Considering Relative Simultaneity  Relying on clocks instead of observersby ryancomplete Tags: clocks, observers, relative, relying, simultaneity 

#1
Jul2307, 10:05 PM

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Einstein’s traincarriage example:
A traincarriage is moving at a constant velocity v relative to the ground. An observer is stationed on the ground perpendicular to the midpoint of the train at time x relative to the ground’s frame of reference. At this time, lightning strikes the front and back of the traincarriage which reflects and reaches the ground observer at the same time. The ground observer therefore concludes that the lightning struck the front and back of the train at the same time. But, for an observer who is stationed on the train at the midpoint of the traincarriage, the light from the front lightning strike will reach him/her before the back lightning strike and thus he/she will conclude that the front of the train carriage must have been struck first. And therefore, based on their respective observations, simultaneity is relative. But what if clocks were used instead of observers in order to detect simultaneity? For example: Two clocks that are stationary with respect to the ground’s frame of reference, clock gr1 and gr2, are synchronous, and two clocks that are stationary with respect to the traincarriage’s frame of reference, clock tc1 and tc2, are synchronous. Clock tc1 is at the very back of the traincarriage and clock tc2 is at the very front of the train carriage. Each clock is light sensitive and will immediately stop ticking the moment light reaches it. At a specific time with regard to the ground’s frame of reference, clock tc1 is at the exact position as clock gr1 and clock tc2 is at the same position as clock gr2. At this specific time with regard to the ground’s frame of reference, lightning strikes the back clocks, gr1 and tc1, and the front clocks, gr2 and tc2. As a result, clocks gr1 and gr2 stop ticking and each record the time to be x. The clocks tc1 and tc2 also stop ticking and both these clocks record the time to be y. Now the fact that the back and front clocks, tc1 and tc2, have recorded the same time would surely demonstrate simultaneity regardless of the differences in the times that the light from the front and back strikes took to reach the observer on the traincarriage. 



#2
Jul2307, 10:18 PM

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#3
Jul2307, 10:25 PM

P: 137

wait, im lost, why are you assuming that tc1 and tc2 will record the same time... the principle of simultaneity says that tc2 should stop before tc1




#4
Jul2307, 11:13 PM

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Considering Relative Simultaneity  Relying on clocks instead of observers 



#5
Jul2307, 11:54 PM

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Hi JesseM,
Many thanks. 



#6
Nov3007, 11:40 AM

P: 13

The same method could be used when the lightning flashes, if the robots were set at each wall facing each other and programmed to start crawling upon "seeing" a lightning flash. Wouldn't each mouse reach the midpoint after having traveled for the same amount of time? 



#7
Nov3007, 12:07 PM

P: 1,545

But from the POV of the Train Stations how fast is each ‘mouse’ moving? As we classically expect as measured in the station frame because of the speed of the train one is moving faster than ‘mouse’ speed the other slower. The whole reason Relativity was even developed; is every measurement ever made said that effect does not happen when you use light speed photons instead of the mice. Light speed c still measured the same c in the other frame even if it required E & Hz of the photons to change. Therefore, what is simultaneous in one frame is not simultaneous in the other. 



#8
Nov3007, 12:20 PM

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You're forgetting about length contraction. If in the ground frame gr1 aligns with tc1 at the same instant that gr2 aligns with tc2, then in the ground frame, the distance between gr1 and gr2 is the same as the distance between tc1 and tc2. BUT, in the ground frame, the distance between tc1 and tc2 is due to length contraction. IOW, if the relative velocity between train and ground is 0.866c and the distance between gr1 and gr2 as measured in the ground frame is 1km, that means that the distance between tc1 and tc2, in the train's frame will be 2km. Also, the in the train's frame, it is the distance between gr1 and gr2 which is contracted, and from this frame this distance is 1/2 Km. Thus, tc1 cannot be aligned wth gr1 at the same time as tc2 aligns with gr2 in the train's frame if tc1 aligns with gr1 at the same time as tc2 aligns with gr2 in the ground frame. You still end up with a difference in simultaneity. 



#9
Nov3007, 12:24 PM

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However, slow clock transport still requires one to specify a frame of reference, the one in which the robot mice move slowly. Relativity predicts that in any given frame, synchronization by light signals in that frame and synchronization by slow clock transport in that frame will be equivalent. 



#10
Nov3007, 12:44 PM

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#11
Nov3007, 01:17 PM

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#12
Nov3007, 01:30 PM

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#13
Nov3007, 02:01 PM

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Two flashes of light separated by any distance will always meet at the half way point at the same time – only makes sense. Doesn’t matter if your on the train or in train stations. BUT only if the two flashes start out at the same time! – again only makes sense right. The issue is: IF lighting strike #1 hits at time = 0.0 for both the train and the station the frame that sees the flashes meet at the halfway point in their frame is the one where strike #2 hits at that same time = 0.0 in their frame. That is only possible in one frame because the relative speed between the two frames, only one frame can have the #2 strike happen at the same time as #1 strike. Again, this makes sense since the two locations (the middle point for the train) and (the middle point for the stations) will be a different places by the time the light reaches either middle point. It was seeing that this only made sense is how SR was found in 1905. You won’t ‘get’ SR till you ‘get’ simultaneity. Focus on that. edit: Then by understanding simultaneity, knowing the speed between them and observing just one clock directly in the other frame an observer in either frame can define all their observations and predict those in the other frame. And ALL will agree with the same locations and times as observed in each frame. Neither observer will be “incorrect” 



#14
Nov3007, 02:19 PM

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#15
Nov3007, 02:41 PM

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#16
Nov3007, 03:17 PM

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#17
Dec107, 09:13 AM

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It is generally understood that "observers" use clocks to measure time and rods to measure distance, both of which are at rest wrt the observer. 


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