On Jul 7, 5:43 pm, colp <c...@solder.ath.cx> wrote: > On Jul 7, 8:52 am, PD <thedraperfam...@gmail.com> wrote: > > > On Jul 6, 3:03 pm, colp <c...@solder.ath.cx> wrote: > > > > On Jul 7, 3:07 am, PD <thedraperfam...@gmail.com> wrote: > > > > The problem, you see, is that the comic-book statement you are using > > > > as your launching point belongs in COLP's Oversimplified Relativity. > > > > It's not a comic book statement any more than Einstein's statement > > > that a moving clock lags behind a stationary clock is a comic book > > > statement. > > > Not so. Einstein's statement included things that you have discounted. > > I haven't discounted them. > > > For example, he makes note of specific events, rather than just making > > the general statement that "moving clocks" run slow. > > The description of the specific events only serves to illustrate that > it is the moving clock that runs slow compared to the stationary > clock.
Then you have misunderstood what he said. The EVENTS do more than that.
> > > Furthermore, he > > makes EXPLICIT mention of the statement that the clocks at points A > > and B are initially synchronized IN THE K FRAME. > > Assuming that they weren't synchonized in my general description of > "the moving clock runs slow" would be arbitrary and illogical.
They are synchronized in the K frame. They are not synchronized in the K' frame. This is essential and cannot be dismissed.
> Remember I was talking about _the_ clock, in reference to the moving > clock described in "Electrodynamics of Moving Bodies", not to a clock > in an arbitrary system.
I understand that completely. There are two clocks involved here: One that moves from A to B and one that remains at B. There is a frame K in which points A and B are at rest, and there is a frame K' in which points A and B are moving and the first clock above is at rest.
> > > A contradiction would > > arise by making the clock at B the moving clock only if the clocks are > > claimed to be intially synchronized also in the K' frame -- but they > > are NOT, and this is the essential detail that you have missed. > > No, it isn't a missing detail, it is an implication of Einstein's > first postulate of relativity.
WHAT is an implication of the first postulate? That they are also synchronized in K'? No.
> > Here is Einstein's description of the clocks: > > "If at the points A and B of K there are stationary clocks which, > viewed in the stationary system, are synchronous; and if the clock at > A is moved with the velocity v along the line AB to B, then on its > arrival at B the two clocks no longer synchronize, but the clock moved > from A to B lags behind the other which has remained at B ..." > > Let us call the moving system K', in which the moving clocks at A' and > B' are synchronized for an observer in K'. The stationary system K > also has two clocks, but these two clocks are synchronized for an > observer in K. Frames K and K' move at a constant velocity with > respect to each other. > > If there is no preferred frame of reference then there is no reason > why the clocks at A' and B' cannot also be synchronized for an > observer in K', just as the clocks at A and B are for an observer in > K, due to the symmetry of the two frames and their respective clocks.
Yes, that is true but the clock that is synchronized with B in K will not initially show the same time as the clock that is synchronized with B in K'.
Now YOU are the one that is adding things beyond what Einstein actually said.
There are only TWO clocks in Einstein's paragraph. One that moves from A to B and one that remains at B. In the frame K, the clocks are synchronized when the clocks are at A and B. In the frame K' that you propose, those same two clocks are not synchronized when the clocks are at A and B. In BOTH frames, when the clocks are next to each other at B, the two clocks will show different times.
To give you a numerical example, A and B and the velocity of one clock from A to B can be arranged such that the following is true:
In the frame K, where A and B are stationary: Clock at A and clock at B both read 1:23:05 at the same moment (simultaneously). They are synchronized. When clock from A arrives at B, it reads 1:23:11. The clock that remained at B reads 1:23:14.
Now, in the frame K', where A and B are moving: Clock at rest reads 1:23:05 when A sweeps over it. The clock that is at B reads 1:23:10 at this instant (simultaneously). They are not synchronized. When point B sweeps over the clock at rest, it reads 1:23:11. The clock that moved along with B reads 1:23:14.
You can see plainly that in the K frame, the moving clock runs slower than the stationary clock, because 6 seconds have elapsed on clock crossing A and B, and 9 seconds have elapsed on clock staying at B. And when the two clocks are adjacent, clock crossing A and B is behind clock staying at B by 3 seconds. You can also see that in the K' frame, the moving clock runs slower than the stationary clock, because 4 seconds have elapsed on clock staying at B and 6 seconds have elapsed on the clock that A and B sweep over. And when the two clocks are adjacent, clock crossing A and B is behind clock staying at B by 3 seconds.
So, you see, there is nothing contradictory in SR about this situation. In either K or K', the moving clock runs more slowly than the stationary clock. In either frame, the difference between the two clocks is identical when the two clocks are together.