Twins Paradox doesn't add up with light
in [Relativity]
|
From: Darwin123 on 9 May 2010 15:29 DSeppala <dsepp...(a)austin.rr.com> Date: Sat, 8 May 2010 06:30:59 -0700 (PDT) >What source did you use to come up with the hypothesis > that the speed of light is not constant as it travels > through empty space, other than the notion of constant c >conflicts with the twin's paradox? Darwin123 09 May 2010 The following is a direct quote from Einstein On the Influence of Gravitation on the Propagation of Light, by Albert Einstein in The Principle of Relativity, by H.A. Lorentz, A. Einstein, H. Minkowski, and H. Weyl. Page 107 If we call the velocity of light at the origin of the co-ordinates c_0, then the velocity of light at a place with gravitational potential phi will be given by the relation, c=c_0(1+phi/c^2) (3) Einstein here says, in no uncertain terms, that an observer under acceleration experiences a speed of light that varies with gravitational potential. I replaced phi by gx. Note that the speed of light still doesnt vary with the motion of the source, even in this equation. The parameter c_0 is what in electtrodynamics would be called the speed of light in a vacuum. DSeppala <dsepp...(a)austin.rr.com> Date: Sat, 8 May 2010 06:30:59 -0700 (PDT) >So when Einstein states "... light is always propagated in >empty space with a definite velocity c which is > independent of the state of motion of the emitting body" > he really means that it is not propagated at a definite > velocity c? Darwin123 09 May 2009 This isnt an entire quote. You clipped a sentence that changes the meaning of your quote. This is in addition to the slight change the quoted sentence. As Androcles would say, You clipping <bad person>. >Or was something lost in the translation? Original source of your quote: On the Electrodynamics of Moving Bodies, by Albert Einstein in The Principle of Relativity, by H.A. Lorentz, A. Einstein, H. Minkowski, and H. Weyl. Pages 37-38 the same laws of electrodynamics and optics will be valid for all frames of reference where the laws of mechanics hold good. We will raise this conjecture to the status of a postulate, and also introduce another postulate, , that light is always propagated in empty space with a definite velocity c which is independent of the motion of the emitting body. all frames of reference where the laws of of mechanics hold good means inertial frames. The laws of mechanics are those listed by Isaac Newton in Principia. The traveling twin is in a frame where at least two laws of mechanics (as listed by Principia) are wrong. 1) Although the centrifugal force is an action force, there is no corresponding reaction force for the traveling twin. 2) The traveling twin experiences a gravitational field that does not have a corresponding gravitational mass. Therefore, the traveling twin is not in an inertial frame. The stationary twin is in an inertial frame. This is the way physicists today understand the laws of relativity. I will quote the postulates as understood by physicists other than Einstein. From A Short Course in General Relativity, by J. Foster and J.D. Nightgale. Appendix A: Special relativity review (page 190) The fundamental postulates are: 1. The speed of light c is the same in all inertial frames. 2. The laws of nature are the same in all inertial frames. Sorry, the traveling twin is not in an inertial frame.
