The Relativity of Simultaneity

Yes. Do you have anything to say about what the train observer and embankment observer can measure?
Pete said:
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
Click to expand...
 
Motor Daddy said:
http://www.bartleby.com/173/9.html

Einstein says:

"Just when the flashes 1 of lightning occur, this point M' naturally coincides with the point M, but it moves towards the right in the diagram with the velocity v of the train."

"Observers who take the railway train as their reference-body must therefore come to the conclusion that the lightning flash B took place earlier than the lightning flash A."

I contend there is no relativity of simultaneity, that the strikes occurred simultaneously, and that the observer on the embankment and the observer on the train will agree on when the strikes occurred.

There is however a distinction between the simultaneity of the strikes, and when the light from the strikes impacts the observers. I realize the light will hit the train observer at different times, as the train is in motion. Therefore, the observer on the train will be hit by the light from the front of the train before the light from the back of the train reaches him. That is a result of the light from the rear of the train having to travel a greater distance until it impacts the train observer.

The light from points A and B hits the embankment observer simultaneously, as the strikes occurred at both points when the train and embankment points coincided, and he was at the midpoint. The light from each strike traveled the same speed and the same distance to reach the observer. The conclusion from that is that the embankment observer could not have had a velocity, he was at a true zero velocity.

The perceived "relativity of simultaneity" in this example is due to the train observer's failure to acknowledge his own velocity, as is clearly shown with the directional arrow in the example. That incorrect assumption leads him to his false claim that the strikes must have occurred at different times.

edit: The board will not allow me to post the URL to Einstein's example. The example can be found in chapter 9 of Einstein's- Relativity
The Special and General Theory.
Click to expand...

I'm going to go ahead and say this makes sense to me. That the lightning strike at the back has a further distance to travel before it hits the embankment observer within the train. But why was this idea not considered before?
 
Pete said:
Yes. Do you have anything to say about what the train observer and embankment observer can measure?
Click to expand...

Great, so whether you know it or not, you have just eliminated every frame the embankment observer can be in except for the absolute zero velocity frame. The same can not be said for the train observer, because the lights did not impact him simultaneously.

If the embankment had any other velocity besides a zero velocity, it would be IMPOSSIBLE for light to strike A and B simultaneously, AND impact the embankment observer simultaneously.

Do you agree? If not, explain in simple terms, not to lengthy, how it would be possible for the lights to impact the embankment observer simultaneously.
 
Motor Daddy said:
Great, so whether you know it or not, you have just eliminated every frame the embankment observer can be in except for the absolute zero velocity frame. The same can not be said for the train observer, because the lights did not impact him simultaneously.

If the embankment had any other velocity besides a zero velocity, it would be IMPOSSIBLE for light to strike A and B simultaneously, AND impact the embankment observer simultaneously.

Do you agree? If not, explain in simple terms, not to lengthy, how it would be possible for the lights to impact the embankment observer simultaneously.
Click to expand...
Of course I agree. In the exercise setup, I defined the embankment to have zero velocity, and the embankment clocks to be synchronized.

The question before you is what experiments the train observer and/or embankment observer can do to confirm that the embankment has zero velocity and the the lightning strikes were simultaneous.
 
Pete said:
Of course I agree. In the exercise setup, I defined the embankment to have zero velocity, and the embankment clocks to be synchronized.

The question before you is what experiments the train observer and/or embankment observer can do to confirm that the embankment has zero velocity and the the lightning strikes were simultaneous.
Click to expand...

Good, so you agree that in this example, the embankment MUST be at a zero velocity. So there is a reality that the train is in motion and the embankment is not.

It can not be said that the train observer is also correct to assume the train is at rest and the embankment is really the one that's in motion.

So in this example, there is no relativity of simultaneity, just a bad assumption on the part of the train observer to assume he is not in motion.
 
Yes, we agree that under the assumptions of the exercise, the train-standard synchronization doesn't directly reflect reality.
 
Pete said:
Yes, we agree that under the assumptions of the exercise, the train-standard synchronization doesn't directly reflect reality.
Click to expand...

