lugita15 said:
ghwellsjr, if you have some arguments or calculations to show that for this particular large light clock slow transport synchronization and Einstein synchronization are the exact same process, I would be happy to take a look at them.
I'm going to present an analogy to Einstein's synchronization and extend it to slow transport. Bear with me:
Imagine a very long ski slope, many miles long and perfectly smooth. There are two rope lifts, a few yards apart, also of many miles that allow skiers to grab on to which take them up the slope at 12 miles per hour. The skiers come down the slope between the two rope lifts at exactly 60 miles per hour. That means that it will take a skier 1 minute to travel one mile down the slope, instantly stop and grab a rope lift and then take 5 minutes to traverse the one mile back to his starting point for a total round-trip time of 6 minutes.
Oh, and the mountain is shrouded in thick clouds so that they can barely see the hand in front of their face. And the skiers have no clocks, watches, cell phones, radios, GPS devices, etc. I will note the times that certain things happen but the skiers are completely unaware of these timings.
Now some skiers decide to do a little experiment. They are located somewhere in the middle of the ski slope, several miles up. They take a steel cable, one mile long and one of them holds on to one end and let's the other end dangle down the slope. They have attached two flags onto the cable, a yellow one at the half-way point and an orange one at the bottom end. The skier holding on to the top end of the cable doesn't move and since he will be counting, we'll call him Counter A. Another skier goes down to the bottom end of the cable, where the orange flag is and stays there. We'll call him Counter B.
After this initial setup, two more skiers, one wearing a red outfit and one wearing a green outfit start together down the slope at 60 mph. A half minute after they start, the skiers get to the yellow flag and the green skier stops and grabs the rope lift on his right. It will take him 2 and a half minutes to get to the top. Meanwhile, the red skier continues down. When he gets to the orange flag at the bottom of the cable, he stops and grabs the rope lift on his right. 60 seconds have gone by since the start. It will take him 5 more minutes to get to the top.
When the green skier gets back to the top at 3 minutes, the stationary skier called Counter A shouts out "1" and the green skier immediately heads back down the slope. This time he continues all the way to the bottom and he tells the skier called Counter B to shout out "2" because it is 1 more than the number he heard when he arrived at the top. It is now 4 minutes into the experiment. When the red skier gets back to the top it is 6 minutes into the experiment and Counter A calls out "2" while the red skier heads back down.
Now it should be easy to list the times and the counts that are being shouted out picking up at time 6:
Time=6, red arrives at top, counter A shouts 2
Time=7, red arrives at bottom, counter B shouts 3
Time=9, green arrives at top, counter A shouts 3
Time=10, green arrives at bottom, counter B shouts 4
Time=12, red arrives at top, counter A shouts 4
Time=13, red arrives at bottom, counter B shouts 5
Time=15, green arrives at top, counter A shouts 5
Time=16, green arrives at bottom, counter B shouts 6
Time=18, red arrives at top, counter A shouts 6
Time=19, red arrives at bottom, counter B shouts 7
Time=21, green arrives at top, counter A shouts 7
Time=22, green arrives at bottom, counter B shouts 8
Notice the patterns: it takes each skier one minute to go down the slope and five minutes to go up the slope. Each counter shouts a new number every 3 minutes. The two counters shout at different times but they don't know that because they can't hear or see each other. As far as they are concerned, they are shouting at exactly the same time, because they have defined time according to Einstein's synchronization process.
And what is that process? Einstein said you note the time on a clock at a light source when you start a pulse of light down to a mirror and reflect it back to the light source where you note the time again. You take the difference in the two times and this is the round-trip time. You divide it in half. You add that to the time on the clock at the light source the moment the next light pulse occurs and when the pulse gets to the clock at the mirror, that is the time you set on that remote clock.
So let's see how that works in our analogy with the skiers. First we note how long it takes for one of the skiers to make the round trip. Remember, they don't know about the actual times in the list above, all they know about is the numbers that the Counters shout out and if you look at either skier's round trip, you will see that it takes 2 counts for both Counter A and Counter B. So Einstein says we divide that by 2 which gives 1. So when a skier leaves a Counter, he adds 1 to that count and when he gets to the other end of the cable, if that is the number the other Counter shouts out, then the two Counters are synchronized. Note that this is what happens in all four cases: red going down, green going down, red going up and green going up.
But one bright skier says he knows how to prove that the Counters are in fact shouting out the same numbers at the same time by another synchronization process called slow transport.
He sets up the identical experiment with the other rope lift on the other side of where the skiers are with a different set of skiers and another one-mile long cable with the flags. After they get everything going, they get the second set synchronized with the first set and the counters counting the same numbers so the both Counter A's are in sync, (they are close enough to hear each other) and both Counter B's are in sync.
The plan is to slowly move the entire setup with the one-mile long cable, Counter A skier at the top and Counter B skier at the bottom, while the second set of red and green skiers are doing their skiing down the slope and coming back up with the second rope lift. The whole apparatus will go down the hill one mile, stopping when the second Counter A reaches the first Counter B.
And so they do it. And what do they find? Yes, indeed, the second Counter A is in sync with the first Counter B, even though they didn't do anything special to make this happen, like in the first setup. So the bright skier feels that he has proved something significant.
But another smart skier says, "wait a minute, you did no such thing, you did exactly what the first set of skiers did and let me explain why." And his explanation went like this:
It should be immediately obvious that while the one-mile long cable is in motion down the hill, the red and green skiers will travel farther downhill than they will travel uphill using the rope lift on each round trip. In fact, they will have added in exactly one additional downhill trip at the expense of one uphill trip. So both the Counters on the second setup will be counting later by the time of one downhill trip than they were before they started moving. And that is exactly what the first setup did to synchronize their two Counters.
lugita15 said:
But tell me this, how does this example get around the general result in the paper I attached, which says that regardless of the kind of clock used, in a world where a(v) is equal to something other than what special relativity predicts, like the world of Maxwell's theory of light, the two synchronization methods MUST give different results?
As I said before, as long as there is no length contraction and the propagation speed for one direction remains constant during the slow transport while the propagation speed for the opposite direction remains constant, then the two synchronization processes are identical for any given instance. But also like I said before, if you rotate the entire apparatus so that round-trip time for the signal propagations is not the same as it was before, then that means that the light clock itself is not dependable in that universe but the two synchronization methods will still be identical to each other in that rotated configuration.
lugita15 said:
Also, do you agree that in our universe, Einstein synchronization using light gives a different simultaneity than sound synchronization? And do you agree that if Earth was pervaded by two different media, say air and water, which did not interact with each other, then Einstein-like synchronization using these two different media would produce different simultaneities? And that this would be true regardless of the kinds of clocks synchronized?
Finally, do you agree that if slow transport synchronization gave the same result as, say, synchronization by sound waves in air, then it could not give the same result as synchronization by sound waves in water?
Again, I'm not saying that two different light clocks will even tick at the same rate (based on the round-trip signal propagation) in all universes or in all media or in all orientations, let alone be capable of being used as a dependable clock but in every one of those situations, as long as the criteria that I outlined are true, then the two synchronization methods are identical in process and in outcome for a given setup of the type that Einstein described in section 1 of his 1905 paper.
But what is really important is that the paper also affirmed that the two synchronization methods agree in our universe. And it's your insistence that slow transport is better than Einstein's synchronization because, for example, it provides experimental proof, as evidenced by your posts #15, #23, #42, #44, #56, etc.
You seem to overlook the fact that slow transport assumes that the clock remains synchronized while being transported and that oversight allow you to think that it has some intrinsic experimental value over Einstein's method.