From: Darwin123 on 9 May 2010 16:02 On May 9, 9:46 am, DSeppala <dsepp...(a)austin.rr.com> wrote: > On May 8, 11:38 pm, eric gisse <jowr.pi.nos...(a)gmail.com> wrote: > > > DSeppala wrote: > Einstein does not say anything about doing the same > observation without using light by simply using synchronized clocks at rest around the circle. No, he didn't tell you to compare the same observation using synchronized clocks at rest around the circle. However, he did tell you to compare the same observation using synchronized clocks located on the spin axis of the earth. >I do agree with you that that is simply > amazing. > I was looking for a clearer explanation from Darwin. Thank you. I am flattered !-) I would even be more flattered if you pay attention. I forgot the exact way Einstein phrased it. His prose wasn't succinct in the early days when he first presented the theory. However, he was using hypothetical observers that were stationary on the spin axis of the earth. For clarity, you may want to consider everything from the standpoint of an observer at the center of the earth. If you look at the articles by Hefele (1972 in Science) you will find that the calculations are done from the same POV. The reason that observers are chosen on the spin axis of the earth (i.e., pole) is that the acceleration is very small there. The acceleration on the surface of the earth is very high. One can approximate the center of the earth, and all other points of the pole, as an inertial frame. The acceleration caused by the earths orbit around the sun, or the suns orbit around the Milky Way, is very small compared to the acceleration on the surface of the earth. The effects on acceleration of orbit is negligible, if one does experiments on the surface of the earth. I think this discussion is about to move into an analysis of the Hefele-Keating experiment. Although HKX isn't precisely the same scenario analyzed by Einstein, it is conceptually similar. In both cases, there is a hypothetical observer at the center of the earth. So I want to make a few comments on the HKX. A lot of people are confused about the Hefele-Keating experiment (HKX). Yes, that was a cutting edge experiment. The experimental uncertainties were rather high. An equivalent experiment was done later with more accuracy (see GPS). However, the experimental accuracy isn't the main issue with these people. The main confusion seems to be the apparent contradiction with the Lorentz time dilation. One clock is running faster than the other clocks. If there was "true relativity" between the clocks, they should tick at the same rate. However, there is no "true relativity" between the clocks because of the acceleration. If Kefele had taken an accurate enough accelerometer with him, he could have measured the acceleration. The clock that is running faster than the other clocks is the one with the most centripetal acceleration. It isn't just the matter of how fast the clocks are going. All three clocks (six clocks really) making time measurements are accelerating. The reason that the acceleration is left out of Hefeles calculation is that his calculations are all done from the viewpoint of the spin axis the earth (e.g., the center of the earth). For practical purposes with this experiment, the center of the earth is an inertial frame. What is interesting from a theoretical viewpoint in the HK experiment is that one doesn't actually use measurements from a real inertial observer. The analysis is done from the POV of a hypothetical observer at the center of the earth. The differences in time are calculated by taking differences in the predicted traveling times as seen by this "inertial" observer. The effects of acceleration can be predicted up to a certain extent using special relativity. However, one has to do all calculations from the point of view of an inertial "virtual" observer. There are equivalent problems in Newtonian mechanics. Yes, "virual" observer are necessary in many classical problems. Fortunately, most physics teachers wait till graduate school before they "wack" the graduate student with them.
From: Darwin123 on 9 May 2010 19:56 On May 7, 11:09 pm, BURT <macromi...(a)yahoo.com> wrote: > On May 7, 6:34 pm, "Androcles" <Headmas...(a)Hogwarts.physics_z> wrote: > If the twin on the train is given to see the clock of the station > going slow as it passes then how can the station age more? > He "sees" the clock at the station go fast when he turning around at distances far from the station.
From: Darwin123 on 9 May 2010 20:29 On May 3, 6:17 pm, DSeppala <dsepp...(a)austin.rr.com> wrote: > The typical analysis of the twin's paradox does a switching of frame > views in which the traveling twin simply disregards the measurements > he makes on the first leg of his journey. Not precisely true. In the typical analysis, the traveling twin disregards the measurements taken during his acceleration. The twin paradox is always presented in the limiting case of an instantaneous "pulse" of acceleration, sufficient to reverse the traveling twin's velocity as seen by the stationary twin. This is actually an unrealistic limiting case. What has to be done is to allow the acceleration to happen during a nonzero time interval, as seen by the traveling twin. The traveling twin can measure his acceleration during that time interval. You also have to take into account the time delay needed for a signal to travel from the stationary twin to the traveling twin. Finally, you have to disregard the irreversible changes