The  Einstein Railway System and the Speed of Light and the Determinination of Simultaneity

Robert Howard Kroepel
Copyright © 2007

The Original Einstein Railway Drawing in Relativity on Page 25

 Einstein Railway Diagram

This reasonable adaptation of the Einstein Railway Drawing is to be used for comments inre the speed of light and simultaneity.

Einstein Railway 1
(Side View)

Einstein Railway 1 

For clarity, M = M1 and M' = M2.

In the Einstein Railway 1 diagram, the Railway Carriage is not moving relative to the Railway Embankment.

The possibility and probability is that the Railway Embankment and the Railway Carriage while at rest relative to each other may in fact be in motion relative to some other physical phenomena.

The most logical physical phenomena to which the Embankment and the Carriage would be in relative motion would be the speed of light, which is c or 186,000 in vacuo, in the absence of other physical phenomena which could alter the speed or/and the direction of a lightray or a lightwave or a lightsphere.

There is no illogic in concluding (1) that there is an absolute velocity (AV) which is the speed of light, c, at 186,000 mps, in vacuo, (2) that when a lightray "goes past" the center of mass (CoM) of any object at c/186,000 mps then the object is—objectively—at AV = 0 mps and therefore at absolute rest (AR) in the absolute rest reference frame (ARRF), and (3) when an object is motion—when an object has been accelerated from AR, then the object's AV = > 0 mps < c.

This phenomenon is theoretically observable only by a Perfect Observer who/which is "independent of the state of motion of [its] body of reference" (his/her/its rate of perception never varies with accelerations and decelerations) and who/which therefore measures space-distances with identical invariable space-intervals on the Perfect Ruler and time-durations with identical invariable time-intervals in the Perfect Clock and who/which uses the Perfect Camera which creates 3-D holograms by sending out detection waves which travel instantaneously to and from all objects and events and therefore records the exact objective spatial and temporal relationships of the objects and events. The 3-D hologram record would enable the Perfect Observer to determine the position and momentum of any and all particles, atoms, molecules, etc., and thereby determine the past record, the present record, and future records of the positions and momentum and any and all particles, atoms, molecules, etc., i.e., the determinism and predictability of the universe would be 100% complete and observable to the Perfect Observer.

Perfect Observers exist only in thought experiments, yet, as theoretical concepts, they reveal the actual principles of physical phenomena and therefore physical reality.

If the Embankment and Carriage when at rest relative to each other have an AV relative to the speed of light, wherein their AV > c when moving in the direction of motion of lightrays or AV = > c when moving opposite the direction of motion of lightrays, an assumption that is not illogical can be made that for determining the simultaneity of events via the Einstein Railway System lightrays will "go past" the centers of mass of observers, embankments and carriages at rest relative to each other at c/186,000 mps.

This assumption permits considering the speed of light "going past" M1 and the embankment to be c and the relative velocity, v, between the Embankment and the Carriage, to be used for the determination of simultaneity.

The Einstein Railway System assumes that the Carriage is in motion relative to the Embankment.

How did the Carriage assume a motion relative to the Embankment?

The logical answer herein, as observed when humans make railway carriages and accelerate them over embankments, is that the Carriage at one timepoint was at rest relative to the embankment and was subsequently accelerated relative to the Embankment.

This answer has to be considered to be a fact which has to be part of the knowledge bases of both M1 and M2. Both M1 and M2 know the Carriage has been accelerated. If M1 and M2 are physicists, then they would also know that when an object is accelerated or decelerated its kinetic mass-energy changes and its rate of operation therefore changes, e.g., inre clocks, the change in the clocks' kinetic mass-energy would cause a change of their time-interval, rate of ticking, and timepoints upon their timelines.

M1 and M2 would have to know that relative to the Embankment Lightrays A and B would "go past" M2's head at c when the Carriage is at rest and at either c-v or c+v when the Carriage is in motion after acceleration.

M1 and M2 would then have to realize that, objectively, Lightrays A and B could not possibly "go past" M2's head at c and that any perception, observation or measurement M2 would have of Lightrays A and B "going past" him/her at c would have to be an illusion and not a reality.

