05-15-11, 08:28 AM #421
05-15-11, 08:29 AM #422
There is a stick on the embankment. How does the embankment observer determine what the length of the stick is, using the speed of light and the unit of measure "metre?"
05-15-11, 08:33 AM #423
05-15-11, 08:36 AM #424
Describe the exact procedure he uses to determine how many meters long the stick is.
05-15-11, 08:38 AM #425
05-15-11, 08:41 AM #426
Do you see what the train observer has done? They have defined a train-standard set of units.
A train-standard second is the duration of 9 192 631 770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of a cesium 133 atom at rest with the train.
A train-standard metre is the distance travelled along the train by light in vacuum during a time interval of 1/299 792 458 of a train-standard second.
In doing so, they implicitly recognize that the embankment-observer's interpretation of the metre and second standards are an 'embankment-standard':
An embankment-standard second is the duration of 9 192 631 770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of a cesium 133 atom at rest with the embankment.
An embankment-standard metre is the distance travelled along the embankment by light in vacuum during a time interval of 1/299 792 458 of an embankment-standard second.
These standards do not conflict - it is easy to convert from one standard to the other. All you need to know is the relative velocity.
05-15-11, 08:47 AM #427
Yes, he realizes that the train's motion affects the travel times.
But he can't detect the train's motion, so the only way to proceed is to define a new standard based on the assumption that the train is at rest.
Although it's not a 'suspicion' so much as an assumption of convenience. The speed of the train doesn't seem to make any difference to his measurements, so he might as well pretend that the speed is zero.
The same applies to the embankment.
05-15-11, 08:49 AM #428
Please think about how the embankment observer will test the synchronization of the embankment clocks, and the speed of the embankment.
05-15-11, 04:54 PM #429
Example: Say there are two cars traveling down the road, one in front of the other, traveling at the same constant velocity, with an unknown distance between them. Light takes 10/299,792,458 of a second to travel from one to the other. How much distance is between the cars?
Last edited by Motor Daddy; 05-15-11 at 05:19 PM.
05-15-11, 05:01 PM #430
Start by telling me how he syncs his clocks.
Last edited by Motor Daddy; 05-15-11 at 05:16 PM.
05-15-11, 05:05 PM #431
Tell me what the train observer knows for sure, starting with how he sync's his clocks, and then measuring the speed of light. If he can't do that he is not in a position to make any statements about his motion, let alone the embankment's motion, or the simultaneity or lack thereof of the strikes at A and B.
05-15-11, 06:28 PM #432
He needs some standard to describe what's happening on the train. He isn't able to determine the train's speed relative to the embankment, so he isn't able to use the embankment standard.
So, he has to define his own standard, which is what I described.
He would happily use the embankment standard, if he were able to somehow measure his velocity or synchronize his clocks to the embankment standard.
Can you help him?
Is there any experiment you can suggest that he can use to test if he is moving?
Is there any experiment you can suggest that he can use to test if his clocks are synchronized?
Is there any experiment you can suggest that he can use to test if his rulers are contracted?
Is there any experiment you can suggest that he can use to test if his clocks are dilated?
05-15-11, 06:33 PM #433
The measurements he makes using his train-standard units and train-standard synchronization scheme are well defined, and can easily be converted to embankment measurements once the relative velocity is known.
Can he do any better?
Suspicion was your word, now you say assumption of convenience, and pretend. Those are not measurements, Pete, they are garbage.
What more do you want?
This morning, I drove about 100km at an average of about 80km/hr... according to the assumption of convenience that the Earth is at rest.
Is that garbage?
Is it foolish to pretend that the Earth is not moving when you make measurements of motion?
Show me the numbers.
Last edited by Pete; 05-15-11 at 06:43 PM.
05-15-11, 06:40 PM #434Originally Posted by Motor Daddy
The train observer knows for sure:
- that his clocks are physically identical to embankment clocks,
- that his rulers are physically identical to embankment metre rulers,
- that moving clocks and rulers measured by embankment standard clocks and rulers are contacted and dilated by a predictable factor,
- that embankment clocks are commonly synchronized by sending light signals between clocks
- that the speed of light measured by embankment standard clocks is 299792458 m/s
Two-way light speed measurement (adaptation of post 331):
- Mirrors are placed at A' at the rear of the train, at B' the front of the train and a timer at M' in the middle of the train.
- When the timer starts, light flashes are sent from the M' clock to the mirrors.
- After 1.25 train-standard milliseconds elapse on the timer, both flashes return to M'
- The train observer calculates that the length of the train is 374740.5725 train-standard metres, and that his physical rulers are accurate train-standard metres.
Synchronization (1), post 393:
(this is a common embankment method of synchronization):
- A light flash is sent from a clock at A' to a clock at B'
- A light flash is sent from a clock at B' to a clock at A'
- If the travel times calculated from the clock readings are equal, then the clocks are synchronized.
- If not, then one clock is adjusted to make the travel times equal
For example, (again adapted from post 331):
- The train observer places a clock at each end of the train.
- A light flash is sent from A' when the clock there reads t'=0.000.
- The light flash reaches B' when the clock there reads 2.1 train-standard milliseconds
- A light flash is also sent from the B' when the clock there reads t'=0.000.
- The light flash reaches A' when the clock there reads 0.4 train-standard milliseconds
- The clock at B' is adjusted backward by (2.1 - 0.4)/2 = 0.85 train-standard milliseconds
- When the light flashes are repeated, the measured travel times are 1.25 train-ms in both directions.
- The clocks are now synchronized according to the train standard
- The measured distance between A' and B' is 374740.5725 train-standard metres.
Last edited by Pete; 05-15-11 at 06:45 PM.
05-15-11, 07:39 PM #435
Do you agree with that statement?
05-15-11, 07:45 PM #436
05-15-11, 07:47 PM #437
05-15-11, 07:48 PM #438
Again, that follows from the assumptions of the exercise.
It is indisputable that the rear lighting bolt struck when A and A' were aligned.
It is indisputable that the front lighting bolt struck when B and B' were aligned.
05-15-11, 07:49 PM #439
05-15-11, 07:52 PM #440
Why are you asking things that have been clearly stated already? Why not summarise the agreed facts in a single post?
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