The Relativity of Simultaneity

I'm happy to use your method of determining absolute velocity:

Motor Daddy said:
The observer on the train measures the time it takes light to go from the rear of the train car to the front of the train car, which is 11.9915 meters in length in the train frame. Light takes .00000004 seconds to travel the length of the train. That means the absolute velocity of the train is 4,958 m/s.
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Yes, we can use that method to determine the train's absolute velocity.

The train observer has limited knowledge (they don't know what clocks are synchronized), but they will try to use that method as best they can with the available tools.

If two clocks are:
- synchronized with each other
- sitting at each end of an x length ruler
And if a light signal leaves goes from one clock the the other:
- leaving when the first clock reads t0
- arriving when the second clock reads t1

Then the measured velocity of the ruler and clocks in the direction of the light signal is given by:
v = c - x/(t1-t0)
 
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Of course, the train observer will also have to account for the length contraction of their rulers and time dilation of their clocks. This will be included in the numbers, when you're happy with the starting assumptions.
 
Pete said:
The train observer will use that method as best they can with the available tools.

If two clocks are:
- synchronized with each other
- sitting at each end of an x length ruler
And if a light signal leaves goes from one clock the the other:
- leaving when the first clock reads t0
- arriving when the second clock reads t1

Then the measured velocity of the ruler and clocks in the direction of the light signal is given by:
v = c - x/(t1-t0)
Click to expand...

So let's do a sample to see if we're on the same sheet of music.

v=(ct-l)/t

It takes .1 seconds for light to travel the length of a 1 meter long stick. I say the stick has a 299,792,448 m/s velocity, what say you?
 
Pete said:
Of course, the train observer will also have to account for the length contraction of their rulers and time dilation of their clocks. This will be included in the numbers, when you're happy with the starting assumptions.
Click to expand...


We'll get to that....
 
Motor Daddy said:
So let's do a sample to see if we're on the same sheet of music.

v=(ct-l)/t

It takes .1 seconds for light to travel the length of a 1 meter long stick. I say the stick has a 299,792,448 m/s velocity, what say you?
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Yes, that's right.
It takes .1 absolute seconds for light to travel the length of a stick that is 1 absolute meter long moving at 299792448 m/s.
 
Pete said:
Yes, that's right.
It takes .1 absolute seconds for light to travel the length of a stick that is 1 absolute meter long moving at 299792448 m/s.
Click to expand...

Good, we're making progress.

So if the distance between A and B on the embankment is 10 meters, and you say the embankment has a zero velocity, how much time does it take light to travel from A to B?
 
If A and B aren't moving,
t = d/c = 33.36 nanoseconds
Obviously.
Is this really necessary? I'm not trying to pull the wool over your eyes. If I do something dodgy in the calculations, you can stop me and thrash out the details then.
 
Pete said:
If A and B aren't moving,
t = d/c = 33.36 nanoseconds
Obviously.
Is this really necessary? I'm not trying to pull the wool over your eyes. If I do something dodgy in the calculations, you can stop me and thrash out the details then.
Click to expand...
Uh, one small correction, maybe you made a typo?


v=(ct-l)/t

so

t = l/(c-v)

You agree?
 
Yes, t=l/(c-v) for absolute t, l, and v.

But you said A and B were on the embankment, which I understood to mean they were at rest. If not, then please specify their velocity.

(Edit - missed a "/")
 
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Pete said:
Yes, t=l(c-v) for absolute t, l, and v.

But you said A and B were on the embankment, which I understood to mean they were at rest.
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You still made a typo? You need to be more precise, Pete.

t = l/(c-v)

Let's do a sample with the embankment having a velocity, to be sure.

It's 10 meters between A and B on the embankment. The embankment has a 1,000 m/s velocity. How much time did it take light to travel from A to B?

I say .000000033356520785191951666614863989887 seconds, what say you?
 
Motor Daddy said:
You still made a typo?
Click to expand...
Thanks.

Let's do a sample with the embankment having a velocity, to be sure.

It's 10 meters between A and B on the embankment. The embankment has a 1,000 m/s velocity. How much time did it take light to travel from A to B?

I say .000000033356520785191951666614863989887 seconds, what say you?
Click to expand...
I agree.
 
Pete said:
Thanks.


I agree.
Click to expand...

So then you agree with all my numbers in this quote?

Let's look at Einstein's train thought experiment in Chapter 9. The Relativity of Simultaneity. Einstein, Albert. 1920. Relativity: The Special and General Theory.

Einstein conveniently forgot to put numbers to the thought experiment, so let's do it for him, shall we?

