The Relativity of Simultaneity

[Pete]

Just double checking figures for his conclusions... no need to respond if it's all clear.

 

[Motor Daddy]

ok.

 

[Motor Daddy]

I need to go now, to be continued...

 

[Pete]

Bah. It's getting late. I keep messing up whether to divide or multiply by gamma for time dilation.

 

[Pete]

Again, he wonders if he might be at rest.
He reasons that if the train is at rest, then:

• The distance between the clocks is 10.000000001367545 metres
• transit = d/c = 33.35640952437684 ns will elapse on his clocks while each flash is in transit.
• He then calculates what the synchronization difference would be given the rear-to-front readings:
  sync_diff = t_front_receive - t_rear_send - transit
  = 10.00055165189787 ns
• ...and checks to see if that matches up with the front-to-rear readings:
  t_rear_receive = t_front_send - sync_diff + transit
  = 23.35585787247897 ns

This matches his measured t_rear_receive, so he concludes that his measurements are consistent with the train being at rest, and the front clock being 10.00055165189787 ns ahead of the rear clock.

(It's interesting to note at this point that if by chance the clocks were perfectly synchronized, the train observer would find that the measurements were consistent with him being at rest, and the clock unsynchronized by .00055165189787 ns)

However, he also notes that it is also consistent with the train having any speed at all, so he still can't be sure how fast the train is moving.


Next, he'll trying synchronizing the clocks.

Any problems or questions?

 

[Motor Daddy]

What does the train observer think the length of the train is?

 

[Pete]

He doesn't know.
He knows that it depends on its speed, and he hasn't been able to measure its speed yet.

The numbers in this scenario are insane.
I'm going to rework it with a 299792.458 metre train going at 0.6c = 179875474.8 m/s, for a gamma factor of 1.25.

 

[Motor Daddy]

He doesn't know.
He knows that it depends on its speed, and he hasn't been able to measure its speed yet.

What does he measure it to be with his sticks on the floor?

The numbers in this scenario are insane.
I'm going to rework it with a 299792.458 metre train going at 0.6c = 179875474.8 m/s, for a gamma factor of 1.25.

No, stick with this scenario. Why do you now want to change it? Not working out like you thought?

 

[Pete]

It's working out fine. I'm just tired of typing ,checking and double checking so many digits.
It will make it easier for you to check the numbers as well.
You can follow through with the original numbers to check that it works out on your own, if you like.

From nine or ten pages ago:

The train observer measures the train to be 10.000000001367545 rulers long.

 

[Motor Daddy]

So he thinks the train is 10.000000001367545 meters in length, correct?

 

[Pete]

The story so far, with more manageable numbers (please check them for typos and miscalcs):

Assumptions:

• The embankment is at rest
• Light travels at c with respect to the embankment
• Clocks on the embankment are synchronized with each other
• The train observer knows that light travels at c with respect to something at rest
• The train observer doesn't know that the embankment is at rest
• The train observer doesn't know that the embankment clocks are synchronized
• The train observer has precise clocks, but he doesn't know if they're synchronized
• Moving clocks run slowly by the Lorentz factor
• Moving rulers are shorter in the direction of motion by the Lorentz factor

The scenario

• Point A and point B are marked c*0.001s = 299792.458 metres apart on the embankment.
• Point A' is moving, marked on the back of the train.
• Point B' is moving, marked on the front of the train.
• An observer M is standing on the embankment, halfway between point A and point B.
• An observer is standing on the train at M', halfway between point A' and point B'.
• The train passes the embankment at 0.6c = 179875474.8 m/s
• gamma = 1 / sqrt(1-v^2/c^2) = 1.25

At t=0.000:

• the front of the train is passing point B
• the back of the train is passing point A
• the train observer M' is passing embankment observer M
• M' has a clock with him that reads t'=0.000
• A bolt of lightning strikes the front of the train and point B
• Another bolt of lightning strikes the back of the train and point A

At t = d/(c+v) = 0.3125 ms :

• The flash from lightning bolt B reaches M' (the train observer)
• The clock at M' reads t' = t/gamma = 0.25 ticks

(a 'tick' is a dilated millisecond)

At t = d/c = 0.5 ms:

• The flash from both lightning bolts reaches M

At t = d/(c-v) = 1.25 ms:

• The flash from lightning bolt A reaches M'
• The clock at M' reads t' = t/gamma = 1 tick

So far, I conclude that:

• the lightning bolts struck simultaneously
• the moving train is 299792.458 metres long.
• rulers on the train are contracted to 0.8 metres long
• clocks on the train are dilated, elapsing 1 ticks every 1.25 milliseconds

The only thing the train observer knows so far is:

• The train is as long as c*0.00125s = 374740.5725 of his rulers
• The lightning flash from the front of the train reached him when his clock read 0.25 ticks
• The lightning flash from the back of the train reached him when his clock read 1 tick.

