The Einstein Light Motion Paradox

Bob Kroepel
Copyright © 2012
Lakeside Studios
20 South Shore Road
New Durham, NH USA 03855

Table of Contents

  1. Introduction
    1. Simultaneity in Physics
    2. Einstein's Conception of Simultaneity
  2. The Concept of a Reference Frame
  3. The Concept of a Reference Body
  4. Chronological Sequences (Time Sequences)
    1. Gross Time Sequences
    2. Precise Time Sequences
  5. Sequences 1, 1b & 1c and Movie 1c
    1. Sequence 1
    2. Sequence 1b
    3. Sequence 1c
    4. Movie 1c
  6. Sequences 2, 2b & 2c and Movie 2c
    1. Sequence 2
    2. Sequence 2b
    3. Sequence 2c
    4. Movie 2c
  7. Comparing Sequences 1, 1b, & 1c & Movie 1c vs Sequences 2, 2b, & 2c & Movie 2c
  8. The Problem: The Einstein Light Motion Paradox
  9. Relative Velocity (RV) Facts
    1. Velocity in Physics
    2. Speed and Direction
    3. Relative Velocities (RVs) and Measured Velocities (MVs)
    4. Relative Velocities
    5. Measured Velocities
    6. Approach and Departure Velocities
    7. The Maximum RV
    8. The Minimum Velocity
    9. Velocities inre Einstein's Fig. 1
    10. Relative Velocities and the Einstein Light Motion Paradox
  10. Simultaneity and The General Principle of Relativity
  11. The Concept of Time
    1. The Temporal Principle
      1. The Time-Interval
      2. The Timerate
      3. Timepoints
      4. Timelines
      5. Timecounts
    2. The Temporal Process
    3. Time: Never Destroyed nor Created
    4. Time: Infinite in Duration
    5. The Essence of Time: The Time-Interval
    6. The Two Types of Clocks
    7. The Two Types of Time
    8. Distortable Time: Local Time
    9. The Continuum of Local Time (CoLT)
    10. Adjustable/Non-Distortable Time: Absolute Time
    11. The Continuum of Absolute Time (CoAT)
    12. The Two Types of Adjustable Clocks: Radio Clocks & Inertial Clocks
    13. Radio Clocks
    14. Inertial Clocks
    15. Simultaneities, Timepoints, and Time-Stamps
  12. The Moving Observer Illusion (MOI)
  13. Summary: The Einstein Light Motion Paradox

Introduction

Simultaneity in Physics

In physics, simultaneity is defined as the occurrence of two or more events at the same timepoint.

Einstein's Conception of Simultaneity

In Relativity, 1961 edition, Chapter IX, Einstein showed that when light is used to determine the simultaneity of events the relativity of different reference frames and observers will prompt an observer in one reference frame to report detecting proof that two events occurred simultaneously while another observer in another reference frame will report detecting proof that the two events did not occur simultaneously.

Einstein:

[Paragraph 1] Up to now our considerations have been referred to a particular body of reference, which we have styled a “railway embankment.” We suppose a very long train travelling along the rails with the constant velocity v and in the direction indicated in Fig. 1. People travelling in this train will with advantage use the train as a rigid reference-body (co-ordinate system); they regard all events in reference to the train. Then every event which takes place along the line also takes place at a particular point of the train. Also the definition of simultaneity can be given relative to the train in exactly the same way as with respect to the embankment. As a natural consequence, however, the following question arises:

[Paragraph 2] Are two events (e.g. the two strokes of lightning A and B) which are simultaneous with reference to the railway embankment also simultaneous relatively to the train? We shall show directly that the answer must be in the negative. [Einstein, Relativity, 1961 edition, Chapter IX]

Inre Relativity, Einstein proposed a unique way to determine the simultaneity of two events.

Einstein presented in Chapter IX of Einstein's Relativity, 1961 edition, the Fig. 1 Einstein Railroad Drawing:

einstein'srailwaydrawing1.jpg
Fig. 1

For the purpose of clarity inre this article, the Einstein Railroad drawing has been redrawn thus:

Einstein RR Fig. 1c.0.jpg
Fig. 1 (Redrawn)

The distinction of Events A' & B' from Events A & B and distinction of the length A'-B' from the length A-B are made ...

(A) to distinguish the lightning strikes that are Events A & B inre (in regards, in relation to, relative to, or about) the Embankment as Events A & B and inre the Train as Events A' & B',

(B) to distinguish Lightrays A & B from Events A & B from Lightrays A' & B' from Events A' & B',

... and ...

(C) to distinguish the length A-B inre M and the Embankment from the length A'-B' inre M' and the Train,

... thus showing better the causal and coincidental relationships inre the M & Embankment reference frame K and the M' & Train reference frame K', especially to show howitiz that the lengths A'-B', A'-M' and B'-M' travel with the Train, and howitiz that because the Train has been in-motion at an unspecified measured velocity (MV) that the lengths A'-B', A'-M' and B'-M' are NOT space-contracted.

Einstein, in Paragraph 1, stated that ...

... the Railway Embankment is one reference frame ...

einsteinrrembankment.jpg
Einstein RR Embankmkent

... and ...

... the Railway Train is another reference frame ...

einsteinrrembankment.jpg
Einstein RR Train

The Concept of a Reference Frame

In this article, a reference frame is a co-ordinate system consisting of three axes, the x-axis, the y-axis, and the z-axis, extending as straight lines from a common origin, within which entities which are at-rest, motionless, no relative velocity, (RV = 0.00c, as explained below), are described as being in the reference frame.

For every possible velocity (speed + direction, as explained below), there is a separate reference frame. Reference frames are distinguished from other reference frames by their velocities (speeds + directions).

In this article, when necessary, the Embankment is described as reference frame K and the Train is described as reference frame K'.

Because M is motionless inre the Embankment, M and the Embankment are in the same reference frame, K; because M' is motionless inre the Train, M' and the Train are in the same reference frame, K'.

The Concept of a Reference Body

In this article, a reference body is an entity to which a reference frame is attached with its origin at the Entity's center of mass (CoM) with the reference frame's co-ordinate system's x-axis aligned parallel to the Entity's direction of motion.

In Fig. 1, the Embankment has a CoM to which the reference frame K co-ordinate system can be attached, therefore the Embankment is a reference body, and thereby the Embankment reference body can also be labeled K, and the Train has a different CoM to which the reference frame K' co-ordinate system can be attached, and thereby the Train reference body can also be labeled K'.

The combination of a reference frame with a reference body means that in essence a reference frame and reference body are the same inre being a point-of-view (PoV) from which observations and measurements can be made and within which the laws of physics are the same (a natural causal relationship observed to have occurred inre one reference frame/body is expected to be observed to occur inre any and all other reference frames/bodies (explained below in Simultaneity and The General Principle of Relativity).

---

In the redrawn Fig. 1, Events A & B have been augmented by the letters A' and B' to show how it is that Events A & B inre the Embankment also occurred as Events A' & B' inre the Train, and how it is that the length A-B inre the Embankment is identical to the length A'-B' inre the Train.

In this article, the phrase Events A & B can mean both Events A & B and Events A' & B'.

The length A-B inre the Embankment is identical in length to the length A'-B' inre the Train. Whereas the Train had been in-motion inre the Embankment prior to Events A & B (A' & B'), the fact that length A-B is identical to length A'-B' means there is no length-contraction inre the length A'-B' inre the Train.

