I would like to introduce what I believe to be a new paradox involving relativity and twin stop clocks. The only mathematics needed to follow along is simply, “if A = B and B = C, then A = C”. The only physics required is that a photon is a singular bundle of light.
In this paradox the Relativity of Simultaneity postulate is setup between a train railcar and a train station wherein the trains sees one event to be simultaneous while the station sees a different event to be simultaneous. But in this scenario, only one of them can be true. The question is which one, if either?
Two clocks are designed identically such that if two photons simultaneously strike receptor cells attached to each clock, the clocks will stop. One, the station clock, is mounted above the tracks at a train station. The other, the train clock, is mounted such as to be in the exact center of an opened-top railcar on the train (by the train’s reference frame) when the moving railcar is centered about the station clock at 4:00-t (by the station’s reference frame).
The twin clocks are then sufficiently desynchronized so as to allow for them both to read exactly 4:00-t o’clock when the train passes the station and the clocks are transversely inline. This of course must be done considering the laws of relativity concerning the acceleration and speed of the train and the effect of that upon its clock. The alternative is merely to accomplish the simultaneity of the clock’s timing by trial an error.
But in addition to the clocks, two photon flashers are mounted on the railcar walls, one on the front and one on the rear walls. Each photon flasher also has a clock identically timed to match the centered train clock at 4:00-t.
Also each flasher is set to fire 2 photons toward the center of the railcar at exactly 4:00 o’clock minus the calculated time for a photon to travel to a centered clock (t). The objective being to have the photons stop each clock at exactly 4:00 o’clock. So with each flasher, one of its photons is aimed slightly upward toward the receptor cell of the station clock and the other slightly downward at the same angle reversed to meet the receptor cell of the train clock.
If the railcar could instantaneously stop at 4:00-t, all four photons would strike a receptor cell at exactly the same time and at exactly 4:00 o’clock. But since the train doesn’t stop, a question comes to mind as to which clocks will be stopped by the simultaneous photon strikes and at what time.
All photons involved are sourced from two equally moving flashers at 4:00-t. The front flasher releases two identical photons that have no reason to travel at different velocities from each other. The back flasher photons similarly have no reason to travel at different velocities than each other. And none of the photons have any means to know of or vary due to being inside or outside of the railcar.
It is speculated that a photon, like a radio wave, travels independently of its source and thus all four photons must travel at the exact same velocity covering the exact same distance in the same amount of time and regardless of which direction the flashers were moving or which frame of reference is used to take the measurements as long as only one is used.
Flash Timing and Positioning
In this scenario, it is not required that any clock or flasher be set to anything in particular at the beginning of the train’s run. The stipulation is merely that when the flashers are equal distance from the station clock (with regard to the station’s reference frame), they must both read 4:00-t and at that time, they are to flash.
Also it is stipulated that the train clock must be centered between the flashers at equal distance (with regard to the train’s reference frame) at the moment that the flashers flash and that all clocks read 4:00-t regardless of any prior settings, even if that means that the train clock and the station clock have to be slightly misaligned at 4:00-t.
Galilean invariance or Galilean relativity is a principle of relativity that states that the fundamental laws of physics are the same in all inertial frames and lead to Einstein’s Special and General relativity theories. What this principle means in this example is that no matter which frame of reference is used to measure the paths of the photons, on the moving train or at the station, all four photons must be measured to travel the exact same distance over the same amount of time (t).
Relativity of Simultaneity
In this setup, there is nothing happening TO the flashers. They are already set to be identical and in sync at 4:00-t. The exact same influence from within both frames is applied to both flashers throughout the scenario. Nothing comes from either frame to set them off as they have their own internal clocks, thus the relativity of simultaneity doesn't get involved and doesn't apply to the setup before the flashing.
The simultaneity of the flashes is guaranteed for both frames due to the predesigned simultaneity through whatever means is necessary to ensure they flash at exactly 4:00-t as measured by both clocks and their internal clocks. Neither flasher has impetus to flash before the other from either reference frame. Thus both reference frames would see a simultaneous flash from the two flashers as by design, there is never an opportunity for the flashers to become asynchronous or misaligned with respect to either reference frame.
If you are one of the many who have become confused regarding relativity of simultaneity and believe that the Lorentz equations demand that the flashes cannot be simultaneous in both the train frame of reference and also the station frame, consider that such has merely been a misunderstanding of how to use the Lorentz equations. Einstein remarked that due to the time it took light to travel from different sources, one person might come to believe that two events were simultaneous even though another person would see them non-simultaneous. And consider the following;
In the following pictorials, two trains are first shown traveling the distance ∆x in the time ∆t. A clock is tossed onto each train, then photo flashed ∆t time later. The image of the train’s clock faces are reflected from each clock displaying their time reading at that moment and seen by everyone regardless of their distance from the flash. Each person will see the image at a different time, but there is only one image to be seen.
