A turn of the tables here; I'm usually the one asking you to GTFO. Anyway I don't own the book you're referring to but you apparently do, so why do you have a problem accepting that as the explanation for the problem listed in the OP?
Relativity paradox
- Thread starter renislaj
- Start date
Where did you crib the solution from, then?
Because you are a liar and a fraud, you've always been one and you don't know when to stop polluting threads with your pseudoscience and to start shutting up.
Years ago I came up with the scenario after reading about the pole/barn paradox, which can be solved by a simple RoS explanation (i.e. what it means to have the doors closed "at the same time"). I did NOT know the answer at the time, I thought I had conjured an unresolvable paradox in SR, but internet searching explained that one frame detects a greater rotation. The same applies here...except the rod's curvature is the only way to accommodate for equal impact forces at both ends when the rod hits the floor. This curvature can be explained physically by Janus' force propagation reference.
you are just continuing to lie. Disgraceful but, coming from you, within character.
No, it can't since there are quite a few errors in Janus' formalism, Janus still has yet to answer. Besides, the scenario from Taylor and Wheeler is quite different from the scenario in the OP. In T-W, both observers agree on the outcome, not so here. So, keep your mouth shut, stop trying to ride the coattails of people who actually know physics, pretender.
Neddy Bate
Valued Senior Member
You are thinking that if one end of the beam impacts the floor before the other, (as it does in the platform frame), then the first impact would cause damage (like a dent). But if you would just do an inverse Lorentz transform, you would find that both ends impact simultaneously in their own frame of reference, thus any damage must be spread out over the entire body. That was what I was trying to say earlier, but you didn't like my method because it did not stay entirely within the platform frame. If you want an explanation from entirely within the platform frame, I think Janus provided the best explanation so far.
But you seem intent on finding a solution in which both ends of the body impact simultaneously in both frames. That is never going to happen unless you figure out a way to make both frames agree on simultaneity. I know of a way, but it means at least one of the frames has to synchronize its clocks using a non-standard procedure instead of Einstein synchronization.
They disagree on whether the shape of the rod is straight or bent during the collision.
They also disagree on whether the train is longer than the platform.
They only disagree on relative measures, not absolutes.
What specifically is ill-posed about the problem?
Is there an ambiguity or impossibility in the scenario setup?
Exactly.
One last time, "doing the inverse Lorentz transform" is not a valid measurement.
Correct, you are unable and unwilling to work within standard experimental confines. You keep trying to dumb down the problem and go back to the results in the train frame via an inverse Lorentz transform. Inverse Lorentz transforms are not a valid form of measurement in experiments. There is no measuring device capable of performing an inverse (or direct) Lorentz transform.
As I already pointed out, there are errors in Janus' explanation. Go back in the thread, so you can look at them.
No, I am not doing any of the above, I am simply pointing out that the dumbed down version of the problem is ill posed, that you cannot reduce this problem to a Relativity of Simultaneity problem.
Precisely. Meaning that trying to dumb down the problem to a Relativity of Simultaneity problem results into irresolvable contradictions, the trademark of an ill posed problem.
Err, wrong. Based on the proper length measurements, i.e. measurements made in their own frames , the two observers arrive to the conclusion that the platform and the train have the same exact proper length. Nice try but no cigar.
I answered this exact question of yours several times, you are getting repetitive.
Please correct my naive understanding of your disagreeing positions. I am confused. If the train observer sees the rod and floor of the train straight and in full contact along their touching lengths, but the platform observer sees a crooked rod, then the platform observer must also see a crooked train too. Is that not the logical thing? The floor of the train must also appear crooked to the platform observer because the train observer testifies that the floor and rod touch all along their lengths while platform observer says the rod is bent. If rod appears bent to platform observer, and if train observer say that rod and floor touch everywhere along rod, then floor must follow rod shape for platform observer, making both rod and train appear bent to platform observer? Is something wrong with this logical conclusion from combining the meanings of your respective posts above? If correct, then both observers are correct that the rod is in contact with train floor perfectly all the contact lengths. The train observer sees the contact line as "straight". The platform sees the contact line as "bent". Both correct because full contact between rod and floor "seen" in both frames?
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An excellent line of reasoning, proving that attempts to dumb down the problem by solving it via a simple minded appeal to Relativity of Simultaneity in SR fails miserably.
Correct, as explained in Markus' post 2.
Thankyou. I read Markus #2 post before. Markus requires some physical process to happen in the train. But if train also appear crooked to platform observer then that Markus explanation is not the same as mine? If Markus explanation depends on things happening in order to "level" the rod, then that is different from my naive conclusion based on the train being bent also for the platform observer, so no special physics inside train necessary to explain rod in full length contact with train floor from both observer frames? Is that a simpler reconciliation of train and platform frame views?
Tach, maybe you can explain a couple of things to me about the view you're advocating, because I'm a little confused.
2. Do you maintain that Markus' post 2 explanation, invoking Thomas precession to negate the rotation, is a correct explanation?
1. By this, do you mean that you think Undefined is correct in saying the platform observer will see the train as bent?
2. Do you maintain that Markus' post 2 explanation, invoking Thomas precession to negate the rotation, is a correct explanation?
