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Show me where in the above I have changed anything.
The important thing to understand is that the diagram, as shown, is INCORRECT. It does NOT show the correct viewpoint of that first set of inertial observers.
That correct diagram shows that, according to the given inertial observers, the two rockets get closer together during the acceleration, and therefore the string does NOT break.
Notice that they (ucr.edu website on Bell's spaceship paradox) do end the discussion with a diagram showing a very different pair of worldlines the objects could have traced out in the lab frame (the one you called IRF in your posts), where the people in the rockets now would find that the distance between the rockets remains constant - but the person in the lab frame no longer does.
WHEN you do that, then the original diagram (that hung over my desk for 20 to 30 years) violates special relativity ... because the inertial observers who are stationary with the rockets immediately before the rockets are fired, claim that the separation between rockets is constant.
Special relativity (via the length contraction equation) says that any inertial observer will conclude that yardsticks that are moving (in the direction of their length) wrt himself are shorter than his own yardsticks (by the gamma factor). I.e., if gamma = 2.0, the yardsticks are only half as long as they would be if they weren't moving relative to the inertial observer. So the inertial observers who are stationary with the rockets immediately before the rockets are fired MUST (according to special relativity) say that the two rockets get closer together as their speed increases.
I'm just not able to follow you, Eternal.
Each rocket has an attached accelerometer, and those two accelerometers always show exactly the same acceleration. (That is part of the initial specification of the scenario).
The INITIAL diagram says that the inertial observers who are stationary wrt the rockets immediately before the rockets fire, say that the separation of the rockets doesn't vary.
But THAT violates special relativity: special relativity says (via the length contraction equation) that an inertial observer MUST conclude that a yardstick moving away from himself (in the direction of its length) is shorter than his own yardsticks.
If you disagree with any of my above statements, identify the first such statement that you disagree with
But that contradicts special relativity
and tell me exactly why you disagree with it.
Hi.Quote from: MikeFontenot on 27/05/2023 17:21:05If you disagree with any of my above statements, identify the first such statement that you disagree withThis one: Quote from: MikeFontenot on 27/05/2023 17:21:05But that contradicts special relativityQuote from: MikeFontenot on 27/05/2023 17:21:05and tell me exactly why you disagree with it. Because I think it's wrong.
What a cop-out!
[...]It appears to me that you came up with an idea that you think shows a flaw in Einstein's relativity [...][...]
And the fact that his exponential equation in gravitational time dilation was wrong (as I've proven)
If you disagree with any of my above statements, identify the first such statement that you disagree with, and tell me exactly why you disagree with it.
crackpot theories
The idea, I think, was that the two curves must have exactly the same shape because of "the Principle of Relativity" ... i.e., it shouldn't matter where in space you start the curve, the curves should always have the same shape.
But the length contraction equation (LCE) of special relativity says that an inertial observer should conclude that a moving yardstick should get shorter and shorter as its speed wrt the inertial observer increases.
The above diagram (without the diagonal straight lines) shows the perspective of the two accelerating observers.
One thing that diagram DOESN'T show is how the ages of those two observers compare, as time progresses.
The inertial observers who are stationary wrt the rockets immediately before the acceleration begins ...
... will say that the rockets get closer together as the acceleration progresses.
I don't believe that SR predicts that.
To obtain the correct diagram, at each instant of the given inertial observers' time, it is necessary to compute the gamma factor (where "v" is the speed of the rockets at that instant), and divide the constant separation "L" of the rockets (according to the observers on the rockets) by gamma. The result is then added to the location of the trailing rocket, to get the location of the leading rocket.
"If you're loosing an argument, change the subject."
Never argue with a fool; onlookers may not be able to tell the difference.
That's ironic, because my postings take the existing diagram (which I've shown VIOLATES special relativity) and replace it with a new diagram (never before defined) which OBEYS special relativity!
NOTE: My use of the phrase "Proper Separation" in the title of this submission means that it is the separation of the two people undergoing the acceleration, ACCORDING TO THOSE TWO PEOPLE THEMSELVES.
Quote from: MikeFontenot on 28/05/2023 17:37:26And the fact that his exponential equation in gravitational time dilation was wrong (as I've proven) No physicists believe that you have proven time dilation as expressed in relativity as wrong.
Einstein's exponential time dilation equation has only been tested for very small values of its argument L*A, where the exponential is essentially linear. It works fine in that linear range. It fails miserably for large values of "A" ... in particular, it disagrees with the outcome of the twin paradox,
Millions of physicists over the past 100+ never noticed this obvious error?
Scan 2023-4-23 17.01.18.jpg (243.13 kB . 1700x2338 - viewed 2304 times)
The above diagram (which I produced many years ago, and until very recently believed to be correct) is INCONSISTENT with special relativity.
Quote from: MikeFontenot on 10/06/2023 17:05:31The above diagram (which I produced many years ago, and until very recently believed to be correct) is INCONSISTENT with special relativity.Then stop bringing it up since wrong and move on.