only real result: objections against Relativity are not disproved. #3 (two clocks in orbit experiment). No one has presented a convincing argument why this experiment doesn't work the way I want. It's a simple application of the rules of mister Einstein. The outcome is devastating for Relativity. #4 (Hafele-Keating). I am curious what convoluted reasoning will be presented to counter the inevitable message from this experiment: RELATIVITY DOES NOT EXIST. I have seen a lot hostile reactions. Calling names, and even the change of the title of one of my postings, by someone who has apparently moderating privileges on this forum. There is a simple psychological explanation for this. Someone who knows for certain that his ideas are right does not behave in a hostile manner. Only if you cling to ideas for other reasons than love for the truth, you will react hostile if your illusions are in danger. Yes, of course you're right. It's truly pathetic how thousands of physicists have blindly followed Einstein's mistakes and unwittingly adopted a logically inconsistent description of the world. However, although your astute insights are right on target, you've not been the first to perceive them. Ken Seto came to the same realization years ago and has created the Improved Relativity Theory (IRT) to reveal Nature's TRUE character. Seto's works are detailed at http://www.geocities.com/kn_seto/index.htm, but to date his promotional efforts haven't been all that successful. Rather than waste your time trying to enlighten indoctrinated Einsteinian disciples, you ought to contact Mr. Seto. A collaboration between two as perceptive as yourselves would no doubt lead to a result the rest of the world couldn't possibly ignore. ))) |
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jem wrote: wrote: In 1971 the Hafele-Keating experiment was conducted. It is a well-known and well documented experiment with two planes, carrying two atomic clocks. One clock flew in western direction around the earth, and one flew in eastern direction around the earth. The purpose was to prove "time delation" as predicted by Einstein's theories of Relativity. The results of the experiments were presented as a big success, proving the theory of Special Relativity. The atomic clocks onboard the planes did walk at a different rate than a stationary atomic clock that was used for reference. However, the results did not PROVE Einsteins Special Relativity but DISPROVED it. One clock walked indeed slower than the reference clock, but the other clock walked FASTER than the reference clock. This phenomenon was explained by noting that one of the clocks flew counter to the rotation of earth, and so was moving even slower than the reference clock. Hm... peculiar! I thought that central to SR was the fact that each inertial frame is equivalent, and there is no "zero" inertial frame AKA "aether". However, the Hafele-Keating experiment showed that the faster one moves with regard to an inertial frame against which also earth moves (through its rotation), the slower your clock goes. So there is a "zero" inertial frame (aether), and experiments conducted in this "zero" frame have results that differ from experiments conducted in inertial frames that move with regard to the "zero" frame. The main difference is that in the zero-frame, clocks walk fastest. The experiment showed that there IS NO RELATIVITY. There might be time delation, but it is a phenomenon that is based on movement with regard to an ABSOLUTE zero-frame. I have recently presented four proofs against Relativity on this forum. A summary of the status of the various discussions. #1 (communication faster than light). The possibility of communication faster than light is denied. I cannot check the claims of certain researchers that they have conducted experiments with information transmission faster than c. What I do know is that if something is not practically realizable, it might be CONCEIVABLE. Immediate communication is theoretically conceivable, and therefore the denial of the existence of absolute time is silly. #2 (stationary and traveling clock experiment). No one has presented a calculation or even a reasoning why my conclusions based on this experiment are wrong. Someone wants to present a calculation, but first I have to prove that I am capable of appreciating the math, by doing some exercises. Ridiculous of course. I think I know why the calculation is "tricky" and why it is not presented. It is so convoluted that it is (in practice) impossible to prove it wrong. Calculations of this kind need to be big and complex. It requires major effort to present such a calculation. Therefore its presentation is delayed with childish conditions. The only real result: objections against Relativity are not disproved. #3 (two clocks in orbit experiment). No one has presented a convincing argument why this experiment doesn't work the way I want. It's a simple application of the rules of mister Einstein. The outcome is devastating for Relativity. #4 (Hafele-Keating). I am curious what convoluted reasoning will be presented to counter the inevitable message from this experiment: RELATIVITY DOES NOT EXIST. I have seen a lot hostile reactions. Calling names, and even the change of the title of one of my postings, by someone who has apparently moderating privileges on this forum. There is a simple psychological explanation for this. Someone who knows for certain that his ideas are right does not behave in a hostile manner. Only if you cling to ideas for other reasons than love for the truth, you will react hostile if your illusions are in danger. Yes, of course you're right. It's truly pathetic how thousands of physicists have blindly followed Einstein's mistakes and unwittingly adopted a logically inconsistent description of the world. However, although your astute insights are right on target, you've not been the first to perceive them. Ken Seto came to the same realization years ago and has created the Improved Relativity Theory (IRT) to reveal Nature's TRUE character. Seto's works are detailed at http://www.geocities.com/kn_seto/index.htm, but to date his promotional efforts haven't been all that successful. Rather than waste your time trying to enlighten indoctrinated Einsteinian disciples, you ought to contact Mr. Seto. A collaboration between two as perceptive as yourselves would no doubt lead to a result the rest of the world couldn't possibly ignore. :-) :-) |
