The Relativity of Simultaneity

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

 

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Good, so you'll also be using it for the measure of the train's velocity as well, correct?

 

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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.

 

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?

 

We'll get to that....

 

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.

 

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.

 

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 "/")

 

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?

 

Thanks.

I agree.

 

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

 

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?

 

I'm not changing anything. What previous agreement do you mean?

 

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:

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!