### The Einstein Railroad, the Speed of Light and Simultaneity

Einstein conceived of simultaneity inre the following diagram.

M = Observer on the Embankment
M’ = Observer on the Train
v = Velocity of the Train (relative to the embankment
A = Lightning Strike on the Embankment
B = Lightning Strike on the Embankment
The Train moves left-to-right at an unspecified velocity v
Light from A and B travels at c relative to the Embankment

The original Einstein Railroad Diagram can be converted to an Adobe Freehand 8 file.

The Einstein’s Railroad Diagram Adapted can be modified to remove the rightside v-arrow, to remove the arrow next to M’, to reposition M’ (the movement of M’ will enable readers to observe the movement of the Train), to reposition the leftside v-arrow, to add the letters A and B above the Train to enable readers to observe better the movement of the Train in relation to the Lightning Strikes, to extend the length of the Embankment (to fit the movement of the Train), and to reposition the words Train and Embankment.

Ole Roemer and others observed that the speed of light in vacuo was c/186,000 mps.

De Sitter and others observed the fact that the speed of light is not affected by the motion of Lightsources; the speed of light as observed by an stationary observer is c/186,000 mps relative to Lightsources moving towards or away from the observer. [NOTE: The motion of a Lightsource affects the frequency and therefore the energy of light emitted from that Lightsource.] Light therefore has an absolute velocity (AV) of c/186,000 mps in vacuo (in subvolumes of space which are devoid of forces including gravity which could accelerate or decelerate a Lightpulse and thereby change a Lightpulse’s velocity—speed and direction—and thereby change a Lightpulse’s inertial state).

The spacepoint (point or location or position in space) at which a Lightsource emits a Lightpulse is essentially at absolute rest (AR) at an absolute velocity (AV) of 0 mps from which the measured velocity (MV), the relative velocity (RV), and the absolute velocity (AV) of light are identical at c/186,000 mps, e.g. AV = MV = RV = c/186,000 mps.

A reference frame is a set of coordinates from which observations and measurements of physical phenomena can be made, in which the laws of physics are identical, and in which objects have the same velocity and therefore are at rest at RV = 0 mps relative to each other.

### The Einstein Railroad 1.0-1.14 Diagrams

At Timepoint 0, the Train is in motion left-to-right at a relative velocity (RV) of v parallel to and relative to the Embankment and lightning has struck the Embankment’s rails at A and B.

At Timepoint 1 the Train moves left-to-right, light from A moves left-to-right while light from B moves right-to-left (see Einstein Railroad 1.1), light from A is traveling at an absolute velocity (AV) of c (AV = c) relative to the Embankment and observer M but at a relative velocity (RV) of less than c (RV < c) relative to the Train and observer M’ while light from B is traveling at an absolute velocity of c (AV = c) relative to the Embankment and observer M but at relative velocity greater than c (RV > c) relative to the Train and to observer M’.

At Timepoint 5, light from B has struck M’ but not M; M’ will report that Event B has occurred.

At Timepoint 7, light from A and B have struck M; M will report that events A and B have occurred simultaneously.

At Timepoint 14, light from A has struck M’; M’ will report that Event A has occurred after Event B.

Results: (A) Light from both A and B traveled at AV = c relative to the Embankment and M, (B) light from A traveled at RV < c light relative to the Train and M’, (C) light from B traveled at RV > c relative to the Train and M’.

Observer M will report that because light from A and B struck him/her/it at the same timepoint (Timepoint 7) then Events A and B occurred simultaneously.

Observer M’ will report that because light from B struck him/her/it at Timepoint 5 and light from A struck him/her/it at Timepoint 14 that Events A and B occurred non-simultaneously—Event B occurred before Event A.

These results depend upon a Lightpulse having an AV or AM of c relative to the spacepoint at which it was emitted and a relative velocity (RV) relative to any objects in-motion with an AV or AM > 0 mps.

These results depend upon a Lightpulse having an RV < c relative to an object which is moving at an AV > 0 mps in the same direction of motion and an RV > c relative to an object which is moving at an AV > 0 mps in the opposite direction of motion.