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harry schreef: The experiment showed that there IS NO RELATIVITY. There might be time delation, but it is a phenomenon that is based on movement with regard to an ABSOLUTE zero-frame. That interpretation is perfectly compatible with "relativity" theory. According to SRT, no such zero frame can be determined. That's all there is to it; just ignore bunkum. Cheers, Harald That's not right. A zero-frame is the frame in which all clocks walk fastest. There is absolute time in system with a zero-frame. If clock K in the zero-frame walks twice as fast as clock K' in a fast moving frame, then clock K' walks twice as slow as K. |
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#10
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wrote in message oups.com... In 1971 the Hafele-Keating experiment was conducted. It is a well-known and well documented experiment with two planes, carrying two atomic clocks. One clock flew in western direction around the earth, and one flew in eastern direction around the earth. The purpose was to prove "time delation" as predicted by Einstein's theories of Relativity. The results of the experiments were presented as a big success, proving the theory of Special Relativity. The atomic clocks onboard the planes did walk at a different rate than a stationary atomic clock that was used for reference. However, the results did not PROVE Einsteins Special Relativity but DISPROVED it. One clock walked indeed slower than the reference clock, but the other clock walked FASTER than the reference clock. This phenomenon was explained by noting that one of the clocks flew counter to the rotation of earth, and so was moving even slower than the reference clock. Hm... peculiar! I thought that central to SR was the fact that each inertial frame is equivalent, and there is no "zero" inertial frame AKA "aether". However, the Hafele-Keating experiment showed that the faster one moves with regard to an inertial frame against which also earth moves (through its rotation), the slower your clock goes. The reference clock was rotating as well, and therefore not inertial. So either you are cheating again, or you are showing your overwhelmingly arrogant ignorance again :-) This is so basic... I posted this before, so it's easily copied and slightly reviewed from http://groups.google.com/group/sci.p...a81f80d2c9ccad and deeper, and http://groups.google.com/group/sci.p...4d4edc8d287d98 Referring to article http://www.eftaylor.com/pub/chapter1.pdf http://www.eftaylor.com/pub/chapter2.pdf http://www.eftaylor.com/pub/projecta.pdf http://hyperphysics.phy-astr.gsu.edu...iv/airtim.html (Using units where c=1 and G=1) In this case the Schwarzschild time rate Schw(va,ra,vb,rb) = sqrt(1-2 M/ra-va^2) / sqrt(1-2 M/rs-vb^2) to make the calculations (although even this is not exact - see section 5 in reference projectA). In the case of Hafele-Keating (and GPS) where M, va and vb are very small, one can use a combination of two effectively independent approximations. One approximation is the so-called "Kinematic time rate" Kine(va,vb) = sqrt(1-va^2) / sqrt(1-vb^2) and it depends on relative motion only. It is a result of special relativity - valid in absence of gravity. The va and vb are seen in an Earth centered non-rotating inertial frame. The other approximation is the so-called "Gravitational potential time rate": Grav(ra,rb) = sqrt(1-2 M/ra) / sqrt(1-2 M/rb) and it depends on location only. It would be valid for non-moving objects only. It is an idealized result from general relativity. For small M/ra, M/rb, va, vb, the Taylor expansion will tell you that Schw(va,ra,vb,rb) =~ Kine(va,vb) Grav(ra,rb) or, since both factors a very close to 1, equivalently: (1 - Schw(va,ra,vb,rb) ) =~ (1 - Kine(va,vb) ) + (1 - Grav(ra,rb) ) Proof: Since K and G are very close to 1, we get K = 1+k (with very small k) G = 1+g (with very small g) so we have 1 - S = 1 - K G = 1 - (1+k) (1+g) =~ - k - g (ignoring the ultra small product k g) = 1-(1+k) + 1-(1+g) = (1-K) + (1-G) The daily kinematic time dilation is then calculated as DayKine = Oneday - Oneday Kine(va,vb) = Oneday ( 1 - Kine(va,vb) ) where Oneday = 24*60*60 seconds as seen on the ground. You can also verify that we can approximate: Kine(va,vb) =~ 1 - 1/2 va^2 + 1/2 vb^2 = 1 - 1/2 (ra W)^2 + 1/2 (rb W)^2 = 1 - 1/2 (ra W)^2 + 1/2 (ra W + v)^2 = 1 + ( 2 ra W v + v^2 ) / 2 where v = relative velocity as seen from the ground. So the daily dilation will be DayKine = Oneday ( 1 - Kine(va,vb) ) =~ - Oneday ( 2 ra W v + v^2 ) / 2 This corresponds to the article's result TA - TS = - TS ( 2 R W v + v^2 ) / (2 c^2 ) where ra = R and TS = Oneday (and c=1). For the daily dilation of the East and West trips you need vEast and vWest DayKineEast = Oneday ( 1 - Kine( vGround, vEast ) ) DayKIneWest = Oneday ( 1 - Kine( vGround, vWest ) ) where Oneday = 24*60*60 seconds vGround = rGround W (and divide by c!) and for the East bound trip: vEast = vGround + 2 pi rEast / (fEast*60*60) rEast = rGround + 8900 (average height) fEast = 41.2*60*60 (time of flight) and for the West bound trip: vWest = vGround - 2 pi rEast / (fWest*60*60) rWest = rGround + 9400 (average height) fWest = 48.6*60*60 (time of flight) Note the plus sign and the minus sign in the expressions for vEast and vWest. And also note the v in the article's expression. For the Eastbound trip v is positive. It is negative for the Westbound trip. Try it out and you'll find (unless I made a mistake somewhere) DayKineEast = -156 nanoseconds DayKineWest = 77 nanoseconds with both calculations. This nicely fits the -184 and 96 nanoseconds of the article where a lot more factors have been taken into account. Likewise, you can calculate the daily gravitational dilation DayGrav = Oneday ( 1 - Grav(ra,rb) ) You will find DayGravEast = 143 nanoseconds DayGravWest = 178 nanoseconds Taken together: DayKineGravEast = -14 nanoseconds DayKineGravWest = 255 nanoseconds which is nicely in the ballpark of the actual results. Dirk Vdm |
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