PD
Posts:
2,970
Registered:
5/25/05
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Re: Preferred Frame Theory indistinguishable from SR
Posted:
Jul 8, 2010 6:09 PM
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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.
PD
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