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From: Sam on 26 Oct 2009 17:47 Jonah Thomas <jethom...(a)gmail.com> wrote: > One beam of light leaves the emitter at speed c > relative to the emitter. It goes through a beam- > splitter which does not change its speed. It doesn't change the speed of the light relative to the beam splitter, but the beam splitter is moving (in tandem with the emitter) at the speed v = wr relative to the hub frame of reference. The light emerges from the beam splitter in two directions, and it has the speed c in both direction relative to the beam splitter. But since the beam splitter is moving at the speed v relative to the rest frame of the hub, the light pulses have the speeds c+v in the forward direction and c-v in the rearward direction relative to the inertial rest frame coordinates of the hub. Of course, the receiver is moving in the forward direction with the speed v as well, so the "closing speed" for the forward pulse is (c+v)-v = c, and the closing speed for the rearward pulse is (c-v)+v = c. They both begin with the same distance to "close", and their closing speeds are the same, so they arrive simultaneously. Jonah Thomas <jethom...(a)gmail.com> wrote: > It bounces off mirrors which do not change its speed. > So the light traveling in opposite directions travel > at the same speed. So one of them arrives early. Nope, see above. The speed of the pulses are always c relative to the local mirror's (or beam splitter's or emitter's) co-moving inertial coordinates, but each mirror (etc.) is moving with the speed v in the forward direction, so, relative to the hub's rest frame the forward pulse is moving at c+v and the rearward pulse is moving at c-v, and these differences cancel with the movement of the receiver, giving each pulse the same closing speed, and hence they arrive simultaneously.
From: Darwin123 on 26 Oct 2009 18:57 On Oct 25, 3:35 am, Jonah Thomas <jethom...(a)gmail.com> wrote: > Darwin123 <drosen0...(a)yahoo.com> wrote: > > Jonah Thomas <jethom...(a)gmail.com> wrote: > > > Darwin123 <drosen0...(a)yahoo.com> wrote: > > > > Jonah Thomas <jethom...(a)gmail.com> wrote: > > > > > Darwin123 <drosen0...(a)yahoo.com> wrote: > I found a link. It appears that there are two ways of measuring the Sagnac effect: one with fringe position and one with time. Here is a link. http://www.cleonis.nl/physics/phys256/sagnac.php The following are my selections from this link. I notice that there are two types of detectors described. In one configuration the experimenter measures spatial fringe shift, and in the other the experimenter measures temporal beats. The supposed observer in the inertial frame is supposed to be measuring differences in wavelength for the fringe shift, and differences in frequency for the temporal beats. 1) Spatial fringe shift Usually several mirrors are used, so that the lightbeams follow a triangular or square trajectory. Fiber optics can also be employed to guide the light. The ring interferometer is located on a platform that can rotate. When the platform is rotating, the point of entry/exit moves during the transit time of the light, so on exit one beam has covered less distance than the other beam. As a consequence, when the platform is rotating the interference pattern will be shifted as compared to the position of the interference fringes when the platform wasn't rotating. The shift is in proportion to the angular velocity of the Sagnac interferometer. In optical rotation sensors the Sagnac effect is used to measure angular velocity. An example of a mechanical rotation sensor is a gimbal mounted gyroscope. This type of ring interferometer is sometimes called a 'passive ring interferometer'. A passive ring interferometer uses light entering the setup from outside. The interference pattern that is obtained is a fringe pattern, and what is measured is a phase shift. 2) Time modulation When a ring laser is rotating, the detector will detect a frequency that is consistent with the laser process generating two frequencies of laser light. (Note: all that can be actually measured is what is detected. In terms of quantum physics the laser process leads to a state where all of the laser light is in the same quantum state. Rather than having half the light propagating in one direction and the other half in the other direction, the state of the light is described as a superposition of propagating clockwise and propagating counterclockwise. The interference pattern is obtained by the specific way that the detector has been set up.) In the case depicted in image 4 the oscillation source has an angular velocity. As in case depicted in image 3 the wavelength of each of the counterpropagating waves will be such that an integer number of wavelengths fits into the length of the ring cavity. When the co- propagating wave returns to the oscillation source it has travelled a longer distance than the actual length of the ring cavity. Therefore the resonant frequency will be lower than in the case of a stationary oscillation source. When the counter-propagating wave returns to the oscillation source it has travelled a shorter distance than the actual ring cavity's length. The two counterpropagating waves have a different frequency. Because of the difference in frequency of the two counterpropagating waves there is a beat frequency.
