This puzzle is mainly for Jack, but others may play too. In this puzzle, we're in a universe much like our own, except that in this universe there is a universal rest frame, in which light moves at c in vaccuum. Length contraction and time dilation still apply. Moving rulers are contracted by a factor of gamma in their direction of motion. Moving clocks run slowly by a factor of gamma. In this parallel Universe, on a parallel Earth, you're in a nice physics lab, with very precise timing devices, laser switches, precise rulers, and so on. You don't know which way your lab is facing, and your lab is shielded from the Earth's magnetic field. Your task is to set up two clocks so that they are synchronized with each other at opposite ends of the lab. How do you do it? Can it be done at all?
By sending a light pulse from one end of the lab to a mirror at the other end, and measuring the time it takes to come back, one can deduce the absolute velocity of the lab. The time dilation and length contraction will cancel each other so that one can forget about these effects when measuring velocity. So the velocity in one direction is c+u, and the other is c-u. From L/(c+u)+L/(c-u)=t we can find u. Then it is easy to synchronize the clocks, for example by sending a light signal from an appropriate point in the room. Edit: On a second thought, it seems that the effects of time dilation and length contraction will actually amplify each other so that in the end we always have 2L=ct. So the above approach will not work.
I can do it. You only need begin with the two clocks synchronized at the same corner of the lab and then slowly move one of them to the opposite end of the lab. The more slowly you move the moving clock, the more perfectly it will be synchronized with the clock on the other side of the lab.
<idea>Midpoint theorem</idea> <hint>(delta t',delta s') = Lorentz(delta t,delta s) implies we don't need to know the lab frame's absolute motion to know what?</hint> Shubert, it will then take an infinite amount of time for your clocks to be actually synchronized at opposite ends of the lab. That's not a useful answer. From 2005: http://www.physforum.com/index.php?showtopic=1099 http://www.physforum.com/index.php?showtopic=1317
Time dilation and length contraction are based on the relativity postulate. Hence, these conditions cannot apply to this model.
The value of correct theory should never be underestimated. Here is a practical equivalent. Place the two clocks C1 and C2 at opposite ends of the lab. Measure the distance between them. Call that d. Let a photon pulse at C1 at time T1=0 be sent to a receiver at C2. When the photon pulse arrives at C2, set the time on C2 to be t=d/c. That's a practical definition of synchronization in a moving frame of reference. The fact that your universe has an absolute frame of reference will not affect this practical synchronization scheme in the moving frame.
Wrong again! But at least you are batting 100, Jack_. Consistency is a good thing or maybe not. Pete's toy universe is essentially the Lorentz Ether Theory (LET) universe. Time dilation and length contraction can still apply -- and they do apply for the simple reason that Pete said so. This is his toy problem. If you want to debate that time dilation and length contraction you need to prove it.
If it is the case that c is absolute, as ST claims with saganc, then you only way you can claim r=d/c is if thee is no motion relative to the fixed absolute light. Otherwise, you will detect a linear sagnac effect.
LOL, I suppose I might do this and know how. But, up front, you are wrong. Assume, light proceeds at c period. It does not keep up with the frame as in Ritz's theory and SR to measure c. I mean think about it. You know the earth is moving right? If you agree and light is always measure c, then it must be the case that the speed light is speed injected in the absolute direction of travel whatever that is. This way a frame always measures c.
No. I'm assuming that there is an absolute frame of reference. I'm claiming that clocks can easily be synchronized in moving frames by the method I've described so that the motion of a photon pulse in the moving frame can be described by the equation x=ct and that no contradictions, under simple conditions, will develop.
If light is absolute, then it is the case you can find this. This is obvious. He said, light is but one speed in this "aether". So, any object moves relative to the fixed aether and can detect their motion just like with sagnac. Why does MMX refuse to detect any type of motion when GPS does?
So, what is you math for clock syncing with an absolute frame for light? I wonder if there is an absolute frame for light since light cannot ever be speed injected beyond c, or so they say.
What? http://web.stcloudstate.edu/ruwang/PRL93.pdf IOP, linear sagnac. Let us see how prepared everyone is for the math of all this.
More http://math.ucr.edu/home/baez/physics/Relativity/SR/experiments.html#moving-source_tests 3.3 Tests of Light Speed from Moving Sources If the light emitted from a source moving with velocity v toward the observer has a speed c+kv in the observer's frame, then these experiments place a limit on k. Many but not all of these experiments are subject to criticism due to Optical Extinction. Experiments Using Cosmological Sources Comstock, Phys. Rev. 10 (1910), pg 267. DeSitter, Koninklijke Akademie van Wetenschappen, vol 15, part 2, pg 1297–1298 (1913). DeSitter, Koninklijke Akademie van Wetenschappen, vol 16, part 1, pg 395–396 (1913). DeSitter, Physik. Zeitschr. 14, 429, (1913) http://www.datasync.com/~rsf1/desitter.htm. DeSitter, Physik. Zeitschr. 14, 1267, (1913) http://www.datasync.com/~rsf1/desitter.htm. Zurhellen, Astr. Nachr. 198 (1914), pg 1. Observations of binary stars. k < 10−6. These are all subject to criticism due to Optical Extinction. K. Brecher, “Is the Speed of Light Independent of the Velocity of the Source?”, Phys. Rev. Lett. 39 1051–1054, 1236(E) (1977). Uses observations of binary pulsars to put a limit on the source-velocity dependence of the speed of light. k < 2×10−9. Optical Extinction is not a problem here, because the high-energy X-rays used have an extinction length considerably longer than the distance to the sources. Heckmann, Ann. d. Astrophys. 23 (1960), pg 410. Differential aberration, galaxies versus stars. This experiment is subject to criticism due to Optical Extinction. Observations of Supernovae A supernova explosion sends debris out in all directions with speeds of 10,000 km/s or more (known from Doppler broadening of spectral lines). If the speed of light depended on the source velocity, its arrival at Earth would be spread out in time due to the spread of source velocities. Such a time spread is not observed, and observations of distant supernovae give k < 5×10−9. These observations could be subject to criticism due to Optical Extinction, but some observations are for supernovas considerably closer than the extinction length of the X-ray wavelengths used. Now, if a frame by luck happened to be at absolute rest, then these experiments confirm light cannot ever exceed one speed c under any conditions. Thus, the light frame is absolute, or so these experiments suggest.
Yes. See problem number 1 and 2 at the end of the page Generalized Lorentz Transformations. I invented those problems and I can solve them also.
How, Jack? Design a simple experiment to do this. Don't forget that clocks moving relative to the aether run slowly, and rulers moving relative to the aether are contracted in the direction of motion.
