I I think the special theory of relativity self-contradicts

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The discussion centers on a claim that the special theory of relativity (SR) contains a self-contradiction regarding the behavior of two rulers in relative motion. The initial argument presents a series of calculations leading to the conclusion that the relative speed must be zero, contradicting the premise of their motion. However, responses emphasize that the perceived contradiction arises from a misunderstanding of the relativity of simultaneity and the proper application of length contraction and time dilation. It is suggested that a more accurate analysis using Lorentz transformations would resolve the issue, reinforcing the consistency of SR. Ultimately, the conclusion is that the contradiction lies in the flawed reasoning rather than in the theory itself.
  • #31
@Leepappas is correct in posts #25 and #28 that I made a mistake in my diagrams. It changes nothing about the conclusions.

The first diagram I posted is correct:
1695578341905.png

I've added labels for the ends A and B of the red rod and A' and B' of the blue rod. The next diagram was where the error began - "State 1" and "State2" are correct, but "State 3" is when the B and B' lines cross. The corrected diagram is:
1695578351150.png

As before, the definition of simultaneity in the primed frame yields sloped lines in this frame:
1695578360187.png

Note that, in the primed frame, "State 2" is after "State 3"! This is the relativity of simultaneity striking - the definitions of the states are anchored to spacelike separated events, and the ordering of spacelike separated events is frame-dependent.

Again we can transform this last diagram into the primed frame:
1695578371378.png

And again, we can switch back to the original unprimed frame and add a green line showing the time ##\Delta t_2/\gamma## that corresponds to what that frame calls "during" the gap between "State 2" and "State 3":
1695578380500.png

And again we can show that in the primed frame:
1695578390370.png

And again, we can see that the green line does not correspond to the gap between any pair of fine blue lines. The relativity of simultaneity cannot be ignored.

Does the green line still not show the interval you were thinking of? It doesn't matter. None of the intervals match up once you take into account the relativity of simultaneity, and this "proof" needs some of them to match up.

This is a rookie mistake. Most of us have made it at some point early in our learning, and understanding why it's a mistake is one of the big steps in developing insights into relativity.
 
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  • #32
Leepappas said:
In my analysis I am not trying to compare the first and last events in the sequence in each frame so I can compare the total time deltas that's not what I'm doing. There are two moments in time or states of the universe that I am focusing on. One moment in time is state one and the other moment in time is state three and I did it right and I got the contradiction what say you?
How can that be only two times for all those length measurements? Even measuring a single length of an object involves the location of the beginning and the end at "the same time" defined by the IRF, IRF1, that the length is being measured in. But the "same time" in IRF1 is two different times in any other IRF. Have you taken that into account?
 
  • #33
Leepappas said:
It's it's child's Play for me so yes.
It is really not. As mentioned above, you clearly don’t understand the relevant concepts and don’t recognize which formulas to use. You simply are not qualified to make the claims you are making.

I challenged you above to post a professional scientific reference that makes the same proof you are claiming here. You have failed to do so. That is the standard used on this forum.

As such, this thread is closed until you find such a proof. Once (if) you do so, just PM me and I can reopen it. Until then the two disproofs you have received and the many recommendations to study the relativity of simultaneity and the Lorentz transform will suffice.
 
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