From: Darwin123 on 26 Oct 2009 19:37 On Oct 25, 3:35 am, Jonah Thomas <jethom...(a)gmail.com> wrote: > Darwin123 <drosen0...(a)yahoo.com> wrote: > > Jonah Thomas <jethom...(a)gmail.com> wrote: > > > Darwin123 <drosen0...(a)yahoo.com> wrote: > > > > Jonah Thomas <jethom...(a)gmail.com> wrote: > > > > > Darwin123 <drosen0...(a)yahoo.com> wrote: I found a link on the Ives-Stilwell effect. > http://en.wikipedia.org/wiki/Ives%E2%80%93Stilwell_experiment The Ives-Stilwell effect came out proving the validity of special relativity. Poor Ives! From the link: The IvesStilwell experiment exploits the Transverse Doppler effect (TDE) described by Albert Einstein in his seminal 1905 paper[1]. Einstein subsequently suggested an experiment based on the measurement of the relative frequencies of light perceived as arriving from a light source in motion with respect to the observer. Herbert E. Ives and G. R. Stilwell undertook the task of executing the experiment and they came up with a very clever way of separating the much smaller TDE from the much bigger longitudinal Doppler effect. The experiment was executed in 1938[2] and it was reprised multiple times (see, e.g.[3]). Ives wanted to do a positive test of time dilation, as followed from the "theory of Lorentz and Larmor" and as was first suggested "by Einstein and Ritz". This was the first direct, quantitative test of the time dilation factor. The IvesStilwell experiment forms one of the fundamental tests of special relativity theory. Other such tests were the MichelsonMorley and KennedyThorndike experiments. A relativistic Doppler effect (not a classical Doppler effect) is needed to explain the results of the Ives-Stilwell experiment. From the same link: When we invert these relationships so that they relate to wavelengths rather than frequencies, Classical Theory predicts redshifted and blueshifted wavelength values of 1+v/c and 1-v/c, so if all three wavelengths (redshifted, blueshifted and original) are marked on a linear scale, according to Classical Theory the three marks should be perfectly evenly spaced. |.....|.....| But if the light is shifted by special relativity's predictions, the additional Lorentz offset means that the two outer marks will be offset in the same direction with respect to the central mark. |....|......| Ives and Stilwell found that there was a significant offset of the centre of gravity of the three marks, and therefore the Doppler relationship was not that of "Classical Theory". Doppler effect is used to explain the Sagnac effect and all its derivative experiments. I suspect that the Doppler shift is embedded in the more standard explanations of the Doppler effect. They may not be using the word Doppler, but the geometry they are describing is fundamentally what causes the Doppler effect.
From: Androcles on 26 Oct 2009 19:37 "Henry Wilson DSc ." <HW@..> wrote in message news:4n9ce5hm0spvgp096t7vk0atcrij0glfrh(a)4ax.com... > On Mon, 26 Oct 2009 21:39:04 -0000, "Androcles" > <Headmaster(a)Hogwarts.physics_p> > wrote: > >> >>"Henry Wilson DSc ." <HW@..> wrote in message >>news:bd3ce5pp336b09ogvhslcq8mg1vkg1aad2(a)4ax.com... >>> On Mon, 26 Oct 2009 18:46:35 -0000, "Androcles" >>> <Headmaster(a)Hogwarts.physics_p> >>> wrote: >>> >>>>http://www.androcles01.pwp.blueyonder.co.uk/Wave/bounce.gif >>> >>> >>> There! Top one! >>> You have shown that, in the ground frame, the ball bounces back at c+2v. >> >>You are fuckin' blind, its moving toward the middle wall at c+v >>and bouncing away at -c-v. The top one has -v added to that, which >>is -c-2v. Bwhahahahaha! > > plus , minus, who cares.... I'll pay you AU$-20,000.00 for that old VW camper van you wanted to trade, and then I'll give you the camper van back for nothing. plus , minus, you don't care but I do. You can send me the bill along with the cheque and the receipt. Oh, and don't forget the cheque. Make it out to Androcles for PLUS AU$20,000 and then I'll have paid you for the van. Did I mention the cheque? I owe you minus AU$20,000, I like to pay my bills on time. Hurry up and send the cheque.
