12/16/24
Author's notes
1.
Mislabeling in Principle of Relativity diagram
and associated text (editions 1 through 6)
Corrected diagram and associated text:
The distance from mirror QA to QB is 0.8 light second
(contracted from 1 light second due to P's absolute speed of 0.6).
P2 is where P is at the moment his light beam reflects at QB2.
Remember -- this is the God's eye view, where simultaneity (a moment)
is not something that is a perception of the parties involved.
Observations made by an omnipresent God are not dependent on the
speed of light. And that omnipresent being need be nothing more
than the reader viewing this static diagram.
2.
As part of the preparation for writing my journal article, I decided
to confirm for myself, by way of diagramming, my assumption that
there was a necessarily unconscious skewed aiming of a pulse of
light as discussed on page 22 in the second and third editions
(and not mentioned in the fourth and fifth editions).
But my diagram quickly confirmed that there could be no such
unconscious skewed aiming.
Therefore, I write (conservatively) in my journal article:
"Although a moving source of light-emission cannot impart additional
speed to light, it is reasonable that it would affect the vector
components of the beam's motion, creating a vector component in
the direction of motion of the source, while the perpendicular
vector component is diminished. A photon does, after all, have a
non-zero amount of momentum. It would be hard to imagine that a
moving source of emission would not have an effect on light's
trajectory."
3.
In editions 1 - 5, I made incorrect commentary on the role of
acceleration on time-keeping: Acceleration of a clock simply
generates a continuous change in its otherwise kinematical
clock-rate, creating what can be considered a non-kinematical
effect in the sense that there is not a uniform speed involved.
The frame that the clock is in as it accelerates is a pseudo-
gravitational field only; therefore there is no slowing of
light within the clock as is the case in the non-kinematical
clock-slowing in a true gravitational field.
There is a great deal of confusion in the literature
about those situations.
Whether one considers the "non-kinematical" effect of
acceleration to be a GR effect or an SR effect is not
important. The clock-slowing equation of SR is employed
along with calculus to allow for its ever-changing
"kinematical" rate.
If you want to call it a GR effect due to the non-uniform
motion, that's fine too.
4.
Beginning with the first edition, (page 64 of edition
six and a different page number in previous editions),
I correctly incorporated the consideration that the
communication of force throughout an accelerating
rigid body is constrained by the speed of light. However,
I misapplied that consideration by considering only the
differing lengths of the clocks in the direction of motion
and then reversed the time-contraction for those two clocks
during the acceleration by considering only the parallel
motions of a light ray within each of those clocks, though
I knew better.
My mistake jumped right out at me all these years later.
The correct consideration is that the trailing clock
is alway keeping time more slowly than the leading clock
due to the fact that it is always moving faster along the
line of motion than the leading clock. And again, that is
of course due to the fact that the communication of force
throughout an accelerating rigid body is constrained by
the speed of light.
That in fact, is in agreement with the non-kinematical
time-contraction of general relativity, which correctly
confers upon the acceleration of a reference frame a
pseudo-gravitational field. The trailing clock will
have the slower clock rate.
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