These results prove that the speed of light is not the same relative velocity for any and all observers in any and all reference frames.

### The Einstein Railroad 2.0-2.14 Diagrams

In another series of Einstein Railroad drawings, the positions of A, M’ and B on the Train have been marked with dotted lines (see Einstein Railroad Fig. 2.). These positions will move with the Train. The movements of the positions of A’ and B’ will not affect the motions of light from A and light from B.

At Timepoint 0 the Train is in motion at RV = v relative to the Embankment and lightning has struck the Embankment’s rails at A and B (see Einstein Railroad 2.0).

At Timepoint 1 the Train moves left-to-right, light from A moves left-to-right while light from B moves right-to-left (see Einstein Railroad 2.1), light from A is traveling at an absolute velocity (AV) of c (AV = c) relative to the Embankment and observer M but at a relative velocity (RV) of less than c (RV < c) relative to the Train and observer M’ while light from B is traveling at an absolute velocity of c (AV = c) relative to the Embankment and observer M but at a relative velocity greater than c (RV > c) relative to the Train and observer M’

At Timepoint 5, light from A has struck M’ but not M; M’ will report Event B has occurred.

At Timepoint 7, light from A and B have struck M; M will report that Events A and B have occurred simultaneously.

At Timepoint 14, light from A has struck M’; M’ will report that Event A has occurred after Event B.

Results: (A) light from both A and B traveled at AV = c relative to the Embankment and M, (B) light from A traveled at RV < c light relative to the Train and M’, (C) light from B traveled at RV > c relative to the Train and M’ and (D) the positions of A and B on the Train have not changed relative to the Train (their distances relative to each other and to M’ have not changed).

If A and B had been Lightsources in motion, then the positions relative to the Embankment and the Train would not have caused any changes in the absolute velocity nor the relative velocities of light emitted from A or B.

The fact that light from A travels at AV = c relative to the Embankment and M but travels at RV < c relative to the Train and M’ and light from B travels at AV = c relative to the Embankment and M but travels at RV > c relative to the Train and M’ proves that the velocity of light is not c for any and all observers in any and all reference frames.

There is an absolute velocity (AV) or absolute motion (AM) of light relative to the positions of the sources of light because observations by de Sitter and others have proven that the motion of a light source does not affect the AV or AM of light emitted from a light source.

Simultaneity as defined by Einstein and illustrated in these diagrams requires an observer to be located equidistant between two (or more) events so if the light from the events strike him/her/it at the same timepoint then the events are simultaneous.

In the Einstein Railroad 2.0-2.14 drawings, the light from events A and B strike M at the same timepoint and therefore M declares the events are simultaneous but the light from A and B do not strike M’ at the same timepoint—in fact, they strike M’ at different timepoints, therefore M’ declares the events to be non-simultaneous.

The modern definition of simultaneity is two or more events occurring at the same timepoint as measured by identical clocks.

Einstein’s conception and definition of simultaneity as illustrated in these diagrams is therefore out-of-date.

The drawings depend entirely on the idea that the motion of light in vacuo is an AV or AM inre a source but otherwise the motion of light is an RV relative to an observer who is in motion at an AV > 0 mps.

### The Einstein Railroad 3.0-3.7 Diagrams

In another series of Einstein Railroad drawings, the positions of A’, M’ and B’ on the Train have been marked with dotted lines (see Einstein Railroad Fig. 3.). The symbols A and B represent lightning strikes on the Embankment; the symbols A’ and B’ represent lightwaves emitted from lightsources A’ and B’ on the train which were emitted when the lightning strikes A and B also struck the Train. The positions of A’ and B’will move with the Train. The movements of the positions of A’ and B’ will not affect the motions of light from A and light from B. Light from A’ and B’ move at AV = c relative to the lightsources A’ and B’ in denial of the results of the observations by de Sitter and others that the motions of lightsources do not affect the motions of lightwaves emitted from those lightsources.