From: Jonah Thomas on 26 Oct 2009 21:18
Darwin123 <drosen0000(a)yahoo.com> wrote: > I found a link. It appears that there are two ways of measuring > the Sagnac effect: one with fringe position and one with time. Here > is a link. > http://www.cleonis.nl/physics/phys256/sagnac.php Thank you! I had seen that page but hadn't given it the attention it deserved. > The following are my selections from this link. I notice that > there are two types of detectors described. In one configuration the > experimenter measures spatial fringe shift, and in the other the > experimenter measures temporal beats. The supposed observer in the > inertial frame is supposed to be measuring differences in wavelength > for the fringe shift, and differences in frequency for the temporal > beats. So any theory about Sagnac should predict both effects. Theories with constant lightspeed will inevitably predict both effects. > 1) Spatial fringe shift > Usually several mirrors are used, so that the lightbeams follow a > triangular or square trajectory. Fiber optics can also be employed to > guide the light. The ring interferometer is located on a platform that > can rotate. When the platform is rotating, the point of entry/exit > moves during the transit time of the light, so on exit one beam has > covered less distance than the other beam. As a consequence, when the > platform is rotating the interference pattern will be shifted as > compared to the position of the interference fringes when the platform > wasn't rotating. The shift is in proportion to the angular velocity of > the Sagnac interferometer. Why does that shift the interference pattern? I've been having trouble understanding that. Maybe my problem is that so far I've only looked at single-slit interference patterns. > In optical rotation sensors the Sagnac effect is used to measure > angular velocity. An example of a mechanical rotation sensor is a > gimbal mounted gyroscope. > This type of ring interferometer is sometimes called a 'passive ring > interferometer'. A passive ring interferometer uses light entering the > setup from outside. The interference pattern that is obtained is a > fringe pattern, and what is measured is a phase shift. > > 2) Time modulation > When a ring laser is rotating, the detector will detect a frequency > that is consistent with the laser process generating two frequencies > of laser light. > (Note: all that can be actually measured is what is detected. That's a vitally important point. > In terms > of quantum physics the laser process leads to a state where all of the > laser light is in the same quantum state. Rather than having half the > light propagating in one direction and the other half in the other > direction, the state of the light is described as a superposition of > propagating clockwise and propagating counterclockwise. The > interference pattern is obtained by the specific way that the detector > has been set up.) At first sight that looks like gobbledegook. But maybe it makes sense even apart from QM. The light doesn't just go around the loop once, all the light that doesn't get taken by the beam sampler will go around again until it gets absorbed or reflected or mangled in a laser cavity. Maybe it makes more sense to think of it as standing waves that move slowly, than as light that quickly reaches its destination. > In the case depicted in image 4 the oscillation source has an angular > velocity. As in case depicted in image 3 the wavelength of each of the > counterpropagating waves will be such that an integer number of > wavelengths fits into the length of the ring cavity. When the co- > propagating wave returns to the oscillation source it has travelled a > longer distance than the actual length of the ring cavity. Therefore > the resonant frequency will be lower than in the case of a stationary > oscillation source. When the counter-propagating wave returns to the > oscillation source it has travelled a shorter distance than the actual > ring cavity's length. The two counterpropagating waves have a > different frequency. Because of the difference in frequency of the two > counterpropagating waves there is a beat frequency. Presumably it would be possible to measure an interference pattern and a beat frequency at the same time. Could you use that to show the lightspeed is constant? Or would it need too many assumptions that might not be true.... |