M1 and M2 are the same height.

M1 and M2 are equidistant from the front and the back of the Carriage.

M1 and M2 are perpendicular to each other.

M1 is standing upon a railway station platform at the same height above the railway embankment as height of the floor of the railway carriage: M1 and M2 are perpendicular to each other and at the same height above the railway embankment.

Lightsources are located at each end of the railway carriage: the Lightsources are at the same height—the height of the heads of M1 and M2—above the railway carriage's floor and the railway station's platform. Lightrays emitted from the Lightsources would strike the heads of M1 and M2.

The Lightsources are offset from the railway carriage's midline.

Einstein Railway 1A
(Overhead View)

Einstein Railway 1A

M1 is offset from the Lightsources' offset line the same distance as M2 is offset from the Lightsources' offset line: M1 -> Lightsources' Offset Line = M2 -> Lightsources' Offset Line.

If the railway carriage were not moving and a Lightsource was triggered from the spacepoint on the Lightsources' offset line at which M1 and M2 are perpendicular to each other, the Lightsphere emitted (represented by the circle in the diagram) would strike M1 and M2 simultaneously (at the same timepoint).

Einstein Railway 2
(Side View)

Einstein Railway 2 
If Lightrays A and C were emitted from a Lightsource at the back of the Carriage simultaneously with Lightrays B and D emitted from a Lightsource at the front of the Carriage, then, considering the length or distance traveled, Lightray A = Lightray B = Lightray C = Lightray D.

Einstein Railway 2A
(Overhead View)

Einstein Railway 2A

All Lightrays are emitted as spherical waves which can be represented as circles in the diagrams: the Lightrays would therefore be emitted from the centers of their Lightspheres, and because all Lightrays are emitted simultaneously then all Lightsphere radii would be equal, therefore the distances traveled by all Lightrays would be identical.

When the Carriage is at rest/not in motion relative to the Embankment, and when assuming that their AV = 0 mps, then Lightrays A and B would therefore go past M2's center of mass (CoM) at c/186,000 mps, and past M1's CoM at c/186,000 mps.

Timepoint T0

Einstein Railway 3
(Side View)

  Einstein Railway 3

Einstein Railway 3A
(Overhead View)

Einstein Railway 3A

In the Einstein Railway 3 and 3A diagrams, at Timepoint T0, the Carriage is moving with velocity v over the Embankment and past M1, M2 is therefore moving with velocity v, M1 and M2 are perpendicular to each other; Lightrays A, B, C, and D are emitted simultaneously from their Lightsources and therefore travel over equal distances represented by the equal radii of their Lightspheres.

The velocities of all Lightrays are independent of the motion of their Lightsources, and, therefore, all Lightrays are traveling at c.

Timepoint T1

Einstein Railway 4
(Side View)

  Einstein Railway 4

Einstein Railway 4A
(Overhead View)

Einstein Railway 4A

In the Einstein Railway Diagrams 2 and 2A, the carriage is continuing to move, and at Timepoint T1, which is of a short enough duration from T0 that the Lightrays do not go past M1 or M2,

1. Lightray A's length/distance traveled = Lightray B's length/distance traveled,
2. Lightray C's length/distance traveled = Lightray D's length/distance traveled,
3. M2 has moved a distance away from M1 and towards Lightray B,
4. Lightray B therefore strikes M2 ahead of, before, and therefore non-simultaneously inre, Lightray A,
5. M2 reports Lightrays A and B did not strike him simultaneously and concludes they were not emitted simultaneously.

The report of M2 cannot occur as stated unless M2 is moving with a velocity v relative to not only to the Embankment but also relative to the Lightrays A and B.

Lightrays A and B are theoretically moving at c = 186,000 mps. The speed of light is not affected by the motion of a lightsource; the speed of light is independent of the state of motion of the body of reference of a lightsource.

M1 perceives and thereby observes Lightray A goes past M2's center of mass (CoM) at c-v and Lightray B goes past M2's CoM at c+v.

Any report from M2 of a perception or an observation that Lightrays A and B are going past M2's CoM at c and not at c-v or c+v is therefore in reality a report of M2's illusion, M2's moving observer's illusion (MOI).