In the third portion of the pictorial, the two train’s are combined into one, showing that each clock face will still show the same time to anyone.
But since there is only one image to be seen regardless of which clock face and that image is broadcast everywhere, on board the train, the same image is seen as the train's clocks readings.
So far, the flashers at the station have been used to produce the flash and thus light has traveled from the flashers to the train clocks. But the direction of the light from the light source hasn’t anything to do with the synchronicity of the clocks, so if we have the clocks flash their face image at that moment instead of the station flashers, we would get the same image.
It is clear that all, on board the train and off, will see the same image of the synchronized clocks on the train.
The flash timers mentioned in the paradox are clocks that flash at a given time setting, “4:00-t”. If they were to show their clock face as a flash, everyone would see the same image of “4:00-t” from both clocks whether on board the train or off. The train timers and clock are therefore synchronous in both frames at that one moment. The question in the paradox isn’t what will be seen or when the flashes occurred, but when they will be seen and by whom.
Summery of the Setup
To summarize the scenario setup, let me go through it again with less explanation.
A station clock is set so that at 4:00-t a railcar will be passing by. On that railcar, fore and aft, two flashers are set to go off exactly when the station clock will be reading 4:00-t and also when they are equal distance from the station clock with respect to the station clock’s reference frame. So by design, the station clock must see both flashers trigger at exactly 4:00-t.
Also aboard the train, a train clock is set to be exactly centered between the two flashers when the station clock reads 4:00-t by its own reference frame regardless of how the station reference frame might view it. The train clock is then adjusted so that it too will read exactly 4:00-t at that same moment.
Thus at 4:00-t as read by either clock, both flashers are designed to flash. Simultaneity of the flashing and centeredness of the clocks from their own reference frames are guaranteed by setup design.
Station Reference Frame
If we examine the paths of the photons from the reference frame of the station, we can see that two photons would strike the station clock simultaneously and stop that clock at exactly 4:00 o’clock. But the train clock, would be moving during the flight time of the photons and thus would no longer be centered. Thus the train clock would not stop.
Train Reference Frame
But if we examine the paths of the photons from the reference frame of the moving train, we see that the two photons aimed at the train clock will strike simultaneously and thus stop the train clock at 4:00. But the from the train’s reference, the station clock is moving in the backwards direction, thus the station clock, no longer being centered, would not stop.
When the train finally stops, each clock is examined to see if either has stopped running. This situation presents us with a paradox;
- A) One clock has stopped – The speed of light is not constant for the other observer.
B) Both clocks have stopped – The speed of light is not constant for either observer.
C) Neither clock has stopped – The speed of light is dependent on an absolute frame.
Only One Clock Stopped
Since from either reference frame, the other clock is moving out of center, the principle of relativity and consistency of the observed speed of light requires that both reference frames must insist that their own still centered clock stops and that the other doesn’t. But since only one stopped, one of the reference frames did not measure the photon travel from fore and aft flashers to be equal. That means that either the principle of relativity and the consistency of the speed of light is incorrect or the simple logic of mathematics involved is incorrect.
Both Clocks Stopped
Since the center distance from the flash was changing for both of the frames with respect to the other, only one could represent an equal distance and speed of travel for the photons. That would imply that the photons inside the train behaved differently than those outside without having influence to do so. This would say that both frames saw the photons within the other frame travel at different speeds. The speed of light is supposed to be the same for any observer.
Neither Clock Stopped
If neither clock stopped, from the perspective of both frames, light did not travel an equal distance in the same time. This directly indicates that the speed of light is NOT constant for all observers, but rather has an absolute frame of reference of its own.
If we temporarily speculate that perhaps a photon carries with it a portion of its source’s velocity, we can rebuild the scenario.
If a photon traveling from the back wall of the train were to travel a little faster because the train wall was moving, we must accept that the distance traveled by the two aft photons will be greater than those of the two forward photons over the same period of time. With this speculation in mind, we can simply reposition both clocks slightly more forward so as to align them with a simultaneous collision with their receptor cells. But in so doing, we run across the exact same paradox merely repositioned.
If for some odd reason photons carry a negative component of their source’s velocity, we could merely reposition the clocks slightly back from center so as to achieve simultaneous collision. But again, we run into that exact same paradox. Each clock must stop if examined by its own reference and not stop if examined from the other reference.
Thus we can remove the concern as to whether photons travel independent of their source, leaving us with;
If Galilean relativity is true, the speed of light is constant for any observer, and the logic of mathematics is true, then both clocks must stop and also not stop, yet each can be seen to either stop or not.
