The real twin paradox.
in [Relativity]
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From: Sue... on 27 Nov 2007 04:16 On Nov 27, 3:55 am, "harry" <harald.vanlintelButNotT...(a)epfl.ch> wrote: [...] > > That there is no need for an observation that "shows that the other clock is > running fast". And you overlooked the illustration that I prepared specially > for you: Indeed... I consider that a good example of the principle of relativity and it inspired my construction of an egg frying experiment that is similarly ignored in droves. I suspect some posters who should know better suddenly realised that a physical response to uniform motion does not support relativty but rather stands in evidence against it. Sue... >
From: Sue... on 27 Nov 2007 05:05 On Nov 27, 1:21 am, colp <c...(a)solder.ath.cx> wrote: [...] > Relativity predicts that we should see their > clocks ticking more slowly (see the Special Relativity lecture). Photons are not balls of light moving inertially as this page suggests: http://www.astronomy.ohio-state.edu/~pogge/Ast162/Unit5/sr.html In fact, they have no inertial coupling at all. <<A Lorentz transformation or any other coordinate transformation will convert electric or magnetic fields into mixtures of electric and magnetic fields, but no transformation mixes them with the gravitational field. >> http://www.aip.org/pt/vol-58/iss-11/p31.html ~Wave Particle Light~ http://nobelprize.org/physics/articles/ekspong/index.html So... when several of the respondents assert a clock slowing with motion, or resposive to inertial fields it is usually on the basis of false assumptions. A real light-clock can be constructed that will respond similarly to motion through the dielectric of free-sapce But it refutes the *basis* of the lecture's conclusion: "There is no absolute time." Einstein admitted the necessity of a dielectric medium but many interpretations do not include it nor consider the absolute frame of reference available in real world light paths. http://en.wikipedia.org/wiki/Wave_impedance http://en.wikipedia.org/wiki/Free_space http://www-ssg.sr.unh.edu/ism/what.html Sue... > Special Relativity predicts that the on-board atomic clocks on the > satellites should fall behind clocks on the ground by about 7 > microseconds per day because of the slower ticking rate due to the > time dilation effect of their relative motion. > > http://www.astronomy.ohio-state.edu/~pogge/Ast162/Unit5/gps.html > > > > > Relativity tells you how much proper time a clock experiences > > for a given path through spacetime. That's an invariant. It's > > not a comparison of two different clocks. > > In the real world different clocks do get compared.- Hide quoted text - > > - Show quoted text -
From: bz on 27 Nov 2007 05:49 colp <colp(a)solder.ath.cx> wrote in news:c3ae81ae-9ac0-4842-afb0-78ddd999b1bc(a)s6g2000prc.googlegroups.com: > On Nov 27, 12:40 pm, bz <bz+...(a)ch100-5.chem.lsu.edu> wrote: >> colp <c...(a)solder.ath.cx> wrote in news:839b939c-528d-4b10-9507- >> 78495beb3...(a)e10g2000prf.googlegroups.com: >> >> >> >> > So how would that work using gamma = 1 / (sqrt (1 - v^2/c^2)) ? >> >> That is what Daryl did. >> He used (4/5 c)^2/c^2 > > O.K. He is using v = 4/5 c. > >> >> .8 = 4/5 right? > > Yes. > >> .8 c = (4/5) c = 4/5 c^2 right? typographical error. Should have read ..8 c = (4/5) c = 4/5 c right? > > No. (4/5) c does not equal 4/5 c^2. > >> >> and >> >> 4/5 c^2 / c^2 = 4/5 right? > > Yes. yes. > >> >> He said [quote] >> Then gamma = 1/square-root(1-(4/5)^2) = 1/square-root(9/25) = 5/3. >> [unquote] >> So, he is using exactly the formula you asked about. > > Yes, gamma is 5/3 for v = 4/5 c using my formula. > >> >> now if you take velocity away from ... as positive and toward ... as >> negative, your other great mystery will be cleared up. > > Oh really? Really. > >> As he said: >> >> [quote] >> t' = gamma (t - vx/c^2) >> [unquote] > > Lets try that again for v = -4/5 c with gamma = 1 / (sqrt (1 - v^2/ > c^2)) > > -0.8 = -4/5 right? right > > -0.8 c = (-4/5) c right? right > > -4/5 c^2 / c^2 = -4/5 right? > > Then gamma = 1/square-root(1-(-4/5)^2) = 1/square-root(9/25) = 5/3. right > > So we get the same gamma value regardless