Good, I will also add that this pertains to EVERY situation in the universe, the same as it does in this example.

EVERY object's motion is relative to the absolute zero velocity reference frame. EVERY OBJECT!

In other words, it could have also been that the train and the embankment were in motion. They would have each had an absolute velocity, and a relative velocity could also be measured.
 
So we have concluded and agreed that in reality, the embankment is at an absolute zero velocity, and that the train has an absolute velocity greater than zero. Let's see what each observer measures and then we'll compare their results.

The train observer has a variety of different length sticks on the train. He picks a stick from the pile and places it inline with the train (front to back).

He uses two battery operated clocks that are not running yet because they have a piece of plastic between the battery and the contact. They will start running when the plastic is pulled.

The train observer places one clock at each end of the random length stick. He attaches a separate wire to each plastic strip. He finds the midpoint of the stick by cutting a string to the exact length of the stick, and then folding the string in half he cuts it. He now has a string that is half the length of the stick. He places one end of the string at one end of the stick and extends the string along the stick. The other end of the string is at the midpoint. He marks the midpoint of the stick at that point.

He places a shaft assembly perpendicular to the stick at the midpoint of the stick, centered at the midpoint of the stick. The shaft assembly rotates on precise bearings. It is supported by triangulated legs on each side. The purpose of the shaft assembly is quite simple, The wires from each clock's plastic tabs are attached to the shaft, so they are equally taught. When the shaft is rotated the wires will pull the plastic tabs on each clock simultaneously, starting each clock simultaneously.

The shaft is rotated and the wires are pulled simultaneously and the clocks are started. As soon as the clocks are started a light pulse is sent from the rear clock to the front clock.

It took .000000012508653569930701859084126792809 seconds for light to travel from the rear clock to the front clock.

The clocks are reset and the procedure is performed again, but this time the light is sent from the front clock to the rear clock.

It took .0000000031271633924826754647710316982024 seconds for light to travel from the front clock to the rear clock.

Using the equation L=(2cTt)/(T+t), the train observer concludes that the length of the stick is 1.5 meters.

The train observer now has the one-way times in each direction, and he has the length of the stick. So it's trivial to find the velocity of the train, using the equation v=(ct-l)/t.

The train observer concludes the absolute velocity of the train is 179,875,474.8 m/s

Using the 1.5 meter long stick he knows to be accurate, he measures the train's length to be 299,792.458 meters in length.

He goes to the midpoint of the train.

At exactly 0.0003125 seconds after 12:00:00 according to his watch he is struck by the light from B (the front of the train).

At exactly 0.00125 seconds after 12:00:00 he is struck from the light from A (the rear of the train).

Knowing the train's absolute velocity and the exact length of the train, and that he was at the midpoint between A and B, the train observer concludes the lightening struck A and B simultaneously at EXACTLY 12:00:00.

The embankment observer performs the same procedure, and finds the embankment's velocity to be an absolute zero velocity. The embankment observer was struck by the lights from A and B at exactly .0005 seconds after 12:00:00. He knows he was at the midpoint between A and B, and therefore concludes the lightening struck A and B simultaneously at 12:00:00.

Both observers agree that the strikes occurred at A and B simultaneously at exactly 12:00:00.

Due to the train observer's 179,875,474.8 m/s absolute velocity, the train observer was struck by the lights from A and B at different times.

The timeline in reality:

12:00:00 Lightening strikes A and B on the embankment and the train.

0.0003125 seconds after 12:00:00 the light from B strikes the train observer.

0.0005 seconds after 12:00:00 the lights from A and B strike the embankment observer.

0.00125 seconds after 12:00:00 the light from A strikes the train observer.


Absolute simultaneity!!!
 
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Motor Daddy said:
So we have concluded and agreed that in reality, the embankment is at an absolute zero velocity, and that the train has an absolute velocity greater than zero. Let's see what each observer measures and then we'll compare their results.

The train observer has a variety of different length sticks on the train. He picks a stick from the pile and places it inline with the train (front to back).

He uses two battery operated clocks that are not running yet because they have a piece of plastic between the battery and the contact. They will start running when the plastic is pulled.