Relativity and Science are entirely embedded in the logic of mathematics. Thus if the logic of mathematics is to be dismissed, both Relativity and Science become useless, whether otherwise true or not. So that proposes that we have to accept that the speed of light is actually dependent on an absolute frame.
So we are left with no choice but to dismiss as a false or useless doctrine either the principle of Relativity and constant observed speed of light with all of its numerous consequential theories and calculations, or dismiss all of Science and the simplest mathematics. Take your pick or keep fantasizing. I choose to keep mathematics and Science and accept that indeed there really is an absolute frame of reference from which all things can be measured.
I predict that if this experiment is done in reality, neither clock will stop which will reveal that indeed light has its own absolute frame of reference. But there is a trick involved in calculating the real time dilation involved.
Einstein relativity down and out. Maxwellian aether back up for round two.
Objection 1; Simultaneity of flashing
A) Flashers will not flash in sync according to one or the other frame
B) Flashers will not flash when they are centered about P1 according to one or the other frame
Math/Logic for belief; "The flashers being in a different position on the train will experience different time dilation"
Revue the pictorials under "Relativity of Simultaneity" show above. The train railcar is already at velocity v and starts this leg of its run when centered at position P0. At that point, flashers F and B (Front and Back) are synchronized and set to flash together when the train reaches the station.
The train continues at constant velocity for an additional distance of d1 where it reaches the station. At the distance d1, the flashers are exactly centered around the station clock at P1. This process takes “tt” seconds to occur as measured by the station clock.
Train’s travel time as per station clock = “tt”
Train distance traveled per station frame = P1 – P0 = d1
Thus as measured by the station clock, at T0+tt, the flashers will be centered and equal distance from the station clock, one fore and aft.
Desiring the flashers to flash simultaneously at T0+tt station time, their internal clocks are set to flash after a time of T0+tt-tf where “tf” is any proposed time dilation component necessary to subtract due to the train being in motion. Since both flashers experience the exact same velocity together, tf is equal for both flashers. At that same moment, the train clock, being centered, is set to 4:00-t - T0 so it will read 4:00-t when the flashers flash.
Time of flash per station’s frame Tfs = T0+tt, at P1; 4:00-t
Time of flash per train’s frame Tft = T0+tt, at P1
Thus when the station clock reads T0+tt (4:00-t) the flashers will each have advanced from T0-tf to T0+tt and flash. The light traveling from the flashers becomes independent of the trains motion and both light rays from the flashers must travel the same distance, “dps”, to reach the station clock, one traveling forward with the train and one backward.
If the light is traveling at a constant speed relative to the station clock, at this point it can be seen that at T0+tt+(dps/c), as measured by the station clock, the station clock will experience simultaneous photon strikes and will stop.
But also back at P0 and T0, the train clock was positioned exactly in the center between the flashers and synchronized to them. The train clock experiences the exact same velocity as the flashers and thus at time T0+tt, when the flashers are centered around P1 and flash, the train clock will still be exactly centered between the flashes.
If the flashed light is traveling at constant velocity relative to the train clock, each ray, fore and aft, will travel the same distance, “dpt” as measured by the train.
Thus at this point it can be seen that at time T0+tt+(dpt/c) as measured by the train clock, the train clock will experience simultaneous photon strikes and stop.
Station clock stops at T0+tt+(dps/c) as measured by itself (4:00).
Train clock stops at T0+tt+(dpt/c) as measured by itself (4:00).
But since each clock and all photons can be measured by both reference frames, each reference frame can make a prediction as to whether the other clock should experience simultaneous strikes.
From the station’s perspective, all 4 photons travel the same distance, “dps”, before stopping the station clock. Thus the 2 photons aimed toward the train clock will also meet together at P1 and T0+tt+(dps/c).
The flashers flashed at T0+tt by the station clock when they were centered around the station clock and the train clock was still centered between them on the railcar at P1, as it never changed its centeredness.
Thus by the time the photons reach the station clock, T0+tt+(dps/c), the station reference purview is that the train clock had moved with the train and is no longer centered between the flash points.
Thus the station reference predicts that the train clock will not stop.
But from the train reference a similar situation must occur reversed. When the train reaches P1 (as precalculated by T0+tt+tf and P1-P0) and the clock and flashers read T0+tt at P1, the flash occurs. At T0+tt+(dpt/c), the photons meet the train clock to stop it. But by that time, P1 and the station clock are no longer centered on the railcar. If all 4 photons travel at the same relative velocity by the train’s reference, the photons aimed toward the station clock will meet at T0+tt+(dpt/c) and miss position P1 and the station clock.
Thus the train reference predicts that the station clock will not stop.