MacM:
What's the difference between "assume" and "accept" in this instance? Where does the acceptance of this postulate come from?
Anyway, let's go with it for a moment.
Wrong, but let's forget that for now.
Ok.
So, you're measuring your seconds in the rest frame of the line. You must specify a frame, or your statements will be meaningless, as you know.
You're mixing frames, as is normal with you.
You want to make marks in the rest frame of the line, while measuring time in the rest frame of the "moving" observer.
Anyway, there's no problem if you want to put marks between each set of marks already there, so let's say you've done that.
This is true according to your "acceptance" that the moving observer's clock is seen to tick slow by the rest observer. Ok.
No. Because you "accepted" that the moving clock ticked slower. Remember?
No. Given your own postulates, of time dilation but no length contraction, the moving observer would say he travelled faster than the rest observer.
In your pretend universe, velocities aren't reciprocal. That's not the case in our real universe, of course, but for the sake of argument, we'll stick with your imaginary one for now.
Yes. Congratulations. You have followed your own set of assumptions through to its logical conclusion.
As I pointed out, if you now want to connect your imagination to the real world, you'll need to somehow reconcile the reciprocity of velocities in the real world with the fact that velocities are observer dependent in MacM fantasyland.
Why are you suddenly talking about SRT now?
First one does not need to even concern himself with the postulates of relativity. You need only to accept (not assume) the fact that at least a clock with velocity which has accelerated while under the enfluence of F = ma, will have a slower clock tick rate (time dilation) than a clock which remains inertial.
What's the difference between "assume" and "accept" in this instance? Where does the acceptance of this postulate come from?
Anyway, let's go with it for a moment.
I specify the above conditions since reciprocity has never been demonstrated and a clock has never been shown emperically to tick slow due to relative velocity alone but only due to actual accelerated velocity.
Wrong, but let's forget that for now.
Now take a long piece of paper and draw a 1m long horizontal line. Mark the scale of this line as 3E8/1. That is each cm is 1 light second. In a rest frame that makes this line 100 light seconds long.
Ok.
Now envision an observer at the right end of the line and a moving observer going from left to right along the line at 0.866c. If we now mark the crafts location along and above this line each second of the trip you will have 115 one second time marks with a minor 0.473 second remainer to the rest observer. Each time mark is 0.866 light seconds long.
So, you're measuring your seconds in the rest frame of the line. You must specify a frame, or your statements will be meaningless, as you know.
We know that it has been emperically demonstrated that a clock with this motion will tick at 1/2 the rate of the rest clock. That is you should make a mark below the 1m line for each two marks made according to the rest clock marks.
You're mixing frames, as is normal with you.
You want to make marks in the rest frame of the line, while measuring time in the rest frame of the "moving" observer.
Anyway, there's no problem if you want to put marks between each set of marks already there, so let's say you've done that.
Therefore based on the rest observers view of velocity the moving clock will only accumulate 57 seconds during the trip and have a 0.7367 remainder to the rest observer.
This is true according to your "acceptance" that the moving observer's clock is seen to tick slow by the rest observer. Ok.
Based on the rest observer velocity, rest line length and rest clock tick rate the moving clock will (can) only accumulate 57 seconds IF the 1m long line remains in 1/1 correspondance between frames.
No. Because you "accepted" that the moving clock ticked slower. Remember?
That is its length CAN NOT have changed otherwise the moving clock could not accumulate the 57 ticks if you acknowledge the fact of time dilation on moving clocks.
No. Given your own postulates, of time dilation but no length contraction, the moving observer would say he travelled faster than the rest observer.
In your pretend universe, velocities aren't reciprocal. That's not the case in our real universe, of course, but for the sake of argument, we'll stick with your imaginary one for now.
Therefore it is clear that spatial length contraction did not and cannot occur but what does occur is that velocity becomes frame dependant, not length.
Yes. Congratulations. You have followed your own set of assumptions through to its logical conclusion.
Let me suggest you forget arguements about invariance of 'c'. Forget arguements about MM. Stick with the facts and then see if they do not mandate that we reconsider our prior interpretations of such matters.
As I pointed out, if you now want to connect your imagination to the real world, you'll need to somehow reconcile the reciprocity of velocities in the real world with the fact that velocities are observer dependent in MacM fantasyland.
I think they must. The failure in SRT is the equating of t and t' time intervals when one is known to be different than the other. SRT changes measurement standards between frames but then treats them as equal in the formula d = vt.
Why are you suddenly talking about SRT now?