of the sign of the velocity. exactly correct, so far. > > The same gammma value means that time dilation is observed regardless > of whether the other frame of reference is approaching or retreating. but now we USE the gamma The Lorentz equation shows us the transformed time as. t' = gamma (t - vx/c^2) so with B going away t' = gamma (t - (.8c)x/c^2) with B coming our way t' = gamma (t - (-.8c)x/c^2) Notice that in the second case, - (-.8c)x/c^2 = + .8c x/c^2 The sign is changed. The correction factor is added rather than subtracted. > >> So using the convention I just mentioned, you will see that when >> traveling away from the other ship (or they are traveling away from us) >> the effect will 'slow' the time we see on the other ships clock. > > I'll take your word for it. Take Lorentz-Einstein's word for it. > >> When traveling toward the other ship, v changes sign, the effect >> changes >> to exactly the effect that you said relativity did not have. > > LOL > > v does change sign, but gamma remains the same using my formula. Yes but minus times minus is plus. > > As in the case of your worked example which ignored relativistic > effects, you have again sidestepped the real issue. NO. No sidestepping. Both explained the real issues which is that people fail to understand and USE relativity correctly. > Instead of using > the same formula for both positive and negative velocities, you only > did one half of the exercise and then quoted Daryl's formula for the > second half. Daryl's formula is the Lorentz equation for time correction. > Using gamma = 1 / (sqrt (1 - v^2/c^2)) you arrive at the following > conclusion: > > When traveling away from the other ship (or they are traveling away > from us) the effect will 'slow' the time we see on the other ships > clock. When traveling toward the other ship, v changes sign, but gamma > remains the same. As gamma remains the same the time dilation effect > is the same regardless of direction. > >> So, Dirk was right, Daryl was right, you were wrong. > > If you use my formula Dirk was wrong. Daryl was right as far as he > went. And you haven't shown how I was wrong. Vectors have direction. In the Lorentz, the velocity is used twice, once as part of the gamma factor, where it is squared and thus direction is unimportant, but once where the correction is subtracted (added for opposite direction of motion). Because minus times minus gives plus. Work it through yourself. Work the doppler version also. You will find that both agree. There is no paradox once the equations are used properly. You have been assuming that the correction was simply gamma times time. It is NOT. Look at the Lorentz transforms. t' = gamma (t - vx/c^2) is the Lorentz transform for time. The other equation often used gives the DELTA t Delta t = t/sqrt(1-(v^2/c^2)) That includes the gamma factor. The fact it is a DELTA means it represents a change. You THEN must take the time and apply the delta to it. That means you must either ADD or SUBTRACT the delta to the time. Whether you add or subtract depends on the direction of the motion. You have been ignoring the direction of the motion. That is your error. -- bz please pardon my infinite ignorance, the set-of-things-I-do-not-know is an infinite set. bz+spr(a)ch100-5.chem.lsu.edu remove ch100-5 to avoid spam trap
From: bz on 27 Nov 2007 07:41 "Sue..." <suzysewnshow(a)yahoo.com.au> wrote in news:1666352e-81c8-4ec7-9a90- fc0dd2440631(a)s12g2000prg.googlegroups.com: > I am not aware of any calculations that that involve a > real geostationary clock but they could contribute a > lot of confidence in the 7us component if they exist. > Gosh, Sue, it is very easy to do such calculations. I would think that an expert on SR and time, such as yourself, would have already done them. My calculations show that the gravity at GPS altitude (orbital radius 26562.463 km) is 3.746% g and at geosync altitude (orbital radius 42165.282 km) the g field is 1.725% g. That gives a 590.217 ppt difference in clock rate (as opposed to 528.428 ppt for the GPS clocks). Or 50.995 us for GeoSync (as contrasted with the 45.532 us for the effect of altitude on GPS clocks). So, the crystal oscillators (and