At Timepoint 7, Lightwaves A and B have struck M simultaneously while, also simultaneously, Lightwaves A’ and B’ have struck M’ simultaneously.

If the postulate of relativity that the speed of light is the same for all observers is true, then, as shown in Einstein Railroad 3.7—Timepoint 7, light emitted from lightsources which are equidistant from observers should always strike the observers simultaneously.

Einstein stated that simultaneity is relative to the motions of observers, and illustrations of this claim are presented in the Einstein Railroad Diagrams 1.0-1.14 and 2.0-2.14 wherein light from B strikes M’ first, then light from A and B strike M simultaneously, and finally light from A strikes M’, and whereas M reports the lightning strikes are simultaneous M’ reports the lightning strikes A and B are sequential and therefore are not simultaneous; but this specification of simultaneity requires light to be traveling at AV = c relative to the Embankment and at RV ≠ c relative to the Train.

If light always moves at AV = c in each and every and any and all reference frames, then the speed of light is c relative to lightsources and therefore the motions of lightsources affect the motions of light.

### Summary: The Einstein Railroad 2.0-2.14 and 3.0-3.7 Diagrams

From this at T0 ...

... at T7 there is either this ...

... or this ...

... but not both.

Q: Why not both?
A: Because either a lightpulse travels at AV = c or 186,000 mps relative to the spacepoint at which it was emitted from a lightsource (as shown by Einstein Railroad 2.7—T7 but also as shown by the Orbiting Stars Diagrams) or it travels at AV= c or 186,000 mps relative to the lightsource from which it was emitted regardless of the spacepoint at which it was emitted (as shown by Einstein Railroad 3.7—T7).

The Orbiting Stars Diagrams (http://www.bobkwebsite.com/orbitingstars.html) reveal that (1) the motion of a lightsource does NOT affect the motion of light emitted from the lightsource and therefore (2) the motion of light is an AV = c or 186,000 mps relative to the spacepoint at which light was emitted.

These twin facts (observations/measurements) inre the motion of light (twin light motion facts—TLMFs)—that (1) the motion of a lightsource does NOT affect the motion of light and (2) light travels at an AV = c or 186,000 mps relative to the spacepoint at which it was emitted—are fundamental to the objective truth inre the motion of light.

The twin light motion facts cannot be refuted. If there should be experiments which appear to refute the twin light motion facts then that experiment is automatically invalid—thus the appearance of experimental results which are the refutation of the twin light motion facts is a sign/symptom of a problem with an experiment and therefore reason to reject its results.

### The Einstein Railroad 4.0-4.7 Diagrams

In another series of Einstein Railroad Diagrams—The Einstein Railroad Series 4.0-4.8 Diagrams, Lightpulses will be emitted simultaneously from Light Source LS1 and will be detected by Light Detectors LD1 and LD2 and Lightpulses will be emitted simultaneously from Light Source LS2 and will be detected by Light Detectors LD3 and LD4. The positions of LD1, LS1 and LD2 on the Embankment have been marked with solid lines; the positions of LD3, LS2 and LD4 on the Train have been marked with dotted lines (see Einstein Railroad Fig. 4).

At Timepoint 0, the Train will be in-motion left-to-right at AV > 0 mps while the Embankment is at-rest at AV = 0 mps at AR in the ARRF and Lightpulses from LS1 and LS2 will be emitted simultaneously.

The Lightpulses from LS1 are labeled LS1A (which travels right-to-left from LS1 towards LD1 at c relative to the Embankment—AV = c inre the Embankment) and LS1B (which travels left-to-right from LS1 towards LD2 at c relative to the Embankment—AV = c inre the Embankment); the Lightpulses from LS2 are labeled LS2A (which travels right-to-left from LS2 towards LD2 at c relative to the Train—AV = c inre the Train) and LS2B (which travels left-to-right from LS1 towards LD4 at c relative to the Train—AV = c inre the Train).

In accord with one of the mantras of special relativity wherein the speed of light is the same (the speed of light is AV = c) for each and every and any and all observers inre each and every and any and all reference frames/bodies, the Lightpulses will move outward/away from their Lightsources but their Lightsources will remain in their centers.