In the drawings in this article, the length A-B and thus the length A-M-B does not move inre the Embankment but the length A'-B' and thus the length A'-M'-B' moves with the Train.

The following comments inre Fig. 1 by Einstein in Paragraph 3 of Chapter IX of Relativity present a sequence of events as observed by M on the Embankment.

Einstein:

[Paragraph 3] When we say that the lightning strokes A and B are simultaneous with respect to be embankment, we mean: the rays of light emitted at the places A and B, where the lightning occurs, meet each other at the mid-point M of the length A -> B of the embankment. But the events A and B also correspond to positions A and B on the train. Let M' be the mid-point of the distance A -> B on the travelling train. Just when the flashes [as judged from the embankment] of lightning occur, this point M' naturally coincides with the point M, but it moves towards the right in the diagram with the velocity v of the train. If an observer sitting in the position M' in the train did not possess this velocity, then he would remain permanently at M, and the light rays emitted by the flashes of lightning A and B would reach him simultaneously, i.e. they would meet him just where he is situated. Now in reality (considered with reference to the railway embankment) he [M'] is hastening towards the beam of light coming from B, whilst he [M'] is riding on ahead of the beam of light coming from A. Hence the observer [M'] will see the beam of light emitted from B earlier than he [M'] will see that emitted from A. Observers [including M'] who take the railway train as their reference-body must therefore come to the conclusion that the lightning flash B took place earlier than the lightning flash A. [Einstein, Relativity, 1961 edition, Chapter IX].

Of special note inre Paragraph 3:

1. "[T]he rays of light emitted at the places A and B, where the lightning occurs, meet each other at the mid-point M of the length [A-B] of the embankment [and] the events A and B also correspond to positions A and B on the train".

Comment: The distance (length) A-B is the same for both the Embankment and the train (A-B = A'-B'). The train is in-motion prior to the occurrences of Events A & B, therefore the x-axis length-contraction inre the Train would have occurred prior to the Events A & B, and, therefore, the length A-B is the same for both the Embankment and the Train (A-B = A'-B'), i.e. there is no length-contraction inre the length A'-B' inre the Train.

2. "Now in reality (considered with reference to the railway embankment) [M'] is hastening towards the beam of light coming from B [and] [M'] is riding on ahead of the beam of light coming from A".

Comment: The relative velocity (RV) inre M' and the Lightray B' from Event B' is greater than 1.00c because the velocity of Lightray B' is to be added to the velocity of M' (and the Train) by the equation ...

... RV = MV1 + MV2 ...

... where ...

... RV = Relative Velocity;
... MV = Measured Velocity;
... MV1 = Measured Velocity of Lightray B';
... MV2 = Measured Velocity of M'.

The MV1 of Lightray B' is assumed to be the speed of light in vacuo (in a subvolume of space which is devoid of matter-energy, m/e, including electromagnetism and gravity), i.e. the MV1 of Lightray B' is assumed to be 1.00c; the MV2 of M' is not given but we can assume that because M' is an entity comprised of m/e that he [M'] will be in-motion at an MV2 < 1.00c but at an MV2 > 0.00c.

The RV inre M' and Lightray A' from Event A' is less than 1.00c because the velocity of Lightray A' is to be subtracted from the velocity of M' (and the Train) by the equation ...

... RV = MV1 - MV2 ...

... where ...

MV1 = Measured Velocity of Lightray A';
MV2 = Measured Velocity of M'.

3. "[M'] will see the beam of light emitted from B earlier than he [M'] will see [the beam of light] emitted from A".

Comment: M' could not 'see' (detect, observe) Lightray B' from Event B' "earlier" than he [M'] would 'see' Lightray A' from Event A' if the RV of Lightray B' & M' was 1.00c and the RV of Lightray A' & M' was also 1.00c.

If the MV of Lightray B' were to equal (be the same as) the MV of Lightray A' and therefore the MV of Lightray A' would be 1.00c and the MV of Lightray B' would also be 1.00c, then Lightrays A' & B' would strike M' simultaneously (at the same timepoint) and therefore he [M'], will 'see' Lightray A' at the same timepoint he [M'] will 'see' Lightray B', and therefore he [M'] would be justified in concluding and reporting that Events A' & B' occurred simultaneously (at the same timepoint).

4. "Observers [including M'] who take the railway train as their reference-body must therefore come to the conclusion that the lightning flash B took place earlier than the lightning flash A."

Comment: Whereas Einstein stated/stipulated that the Events A & B ( and Events A' & B') occurred simultaneously for both the Embankment and the Train, and, theoretically, if the speed of light is the same for all observervs, which, interpreted, means that Lighrays should have traveled past both M and M' at 1.00c, then both M and M' should have detected Lightrays simultaneously (at  the same timepoint) and therefore both M and M' should have judged and reported that Events A & B (and Events A' & B') occurred simultaneously.

But Einstein does not say so in the #4 quote cited.

Instead, in the quote #4 cited, he says that observers inre the Train reference frame/body should detect Lightray B' before detecting Lightray A', and that means M', being obviously an observer inre the Train reference frame/body, along with any other observers inre the Train reference frame/body, should have detected Lightray B' before detecting Lightray A'.

Inre the light motions inherent in Fig. 1, the concept of a chronological sequence, or time sequence, is critical.

Chronological Sequences (Time Sequences)

A chronological sequence is a time sequence or listing of the occurrences of events at timepoints (time marks) on a timeline (continuum of time, a history, or record, of events).

Gross Time Sequences

A gross time sequence presents a chronological sequence in terms of the timepoints at which specific events occurred without regard for—without the requirement for—equivalent durations between timepoints nor equivalent durations of timepoints.

Ex(ample): In the game of baseball, there is no game clock which keeps precise timepoints on a timeline because the game is played by a total of nine innings and the duration of an inning typically is unpredictable and therefore variable, with the result that events (home runs, triples, doubles, singles, strikeout, double-plays, triple-plays, runs scored, etc.) are listed by innings in a gross time sequence.

Precise Time Sequences

A precise time sequence presents a chronological sequence in terms of equiduration and equidistant timepoints (timepoints of equal duration separated by equal durations) at which specific events occurred.

Ex: In some games, including football, basketball, and hockey, game clocks are used and events are often listed according to the game clock timepoint at which they occurred. In football, the game clock is split into four quarters of fifteen minutes, fifteen timepoints, each. Events in a football game (touchdowns, field goals, passes completed, pass intercepted, runs scored, ... etc.) can be listed as occurring at minutes on the game clock. A game clock often differs from a 24-hour clock because of timeouts, or pauses in the game action, which cause timekeepers to stop the game clock. Nevertheless, when the game clock is running, the durations of timepoint (minutes) are equal and the durations between the minutes are also equal.

Ex: A 24-hour clock is a standard clock for most people, in which there are twenty-four hours divided into 60 minutes per hour divided into 60 seconds per minute, and if a 24-hour clock is operating properly, then the durations of the seconds, minutes, hours, etc., are equal, and the durations between the ticks of the seconds, minutes, hours, etc., are also equal. The USNO (US Naval Observatory), the US NIST (US National Institute of Standards and Technology), and the BIPM (Bureau Internationale des Poids et Mesures, in France) use adjustable clocks which are the standard clocks which are used to maintain the standard second and which are therefore the time standard for civilians, military personnel, and scientists wherein the durations of seconds are equal and the durations between seconds are equal. The US GPS nav system's tming system consists of a master clock which controls the timerates of slave clocks in the GPS satellites; the GPS master clock is synchronized with the USNO standard clocks and thereby broadcast the USNO standard time to any individuals and organizations whose time standard requirements are satisfied by the precision of the USNO standard clocks.