frequencies of transmission) for Geosync satellites should be off by 590.217 ppt. That amounts to a 0.59 Hz shift in a 1 GHz transmitter's output frequency. Certainly measurable, but probably swamped by drift due to component aging and temperature variations as it will NOT be cumulative (unless someone decides to count cycle on the carrier frequency over a period of time, THEN it would be cumulative AND would allow a long term test WITHOUT orbiting a cesium clock). Telemetry of temperature conditions could be used to compensate somewhat, as well as comparison with a similar circuit kept on earth under similar pressure and temperature conditions. -- bz please pardon my infinite ignorance, the set-of-things-I-do-not-know is an infinite set. bz+spr(a)ch100-5.chem.lsu.edu remove ch100-5 to avoid spam trap
From: Sue... on 27 Nov 2007 09:48
On Nov 27, 7:41 am, bz <bz+...(a)ch100-5.chem.lsu.edu> wrote: > "Sue..." <suzysewns...(a)yahoo.com.au> wrote in news:1666352e-81c8-4ec7-9a90- > fc0dd2440...(a)s12g2000prg.googlegroups.com: > > > I am not aware of any calculations that that involve a > > real geostationary clock but they could contribute a > > lot of confidence in the 7us component if they exist. > > Gosh, Sue, it is very easy to do such calculations. I would think that an > expert on SR and time, such as yourself, would have already done them. > My calculations show that the gravity at GPS altitude (orbital radius > 26562.463 km) is 3.746% g and at geosync altitude (orbital radius 42165.282 > km) > the g field is 1.725% g. > > That gives a 590.217 ppt difference in clock rate (as opposed to 528.428 > ppt for the GPS clocks). > Or 50.995 us for GeoSync (as contrasted with the 45.532 us for the effect > of altitude on GPS clocks). What is the name of the SV? Where did you get the raw data on its clock stability? How was it compared to GPS clocks ? > > So, the crystal oscillators (and frequencies of transmission) for Geosync > satellites should be off by 590.217 ppt. > That amounts to a 0.59 Hz shift in a 1 GHz transmitter's output frequency. > > Certainly measurable, but probably swamped by drift due to component aging > and temperature variations as it will NOT be cumulative (unless someone > decides to count cycle on the carrier frequency over a period of time, THEN > it would be cumulative AND would allow a long term test WITHOUT orbiting a > cesium clock). > Telemetry of temperature conditions could be used to compensate somewhat, > as well as comparison with a similar circuit kept on earth under similar > pressure and temperature conditions. Calculations look great! What is the status of your oscillator? Proceedings of the 2003 IEEE International << Summary: A science-quality space GPS receiver is being studied for the primary atomic reference clock in space (PARCS) mission. The PARCS flight experiment is an International space station (ISS) payload that will conduct investigations into the laser cooling of atoms, time interval measurement, and fundamental physics. The receiver will make GPS carrier phase observations, to transfer the frequency measurements made by other PARCS subsystems to the ground and to determine the experiment's precise position and velocity. The receiver is based on the Jet Propulsion Laboratory's BlackJack radiometric instrument. This is a dual frequency, codeless design that is a veteran of multiple spaceflights. The major challenges for its use on PARCS derive from the ISS environment, for example, the antenna field of view, multipath sources, and potential electromagnetic interference. Simulations indicate that the restricted field of view will be the main limitation, and that the receiver antenna should be tilted away from the ISS structure by /spl sim/30/spl deg/ for better results. The use of GPS ground networks and data analysis techniques to provide a total measurement system adequate to meet PARCS' requirements will need to be examined further. >> http://ieeexplore.ieee.org/iel5/8990/28531/01275085.pdf (subscription) Sue... > > -- > bz > > please pardon my infinite ignorance, the set-of-things-I-do-not-know is an > infinite set. > > bz+...(a)ch100-5.chem.lsu.edu remove ch100-5 to avoid spam trap |