LS1, LD1 and LD2 will remain at-rest on the Embankment; LS2, LD3 and LD4 will move with the Train. The distances between LD3, LS2 and LD4 will not change because they were marked out specifically to be identical to the distances between LD1, LS1 and LD2 at Timepoint 0 while the Train was moving left-to-right at AV < 0 mps.

As the Train moves left-to-right at AV < 0 mps, the Lightpulses LS2A and LS2B from LS2 travel at c or 186,000 mps (AV = c) relative to the Train while the Lightpulses LS1A and LS1B from LS1 move at c or 186,000 mps (AV = c) relative to the Embankment (see Einstein Railroad 4.1).

At Timepoint 0, Lightpulses from LS1 and LS2 are emitted simultaneously.

At Timepoint 1, the Lightpulses from LS1 and LS2 begin their movements towards the Light Detectors.

At Timepoint 8, the Lightpulses simultaneously strike and are thereby detected by their Light Detectors: LS1A strikes LD1 at the same timepoint as when LS1B strikes LD2 and LS2A strikes LD3 as the same timepoint as when LS2B strikes LD4.

In the Einstein Railroad Series 4.0-4.8 Diagrams, the Embankment is either at-rest/not-in-motion at AV = 0 mps at AR in the ARRF or it is in-motion/not-at-rest at AV > 0 mps, but, either way, the Train is moving in the same direction and therefore observers can determine that the Train is moving at an RV relative to the Embankment and therefore the Train is in-motion faster than the Embankment.

If the special relativity (SR) mantra that the speed of light is the same for all observers is true, then the Lightpulses from LS1 and LS2 should strike their respective Light Detectors simultaneously.

In reality, instead of the set of conditions described/illustrated in the Einstein Railroad Diagrams 4.0-4.7, observers actually observe the set of conditions illustrated in the Einstein Railroad Diagrams 1.0-1.15 and 2.0-2.15, which are necessary to demonstrate the non-simultaneity of events because Lightpulses from Events A and B strike observer M’ on the Train at multiple timepoints which are different from the single timepoint at which Lightpulses from Events A and B strike observer M on the Embankment. This is the set of conditions Einstein intended to illustrate in his railroad diagram.

This set of conditions in the Einstein Railroad Diagrams 1.0-1.15 and 2.0-2.15 requires Lightpulses to be traveling in vacuo (in subvolumes of space which are devoid of m/e and therefore are devoid of forces including gravitational forces which could alter their motions) at AV = c or 186,000 mps relative to the spacepoints at which they were emitted from their Lightsources.

This requirement requires Lightpulses to be traveling either at AV = c or 186,000 mps relative to the Embankment if the Embankment has an AV = 0 mps at AR in the ARRF or otherwise at an RV < c relative to the Embankment if the Embankment has an AV > 0 mps and at an RV ± c relative to the Train.

If Lightpulses are traveling at an RV < c relative to either the Embankment or the Train, then the Lightpulses cannot be and therefore are not traveling at AV = c relative to the Embankment and the Train, which contradicts the SR mantra that the speed of light is the same, e.g. AV = c, for all observers, and it contradicts the Result B of the Michelson-Morley and Fizeau Interferometer Experiments which says that because there are no detected changes of interference patterns regardless of the orientation or velocity of an interferometer then the speed of light is the same in all directions and therefore the speed of light is the same for all observers.

Therefore, the Result B of the MM/F Interferometer Experiments is false: the speed of light is not AV = c for all observers inre all reference frames/bodies.

### The Einstein Railroad 5.0-5.7 Diagrams

If the special relativity (SR) mantra that the speed of light is the same for all observers in all reference frames (light AV = c for all observers), and if Lightpulses move outward from their Lightsources while their Lightsources remain at their centers, then Lightpulses emitted from Lightsources which are equidistant from Light Detectors should strike the Light Detectors simultaneously regardless of the motions of the Lightsources and their reference frames/bodies.