Measuring speed, attempt 1
Next, the train observer will measure the velocity of the train using a single clock, a light flash, and a mirror:

• The mirror is placed at B' the front of the train and a timer at M' in the middle of the train.
• The mirror is c*0.0005s = 149896.229 metres from the timer.
• The train observer measures this distance to be c*0.000625s = 187370.28625 train rulers.
• When the timer starts, a light flash is sent from the M' clock to the mirror.
• d/(c-v) = 1.25 ms later, the light flash reflects off the mirror.
• d/(c+v) = 0.3125 ms later again, the light flash returns to M'.
• The total time is t=1.5625 ms

The train observer measures an elapsed time of t/gamma = 1.25 ticks for the round trip.

Measurement analysis
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 of 187370.28625 rulers is actually 187370.28625 metres.
• The time taken of 1.25ticks was actually 1.25ms
• The average speed of the light flash was
  = 374740.5725m / 1.25ms = 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.


Measuring speed, attempt 2
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 374740.5725 rulers.
• The clock at the front of the train reads sync = 0.1 ticks 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.
• 2.5 ms later (forward = d/(c-v)), the light flash reaches the front clock, which reads:
  t_front_receive = t_rear_send + sync + (forward / gamma)
  = 2.1 ticks
• A light flash is also sent from the front clock toward the rear when the front clock reads t_front_send = 0.000.
• 0.625 ms later (rearward = d/(c+v)), the flash reaches the rear clock which reads:
  t_rear_receive = t_front_send - sync + (rearward / gamma)
  = 0.4 ticks

Measurement analysis
Again, he wonders if he might be at rest.
He reasons that if the train is at rest, then:

• The distance between the clocks is 374740.5725 metres
• transit = d/c = 1.25 ms will elapse on his clocks while each flash is in transit.
• He then calculates what the synchronization difference would be given the rear-to-front readings:
  sync = t_front_receive - t_rear_send - transit
  = 2.1 - 0 - 1.25 = 0.85 ms
• ...and again with the front-to-rear readings:
  -sync = t_rear_receive - t_front_send - transit
  = 0.4 - 1.25 = -0.85 ms

He concludes that his measurements are consistent with the train being at rest, and the front clock being 0.85 ms ahead of the rear clock.

(It's interesting to note at this point that if by chance the clocks were perfectly synchronized, the train observer would find that the measurements were consistent with him being at rest, and the clocks unsynchronized by .0.75 ms)

However, he also notes that it is also consistent with the train having any speed at all, so he still can't be sure how fast the train is moving.


Next, he'll trying synchronizing the clocks.

 

[Pete]

So he thinks the train is [374740.5725 (Pete)] meters in length, correct?

He doesn't know.
He knows that it depends on its speed, and he hasn't been able to measure its speed yet.

His measurements so far are consistent with the train at rest and a length of 374740.5725m, but not conclusive.

 

[Motor Daddy]

His measurements so far are consistent with the train at rest and a length of 374740.5725m, but not conclusive.

He measures the train to be 374740.5725 m in length with his sticks, correct? Why would he think that it's inconclusive? Does he doubt that his meter sticks are an actual meter?

 

[James R]

Motor Daddy:

So, let's be clear. Your claim is that postulate 2 of Einstein's special theory is false. We have:

2. (Einstein) The speed of light is the same in all inertial reference frames.
2. (Motor Daddy) The speed of light is different in every reference frame, and only has the value 299792458 m/s in a single, absolute frame. In every other frame, the speed of light will have a different measured value.

Correct. Except light always travels at the same speed. You mean to say that light is measured to be different if measured from a frame with a velocity.

We're using language in a different way, and that's part of the problem, perhaps.

When I say "light has speed X in frame F", I always mean "if you measure the speed of light in frame F, the result you will get will be X". In other words, I say that the speed of light is always what you measure it to be.

You say "light always travels at the same speed". But by that you mean it always travels at the same speed in "space". If you measure the speed, unless you're stationary in "space" you won't ever measure the "correct" speed of light. So, you're saying that the speed of light is, practically, never what you measure it to be - it is always what it is defined to be in "space".