Timepoint T2

Einstein Railway 5
(Side View)

Einstein Railway 5

Einstein Railway 5A
(Overhead View)

Einstein Railway 5A

At Timepoint T2, Lightrays C and D strike M1; M1 reports Lightrays C and D have struck him simultaneously (at the same timepoint, Timepoint 2).

M1 observes Lightrays C and D continue to go past his CoM at c and Lightray A goes past M2's CoM at c-v while Lightray B goes past M2's CoM at c+v.

For simultaneity, the Einstein Railway System requires (1) that events or Lightsources be equidistant from a single observer (M1) at rest relative to the events or Lightsources, (2) the events or Lightsources lie in a perfectly straight line parallel to the directions of motion of light rays—events are automatically non-simultaneous when they are not equidistant from the single observer, and (3) the lightrays from the events strike the single observer at the same instant or timepoint—events are automtically non-simultaneous when lightrays from them do not strike the single observer at the same instant or timepoint.

Imagine that there are identical synchronized clocks which have the same time-intervals which generate identical rates of ticking and identical timepoints and identical timelines and are placed near enough to the Lightsources that light-based information transmission delays were negligible; imagine that when the Lightrays were emitted simultaneously, each clock triggered a companion camera that photographed the Lightray emissions and time-stamped the photos.

Whenever the Lightrays were emitted, the timestamps would all be identical.

The current definition of simultaneity is two or more events occurring at the same timepoint.

From Wikipedia, the free encyclopedia

Simultaneity is the property of two events happening at the same time in at least one reference frame.

The Oxford Dictionary of Physics
Alan Isaacs, ed.
Oxford University Press, Fourth Edition, 2000

simultaneity The condition in which two or more events occur at the same instant.

Because the time-stamped photos could be examined by M1 or M2 at any spacepoint at any timepoint and the information inre the time-stamps would be identical for both M1 and M2, then M1 and M2 could agree that the identical time-stamps on the photos prove the photos were taken at the same timepoint and that the events which were the emissions of the Lightrays were all simultaneous.

Thus, when simultaneity is defined as two or more events occurring at the same timepoint, simultaneity is thus relevant to time and is independent of geometry or geography.

Here is an operational definition of time:

Time is the use of a duration, which is a time-interval, and which is modeled after a physical periodic or cyclic motion, as a unit of measurement of the occurrences of events, which are relationships between or among people, organisms, and/or objects comprised of matter and/or energy, or for the measurement of the duration of a single event, for predicting, coordinating, scheduling, or synchronizing events, for the determination of the simultaneity of events, or for the determination of the causality or coincidence between or among people, organisms, and/or objects.

Object = Group of particles/atoms/molecules which retains its organization and unity and identity for a longer duration than a relevant event.

Event = A causal relationship between/among people/organisms/objects.

Causality = People/Organisms/Objects/Events who/which are comprised of matter/energy and who/which are causes and who/which cause the effects which are (A) changes of inertial states in pre-existing people/organisms/objects/events or (B) new people/organisms/objects/events.

The causal sequence is (1) cause(s) -> (2) effect(s)

Note that in a causal sequence the causes do not exist as causes at the same time/at the same timepoint as the effects exist as effects; a causality is observed to occur abefore and during one timepoint after which the effects are observed.

Coincidence = The appearance at the same timepoint of people/organisms/objects/events who/which are not causally related.

Note that in a coincidence the relevent people/organisms/objects/events may appear (A) simultaneously, which is to appear at the same timepoints, (B) sequentially at contiguous timepoints, or (C) overlapping at some timepoints but not others.

People/organisms/objects/events are thus related either by being causal or coincidental.

Simultaneity = Two or more events occurring at the same timepoint on the same timeline/timemap.

Because simultaneity involves timepoints, only a time system which uses time-intervals/TIs to generate a clock's rate of ticking/RoT and therefore a set of timepoints on a timeline can be used to determine simultaneity.

The essence of time is the time-interval/TI which is the unit of measurement of time.

