The Relativity of Simultaneity

[Pete]

You don't seem to understand, Pete.

For instance, there is a stick on the train. How does he determine what the length of the stick is, using the speed of light and the unit of measure "meter?"

He uses his clocks to time how long light takes to travel from one end to the other, of course.

[Pete]

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?"

[Pete]

You don't seem to understand, Pete.

For instance, there is a stick on the train. How does he determine what the length of the stick is, using the speed of light and the unit of measure "meter?"

For example, a flash of light going through the train takes 1.25ms according to train-standard clocks.
So the train-standard length of the train is 374740.5725 metres.

[Motor Daddy]

He uses his clocks to time how long light takes to travel from one end to the other, of course.

Does he realize that if the stick was in motion it would affect the time it takes light to travel the length of the stick, or does he just base his measurements on his suspicion that it isn't in motion?

Describe the exact procedure he uses to determine how many meters long the stick is.

[Motor Daddy]

For example, a flash of light going through the train takes 1.25ms according to train-standard clocks.
So the train-standard length of the train is 374740.5725 metres.

Again, he is assuming the train to have a zero velocity, which he hasn't proven to be true, so his measurements are all based on his suspicion that the train is at rest.

[Pete]

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.

[Pete]

Does he realize that if the stick was in motion it would affect the time it takes light to travel the length of the stick, or does he just base his measurements on his suspicion that it isn't in motion?

Describe the exact procedure he uses to determine how many meters long the stick is.

I believe that's been covered in the thread.
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.

Again, he is assuming the train to have a zero velocity, which he hasn't proven to be true, so his measurements are all based on his suspicion that the train is at rest.

Correct.
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.

[Pete]

Goodnight.

Please think about how the embankment observer will test the synchronization of the embankment clocks, and the speed of the embankment.

[Motor Daddy]

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.

You are mistaking, Pete. Where in the definition of a meter does it say the distance light travels is relative to the train? A meter is inseparable from the distance light travels in a vacuum in 1/299,792,458 of a second. In other words, if light travels for 2/299,792,458 of a second, light traveled 2 meters in space, but that says nothing of the length between co-moving clocks that are traveling in the same direction.

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?

In doing so, they implicitly recognize that the embankment-observer's interpretation of the metre and second standards are an 'embankment-standard':

Wrong, the embankment has an absolute zero velocity, it's not even debatable and I will explain why when you rest your case for the train observer.

[Motor Daddy]

I believe that's been covered in the thread.
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.

He never sync'd his clocks so he knows nothing other than it takes 1.25 ticks to travel each way between asynchronous clocks. The train observer did NOT measure ANYTHING yet!

Correct.
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.

Suspicion was your word, now you say assumption of convenience, and pretend. Those are not measurements, Pete, they are garbage. You can 't base your measurements on garbage and "pretend" they are accurate. It doesn't work that way.

Start by telling me how he syncs his clocks.

[Motor Daddy]

Goodnight.

Please think about how the embankment observer will test the synchronization of the embankment clocks, and the speed of the embankment.

I already know the embankment is at an absolute zero velocity and I can prove it. I don't need to pretend, or assume, or suspect that it is, I KNOW it is and I can prove it.

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.

[Pete]

You are mistaking, Pete. Where in the definition of a meter does it say the distance light travels is relative to the train?

This is a new standard the train observer has derived, MD, because he doesn't have access to the embankment standard.

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?

[Pete]

He never sync'd his clocks so he knows nothing other than it takes 1.25 ticks to travel each way between asynchronous clocks. The train observer did NOT measure ANYTHING yet!

He has set up his clocks in a reproduceable way.
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.

They're well defined, reproducable, internally consistent, and can be reliable converted to whatever system you prefer.
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?

I already know the embankment is at an absolute zero velocity and I can prove it. I don't need to pretend, or assume, or suspect that it is, I KNOW it is and I can prove it.

So do it.
Show me the numbers.

[Pete]

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.

Background:
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:

Two clocks are synchronized at the back of the train.
One of the clocks is slowly moved to the front of the train.

Synchronization (2), and one-way speed of light measurement
(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.

[Motor Daddy]

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?

From a purely reality standpoint, irrelevant to what the embankment observer thinks or the train observer thinks, the A and B points on the train were at one point in time aligned with the A and B points on the embankment, simultaneously. There is no duration evolved in that statement, it is timeless, there is no motion evolved. It is a fact that A and B on the train were aligned with A and B on the embankment, simultaneously.

Do you agree with that statement?

[Pete]

From a purely reality standpoint, irrelevant to what the embankment observer thinks or the train observer thinks, the A and B points on the train were at one point in time aligned with the A and B points on the embankment, simultaneously. There is no duration evolved in that statement, it is timeless, there is no motion evolved. It is a fact that A and B on the train were aligned with A and B on the embankment, simultaneously.

Do you agree with that statement?

Yes, that follows from the assumptions of this exercise.

[Motor Daddy]

Yes, that follows from the assumptions of this exercise.

Good, I also agree.

Do you also agree that the lightening struck A and B when the points were aligned?

[Pete]

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.

[Motor Daddy]

Again, that follows from the assumptions of the exercise.

Good, I agree.

Do you agree that the embankment observer was hit by both lights at the same time?

[Pete]

Yes.

Why are you asking things that have been clearly stated already? Why not summarise the agreed facts in a single post?