in the traveling twin caused by the acceleration. The traveling twin can not reset any of his clocks during the acceleration. Resetting the traveling twin clock during acceleration is equivalent to "squishing" him. The traveling twin watches the stationary twin all throughout. At the moment of acceleration, when he feels the squish, there is no big change in the metabolism of the observed stationary twin. This is because there is a delay caused by the speed of light between him and the twin. However, the traveling twin can correct for this delay. He knows he is getting a message from the stationary twin as he was in the past. One the way home, with the acceleration turned off, the traveling twin can continue to watch signals from the stationary twin. He will arrive at some point where the signals from the stationary twin come from a time when he projects the acceleration occurred in his frame. At that point, he will see the metabolism of his stationary brother speed up. He will see the hands on stationary clock run quickly around the face. The smaller the time of acceleration, the faster the hands on the stationary clock will run. However, the signals came from the past. It is only after he corrects for time delay that the traveling twin realizes that the increase in metabolism occurred instantaneously with the acceleration in the traveling frame. The "standard" way to introduce relativity takes the limit as the time goes to zero. However, this is a bit unphysical. A sudden turn around like that would crush the traveling clock. I think it would be better if the physics teacher tries to address the accelerating frame qualitatively. He should mention that the speed up occurs during acceleration. He doesn't have to go into quantitative detail. As long as he gets the inertial case story straight, he can just suggest what happens during the acceleration. However, I think it is a bad thing to ignore the accelerating frame case entirely. Perhaps some physics teacher will show a movie where the characters are actually doing the twin paradox scenario. The two twins, stationary and traveling, are watching each other with time delayed signals. An SF movie director could also do this, but he would have to find some interesting dramatic conflict as a vehicle for this hypothetical situation. Finding a convincing dramatic conflict will be harder than doing the calculation. Your circular orbit could be in the sequel. The third sequel could be descent into a black hole. Twin Paradox III: Now Its Massive! I think even a lay audience could appreciate this sort of thing. I think everyone has been spoiled by the Star Trek/Star Wars space opera formula. It actually crimps the imagination. I think future SF should portray a universe with massive delay times in signal, a weightless environment in space, and planets where the aliens don't speak English! Down with translation devices and artificial gravity! BTW: Did you deduce the "event horizon" implied by the speed of light formula in the traveling twin frame? When the speed of light as seen by the traveling twin is zero, that corresponds to an event horizon as seen by the traveling twin. The accelerating twin has an event horizon without a "black hole".
From: PD on 10 May 2010 10:38
On May 8, 8:56 pm, DSeppala <dsepp...(a)austin.rr.com> wrote: > On May 7, 11:31 am, Darwin123 <drosen0...(a)yahoo.com> wrote: > > > > > On May 6, 10:05 pm, DSeppala <dsepp...(a)austin.rr.com> wrote: > > > > On May 6, 8:29 pm, Darwin123 <drosen0...(a)yahoo.com> wrote: > > > > > On May 6, 4:53 pm, DSeppala <dsepp...(a)austin.rr.com> wrote: > > > > > > On May 5, 3:39 pm, Darwin123 <drosen0...(a)yahoo.com> wrote: > > > > > > > On May 3, 6:17 pm, DSeppala <dsepp...(a)austin.rr.com> wrote:> Can anyone explain how the moving twin explains why his emitted > > > Let's say he has every piece of measuring equipment there is. Why > > > does the traveling twin say that if the speed of light is constant and > > > independent of the velocity of the light source in a vacumm that light > > > travels two different distances during the same time interval? > > > I already addressed that. However, to repeat the obvious: > > The traveling twin does not say that the speed of light is constant > > in every region of space. The traveling twin is not in an inertial > > frame, so the postulates of special relativity do not apply to him. He > > knows he is not in an inertial frame because his accelerometer, > > whatever form it is in, shows a nonzero acceleration. > > The traveling twin can observe the speed of light as constant > > only over a small spacial region near him. At large distances from > > him, he observes the speed of light as different than that in that > > small region of space. > > Suppose both twins have a clock that is based on a pulse of light > > bouncing between two mirrors. Every time it hits a detector, it blips. > > The traveling twin sees the rate of blip of his traveling clock being > > at a certain rate near him. If stationary twin is within the small > > region of space that surrounds the traveling twin, the blip rate will > > be the same for both clocks. However, in your scenario, the two twins > > are at times very far apart. At the time that both twins are on > > opposite sides of the circle, the speed of light is very different for > > the two clocks. The traveling twin observes the blip rate of the > > stationary twin as much faster than his own blip rate. Thus, he > > concludes that the speed of light is bigger for the stationary