Sequences 1, 1b & 1c and Movie 1c

Sequence 1 is a paraphrase of Paragraph 3 of Chapter IX of Relativity in which the sequence of events inherent in Fig. 1 as described by Einstein in Paragraph 3 are presented in a numerical sequence (numbered sequence).

Sequence 1

1. Lightning strikes A & B; Events A & B occur simultaneously inre distance A-B inre both the Embankment & the Train;
2. Light from B' strikes M' (M' reports detecting Lightray B' from Event B');
3. Light from A and B strike M (M reports detecting Lightrays A & B from Events A and B and his judgment that Events A & B occurred simultaneously);
4. Light from A' strikes M' (M' reports detecting Lightray A' from Event A' and his judgment that Events A' & B' occurred non-simultaneously).

Sequence 1 is a gross time sequence.

A gross time sequence presents a chronological sequence in terms of the timepoints at which specific events occurred without regard for—without the requirement for—equivalent durations between timepoints nor equivalent durations of timepoints.

The gross time sequence for Sequence 1 is presented as Sequence 1b, wherein T = Timepoint and there are four timepoints, T1, T2, T3, & T4.

Sequence 1b

NOTE: T = Timepoint

1. T1: Lightning strikes A & B; Events A & B occur simultaneously inre distance A-B inre both the Embankment & the Train;
2. T2: Light from B' strikes M' (M' reports detecting Lightray B' from Event B');
3. T3: Light from A and B strike M (M reports detecting Lightray A & B from Events A and B and his judgment that Events A & B occurred simultaneously);
4. T4: Light from A' strikes M' (M' reports detecting Lightray A' from Event A' and his judgment that Events A' & B' occurred non-simultaneously).

There are four timepoints in the gross time sequence which is Sequence 1b; these timepoints are not necessarily of equal durations nor are the durations between them necessarily of equal durations.

The following drawings illustrate the causal and coincidental relationships inre the movements of lightrays from Events A & B, the motion of the Train, and the motion of M' relative to M and the Embankment illustrated in Fig. 1, in Sequence 1 and in Sequence 1b at Timepoints T1, T2, T3, & T4.

einsteinrr1c.0.jpg
1. T1: Events A & B occur simultaneously inre the Embankment and the Train.

einsteinrr1c.5.jpg
2. T2: Light from B' strikes M'.

einsteinrr1c.8.jpg
3. T3: Light from A & B strike M.

einsteinrr1c.15.jpg
4. T4: Light from A' strikes M'.


Sequence 1c, is a precise time sequence in which the causal and coincidental events inherent in Einstein's Fig. 1 are presented as timepoints T1-T16.

Sequence 1c


einsteinrr1c.0.jpg
1. T1: Einstein RR (Sequence 1c: Movie 1c)

einsteinrr1c.1.jpg
2. T2: Einstein RR (Sequence 1c: Movie 1c)

einsteinrr1c.2.jpg
3. T3: Einstein RR (Sequence 1c: Movie 1c)

einsteinrr1c.3.jpg
4. T4: Einstein RR (Sequence 1c: Movie 1c)

einsteinrr1c.4.jpg
5. T5: Einstein RR (Sequence 1c: Movie 1c)

einsteinrr1c.5.jpg
6. T6: Einstein RR (Sequence 1c: Movie 1c)

einsteinrr1c.6.jpg
7. T7: Einstein RR (Sequence 1c: Movie 1c)

einsteinrr1c.jpg
8. T8: Einstein RR (Sequence 1c: Movie 1c)

einsteinrr1c.8.jpg
9. T9: Einstein RR (Sequence 1c: Movie 1c)

einsteinrr1c.9.jpg
10. T10: Einstein RR (Sequence 1c: Movie 1c)

einsteinrr1c.10.jpg
11. T11: Einstein RR (Sequence 1c: Movie 1c)

einsteinrr1c.11.jpg
12. T12: Einstein RR (Sequence 1c: Movie 1c)

einsteinrr1c.12.jpg
13. T13: Einstein RR (Sequence 1c: Movie 1c)

einsteinrr1c.13.jpg
14. T14: Einstein RR (Sequence 1c: Movie 1c)

einsteinrr1c.14.jpg
15. T15: Einstein RR (Sequence 1c: Movie 1c)

einsteinrr1c.15.jpg
16. T16: Einstein RR (Sequence 1c: Movie 1c)

Movie 1c

Movie 1c: http://www.bobkwebsite.com/einsteinrr1c.mov

Sequence 1, Sequence 1b and Sequence 1c are paraphrases of Einstein’s description in Paragraph 3 of Chapter IX of Relativity of the motions of Lightrays from Events A & B (and Events A' & B') in relation to M, the Embankment, M', and the Train which are inherent in Fig. 1.

Sequences 2, 2b & 2c and Movie 2c

Sequence 2 is a gross time sequence which describes the motions of Lightrays from Events A & B in relation to M, the Embankment, M', and the Train when the length A-B (A'-B') moves with the M' and the Train and Lightrays A' & B' travel at 1.00c towards M'.

Sequence 2

1. Events A & B occur simultaneously inre the Embankment and the Train.
2. Lightrays from A & B strike M and M' simultaneously (both M & M' report detecting Lightrays from Events A & B simultaneously and their judgments that Events A & B occurred simultaneously).
NOTE: Because Lightrays from A & B struck M and M' simultaneously, there is no need for a T3 or a T4 inre Sequence 2.

Sequence 2b is a gross time sequence which describes the motions of lightrays from Events A & B in relation to M, the Embankment, M', and the Train when the length A-B (A'-B') moves with the M' and the Train at timepoints T1, T2, T3, & T4.

Sequence 2b

1. T1: Events A & B occur simultaneously inre the Embankment and the Train.
2. T2: Lightrays from A & B strike M and M' simultaneously (both M & M' report detecting Lightrays from Events A & B simultaneously and their judgments that Events A & B occurred simultaneously).
NOTE: Because Lightrays from A & B struck M and M' simultaneously, there is no need for a T3 or a T4 inre Sequence 2b.
einsteinrr2c.0.jpg
1. T1: Einstein RR (Sequence 2b)

einsteinrr2c.7.jpg
2. T2: Einstein RR (Sequence 2b)

Because Sequence 2b is a gross time sequence, there are only two timepoints, T1 & T2.

When the Lightrays A' & B' from Events A' & B' travel with distance A-B (A'-B') and M' and the Train, then Lightrays A' & B' travel towards-past-away-from M' at 1.00c while Lightrays A & B also travel towards-past-away-from M at 1.00c.

Sequence 2c is the precise time sequence of events at timepoints T1-T8 when the length A-B (A'-B') moves with M' and the Train and Lightrays A' & B' from Events A & B also move with M' and the Train.

