Re: SR examination question

["John S. Denker" <jsd@MONMOUTH.COM>]

At 10:19 AM 5/21/01 -0400, Michael Edmiston wrote:
> * * * * Questions for all concerning the implication of Moloney's and Nunes'
> comments.
>
> Is this the way you understand it?  That we need multiple observers in the
> frame?

Yes, that is exactly how I understand it.

The usual nomenclature for this is "a lattice of rods and clocks".  The
rods mark off space, and the clocks mark off time, as shown in
  http://www.monmouth.com/~jsd/physics/sp-rel.gif

> Sam and Jane are in the same reference frame, but vastly different positions
> in that frame.  Please tell me how they synchronized their clocks.

Good question.  There are standard protocols for doing this.

The first step is to put the rods into place, so Sam and Jane can maintain
their relative positions with confidence.

In the second step, they exchange pulses of light OR SOUND.  If necessary,
they can measure the propagation delay by measuring the round-trip time.
They correct for this propagation delay when synchronizing their clocks.
Therefore, the equal-time contours in the figure
  http://www.monmouth.com/~jsd/physics/sp-rel.gif
really are equal-time contours, and every clock on such a contour reads the
same value.  (Jane's equal-time contours are the red lines that slope
gently up and to the right.  They cross her worldline, which slopes much
more steeply.)

> Do you agree that Jane does not observe Peter's clock to hit one
> minute when she observes it located at x = -6.19x10^8?

I would rather say that Jane herself is not in a position to directly
"observe" Peter's clock or anything else at that location.  She might
eventually observe the light and/or sound coming from that location, but
that's different.

The gold standard is to speak of spacetime events.  Sam (a member of Jane's
team) is in a position to observe the critical event, and measure it
against the rods and clocks at that location.

> If this is true, how
> do you interpret the meaning of the Lorentz transformation?  Isn't part of
> the basis for the L-transformation the time it takes the light signal to
> propagate to Jane?

No, that is not the basis of the Lorentz transformation.  What if the event
did not give off any light, and Jane observed only the sound coming
therefrom?  Would her definition of time involve the speed of sound?  I
don't think so.

As mentioned above, ordinary hardware-store rods and clocks can be used to
specify everything Jane and Sam and the rest of that team need to know.
The clocks can be synchronized using sound waves.  Electromagnetic signals
are !not! necessary.

Calling c the speed of "light" greatly understates its significance.  The
rhombic shape of the rods and clocks in the spacetime diagram is given by
v/c, even if no electromagnetism is involved.