twin > > while on the opposite side of the circle. > > The faster blip rate doesn't bother the traveling twin because > > his accelerometer says he has a nonzero acceleration. The Lorentz time > > dilation shouldn't apply to a distant object when the accelerometer > > says nonzero. The stationary twin sees the blip rate of the stationary > > twin as slower than his own. However, his accelerometer says zero. So > > he expects that the Lorentz time dilation to apply over all space and > > time. For the stationary twin, the speed of light is constant > > everywhere. The speed of light is constant over all space only when > > the accelerometer says zero. > > The traveling twin spends a lot of time at the far point of the > > circle. The smaller the acceleration, the longer he spends at > > distances far from the stationary twin. > > I'll give you an estimate of the region over which the traveling > > twin can expect the speed of light to be constant to first order. Let > > "L" be the radius of a sphere around the traveling twin where the > > speed of light determined by the traveling twin is nonzero. Then, > > gL/c^2<<1 > > where g is the acceleration measured by the traveling twin, and c is > > the speed of light. Of course, the above equation is an approximation. > > "First order" means that assuming the speed of light is constant will > > cause fractional errors on the order of "gL/c^2". > > Please note that one only has to to be concerned with acceleration > > if "L<<R", where "R" is the radius of the circle traveled. If the > > velocity of the traveling twin relative to the center of the circle is > > "v", and "v<<c", then > > g=v^2/R, > > just as in Newtonian theory. > > Also note that I am ignoring the "squish". If "g" is too big, > > the measuring instruments will be warped by the centripetal force. > > Unmentioned in your scenario is the reason the traveling twin is > > traveling in a circle. He has to be using some type of rocket, or > > maybe a rope, to force his trajectory in a circle. He and his > > instruments feel "g" forces, which we both are ignoring for now. If g > > is too big, the clocks and rulers don't work. The traveling twin is > > dead. So there are pragmatic limits on "g". "g" has to be fairly > > small. So the time that the round trip takes has to be fairly big. So > > you can't let the round trip time go to the limit of zero. The > > traveling twin is going to take a long time to meet his stationary > > brother again. Unless we are talking about small people. > > These "pragmatic limits" can be addressed by using instruments > > that are very small, or by using certain mechanical corrections in the > > calculations. However, you implied that the instruments were suitably > > small by ignoring the centripetal "squish." So I am also reasonably > > that all your instruments are small enough to fit in the small region > > where the speed of light is constant. > > In my analysis, I am assuming that the effect of gravitational > > mass is negligible. As long as gravitational can be ignored, we are in > > the realm of special relativity. The precise way to analyze the effect > > of acceleration and gravity involves general relativity. Our > > discussion hasn't left special relativity. However, we are just on the > > border to general relativity. Since I admit to not fully understanding > > general relativity yet, you will kindly refrain from dragging gravity > > in the discussion. I am sure of what I am saying up to now, in terms > > of special relativity. In SR, acceleration is important. No matter > > what anybody else says |:-) > > > In the > > > > problem two beams leave a common point in space at the same time, and > > > they return to a common point at the same time, yet the traveling twin > > > says that one beam travels a different distance than the other beam, > > > and that the speed of light is independent of the velocity of the > > > light source. > > > David > > > That's what I don't understand.- Hide quoted text - > > > - Show quoted text - > > Einstein's theory has two stated postulates, one is that the speed of > light is always propagated in empty space with a definite velocity c > which is independent of the state of motion of the emitting body. As measured LOCALLY. > The > other is that unsuccessful attempts to discover any motion of the > earth relatively to the "light medium" suggest that the phenomena of > electrodynamics as well as of mechanics possess no properties > corresponding to the idea of absolute rest. This is not the postulate. Try again. It's called the principle of relativity, in case you want to google it. > Einstein states that the > same laws of electrodynamics and optics will be valid for all frames > of reference for which the equations of mechanics hold good. > You seem to take the constant speed of light postulate to mean that > it is only constant in inertial frames and not valid for all frames of > reference as Einstein stated. Where did your concept come from? > We should note that Einstein states that the velocity of light is > independent of the motion of the emitting body. I don't know if that > is an error in the translation or not, or whether the word velocity > had a different meaning a hundred years ago, but we all know that the > velocity of light is dependent on the motion of the emitting body, > whereas the accurate phrasing is that the speed of light is > independent of the motion of the emitting body, but not the light's > velocity (speed and direction). > David |