The observer on the train measures the time it takes light to go from the rear of the train car to the front of the train car, which is 11.9915 meters in length in the train frame. Light takes .00000004 seconds to travel the length of the train. That means the absolute velocity of the train is 4,958 m/s.

The observer on the tracks measures the time it takes light to travel the distance between two clocks on the track, which is 1 meter. It takes light .0000000033356409519815204957557671447492 seconds to travel the distance, which means the track has an absolute zero velocity.

It is 10 meters from A to B on the train in the train frame, and 10 meters from A to B on the embankment in the embankment frame. Both observers are at the midpoint between A and B in their respective frames.

Lightening strikes A and B as the two points on the train coincide with the two points on the embankment.

Light takes .000000016678204759907602478778835723746 seconds for each light from A and B to strike the embankment observer. The embankment observer was struck simultaneously from each light at precisely .000000016678204759907602478778835723746 seconds after 12:00:00. That means the strikes occurred at A and B at exactly 12:00:00.

It takes .00000001667792893852027063502108370407 seconds for light to travel from B on the train to the train observer at the midpoint. It takes .000000016678480590418212900804736688488 seconds for light to travel from A on the train to the midpoint observer on the train.

So, the train observer had the light from B impact him .00000000000055165189794226578365298441767877 seconds before the light from A impacted him.

Since the light from B impacted the train observer .00000001667792893852027063502108370407 seconds after 12:00:00 and it took light .00000001667792893852027063502108370407 seconds to travel from B to his midpoint position, the train observer concludes the strike occurred at B at exactly 12:00:00. Since the light from A impacted the train observer .000000016678480590418212900804736688488 seconds after 12:00:00 and it took light .000000016678480590418212900804736688488 seconds to travel from A to his midpoint position, the train observer concludes the strike occurred at A at exactly 12:00:00.

So both observers acknowledge that the strikes occurred at exactly 12:00:00 at A and B. The embankment observer had both lights hit him simultaneously, and the train observer had the lights hit him at different times due to his 4,958 m/s velocity.

Absolute simultaneity!!!
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Yes, those numbers appear to be correct in a mathematical world with no time dilation and no length contraction, and under the assumption that the train observer has absolutely synchronized clocks.

Are you ready to see my numbers now?

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

Are these premises acceptable to you?
All my calculations must be perfectly consistent with these premises.


From these premises, I believe I can prove that:
Conclusions
  • The train observer can't tell how fast he's going.
  • His best measurements tell him he's at rest.
  • His best measurements tell him that the speed of light is c with respect to the train.
  • He can't synchronize his clocks. His best synchronization methods make his clocks out of sync with the embankment clocks
  • The clocks he synchronized as well as he possibly could tell him that the lightning strike at the front of the train happened before the lightning strike at the back of the train.

I'll go one step at a time, and wait for your questions and corrections before proceeding.

In return, I expect that if I am able to do this to your satisfaction, then you will agree:
  • that Einstein's world is a logically consistent world, and
  • that if actual measurements in the real world match Einstein's world better than your own conceptual model, then your own conceptual model is wrong at relativistic speeds.

Agreed?
 
What is this time dilation and length contraction you speak of? Are you now going to change what you previously agreed to?
 
Pete said:
I'm not changing anything. What previous agreement do you mean?
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You just agreed to a world with no length contraction or time dilation. Now you are gonna give me different numbers?

According to your assumptions, how much time does it take for light to travel 10 meters in the embankment frame? How much time does it take for light to travel 10 meters in the train frame?
 
I agree that your numbers are correct in the world of no time dilation and no length contraction.
But that's not Einstein's world. Remember the agreement:
Pete said:
Here's a deal for you:
We're considering two mathematical worlds: Newton's world and Einstein's world.
You think that Newton's world is a better match for the real world than Einstein's.
I think that Einstein's world is a better match.

If you agree that only actual measurements of the real world (ie experiments) can decide who is right, then I'll show you the numbers in Einstein's world, one small step at a time, so you can point out any problems.

Deal?
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Motor Daddy said:
How about this. We have a deal, but first you prove to me a relativity of simultaneity exists before you start using it in your method of calculations. Show me your numbers of Chapter 9 and prove to me that a relativity of simultaneity actually exists as Einstein claims it does. Prove it! Show me the numbers!
Click to expand...

We agree on the numbers in your mathematical world.
Do you want to see the numbers in Einstein's mathematical world?
 
Pete, I'm following this discussion with interest; I'm curious to see if you succeed where I failed. Anyway, MD does not accept time or length contraction. Length is length is length, period. He believes that there exists a preferred frame of "true rest", and that light travels at c in absolute motion only from that frame. When I would bring up well established observations that contradict this way of thinking they would never seem to penetrate.

Anyway, good luck!
 
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