Sequence 2c


einsteinrr2c.0.jpg
1. T1: Einstein RR (Sequence 2c: Movie 2c)

einsteinrr2c.1.jpg
2. T2: Einstein RR (Sequence 2c: Movie 2c)

einsteinrr2c.2.jpg
3. T3: Einstein RR (Sequence 2c: Movie 2c)

einsteinrr2c.3.jpg
4. T4: Einstein RR (Sequence 2c: Movie 2c)

einsteinrr2c.4.jpg
5. T5: Einstein RR (Sequence 2c: Movie 2c)

einsteinrr2c.5.jpg
6. T6: Einstein RR (Sequence 2c: Movie 2c)

einsteinrr2c.6.jpg
7. T7: Einstein RR (Sequence 2c: Movie 2c)

einsteinrr2c.7.jpg
8. T8: Einstein RR (Sequence 2c: Movie 2c)

Movie 2c illustrates the specific sequence of events when the length A'-B' moves with M' and the Train and Lightrays A' & B' from Events A & B also move with M' and the Train.

Movie 2c

Movie 2c: http://www.bobkwebsite.com/einsteinrr2c.mov

Comparing Sequences 1, 1b, & 1c & Movie 1c vs Sequences 2, 2b, & 2c & Movie 2c

Here are T1 and T3 from Sequence 1b and T1 and T2 from Sequence 2b:

Einstein RR 1c.0.jpg @ T1
Sequences 1b & 2b: T1: Events A & B Occur Simultaneously inre the Embankment and the Train.

einsteinrr1c.7.jpg
Sequence 1b: T3: Lightrays from Events A & B strike M Simultaneously. 

Einstein RR 2c.7.jpg @ T3
Sequence 2b: T2: Lightrays from Events A & B Strike M and M' Simultaneously.

Sequence 1, Sequence 1b and Sequence 2b start at T1 with Events A & B occurring simultaneously inre the Embankment and the Train.

Inre Sequence 1, at T3, when light travels at RV = 1.00c inre M & the Embankment and at RV ≠ 1.00c inre M' & the Train, Light from B' has already struck M' and Light from A & B strike strike M simultaneously.

Inre Sequence 2b, at T2, when light travels at RV = 1.00c inre M & the Embankment and M' & the Train, then Light from A & B strike M and M' simultaneously.

Therein lies the Einstein Light Motion Paradox: For Events A & B to be non-simultaneous inre M' & the Train in Sequence 1b, then the RV of light inre M & the Embankment ≠ the RV of light inre M' & the Train; for Events A & B to be simultaneous inre M & the Embankment AND inre M' & the Train, then the RV for light inre M & the Embankment = RV for light inre M' & the Train.

The Problem: The Einstein Light Motion Paradox

Problem: In Paragraph 3, Einstein stated/stipulated clearly that Events A & B (and Events A' & B' in the redrawn Fig. 1) occurred simultaneously inre both the Embankment—reference frame K and the Train—reference frame K', but then, also in Paragraph 3, he stated that, as observed from either K or K', M or M' would detect Lightrays at different timepoints and therefore there is a relativity of simultaneity that conflicts with the objective fact that Events A & B (and Events A' & B' in the redrawn Fig. 1) occurred simultaneously inre K & M and inre K' & M'.

If Events A & B (and Events A' & B' in the redrawn Fig. 1) occurred simultaneously inre both the Embankment/reference frame K and the Train/reference frame K', and if the motions of the Lightrays A, B, A', & B' were RV = 1.00c for both M in K and M' in K', as described by Einstein's light motion equation, RV = (MV1 + MV2)/(1 + MV1 x MV2/C2), then both M and M' should have reported detecting Lightrays from Events A & B (and A' & B' in the redrawn Fig. 1) simultaneously, at #2 in Sequence 2 and at #2. T2 in sequence 2b.

Because of their relative velocity difference (because their reference frames/bodies have different MVs and therefore they have different MVs), M and M', at least in theory, ought to observe each other detecting Lighrays from Event A & B at different timepoints and conclude that there is a relativity of simultaneity which ought to mean that, if true, then Events A & B did not occur simultaneously inre both M in K and M' in K'.

The Problem herein is the Einstein Light Motion Paradox wherein there is an objective fact of simultaneity (Events A & B occurred simultaneously—at the same timepoint—inre K & M and K' & M') which conflicts with the concept of the relativity of simultaneity (wherein because of their relative velocity difference M and M' would detect Lightrays at different timepoints and thereby judge that the Events A & B did not occur simultaneously).

Relative Velocity (RV) Facts

Velocity in Physics

In physics, velocity is the combination of an Entity's speed and direction of motion.

Speed and Direction

Speed and direction are two different characteristics of motion (another characteristic is the change of speed, particularly the rate of change of speed, caused by acceleration or deceleration forces; another characteristic is change of direction, particularly the rate of change of direction, caused by acceleration and deceleration forces).

Speed is motion without regard for direction while direction is motion without regard for speed.

Although speed and direction are interconnected in the concept of velocity, when either necessary or otherwise convenient, it is logical and therefore possible for people to refer to speed in any direction and thereby disregard speed in a specific direction (someone could talk about the top speed of a car regardless of direction) or to refer to direction and thereby disregard direction with any specific speed (a person could travel in a direction at any speed).

Relative Velocities (RVs) and Measured Velocities (MVs)

Relative Velocities

Relative velocities (RVs) are the combinations or differences inre the measured velocities (MVs) of Entities.

Relative velocities (RVs) occur when Entities have different measured velocities (MVs).

A relative velocity (RV) is the combination or difference inre the measured velocities (MVs) of two Entities.

Measured Velocities

A measured velocity (MV) is the velocity of an entity as measured in relation to a reference point or object (entity). In Fig. 1, the v of the Train (and M') is an MV inre the Embankment, or inre M as M stands on and is thereby motionless inre the Embankment. In that regard, an MV is an RV because it is the difference between the velocity of an entity in relation to (inre) the velocity of a reference point.

A relative velocity (RV) is either ...

(1) the combination of the measured velocity (MV) of one entity (MV1) and the measured velocity of another entity (MV2) described by RV = MV1 + MV2,

... or ...

(2) the difference between the measured velocity (MV) of one entity (MV1) and the measured velocity of another entity (MV2) described by RV = MV1 - MV2.

Approach and Departure Velocities

In aviation, a relative velocity (RV) can be described as an approach velocity (herein referred to as an approach relative velocity, or ARV) or as a departure velocity (herein referred to as a departure relative velocity, or DRV).

NOTE: In aviation, approach-departure velocities are generally restricted to aircraft inre fixed locations on the ground (the Earth's surface), but for the theory of relative velocities approach-departure velocities can be described inre entities in-motion and/or positions in space (spacepoints) in addition to fixed locations on the ground.

An ARV occurs (A) when two Entities approach—move towards—each other from opposite directions or (B) when one Entity moves towards another Entity in the same direction; a DRV occurs (A) when two Entities depart—move away—from each other in opposite directions or (B) when one Entity moves away from another Entity in the same direction.

Fact: An ARV can be the sum of two Lightrays traveling in opposite directions and parallel to each other with the MV1 of a Lightray traveling at 1.00c and the MV2 of an Entity traveling less than 1.00c, by RV = MV1 + MV2, without either the Lightray or the Entity traveling faster than 1.00c.

Fact: A DRV can be the difference between the MV1 of a Lightray traveling at 1.00c and the MV2 of an Entity traveling less than 1.00c, by RV = MV1 - MV1.

The Maximum RV

Fact: The maximum RV would be the ARV inre two Lightrays, Lightray A & Lightray B, which are approaching each other from opposite directions and are traveling parallel to each other and each Lightray is traveling at MV = 1.00c or the DRV inre two Lightrays, A & B, which are departing from each other by traveling parallel to each other in opposite directions at 1.00c each.

