The Relativity of Simultaneity

[Motor Daddy]

So the train observer lays rulers end to end along the length of the train. How many times does he bend over to place full length rulers down on the floor, and I presume he needs to cut another piece to fill the final gap, so you are saying he bends over 11 times, correct?

[Pete]

Yes

[Motor Daddy]

Next, the train observer will measure the velocity of the train using a single clock, a light flash, and a mirror.

He puts the mirror at the front of the train and a timer in the middle of the train.
The mirror is 5 metres from the timer.
The train observer measures this distance to be 5.00000000068377 train rulers.

When the timer starts, a light flash is sent from the M' clock to the mirror.

d/(c-v) = 16.67848059041821 ns later, the light flash reflects off the mirror.
d/(c+v) = 16.67792893852027 ns later again, the light flash returns to M'.

The timer has elapsed t/gamma = 33.35640952437684 ns for the round trip.

Next, I'll present the train observer conclusions from this measurement.

So the train observer acknowledges that it takes light a different amount of time to get to the mirror than it does for it to return to his midpoint position. Does he acknowledge that in his frame, light takes a different amount of time to travel the same length of the train, depending on which way he measures it? How does he explain that?

[Motor Daddy]

Yes

IF someone where to have been watching him from outside the train, would they see him bend over 11 times?

[wellwisher]

Although we can accept the speed of light or C is constant, we don't hear any explanation for why this is so. A dogmatic assertion, without support logic, even if correct via experimentation, does not settle well with a rational mind who seeks a logical explanation more than an empirical explanation.

It would be like saying, why do we drive on one side of the road? The answer is because that is the law. But why is it the law? Because it is. This is all true, but here is a layer of irrational on top of this empirical assertion.

Don't get me wrong. I believe C is independent of reference. But why is this so is a valid question to ask.

I my opinion, there is not only the fixed C reference, but also a fixed zero reference that is the same for all references. This allows the laws of physics to be the same in all references.

If C is constant, and there was no absolute zero reference, C speed energy exchange with matter would mean going from C to a variable velocity based on reference. This would make the laws of physics dependent on reference and how C has to change. With an absolute zero reference, there is consistency in all references.

The Uncertainty Principle appears to be an artifact of transitions from C to zero reference, while occurring in finite reference. The transition max from C to 0, adds potential to any reference. This difference provides the energy needed to increase the entropy which defines uncertainty.

[Pete]

So the train observer acknowledges that it takes light a different amount of time to get to the mirror than it does for it to return to his midpoint position. Does he acknowledge that in his frame, light takes a different amount of time to travel the same length of the train, depending on which way he measures it? How does he explain that?

He doesn't know how long it took to get to the mirror. He doesn't have a synchronized clock there yet.
The only number he has is the 33.35640953350012 ticks for the round trip.
(I actually had that number wrong and had to edit it - I divided instead of multiplied by gamma).
Edit - No, it was right the first time. 33.35640952437684 ticks.
Getting late

IF someone where to have been watching him from outside the train, would they see him bend over 11 times?

Yes. Everyone would agree that the train is as long as 10.000000001367545 train rulers.

[Motor Daddy]

He doesn't know how long it took to get to the mirror. He doesn't have a synchronized clock there yet.
The only number he has is the 33.35640953350012 ticks for the round trip.
(I actually had that number wrong and had to edit it - I divided instead of multiplied by gamma).

So just to be clear, all he knows from the measurements is that the clock at the midpoint elapsed 33.35640953350012 ns for the round trip?

He doesn't know the one way times, or that they are different? But he does know that IF the times were different, he still hasn't performed a proper measurement, as a round trip would hide the different one way times.

[Motor Daddy]

Yes. Everyone would agree that the train is as long as 10.000000001367545 train rulers.

I didn't ask you that, I asked if everyone would agree he bent over 11 times?

...and for that matter, would they agree he had to cut a small piece to fill the final gap?

[Pete]

So just to be clear, all he knows from the measurements is that the clock at the midpoint elapsed 33.35640953350012 ns for the round trip?