So my postulate is: The speed of light is a constant. Measurements of the speed of light will vary depending on the velocity of the frame the measurements are taken in.

Yes. I agree. That's an equivalent way of putting it using your terminology. You agree that this is very different from Einstein's second postulate, don't you?

Light travels at a constant speed in space. The speed of light is not determined or changed by another object's speed.

Yes, according to you.

Einstein agrees that the speed of light is not determined by the speed of any object. But Einstein says the speed of light is the same in all reference frames. So, not only is it not determined by objects, it is not determined by your kind of "space" either.

If you are on the train moving .5c, you will measure light to be .5c in that train.

As a matter of reality, you will not. IF your assumption of absolute space were correct, then your conclusion would be correct, too. But you're wrong, as a matter of actual fact, verified by countless actual real-world experiments.

You can think of a light source in space. Light is emitted and one second later the light sphere has a 299,792,458 meter radius. If the source were to have traveled during that one second, the source would not be at the center of the light sphere, it would be closer to the outer edge of the sphere, and from that you can determine absolute velocity of the source. So if a light was emitted in space, and one second later the light was 150,000,000 meters from the source, the source had a .5c absolute velocity. An absolute velocity of .5c relative to distance and time in space.

All of that is true in actual fact in the frame of the embankment. It is NOT, in fact, true in the frame of the the train. Or, to put it another way, the train never moves in its own frame, so the speed of light must be 299792458 metres per second in its frame, if Einstein's second postulate is correct. If Einstein's second postulate were wrong and you were correct, then the measured speed of light on the train would have to change.

You say that the source is always at the center of the sphere 1 second later. That is pure rubbish, James, and you know it!!!

It's not rubbish. It's just counterintuitive. Your gut feeling that it is wrong doesn't prove anything. That's what you don't seem to understand. You imagine how you think things ought to work, but they don't in fact work that way. Why do you get things wrong when you apply your common sense? Answer: you live in a "low speed" world, where nothing you encounter in your daily life ever moves at a reasonable fraction of the speed of light. So, in your everyday experience, relativistic effects are so tiny that you never notice them. But that doesn't mean they aren't there. And, moreover, they become very significant indeed when you deal with higher relative speeds.

If a light travel time on an embankment is the same one-way as it is the other way, the embankment has a zero velocity, so you are wrong.

No, I'm not wrong. The embankment always has zero velocity in its own reference frame. And the train always has zero velocity in its own reference frame. You have to start taking this reference frame stuff seriously if you want to understand relativity - even common-sense Newtonian relativity.

In the embankment's frame, the train moves and the embankment is stationary. In the train's frame, the embankment moves and the train is stationary. And there's no physical experiment you can do that will tell you which frame is "absolutely" stationary. That's in spite of your claim that you can use light to measure the absolute speeds, because your assumption that you can do that is wrong as a matter of observed fact.

If the times are different a velocity can be calculated. Simple as that.

Right. IF the times are different. But in a single frame, they never are, as a matter of fact.

Think of a light sphere, James. You can't understand that because you think the source is always at the center 1 second later. You are dead wrong!

In a frame where the source is moving, you're right - the source is not at the centre of the light sphere 1 second later. But in a frame where the source is stationary, the source stays at the centre of the sphere at all times.

What Einstein's postulate says is that the speed of light emitted from a source in the middle of your train is observed to move at speed c in both directions by somebody on the train. Therefore, the light wavefront is always the same distance from the source in both directions and the source remains stationary at the centre. The motion of the train is irrelevant.

According to YOUR postulate, things are very different. You say light moves at different speeds in the two directions, as measured in the train's frame. So, light spreads out from the source at different rates depending on its direction of travel and the source does not remain at the centre of the light sphere.

Looking at things from the embankment frame, Einstein says that the source does NOT remain at the centre of the light sphere because light travels at c in both directions in the embankment frame and the source on the train is moving. And you agree with Einstein about the embankment picture, because in your mind the embankment frame is the only truly valid frame (provided it is stationary in "space").

As a matter of reality, Einstein is right and you are wrong, as proven by countless experiments. Nothing you imagine or assert can change that.

 

[Pete]

He measures the train to be 374740.5725 m in length with his sticks, correct? Why would he think that it's inconclusive? Does he doubt that his meter sticks are an actual meter?

He measures the train to be 374740.5725 rulers long.

He knows that the length of the rulers depends on their speed.
He knows that if the train is moving, then the rulers are not an actual meter long.