There are no irresolvable contradictions in this scenario. At least none that have been pointed out.
The observers disagree on the relative shape of the rod during the collision.
So what? Shape is relative.
What absolute measures do they disagree on?
And no one disagrees about the shape of the rod measured in its own frame.
There is no disagreement about the absolute measures such as proper length.
There is disagreement about the relative measures:
In the train frame, the train is longer than the platform.
In the platform frame, the platform is longer than the train.
But this is of course not a contradiction - relative measures (like length, simultaneity and shape) are relative.
I haven't asked those exact questions before.
All you've said is that the scenario leads to a contradiction (it doesn't), that the two observers disagree on the outcome of the experiment (they only disagree on relative measures such as length and simultaneity) therefore you conclude it must be ill-formed.
But you haven't attempted to discern what exactly is ill-formed about it.
Try this, the scenario is posed a little more formally, and leaves it to you to determine the outcome:
A train is at rest in frame S(x,y,t).
The floor of the train is at y=0 (ie along the x-axis).
A rod of negligible mass is above the floor, parallel to the floor, moving toward the floor at velocity $$\vec{v_r}(x,y) = (0, -v_r)$$
At t=0, the rod collides inelastically with the floor.
Frame S' is moving relative to S at $$\vec{v}(x,y) = (v, 0)$$
What happens to the rod in frame S'?
The floor of the train is at y=0 (ie along the x-axis).
A rod of negligible mass is above the floor, parallel to the floor, moving toward the floor at velocity $$\vec{v_r}(x,y) = (0, -v_r)$$
At t=0, the rod collides inelastically with the floor.
Frame S' is moving relative to S at $$\vec{v}(x,y) = (v, 0)$$
What happens to the rod in frame S'?
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Yes, the explanation based on Thomas precession is correct. Both observers see the rod parallel with the train car floor, respectively the platform. See next post for the mathematical proof.
Wrong, we aren't talking about the shape of the rod in the train car frame as viewed from the platform frame.
We are talking about the shape of the rod in the platform frame as measured in the platform frame vs. the shape of the rod in the train car frame as measured in the train car frame. We are talking about a comparison of the proper shapes of the rod.
Actually, according to the discussion, they would, IF the rod were to be measured to fall at a non-zero angle in the platform frame. Turns out that I can prove that is not the case.
Actually you have been disagreeing on that by virtue of disagreeing on the angle of fall. You may not realize or admit it but this is the case.
I have, several times. But you won't admit to it.
I am glad that you are attempting to formalize a little the dumbed down version of the problem. Since you are so intent on solving the dumbed down version instead of the realistic one, I'll solve this version for you.
First off, there are THREE frames of reference that you must consider, not TWO:
$$S"=$$ the frame of the train car
$$S'=$$ the frame of the falling rod
$$S=$$ the frame of the platform
There are two speeds that we need to consider:
$$v'=(0,-u)$$ the speed between $$S'$$ and $$S"$$
$$v=(V,0)$$ the speed between $$S$$ and $$S'$$
This is a classical problem of Thomas precession.
The angle made by the rod with the floor of the car , in the frame of the car $$S"$$ is $$\theta"$$.
The angle made by the rod with the platform , in the frame of the platform is $$\theta$$.
Form the description of Thomas precession:
$$tan(\theta)=\frac{v'}{v \gamma(v)}$$
$$tan(\theta")=\frac{v'\gamma(v')}{v}$$
So:
$$\tan(\theta")=tan(\theta) \gamma(v)\gamma(v')$$
Since $$\tan(\theta")=0$$ it follows $$tan(\theta)=0$$.
In other words:
$$\theta"=0 => \theta=0$$
QED.
Now, having solved the dumbed down version of the problem, I'll let you ponder on how to solve the much more difficult problem in the realistic case of accelerated motion in the presence of the gravitational field. Hint: you will no longer be able to use the Lorentz transforms, you will need to use the equations of accelerated motion (Rindler coordinates).
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Motor Daddy
Valued Senior Member
A question for Tach:
If in the train frame the wires are cut simultaneously, and the rod lands flat on the floor, then we can calculate the acceleration of the rod to the floor, since gravity is in fact included.
Let's assume the rod is dropped from a height of 16.087 feet in the train frame and the rod takes one second to land on the floor flat. That is an acceleration of 32.174 ft/sec^2. So we now know that from the time the wires are cut to the time the rod hits the floor is exactly one second, correct?
If in the train frame the wires are cut simultaneously, and the rod lands flat on the floor, then we can calculate the acceleration of the rod to the floor, since gravity is in fact included.
Let's assume the rod is dropped from a height of 16.087 feet in the train frame and the rod takes one second to land on the floor flat. That is an acceleration of 32.174 ft/sec^2. So we now know that from the time the wires are cut to the time the rod hits the floor is exactly one second, correct?
$$t=\sqrt{\frac{2h}{g}}$$
Motor Daddy
Valued Senior Member
"g" being what?
gravitational acceleration, please open your own thread , you seem to be trying to learn 9-th grade physics on the cheap, don't pollute this thread
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