This set of conditions would require Lightpulses to have an AV = c or 186,000 mps relative to their Lightsources and their reference frames/bodies; this set of conditions, however, would require that there would be an RV between the Lightsources, Light Detectors and Lightpulses of one reference frame/body and the Lightsources, Light Detectors and Lightpulses of another reference frame/body, and that RV would require the forward edge of the Lightpulse from the faster Lightsource traveling in the same direction of motion as the reference frames/bodies to travel ahead of and therefore faster than the forward edge of the Lightpulse from the slower Lightsource.

For clarity, in the Einstein Railroad 5.0-5.7 Diagrams LD1 and LD3 have been removed and the Lightpulses LS1A and LS1A are not shown. LS2 and LD4 are co-located on the Train while LS1 and LD2 are co-located on the Embankment; the distance between LS1 and LD2 is the same as the distance between LS2 and LD4. Lightpulse LS1B will be emitted from LS1 at the same timepoint as LS2B is emitted from LS2; LS1B will travel at c or 186,000 mps relative to the Embankment (LS1B AV = c inre the Embankment) while LS2B will travel at c or 186,000 mps relative to the Train (LS2B AV = c inre the Train). The Train is moving at .86c or 159,960 mps relative to the Embankment therefore there will be an RV = 26,040 mps between the Train and the Embankment which will also be the RV = 26,040 mps between LS1 and LS2 and between LD2 and LD4. If LS1B and LS2B travel at c or 186,000 mps relative to their Lightsources, then there has to be and therefore is an RV = 26,040 mps between LS1B and LS2B.

At Einstein Railroad 5.0-T0 (Timepoint 0), Lightpulse LS1B is emitted from LS1 and Lightpulse LS1B is emitted from LS2 (LS1B and LS2B are emitted simultaneously).

### The Einstein Railroad 6.0-6.14 Diagrams

If the motion of a lightsource does NOT affect (add to or subtract from) the velocity of a lightpulse emitted from the lightsource and if the speed of light is c relative to the spacepoint at which a lightpulse is emitted (light AV = c inre a light emission spacepoint) and if there is an RV between two objects or reference bodies/frames, then there will be an RV inre the motion of a lightpulse relative to the RV between the slower and the faster moving objects or reference bodies/frames.

In the Einstein Railroad 6.0-6.14 Diagrams, the Train travels at .86c or 159,960 relative to the Embankment. LS2 and LD4 are co-located on the Train while LS1 and LD2 are co-located on the Embankment; the distance between LS1 and LD2 is the same as the distance between LS2 and LD4. Lightpulse LS1B is emitted from LS1 towards LD2 simultaneously with the emission of Lightpulse LS2B from LS2 towards LD4; the motion of the Train and therefore the motion of LS2 does not affect the motion of Lightpulse LS1B; LS2B travels at c relative to the spacepoint at which it was emitted from LS2 (LS2B travels at AV = c inre its emission spacepoint); LS1B travels at c relative to the spacepoint at which it was emitted from LS1 (LS1B travels at AV = c inre its emission spacepoint). The forward edge of Lightpulse LS1B travels the same distance in the same time as the forward edge of Lightpulse LS2B; therefore the forward edges of Lightpulses LS1B and LS2B keep pace with each other—neither moves ahead of or behind the other. The motions of Lightpulses LS1B and LS2B are therefore AV = c or 186,000 mps relative to both their emission spacepoints and the Embankment. The motions of Lightpulses LS1B and LS2B are RV = 26,040 mps relative to the Train.

At T7, LS1B has struck LD2 while LS2B is still chasing LD4; this observation/measurement/fact proves that there is an RV of 26,040 mps between LS2B and the Train.

At T14, LS2B has struck LD4 while LS1B is running past LD2; this observation/measurement/fact also proves that there is an RV of 26,040 mps between LS2B and the Train.

### Summary: The Einstein Railroad 5.0-5.7 and 6.0-6.7 Diagrams

From this at T0 ...

... at T7 there is either this ...

... or this ...