03/15/26
Author's notes
1.
Mislabeling in Principle of Relativity diagram and associated text (editions 1 through 5)
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: The acceleration of a clock simply generates a continuous change in its otherwise uniform kinematical clock-rate, and is not a true non-kinematical effect.
The frame that the clock is in as it accelerates is a pseudo- gravitational field only; therefore there is no additional 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 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 implementing a misleading static diagram, then reversed the time- contraction, though I knew better.
My mistake jumped right out at me all these years later.
The correct consideration is that the trailing clock is always 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 an accelerating reference frame a pseudo- gravitational field. The trailing clock will have the slower clock rate.
Author's notes
1.
Mislabeling in Principle of Relativity diagram and associated text (editions 1 through 5)
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: The acceleration of a clock simply generates a continuous change in its otherwise uniform kinematical clock-rate, and is not a true non-kinematical effect.
The frame that the clock is in as it accelerates is a pseudo- gravitational field only; therefore there is no additional 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 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 implementing a misleading static diagram, then reversed the time- contraction, though I knew better.
My mistake jumped right out at me all these years later.
The correct consideration is that the trailing clock is always 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 an accelerating reference frame a pseudo- gravitational field. The trailing clock will have the slower clock rate.