The RV equation for the maximum ARV is RV = MV1 (Lightray A) + MV2 (Lightray B), for an RV = 1.00c + 1.00c, or RV = 2 x 1.00c or 2.00c without either Lightray traveling faster than 1.00c.

The RV equation for the maximum DRV is DRV = MV1 + MV2 = 1.00c + 1.00c = 2 x 1.00c = 2.00c without either Lightray traveling faster than 1.00c.

The Minimum Velocity

Fact: The minimum RV would be the RV inre two Entities that are at-rest in a single reference frame or on a single reference body, described by RV = MV1 (Entity 1) - MV2 (Entity 2) = 0.00c. The Entities would neither approach nor depart from each other.

Because inre the minimum RV the entities are not moving inre each other, then the minimum RV equation is RV = MV1 ± MV2 = 0.00c ± 0.00c = 0.00c, e.g. RV = MV1 + MV2 = 0.00c + 0.00c = 0.00c and RV = MV1 - MV2 = 0.00c - 0.00c = 0.00c.

Velocities inre Einstein's Fig. 1

Fact: Inre Einstein's Fig. 1, Lightray B' approaches M' at an ARV that is the combination of the sum of the MV1 of Lightray B' and the MV2 of M' given by ARV = MV1 + MV2.

Fact: Inre Einstein's Fig. 1, Lightray A' approaches M' at an ARV that is the difference between the MV1 of Lightray A' and the MV2 of M' given by ARV = MV1 - MV2.

The Einstein light motion relative velocity equation, ...

RV = (MV1 + MV2)/(1 + MV1 x MV2/c2

... always produces the result RV = 1.00c, which fits the relativistic claim that the speed of light is the same for all observers.

If the Einstein light motion relative velocity equation always produces the result of RV = 1.00c, which is implied in Chapter XIII, then it is not possible for the Einstein light motion relative velocity equation to describe accurately the ARV inre Lightray A' and M' nor the ARV inre Lightray B' and M' because of the description of the RVs inre Lightrays A' & B' inre M' given by Einstein in Paragraph 3 and by paraphrases of Einstein's Paragraph 3 in my Sequence 1, Sequence 1b and Sequence 1c, and animated in Movie 1c, wherein M' approaches Lightray B' and is struck by Lightray B' before being struck by Lightray A', and Lightray A' approaches M' and strikes him after he has been struck by Lightray B'.

When M' is traveling at an unspecified MV2 parallel to and towards Lightray B' which is traveling at MV1 = 1.00c parallel to M' but in the opposite direction, then M' has an MV2 which has to be added to the MV1 of Lightray B' via RV = MV1 + MV2.

As observed from reference frame K/the Embankment, the ARVs inre Lightrays A & B inre M are 1.00c but the ARVs inre Lightrays A' & B' inre M' inre reference frame K'/the Train are not 1.00c.

ARV = MV1 ± MV2 gives the correct ARVs inre Lightrays A' & B' inre M' as well as the correct ARVs inre Lightrays A & B inre M but although RV = (MV1 + MV2)/(1 + MV1 x MV2/c2 gives the correct RVs inre Lightrays A & B inre M it does not give the correct ARVs inre Lightrays A' & B' inre M'.

Relative Velocities and the Einstein Light Motion Paradox

Inre Einstein's Fig. 1, because of the fact that ARV = MV1 ± MV2 gives the correct ARVs inre Lightrays A' & B' inre M' but RV = (MV1 + MV2)/(1 + MV1 x MV2/c2 does not give the correct ARVs inre Lightrays A' & B' inre M', we have the Einstein Light Motion Paradox.

Simultaneity and The General Principle of Relativity

The general principle of relativity states describes the fact that the laws of physics are the same for any reference frame or reference body.

Einstein's theory of relativity depends upon laws of physics in one reference frame or on one reference body being the same in any and all other reference frames or on any and all other reference bodies.

Inre Fig. 1 of Chapter IX of Relativity, in Paragraph 3, Einstein stated that, as M would observe from reference frame K (in which are located M & the Embankment), the following sequence occurred:

Sequence 1

1. Lightning strikes A & B; Events A & B occur simultaneously inre distance A-B inre both the Embankment & the Train;
2. Lightray B' from Event B' strikes M' (M' reports detecting light from Event B');
3. Lightrays A & B from Events A and B strike M (M reports detecting light from Events A and B and his judgment that Events A & B occurred simultaneously);
4. Lightray A' from Event A' strikes M' (M' reports detecting light from Event A' and his judgment that Events A' & B' occurred non-simultaneously).

When timepoints T1, T2, T3, & T4 are added to Sequence 1, we get Sequence 1b:

Sequence 1b

1. T1: Lightning strikes A & B; Events A & B occur simultaneously inre distance A-B inre BOTH the Embankment & the Train;
2. T2: Lightray B' from Event B' strikes M' (M' reports detecting light from Event B);
3. T3: Light from A and B strike M (M reports detecting light from Events A and B and his judgment that Events A & B occurred simultaneously);
4. T4: Lightray A' from Event A' strikes M' (M' reports detecting light from Event A' and his judgment that Events A' & B' occurred non-simultaneously).

According to the general principle of relativity, from reference frame K' (in which are located M' & the Train), M' should observe Sequences 1 and1b inre reference frame K and M and the Embankment:

Sequence 1 (As observed by M' from reference frame K')

1. Lightning strikes A & B; Events A & B occur simultaneously inre distance A-B inre BOTH the Embankment & the Train;
2. Lightray B from Event B strikes M (M reports detecting light from Event B);
3. Lightrays A' & B' from Events A' and B' strike M' (M' reports detecting light from Events A' and B' and his judgment that Events A' & B' occurred simultaneously);
4. Lightray A from Event A strikes M (M reports detecting light from Event A and his judgment that Events A & B occurred non-simultaneously).

Sequence 1 (As observed by M' from reference frame K')

1. T1: Lightning strikes A & B; Events A & B occur simultaneously inre distance A-B inre BOTH the Embankment & the Train;
2. T2: Lightray B from Event B strikes M (M reports detecting light from Event B);
3. T3: Lightrays A' & B' from Events A' and B' strike M' (M' reports detecting light from Events A' and B' and his judgment that Events A' & B' occurred simultaneously);
4. T4: Lightray A from Event A strikes M (M reports detecting light from Event A and his judgment that Events A & B occurred non-simultaneously).

Note that, according to the general principle of relativity, by simply exchanging the symbol M' for M in Sequences 1 & 1b we get the same results: the observer (M or M') in the reference frame that is supposed to be at-rest will observe that he will detect Lightrays from Events A & B (or Events A' & B') simultaneously, at the same timepoint, and thereby he can judge and report that Events A & B (or Events A' & B') occurred simultaneously while he supposedly will observe that the other observer in the reference frame that is supposed to be moving will detect one Lightray from Event A or B (or Event A' or B') before detecting the other Lightray from the other Event and supposedly will judge and report that Events A & B (or Events A' & B') did NOT occur simultaneously.

Because (P) we have two reference frames and either could be the at-rest or  the moving reference frame and therefore either observer (M or M') could be the at-rest observer while the other is the moving observer, then (Q) we therefore have two possibilities for two conflicting judgments and reports: (1) The observer in the at-rest reference frame will judge and report Events A & B (or Events A' & B') occurred simultaneously but (2) the observer in the moving reference frame will judge and report that Events A & B (or Events A' & B') did NOT occur simultaneously.