Have to go. My next post will be after you're asleep, I think.

 

[Motor Daddy]

He measures the train to be 374740.5725 rulers long.

He knows that the length of the rulers depends on their speed.
He knows that if the train is moving, then the rulers are not an actual meter long.

Have to go. My next post will be after you're asleep, I think.

1. He doesn't know the length of the train.
2. He doesn't know the length of his rulers.
3. He doesn't know the velocity of the train.
4. He doesn't have sync'd clocks.
5. He doesn't know if his clocks are accurate to the standard second.

Noted.

Good night.

 

[Motor Daddy]

Still working on it, Pete?

 

[Pete]

Now the train observer will set up synchronized clocks at each end of the train, and use them to measure the train's velocity.

He proceeds like this:

• Two clocks are synchronized while together at the rear of the train.
• One clock is slowly moved to the front of the train.
• A flash of light is sent from the rear clock to the front clock.
• A flash of light is sent from the front clock to the rear clock.
• One distance measurement (in rulers) is taken
  • d' = the distance between the clocks
• Four time readings (in ticks) are taken:
  • t_1a' is the reading on the rear clock when the forward flash is sent.
  • t_1b' is the reading on the front clock when the forward flash is received.
  • t_2a' is the reading on the front clock when the rearward flash is sent.
  • t_2b' is the reading on the rear clock when the rearward flash is received.

The readings will be used to calculate the train velocity, after a little algebra:

• d / t_forward = c - v
• d / t_rearward = c + v
• therefore:
  $$\frac{c-v}{c+v} = \frac{t_{rearward}}{t_{forward}}$$
• t_forward = time in milliseconds = gamma.(t_1b' - t_1a')
• t_rearward = time in milliseconds = gamma.(t_2b' - t_2a')
• therefore:
  $$\frac{c-v}{c+v} = \frac{t_{2b}' - t_{2a}'}{t_{1b}' - t_{1a}'}$$
• rearranging:
  $$v = c \frac{(t_{1b}' - t_{1a}') - (t_{2b}' - t_{2a}')}{(t_{1b}' - t_{1a}') + (t_{2b}' - t_{2a}')}$$

OK?

 

[Motor Daddy]

Now the train observer will set up synchronized clocks at each end of the train, and use them to measure the train's velocity.

He proceeds like this:

• Two clocks are synchronized while together at the rear of the train.
• One clock is slowly moved to the front of the train.
• A flash of light is sent from the rear clock to the front clock.
• A flash of light is sent from the front clock to the rear clock.
• One distance measurement (in rulers) is taken
  • d' = the distance between the clocks
• Four time readings (in ticks) are taken:
  • t_1a' is the reading on the rear clock when the forward flash is sent.
  • t_1b' is the reading on the front clock when the forward flash is received.
  • t_2a' is the reading on the front clock when the rearward flash is sent.
  • t_2b' is the reading on the rear clock when the rearward flash is received.

The readings will be used to calculate the train velocity, after a little algebra:

• d / t_forward = c - v
• d / t_rearward = c + v
• therefore:
  $$\frac{c-v}{c+v} = \frac{t_{rearward}}{t_{forward}}$$
• t_forward = time in milliseconds = gamma.(t_1b' - t_1a')
• t_rearward = time in milliseconds = gamma.(t_2b' - t_2a')
• therefore:
  $$\frac{c-v}{c+v} = \frac{t_{2b}' - t_{2a}'}{t_{1b}' - t_{1a}'}$$
• rearranging:
  $$v = c \frac{(t_{1b}' - t_{1a}') - (t_{2b}' - t_{2a}')}{(t_{1b}' - t_{1a}') + (t_{2b}' - t_{2a}')}$$

OK?

Not exactly.

1. You say the clock was slowly moved to the front? Are you now saying that it will be in sync with the other clock when it gets there? If it moves faster will it still work? How about even faster? What is the limit to still being in sync when it gets there and being out of sync when it gets there, as far as the rate at which you move it there?

2. You mention milliseconds. What is that?? How would he know such a thing when he doesn't know if his clocks are calibrated to the standard second?

 

[origin]

James, I have asked him several times for any evidence that the speed of light will change relative to the observers movement and he simply ignores the request. I think that he has realized at some point that he is wrong but is stubbornly refusing to admit it. It is really very simple, if MD is correct then the speed of light as measured from earth should vary continuously through the year as the direction of our orbital speed changes relative the stationary frame (wherever that is). MD knows this is not true so he just ignores the whole problem. Not to scientific...