The TI in a clock generates the clock's rate of ticking/RoT, set of timepoints and timeline (the set of timepoints fits upon the timeline).

There are two TIs: (1) The variable time-interval/VTI which is found in variable time-interval clocks/VTICs whose rates of ticking/RoTs are variable/not constantchanged by, and not adjusted to compensate for, the inverse effects caused by accelerations/decelerations; (2) The invariable time-interval/ITI which is found in invariable time-interval clocks/ITICs whose RoTs are invariable/constant because they are adjusted to compensate for the inverse effects caused by accelerations/decelerations.

There are two types of clocks: (1) The variable time-interval clock/VTIC whose TI is a VTI because the VTIC's RoT is variable/not constant because it is not adjusted to compensate for the inverse effects caused by accelerations/decelerations; (2) the invariable time-interval clock/ITIC whose TI is an ITI because the ITIC's RoT is invariable/constant because it is adjusted to compensate for the inverse effects caused by accelerations/decelerations.

There are two types of ITICs:
(1) The motion-sensing self-adjusting invariable time-interval clock/MSSAITIC whose ITI is created by the process which by accelerometers/decelerometers sense changes of motion/velocity caused by acceleratons/decelerations and a computer adjusts the TI to make it an ITI;
(2) The master invariable time-interval clock/MITIC, which sends radio signals to control slave invariable time-interval clocks/SITICs found in different inertial reference frames/IRFs.

LT = Local Time = Time measured by local time-intervals/LTIs in local time clocks/LTCs in individual IRFs.

Events occurring within an IRF can be measured by VTIs in VTICs provided that the VTIs are identical and thereby generate identical timepoints which generate identical timelines/timemaps for each VTIC; events occurring within an IRF are not required to lie in a straight line--they can be in any positions/locations within the IRF.

AT = Absolute Time/AT = Time measured by absolute time-intervals/ATIs in absolute time clocks/ATCs in any IRFs.

Events occurring within different IRFs can be measured by ITIs in ITICs provided the ITIs are identical and thereby generate idential timepoints which generate identical timelines/timemaps for each ITIC; events occurring in different IRFs are not required to lie in a straight line--they can be in any positions/locations with the IRFs.

The Law of Inertia: An object which has an inertial state of (A) being at rest or or (B) being in uniform motion will retain its inertial state of being at rest or in uniform motion until acted upon by a force.

At Rest = Having no velocity or direction
Uniform Motion = No change of direction or velocity
Velocity = Speed + Direction

Force = A push or a pull

Corollaries to the Law of Inertia:

1. A force is the cause of a change of an inertial state.
2. The observance of a change of an inertial state implies the cause to be a force of some kind.

Inertial Reference Frame = Condition of having the same velocity

Forces which accelerate/decelerate people/organisms/objects cause those people/organisms/objects to leave one inertial reference frame and enter into a different inertial reference frame; thus, the common link between inertial reference frames is the velocity of the people/organisms/objects.

People/organisms/objects have fundamental rates of operation, functioning, vibration, frequency, metabolism, perception, ticking, etc.

These fundamental rates change inversely with accelerations and decelerations.

In each specific reference frame, a person has a specific rate of metabolism and a specific rate of perception, an organism has a specific rate of metabolism, an object has a specific rate of operation, rate of functioning, rate of vibration, frequency, and a clock has a specific rate of ticking and therefore a specific time-interval, timepoints and timeline.

Every occurrence in which a person/organism/object returns to a specific reference frame—when the person/organism/object is accelerated or decelerated to a previous speed, then the person assumes his/her previous rate of metabolism and rate of perception, the organism assumes its previous rate of metabolism, an object assumes its previous rate of operation/functioning/vibration/frequency/etc., and a clock assumes its previous rate of ticking.

If time-intervals were invariable, never varying despite accelerations or decelerations of their host clocks, then those invariable time-intervals would generate identical rates of ticking of their host clocks and identical timepoints on identical timelines and therefore would be "independent of the state of motion of [their bodies] of reference" (their host clocks) and they would measure absolute time and the identical timepoints they generated would determine the absolute simultaneity of events in different reference frames (on different bodies of reference).