There is a problem herein: If we disregard the concept of the general principle of relativity wherein the relationships observed from one reference frame by observers in that reference frame should also be observed from another reference frame by observers in that reference frame, a fact which could produce conflicting observations, measurements and reports inre WIGO inre the relationships, there is a possibility a relationship, such as the simultaneity of events, can be determined objectively, without the viewpoint (point-of-view, or PoV) of an oberver in either of the reference frames.

We could use the concept and relevant principles of time to create the physical evidence which would serve as proof of  the simultaneities of events, as well as the sequences of events, the causalities of events, and the changerates (rates of change) of events inre different reference frames/bodies.

The Concept of Time

Time is the combination of The Temporal Principle and The Temporal Process.

The Temporal Principle

The Temporal Princple: Time is the use of a chosen duration (recurring event, cycle, or a model of a chosen duration) to be used as a time-interval to be used as the unit of temporal meaurement for the measurement of the durations between the occurrences of events, the durations of single events, and the durations (ages) of people and objects, and for the generation in timepieces (clocks, watches, etc.) of their timerates (rates of ticking, RoTs, tick-rates), timepoints (marks on a timeline), timelines (histories, records of timepoints, continuums of time), and timecounts (accumulations of timepoints inre a timeline, by addition, from a chosen timepoint origin, T0, from the past through the present into the future, with the arrow of time pointing from the past through the present into the future), and for the determination of the sequences, the simultaneities, the causalities, and the changerates of events, or for the coordination (synchronization) of events, inre single or multiple reference frames/bodies.

The Time-Interval

A time-interval (TI) is a chosen duration which can be modeled after a physical recurring event, periodic motion, or cycle, or modeled from an abstracted duration.

Ex: The standard second is the duration of 9b c-atom oscillations at the Earth's surface.

Ex: Mechanical clocks could mimick or imitate the 9b c-atom oscillation duration b/c that 9b c-atom oscillation can be abstracted when designers and fabricators set the mechanical clock's timerate to match that, be identical to, the timerate set by the duration of the 9b c-atom oscillations.

The Timerate

A timerate is the rate of ticking (RoT), the rate of operation (RoO), the rate of functioning (RoF), of a timepiece (watch, clock, etc.).

For temporal accuracy, the durations between the ticks of a clock should be equal, and the durations of the ticks should also be equal.

Timepoints

A timepoint is a mark inre a timeline.

For mechanical clocks, a timepoint is a number on the clock's face; when the hour, minute, and second hands of a mechanical clock move, their positions determine the clock's timepoints.

For digital clocks, a timepoint is the timepoint which shows in the clock's readout or display.

Timepoints occur inre timelines.

Timelines

A timeline is a record, history or continuum of time, a list of timepoints.

At each timepoint on a timeline, there is a unique configuration of the universal m/e system (matter-energy system); thus, there is a combination of a unique/specific timepoint and a unique/specific m/e configuration which, together, as a combination, occur once in the history/timeline of the universe and never again.

A timeline is dated from a chosen timepoint, T0, which is a chosen origin.

A timeline can be a uni-directional timeline (single direction timeline) or a bi-directional timeline (double direction timeline)

A uni-directional timeline begins at a chosen origin timepoint, T0, and is counted forward from that T0.

T0 -> T+1 -> T+2 -> ... -> Infinity Future

A bi-directional timeline begins at a chosen timepoint origin, T0, and is counted backwards and forwards from T0.

Past Infinity <- ... <- T-2 <- T-1 <- T0 -> T+1 -> T+2 -> ... -> Infinity Future

Despite the fact that there are two types of continuums of time, uni-directional and bi-directional, new, unique, timepoints are always accumulated in the future from the past and the present.

Therefore, the timepoints on the timeline of the universe have accumulated from the past through present and will accumulate from the present into the future.

Thus, there is an arrow-of-time which always and only "travels" from the past through the present into the future.

The uniqueness of each timepoint & m/e configuration means that timepoint & m/e combination, regardless of when/where on the universal timeline it occurred, will never occur again.

Ex: You, and I, as we are at this present timepoint and within the present universal m/e configuration, are in a unique timepoint & m/e combination, have changed in past timepoint & m/e combinations and will change inre future timepoint & m/e combinations, and whereas today we are not what we were yesterday tomorrow we will not be what we are today, and therefore we will never be as we were.

The fact that a unique timepoint & m/e combination occurs once on the universal timepoint means time travel is impossible.

Timecounts

A timecount is the accumulation, by addition, of the timepoints on a timeline.

To determine a timecount, such as a duration between events, or the duration of a single event, a timepoint origin must be chosen in order for timepoints to accumulate by addition from that timepoint origin to the present timepoint.

Ex: The timecount for a mechanical clock is the change from a previous hand alignment inre the clock's face numbers to the present hand alignment inre the clock's face numbers, always clockwise; timekeepers will have to do mentally or manually the calculations of timepoints from the previous hand alignment to the current or anticipated hand alignment.

Ex: The timecount for a digital clock is the change from a previous readout to the present readout, which is always larger/greater than the previous readout; timekeepers will have to do mentally or manually the calculations of timepoints from the previous readout to the current or anticipated readout.

When timepoint origins are marked on a timeline, the accumulation of timepoints becomes a line of marks from the timepoint origin to the present timepoint.

The Temporal Process

The Temporal Process: Time is the use of a chosen duration for the time-interval which is to be the unit of temporal measurement for the design, fabrication and deployment of timepieces which are to have designed timerates, timepoints, timelines, and timecounts to be used for the temporal measurement process for the measurement of the durations between the occurrences of events, the durations of single events, and the durations (ages) of people and objects, and for the generation in timepieces (clocks, watches, etc.) of their timerates (rates of ticking, RoTs, tick-rates), timepoints (marks on a timeline), timelines (histories, records of timepoints, continuums of time), and timecounts (accumulations of timepoints inre a timeline, by addition, from a chosen timepoint origin, T0, from the past through the present into the future, with the arrow of time pointing from the past through the present into the future), and for the determination of the sequences, the simultaneities, the causalities, and the changerates of events, or for the coordination (synchronization) of events, inre single or multiple reference frames/bodies.

Thus, time is the combination of the Temporal Principle and the Temporal Process.

---

All biologicals including human biologicals must use the temporal principle to "do time", i.e. to engage in the temporal process. That means space aliens, if they exist, would have to use the temporal principle to create timepieces to engage the temporal process.

All machines, especially computers, are designed to incorporate the temporal principle into the temporal processes they need to operate as designed.

Time: Never Destroyed nor Created

Time is never destroyed nor created.

Ex: If you drop your watch and it no longer functions as designed, then, although the temporal process inre that watch is destroyed, time is not destroyed because the principle of time is never destroyed, and the principle of time means you can once again engage the temporal process by repairing your watch or by buying another watch.

By being never created nor destroyed, time, as the temporal principle, has always been, is now, and forever will be, a universal reality from the past through the present into the future.

Time: Infinite in Duration

As the temporal principle, time is indestructible, and infinite in duration.

The Essence of Time: The Time-Interval

The essence of time is the time-interval—the chosen duration which is the unit of temporal measurement.

