Re: New Light On The Speed of Light


Symmetry Observer wrote:
> Sue... wrote:
> > Symmetry Observer wrote:
> > > Martin Hogbin wrote:
> > > > "Symmetry Observer" <mathexpert@xxxxxxxxxxxxx> wrote in message
> > > > news:1134715336.702598.59790@xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
> > > > >
> > > > > > Symmetry Observer wrote:
> > > > > > > If in Special Relativity, we let u denote the
> > > > > > > proper time of an observer (the invariant time carried by an observer
> > > > > > > in his rest frame). We have
> > > > > > >
> > > > > > > u = t(1 - (v/c)^2)^(0.5)
> > > > > > > (eq.1)
> > > > > > >
> > > > > > > where v is the absolute value of the velocity of the observer with
> > > > > > > respect to a fixed frame with (conventional ) time coordinate t. Now
> > > > > > > if we solve (eq.1) for c we obtain
> > > > > > >
> > > > > > > c = [v]/( 1 - (u/t)^2)^(0.5)
> > > > > > > (eq.2)
> > > > > > >
> > > > > > > where [v] denotes the absolute value of v.
> > > > > > >
> > > > >
> > > > > > > A Proposed Experiment
> > >
> > > Let us consider two (one spatial dimensional) coordinate systems R
> > > (with
> > > coordinates x and t) and M (with coordinates X and T). Let an observer
> > > (or an "observing apparatus") be moving with the origin of the M frame,
> > > at a constant velocity v, in a direction parallel and coinciding with
> > > the
> > > x - axis of the R frame. Moreover let (X, T) = (0, 0) when (x, t) = (0,
> > > 0).
> > > As a matter of arbitrary choice we may consider the R frame to be
> > > fixed.
> > >
> > > As the reader well knows, space - time is a continuum. At each point
> > > along the x - axis of the R frame, in theory, is a clock. This of
> > > course
> > > is an idealized conception. A physical representation is impossible but
> > > it is also unnecessary. All that we need is that for one clock, from a
> > > set
> > > of identical clocks, to be placed at a finite number of points along
> > > the x - axis
> > > of the R frame. The points in question could be labled as x_i ( i = 1
> > > to n)
> > > where n is a finite integer.
> > >
> > > The clocks could be synchronized in the usual way using light signals.
> > > There are many excellent references on the internet that explain the
> > > details.
> > >
> > > Many have tried to synchronize their clocks
> > > in the market for bonds and stocks
> > > but the best at buying and selling shares
> > > are still the Bulls and the Bears.
> > >
> > > The experiment is simply this: The x - axis of the R frame could be
> > > represented by a tape measure of say 200 meters (set up in the
> > > Salt Flats of Utah (?). At 50 meter intervals along the tape a "clock"
> > > could be set up. For concreteness, we will say that clocks are set up
> > > at
> > > points whose coordinates along the x - axis are x_1, x_2, x_3 and x_4
> > > which
> > > are located 50, 100, 150 and 200 meters respectively, from the origin
> > > of the
> > > R frame.
> > >
> > > The origin of the moving M frame, referred to above, could be
> > > considered to
> > > be attached to a moving mechanism denoted by W. W could be fitted
> > > on a monorail that is parallel to the tape measure (which represents
> > > the x - axis
> > > of the R frame) and run either directly above it or directly beside it.
> > >
> > >
> > > The moving mechanism W could be set in motion so that when it passes
> > > the
> > > space - time point (X, T) = (x, t) = (0, 0) it is moving at a constant
> > > velocity of
> > > say 25 meters/sec. W will carry it's own proper time which we will
> > > denote by u.
> > >
> > > A device could be implanted in W that will automatically record the
> > > proper
> > > times u_i (i = 1 to 4) when it passes the points x_i ( i = 1 to 4)
> > > along the
> > > x - axis of the R frame. In addition to this, the clocks at the points
> > > x_i (i =1
> > > to 4) on the x - axis, could be programmed to automatically record the
> > > times
> > > t_i (i = 1 to 4) when the moving apparatus W passes these points.
> > >
> > > The following is a reproduction from the original post:
> > >
> > > If in Special Relativity, we let u denote the
> > > proper time of an observer (the invariant time carried by an observer
> > > in his rest frame). We have
> > > u = t(1 - (v/c)^2)^(0.5)
> > > (eq.1)
> > > where v is the absolute value of the velocity of the observer with
> > > respect to a fixed frame with (conventional ) time coordinate t. Now
> > > if we solve (eq.1) for c we obtain
> > > c = [v]/( 1 - (u/t)^2)^(0.5)
> > > (eq.2)
> > > where [v] denotes the absolute value of v.
> > >
> > > So now we have four sets of data
> > >
> > > u = u_i and t = t_i for i = 1 to 4
> > > all recorded for v = 25 meters/sec
> > >
> > > Now for i = 1 to 4, plug these values all into the right side of
> > > (eq.2).
> > > I am predicting, if the measurements are recorded with a high level
> > > of precision, that we will get c = 3.0 x 10^10 cm/sec (+ or (-) a very
> > > small eror) in each case. The experiment could be repeated for
> > > various values of v.
> > >
> > > This expectation should be a foregone conclusion because, as
> > > was stated before, eq.(1) is at the very core of SR and eq.(2)
> > > follows directly from it.
> > >
> > << The experiment could, in reality, serve as a test of the precision
> > of clocks. >>
> >
> > I fail to see how it incorporates the only inflexible definition of
> > time that we know of.
> > <<the energy is conserved if and only if the physical laws are
> > invariant under time translations (if their form does not depend
> > on time) >>
> > http://en.wikipedia.org/wiki/Noether's_theorem
> >
> > Sue...
> > >
> > >
>
> Every algebraic re-arrangement of the equation associated with a
> fundamental law (or
> definition)
> has an interpretation (on a fundamental level). This does not affect
> the invariance
> property that you referred to.

Where will we find clocks that behave motionally
as *your* equations describe and why should they
need calibration?

Sue...

.

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