Motor Daddy
Valued Senior Member
Prove yours
I make no assertion.
I've already proved it. It is impossible for the train to have been at rest, because the lights impacted the train observer at different times.
Prove yours
I make no assertion.
We agree on that point.
I'm asking you to prove in this mathematical world of time dilation and length contraction, your assertion that the propagation of the signal through the wire is equal in both directions.
But, I can see that we won't make any progress on that front, so let's explore what we have established, shall we?
James is talking about the real world.But James doesn't agree,
No, I'm thinking of the dynamic analysis of the wave propagating through the rope, not the overall movement.How does your length contraction factor into the length of the ropes and the time they are pulled? Are you saying one rope would be pulled a shorter distance than the other, using just one crank to pull on both ropes?
James is talking about the real world.
I'm talking about the mathematical world I defined for this exercise.
No, I'm thinking of the dynamic analysis of the wave propagating through the rope, not the overall movement.
It's too hard for me to analyse. I really don't know how to approach it.
What if the train observer didn't have such materials available?
Do you see that he can't synchronize his clocks or calculate his velocity using rulers, clocks, and light signals alone?
Don't you find that surprising?
I can see you're not interested. It's a shame you're not willing to explore the possibilities.
You don't seem interested in exploring different mathematical worlds.I'm not interested in what, illusions? Correct, I'm not.
In the particular mathematical world of the exercise.You've already admitted that the train observer is wrong to assume the train to be at rest.
How can you tell?That is the real world.
Does it matter?I'm not interested in illusions in which the train observer assumes the train to be at rest and the embankment to be in motion. That is his illusion, and it is absolutely FALSE!!!
You don't seem interested in exploring different mathematical worlds.
You also don't seem interested in exploring the real world.
You only seem to want to explore your own particular preferred mathematical world.
Does it matter?
If he can't tell the difference, if all his measurements are consistent with the train being at rest, then does it matter that he pretends the train is at rest?
What will be the consequences?
Don't you remember? We worked through several measurements of the train velocity. None were successful.I'm all ears, but you are wanting to start with false assumptions. If you want to be the train observer scientist, than you don't start with the notion that the train is at rest. You TEST and MEASURE the train's velocity. You start with a solid foundation of your measurements. You don;t start with the assumption that the train is at rest and continue to base everything on that garbage.
So what? What are the practical consequences?Yes it does matter. We are talking about the difference between absolute motion and relative motion, do you understand the difference? One is absolute, which is each object's velocity in the universe, relative to light. The other is relative motion, based on the motion between two objects, of which you don't know the absolute velocity of either in the universe.
Don't you remember? We worked through several measurements of the train velocity. None were successful.
So, if the train observer has no way of synchronizing his clocks or measuring his true velocity...
What advice do you give him?
Should he use his ad-hoc train standard until he is able to determine his velocity?
So what? What are the practical consequences?
Will his microwave oven not work?
Will his two-way radios need rebuilding?
But it is clearly stated in Einstein's chapter 9 that the lights impacted the train observer at different times.
As measured by the observer on the embankment. The observer on the train sees them as simultaineous.
As measured by the observer on the embankment. The observer on the train sees them as simultaineous.
...another idea for the sync of clocks.
Place a light transmitter and a receiver a distance apart from each other on a table, inline with the train from front to rear, roughly an arm's length apart from each other. Make a steel wheel that is a circle, roughly an arms length in diameter. Place steel tabs sticking out 180 degrees apart from each other on the wheel. Install a bearing in the center of the steel circle. Find the center of the distance between the transmitter and receiver on the table. Mount the wheel on a shaft at the center in such a fashion that when the wheel rotates, the tabs come in contact with the actuator on the transmitter and receiver. Rotate the wheel so the tabs are almost touching the actuators. Calibrate each actuator so that when the wheel is spun the tabs contact the two actuators simultaneously.
Now spin the wheel. As soon as the tabs make contact, the transmitter sends a light pulse to the receiver, and at the same time the receiver starts a clock. So when the light arrives at the receiver the clock is stopped and the elapsed time is shown.
Now repeat the test in the opposite direction.
Mind you, the distance between the transmitter and receiver is still unknown, but the two one-way times are known.
Use the equation L=(2cTt)/(T+t) to find the distance between the transmitter and receiver.
Use the equation v=(ct-L)/t to find the velocity of the train.
No sticks required.
... and no suspicions, illusions, assumptions of convenience, or pretending involved! Just straight up measurements of distance and time!
When JamesR said the light reaches the ends of the train simultaneously, he was talking about light from a single light source at the center of the train.
Motor Daddy,
What I'm about to say is going to blow your mind. The apparatus you describe above will work for synchronizing two clocks, but the clocks will only be synchronized in the frame in which the transmitter and receiver are at rest. For example, if you do this procedure on the embankment, the clocks will only be synchronized on the embankment.
Here is what it will look like from the train's point of view: The steel wheel on the embankment is distorted such that the two steel tabs are no longer exactly at opposite sides of the circle. The reason is because one side of the wheel is "ahead" in time, and the other side of the wheel is "behind" in time. The steel itself does not bend, its just that those parts of the wheel are in different "time zones" so-to-speak. This means that the train observer will say that the embankment started his clocks at different times, because the tabs on the wheel were not located exactly opposite each other.