There are two types of time-intervals: (1) the distortable time-interval, or d-time-interval, whose duration is distorted by accelerations and decelerations, whose duration is increased by accelerations and whose duration is decreased by decelerations; (2) the adjustable time-interval, or a-time-interval, whose duration is not distorted by accelerations or decelerations because it (the a-time-initerval's duration) is adjusted to maintain a pre-set or original duration.

The Two Types of Clocks

There are two types of clocks: (1) distortable clocks, d-clocks, whose timerates (tick-rates, rates of ticking) are distorted by accelerations and decelerations, wherein accelerations cause decreases in d-clocks' timerates and decelerations cause increases in d-clocks' timerates, and (2) adjustable clocks, a-clocks, whose timerates are not distorted by accelerations and decelerations because their timerates are adjusted to maintain a pre-set original timerate despite accelerations and decelerations so the a-clocks essentially are "independent of the state of motion of [their bodies] of reference" [Einstein, Relativity, 1961 edition, p. 27]. Thus, when the state of motion of the body of reference of a d-clock is changed by acceleratons or decelerations, the d-clock's timerate is changed, but when the state of motion of the body of reference of an a-clock is changed by accelerations or decelerations, the a-clock's timerate is essentially unchanged.

D-clocks are also called local time clocks (LTCs); a-clocks are also called absolute time clocks (ATCs)

The Two Types of Time

A d-clock essentially measures distortable time, or d-time, or local time, or l-time—the time for a single unique reference frame/body, whereas an a-clock thereby measures absolute time or a-time—the universal time for multiple different reference frames/bodies.

Thus, there are two types of time: (1) distortable time, d-time, which is also local time, l-time; (2) absolute time, a-time.

Distortable Time: Local Time

Distortable time, or d-time, or local time, or l-time is the time for a single unique reference frame/body generated by the timerates, timepoints, timeines, and timecounts of distortable clocks, d-clocks, or local time clocks (LTCs).

D-time changes when d-clocks are accelerated or decelerated. Accelerations and decelerations cause distortions of the mechanisms of mechanical clocks and distortions of the oscillations of digital clocks which result in distortion of the d-clocks' timerates, timppoints, timelines, and timecounts.

The Continuum of Local Time (CoLT)

A continuum of local time (d-time) can be created by either a uni-directional timeline or a bi-directional timeline.

A local time or d-time uni-directional timeline is unique, specific, to a single reference frame/body and begins at a chosen origin timepoint, T0, and is counted forward from that T0.

T0 -> T+1 -> T+2 -> ... -> Infinity Future

A local time or d-time bi-directional timeline is unique, specific, to a single reference frame/body and begins at a chosen timepoint origin, T0, and is counted backwards and forwards from T0.

Past Infinity <- ... <- T-2 <- T-1 <- T0 -> T+1 -> T+2 -> ... -> Infinity Future

A CoLT will distort as its d-clock and/or its d-clock's reference body is accelerated or decelerated.

Adjustable/Non-Distortable Time: Absolute Time

Absolute time or a-time, or absolute time, also a-time, is the universal time for multiple different reference frames/bodies generated y the timerates, timepoints, timelines, and timecount of adjustable clocks, a-clocks, also non-distortable clocks, nd-clocks, also asbslute time clocks (ATCs)

The Continuum of Absolute Time (CoAT)

A continuum of absolute time (a-time) can be created by either a uni-directional timeline or a bi-directional timeline.

An absolute time or a-time uni-directional timeline is universal to all reference frames/bodies and begins at a chosen origin timepoint, T0, and is counted forward from that T0.

T0 -> T+1 -> T+2 -> ... -> Infinity Future

An absolute time or a-time bi-directional timeline is universal to all reference frames/bodies and begins at a chosen timepoint origin, T0, and is counted backwards and forwards from T0.

Past Infinity <- ... <- T-2 <- T-1 <- T0 -> T+1 -> T+2 -> ... -> Infinity Future

A CoAT will not distort as its a-clock and/or its a-clock's reference body is accelerated or decelerated because the a-clock is designed to be adjusted (radio a-clock) or adjust itself (inertial a-clock) to compensate for the distortions caused by acceerations and decelerations.

The Two Types of Adjustable Clocks: Radio Clocks & Inertial Clocks

There are two types of a-clocks: (1) radio a-clocks, wherein a master clock sends radio signals to slave clocks and thereby controls the slave clocks' timerates;  (2) inertial a-clocks, wherein accelerometers detect changes of the state of motion (inertial state) of the body of reference (the body of reference being either the a-clock or the Entity upon which the a-clock is at-rest) and computers adjust the inertial a-clocks' timerates.

For the measurement of absolute time, an a-clock must tick with equal time-intervals—equal durations—between ticks and equal time-intervals—equal durations—of ticks.

A clock-tick will have a duration. That duration can be measured by the chosen time-interval.

There will be a duration between clock-ticks. That duration can be measured by the chosen time-interval.

Moreover, an a-clock must continue to tick at the same timerate (tickrate) despite accelerations and decelerations which would cause timerate changes in d-clocks. This means an a-clock must be "independent of the state of motion of the body of reference" [Einstein, Relativity, 1961 edition, p. 27]. This means an a-clock must be independent of inertial state changes inre whatever reference body upon which or within which it is located. This means that if an a-clock is located/positioned within a spaceship, then the a-clock must function in such a way that its timerate remains steady and thus must be independent of the spaceship's inertial state changes caused by accelerations and/or decelerations inre the spaceship. The design and fabrication of a-clocks causes both radio clocks and inertial clocks to function independently of the state of motion of their bodies of reference in accord with Einstein's a-clock requirements.

Radio Clocks

In the radio clock design, a master clock sends radio signals to slave clocks and thereby controls the slave clocks' timerates, timepoints, timelines, and timecounts.

Radio a-clocks are in-use as the standard clocks which generate the standard second and which are in-use by the USNO (United States Naval Observatory), the US NIST (US National Institute of Standards and Technology) and and the BIPM (Bureau Internationale des Poids et Mesures) and for the US GPS (United States Global Positioning Satellite) navigation system (which uses a master clock which is synched to the USNO standard clocks). Thus, radio clocks are realities.

The operation of a radio clock depends on the stability of the reference body upon which the radio clock is located/positioned. So long as a radio clock's reference body is not accelerated or decelerated and thus its inertial state is unchanged and therefore the reference body and the radio clock is stable, then the radio clock will continue to function as designed. So long as the Earth is stable inre its rotation about its axis and its orbit about the Sun and the Sun's orbit about anything else in the universe, then a radio clock on the Earth's surface will continue to measure absolute time, a-time.

Inertial Clocks

In the inertial clock design, accelerometers detect changes of the state of motion (inertial state) of the body of reference (the body of reference being either the a-clock or the Entity upon which the a-clock is at-rest) and computers adjust the inertial a-clocks' timerates.timepoints, timelines, and timecounts.

Inertial a-clocks are in-use by the US Military for inertial navigation systems for aircraft, ships, and submarines; in the US Military, an onboard inertial navigation system is called the INS.

The operation of an inertial clock is independent of the state of motion (inertial state) and/or stability of its reference body upon which the inertial clock is located/positioned. Inherent in the design of an inertial clock is the independence of the clock from the state of motion of any reference body upon which it is located/positioned. Accelerations and/or decelerations of an inertial clock's reference frame will be automatically detected by the inertial clock's accelerometers and the clock's computer will automatically adjust the clock's timerate to maintain the clock's pre-set/original timerate and timepoints, timeline, and timecount.