He doesn't know the one way times, or that they are different? But he does know that IF the times were different, he still hasn't performed a proper measurement, as a round trip would hide the different one way times.

Yes, that's correct.

I didn't ask you that, I asked if everyone would agree he bent over 11 times?

...and for that matter, would they agree he had to cut a small piece to fill the final gap?

Of course.

[Motor Daddy]

Noted. Continue.

[Pete]

The train observer first wonders if the train is at rest

He reasons that if the train is at rest, then:

• The clock-mirror distance is 5.00000000068377 metres.
• The time taken was 33.35640953350012 ns
• The average speed of the light flash was
  2 * 5.00000000068377m / 33.35640953350012ns = 299792458 m/s
• This matches what the measured speed of light should be if the train were at rest

However... he also realises that he would get the same measurement no matter how fast he was going.
The measurement is consistent with the train being at rest, but also consistent with any speed.

He'll try another method in the next post.

Questions or problems?

[Motor Daddy]

The train observer first wonders if the train is at rest

He reasons that if the train is at rest, then:

• The clock-mirror distance is 5.00000000068377 metres.
• The time taken was 33.35640953350012 ns
• The average speed of the light flash was
  2 * 5.00000000068377m / 33.35640953350012ns = 299792458 m/s
• This matches what the measured speed of light should be if the train were at rest

However... he also realises that he would get the same measurement no matter how fast he was going.
The measurement is consistent with the train being at rest, but also consistent with any speed.

He'll try another method in the next post.

Questions or problems?

What is his concept of "at rest?" At rest compared to what?

[Pete]

What is his concept of "at rest?" At rest compared to what?

At rest means that light takes the same time to go from front to back as back to front.

[Motor Daddy]

At rest means that light takes the same time to go from front to back as back to front.

So he bases his concept of "at rest" on light, not on objects such as tracks etc...

In other words, if he thought the train was riding on tracks, he couldn't measure the train's velocity by measuring the distance the train traveled down the tracks and get a correct answer unless he knew the tracks to have a zero velocity. So he realizes that the tracks could have a velocity and the train could have a separate velocity, correct?

[Pete]

So he bases his concept of "at rest" on light, not on objects such as tracks etc...

In other words, if he thought the train was riding on tracks, he couldn't measure the train's velocity by measuring the distance the train traveled down the tracks and get a correct answer unless he knew the tracks to have a zero velocity. So he realizes that the tracks could have a velocity and the train could have a separate velocity, correct?

Yes

[Motor Daddy]

So since he bases his concept of "at rest" on light, does he realize that IF the train were to have a velocity that he would not measure the speed of light to be c in the train?

[Pete]

Yes.

[Motor Daddy]

Noted. Continue.

[Pete]

Next, the train observer tries to measure his velocity using a clock at each end of the train. Unfortunately, he hasn't yet decided how to synchronize them with each other, so he's going to try taking readings when they are unsynchronized and see what he can figure out.

He places a clock at each end of the train, separated by 10.000000001367545 rulers.
(The clock at the front of the train reads sync_diff = 10 nanoticks ahead of the rear clock at that time, but the train observer doesn't know it.)

When the rear clock reads t_rear_send = 0.000, a light flash is sent from the rear clock toward the front.

33.35696118083643 ns later (forward_time = d/(c-v)), the light flash reaches the front clock, which reads:
t_front_receive = t_rear_send + sync_diff + (forward_time / gamma)
= 43.35696117627471 nanoticks

A light flash is also sent from the front clock toward the rear when the front clock reads t_front_send = 0.000.

33.3558578770405 ns later (rearward_time = d/(c+v)), the flash reaches the rear clock which reads:
t_rear_receive = t_front_send - sync_diff + (rearward_time / gamma)
= 23.35585787247898 nanoticks


What can the train observer conclude from these measurements?
t_rear_send = 0.000 ns
t_front_receive = 43.35696117627471 nanoticks

t_front_send = 0.000 ns
t_rear_receive = 23.35585787247898 nanoticks

[Motor Daddy]

Do you want me to respond now or are you still posting?