The train observer places one clock at each end of the random length stick. He attaches a separate wire to each plastic strip. He finds the midpoint of the stick by cutting a string to the exact length of the stick, and then folding the string in half he cuts it. He now has a string that is half the length of the stick. He places one end of the string at one end of the stick and extends the string along the stick. The other end of the string is at the midpoint. He marks the midpoint of the stick at that point.

He places a shaft assembly perpendicular to the stick at the midpoint of the stick, centered at the midpoint of the stick. The shaft assembly rotates on precise bearings. It is supported by triangulated legs on each side. The purpose of the shaft assembly is quite simple, The wires from each clock's plastic tabs are attached to the shaft, so they are equally taught. When the shaft is rotated the wires will pull the plastic tabs on each clock simultaneously, starting each clock simultaneously.

The shaft is rotated and the wires are pulled simultaneously and the clocks are started.
Click to expand...

How long after the observer pulls the wire does each clock start?
Please don't use a signalling method that hasn't been analysed according to the assumptions of this mathematical world. Light signals, clocks, and rulers.
 
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Pete said:
How long after the observer pulls the wire does each clock start?
Please don't use a signalling method that hasn't been analysed according to the assumptions of this mathematical world. Light signals, clocks, and rulers.
Click to expand...

It doesn't matter how long it takes to start each clock, the point is that they start simultaneously.

It could take hours for each clock to start ticking, but when they do start, they start simultaneously. You seem to have a problem grasping the concept of simultaneous.

I'll use any method necessary in order to measure as accurately as I can. I don't live by the notion that there is no experiment that can prove an absolute motion. That's BS! That's a cop out to try to save his theory. Einstein doesn't tell me what is, and what isn't possible! I measure the velocity of a box from within the box using light as the standard, because the meter is defined by light travel time!
 
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Poor Pete. I saw this coming, but there was nothing I could to to help. The windmill has slain Don Quixote.

Motor Daddy used the same argument on me back in December:
http://www.sciforums.com/showthread.php?p=2663405&#post2663405

You see, in Motor Daddy's universe, tension travels through a wire at a constant speed in all directions, in all frames of reference. So he is able to establish synchronicity between two clocks, by simply pulling two wires at the same time.

So, if the train were moving at 1.0c, light would propagate toward the front of the train at 0.0c in the train frame. The speed of tension through the wire would be faster than light travelling toward the front of the train. Such is life in Motor Daddy's universe.
 
...and one more thing to add, Pete.

Unlike Einstein's methods, my numbers are not based on suspicion, assumption of convenience, pretend, superstition, religion, nor were they implanted in me by aliens.

My numbers are based on the constant speed of light, and the definition of the meter. Believe it or not, I don't have to pretend the train has a zero velocity, I measure its velocity.

Of course, if you live in Einstein's world, pretending is the standard, and illusions and paradoxes are the norm.
 
Neddy Bate said:
You see, in Motor Daddy's universe, tension travels through a wire at a constant speed in all directions, in all frames of reference. So he is able to establish synchronicity between two clocks, by simply pulling two wires at the same time.
Click to expand...
The difference is that we're not conducting this exercise in his universe, but in a specific mathematical world with agreed rules.
Motor Daddy said:
It doesn't matter how long it takes to start each clock, the point is that they start simultaneously.
Click to expand...
It certainly matters.
In this mathematical world, motion affects clocks, which includes all time-related processes such as tension waves through materials.

You have a wave moving through a wire. How does that motion affect the process of signal propagation?

I don't know, and neither do you.

I'll use any method necessary in order to measure as accurately as I can.
Click to expand...
Please do. That means you must be able to accurately predict the result of your method in this mathematical world.
 
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Motor Daddy said:
Good, so you agree that in this example, the embankment MUST be at a zero velocity. So there is a reality that the train is in motion and the embankment is not.
Click to expand...

This would be extremely tough. Last I checked, the embankment moved with the Earth and the Earth rotated at 330m/s while in revolution around the Sun with 30km/s while the Sun moved wrt the distant stars at 337km/s. Tough!
 
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