Simultaneities, Timepoints, and Time-Stamps

If we could use a-clocks to measure a-time and time-stamp photos or videos of events taken by cameras linked and synched to the a-clocks, then identical time-stamps of photos or videos of events would be the physical evidence that would be the proof that could be used to determine the simultaneities of events.

If we were to use camera and a-clock combinations to photograph or videorecord and time-stamp Events A & B (or/and Events A' & B') inre Fig. 1, then the timestamps would determine the simultaneity of Events A & B (or Events A' & B') without, or regardless of, judgments from M or M'. These time-stamped proofs would be independent of the observations, measurements, and judgments of observers inre different reference frames/bodies. These time-stamped proofs would prove that Events A & B (and Events A' & B') occurred simultaneously—at the same a-clock timepoint.

These time-stamped photos/videos would destroy the relativity of siimultaneity. No one would care what M or M' detected, judged or concluded from K or K' inre the light motions of Fig. 1.

The Moving Observer Illusion (MOI)

In Paragraph 2 inre Fig. 1 of Chapter IX of Relativity, Einstein stated that Events A & B occurred simultaneously inre both the Embankment and the Train. He needed Events A & B to occur simultaneously inre both the Embankment and the Train for the phenomena wherein (A) M is struck simultaneously—at the same timepoint—by Lightrays A & B and (B) M' is struck non-simultaneously—at different timepoints—by Lightrays A' & B' from Events A' & B'.

Einstein also needed the length A-B inre the Embankment to be the same physical length as length A'-B' inre the Train.

Clarification: If (P) identical a-clocks are used for the definition of time and the temporal measurement inre both the Embankment and the Train, then, because their time-intervals—their units of temporal measurement—will be identical, (Q) the timerates, timepoints, timelines, and timecounts of all identical a-clocks will be identical and therefore simultaneity, two or more events occurring at the same timepoint, can be defined and determined by the use of the identical a-clock timepoints and timeline.

Timepoint T1 inre the Embankment is identical to timepoint T1 inre the Train.

Thus, when (P) Events A & B occur at timepoint T1 inre the Embankment, then (Q) Events A & B also occur at timepoint T1 inre the Train. Thus, Events A & B are simultaneous—Events A & B occur simultaneously—inre both the Embankment and the Train.

If (P1) M' reports that because (P2) Lightrays A' & B' did not strike him at the same timepoint then (Q2) Events A & B did not occur simultaneously, then (Q1) is reporting a false claim—an illusion—because of the fact that Events A & B occurred simultanesouly—at the same timepoint—inre both the Embankment and the Train.

This illusion occurs because M' is moving inre Lightrays A' & B'. In Paragraph 3 of Chapter IX of Relativity, Einstein is specific inre the motions of Lightrays A' & B' inre M': M' is moving towards Lightray B' and away from Lightray A'.

This fact means there is an RV difference inre the motion of Lightray A' inre M' and the motion of Lightray B' inre M'.

This RV difference can only be described by RV = MV1 ± MV2.

This illusion can be called the moving observer illusion (MOI). The MOI is apparent when lightrays have different directions of motion inre an observer and are therefore moving at different RVs inre the observer.

Summary: The Einstein Light Motion Paradox

Inre Einstein's Fig. 1 drawing from Chapter IX of Relativity, 1961 edition, there are two mutually exclusive possibilities:

Either ...

... (A) Light travels at ...

RV = MV1 ± MV2

... inre observers and objects who/which are in-motion at an AV > 0.00c or otherwise are at-rest at an AV = 0.00c and therefore the causal and coincidental relationships inre light motion, M, the Embankment, M' and the Train are as Einstein himelf described in Chapter IX and as summarized in Sequence 1, ...

Sequence 1

1. Lightning strikes A & B; Events A & B occur simultaneously inre distance A-B inre both the Embankment & the Train;
2. Lightray B' from Event B' strikes M' (M' reports detecting light from Event B');
3. Lightrays A & B from Events A and B strike M (M reports detecting light from Events A and B and his judgment that Events A & B occurred simultaneously);
4. Lightray A' from Event A' strikes M' (M' reports detecting light from Event A' and his judgment that Events A' & B' occurred non-simultaneously).

... and in Sequence 1b, ...

Sequence 1b

1. T1: Lightning strikes A & B; Events A & B occur simultaneously inre distance A-B inre BOTH the Embankment & the Train;
2. T2: Lightray B' from Event B' strikes M' (M' reports detecting light from Event B');
3. T3: Lightrays A & B from Events A and B strike M (M reports detecting light from Events A and B and his judgment that Events A & B occurred simultaneously);
4. T4: Lightray A' from Event A' strikes M' (M' reports detecting light from Event A' and his judgment that Events A' & B' occurred non-simultaneously).

... and in Sequence 1c ...

Sequence 1c

Einstein RR 1c.0.jpg @ T1
1. T1: Events A & B Occur Simultaneously inre the Embankment and the Train.

Einstein RR 1c.5.jpg @ T2
2. T2: Lightray B' from Event B Strikes M'.

Einstein RR 1c.7.jpg @ T3
3. T3: Lightrays A & B from Events A & B Strike M.

Einstein RR 1c.15.jpg @ T4
4. T4: Lightray A' from Event A Strikes M'.

... or ...

... (B) Light travels at ...

RV = (MV1 + MV2)/(1 + MV1 x MV2/c2) = 1.00c

... inre observers and objects who/which are in-motion at an AV > 0.00c or otherwise are at-rest at an AV = 0.00c and therefore the causal and coincidental relationships inre light motion, M, the Embankment, M' and the Train are as described and summarized in Sequence 2, ...

Sequence 2

1. Events A & B occur simultaneously inre the Embankment and the Train.
2. Lightrays from A & B strike M and M' simultaneously (both M & M' report detecting Lightrays from Events A & B simultaneously and their judgments that Events A & B occurred simultaneously).
NOTE: Because Lightrays from A & B struck M and M' simultaneously, there is no need for a T3 or a T4 inre Sequence 2.

... and in Sequence 2b ...

Sequence 2b.

1. T1: Events A & B occur simultaneously inre the Embankment and the Train.
2. T2: Lightrays from Events A & B Strike M and M' Simultaneously (Both M & M' report detecting Lightrays from Events A & B simultaneously and their judgments that Events A & B occurred simultaneously).
NOTE: Because Lightrays from A & B struck M and M' simultaneously, there is no need for a T3 or a T4 inre Sequence 2b.

... and in Sequence 2c ...

Sequence 2c

Einstein RR 2c.0.jpg @ T1
1. T1: Events A & B Occur Simultaneously Inre The Embankment And The Train.

Einstein RR 2c.7.jpg @ T3
2. T2: Lightrays from A & B Strike M and M' Simultaneously.

Light cannot travel at both ...

(A) RV = MV1 ± MV2 ≠ 1.00c

... and ...

(B) RV = (MV1 + MV2)/(1 + MV1 x MV2/c2).

The Einstein Light Motion Paradox: Einstein claimed inre Fig. 1 of Chapter IX of Relativity that light can travel at (A) RV = MV1 ± MV2 and he also claimed in Chapter XIII of Relativity that light can travel at (B) RV = (MV1 + MV2)/(1 + MV1 x MV2/c2).