Basic Special Relativity Question

The original scenario simply involved a rod moving inertially toward the floor of the train. It was never attached to the ceiling, it is simply in inertial motion (like the train and the platform).

We can define a release from the ceiling if you like. but it won't simply be "cut the wires" (which were never part of this thread):
In the rest frame of the train, the entire length of the rod is pushed off the ceiling at once.

 

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Nope , the dumbed down scenario you concocted was simply supposed to remove the gravitational field from the original scenario. Now, that I showed you that the scenario you created contains an internal contradiction, you are trying to change it.

You created a self-contradictory scenario, live with it.

 

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The scenario is as posted. Changing it to suit yourself doesn't help us find out what's going on.

 

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Don't bite, Pete; Tach is in full-fledged baiting mode but I want this analysis to be concluded in a consensus

 

Thanks Rod.
Tach, there are no wires in this scenario. There's no gravity, so cutting wires wouldn't do anything anyway.
The only thing that fits with the OP is if all parts of the rod are pushed from the ceiling simultaneously.


Is that unphysical?

 

Nothing to do with any wires, nothing to do with any gravitation, I just showed you that you created a self-contradictory scenario.

In the platform frame:
The \(B"\) endpoint starts moving \(\gamma' \frac{VL}{c^2}\) earlier than \(A"\) . By virtue of being connected to \(A"\) , \(B"\) describes a circular arc with the center in \(A"\), exactly like a moving pendulum.
To make matters worse, when \(A"\) starts \(\gamma' \frac{VL}{c^2}\) later, it is \(A"\) turn to pivot around \(B"\), so contrary to your beliefs, neither end moves inertially in the platform frame. You created a self-contradictory scenario, now you will have to live with it.
PS: the fact that you have the "seal of approval" from the forum resident crackpot RJBeery, doesn't bode very well.

 

Nah, I am done pointing out the math and physics mistakes in the scenario. How is your stalking going, RJ?

 

You say people are "stalking" again?

Your not a celebrity, no one wanna stalk you. Weird, you know?

 

Right on cue!

 

I am quietly lurking for the sake of the analysis. If I didn't care about letting you guys complete the analysis I would let people know when they were being complete douche-nozzles. The fact that you say you're done pointing out errors is actually a sign that you realize that Pete and Fednis48's analysis is correct after accounting for their errors.

 

You are always lurking, never contributing anything. Too bad that you can never follow the science. You compensate by being always entertaining in your ignorance, your "seal of approval" is the kiss of death, on par with getting Motor Daddy, Prof. Layman or Farsight's "seal of approval".

 

http://www.wolframalpha.com/input/?i=Integrate[Sqrt(x+x^3)]

This is just one of my favorite websites, but I don't think it's what you want or what you want actually exists.

 

Looking back at my OP, Pete is quite right here. I did say that the rod "is dropped from the ceiling," but I didn't specify how. The obvious way - just holding onto it and then letting go at some train-frame time - doesn't work because letting go won't do anything absent any gravity.

Given this, there are two ways to proceed. One would be to come up with a gravity-free release mechanism and apply it to the problem retroactively. But I think this would be a waste of time, since the impact is the part of the problem we're interested in. Option two is to remove the release from the problem entirely, and just say that the rod starts in a downward-moving inertial state. I suppose for this scenario to occur, the rod would have had to be launched at some point in the past. But ignoring this launch and focusing on the inertial movement and impact is no less physical than ignoring the past acceleration of the train when we call it an inertial frame.

 

Neither approach makes the fact that \(B"\) starts \(\gamma \frac{VL}{c^2}\) earlier than \(A"\) making \(B"\) ROTATE about \(A"\) go away. Pete understood that his goose was cooked when I pointed this out to him. It is even further cooked when \(A"\) starts moving as well, because it starts rotating about \(B"\). So, NEITHER point can move inertially. On the other hand, in the frame of the car, BOTH move inertially, since both frames are inertial, one would expect for the endpoints to move inertially in the frame of the platform (but they don't). So, you created a scenario that contains a self-contradiction. Not that SR is self-contradictory, your scenario is.

 

How does \(B"\) start earlier than \(A"\) if we go with option two? If we just say that the rod is initially in a downward-moving inertial state, \(A"\) and \(B"\) are both moving the whole time (at least until they hit the ground). \(A"\) is never pinned to the ceiling of the train, so \(B"\) never has to rotate around it.

 

Relativity of Simultaneity, remember? In \(S'\) the two ends start simultaneously, in \(S"\) , not so much.

LOL, they need to start at one point in time, Pete already tried this desperation curved ball.
Heck, the train car has a roof at finite height.
You need to come to grips that when you dumb down scenarios you end up with self-contradictory ones. This is the lesson that you need to take away from this attempt.

 

Tach, this is a sincere comment so please take it as such: forget the other thread. Surely you have to agree that the OP describes a physically plausible thought experiment, yes? Take the roof off of the train; put it in deep space. Send the rod toward the floor in a parallel fashion from the floor's frame (doesn't matter how). Now...would other (arbitrary) frames see the rod as remaining parallel with the floor? It's an interesting question and should be answerable by the brainpower on this site.

 

Woah. I thought I was misunderstanding you; I didn't think you were actually going this route. I have two responses to this, and I can't decide which I like more, so I'll post both.

1. The detailed argument, via painstaking deductive logic:

A. I want to ignore the release of the rod and treat an inertial, downward-moving rod as our initial condition.
B. You say this isn't ok, because the rod needed to start moving at some point in time.
C. The only constraint on when in the past the rod could have started is that the roof is at finite height.
D. Since there's no gravity to worry about, the roof could be made arbitrarily high without changing the problem.
E. From C and D, the rod could have started moving at an arbitrarily early point in time.
F. From B and E, you say it's not ok to treat an inertially moving rod as our initial condition if the rod started moving at any point in time.
G. There is nothing unique about rods as compared to other objects in relativity.
H. From F and G, you say it's not ok to treat any inertially moving object as our initial condition if that object started moving at any point in time.
I. All trains are man-made objects that had to be built and started moving at some point in time.
J. From H and I, you say it's never ok to treat an inertially moving train as our initial condition.
K. From J, your reasoning implies that all SR thought experiments on trains are ill-posed.

2.The short version

When I say that I want to treat the rod as initially in a downward-moving inertial state, that removes the release from the problem, and we haven't even gotten to the impact yet. With both the release and the impact out of the picture, my proposed scenario becomes: "A rod is moving downward at constant velocity in a moving train." If you think that is a self-contradictory scenario, you have bigger issues than I thought.

 

You can't wish away the starting conditions. Pete wanted to do the same thing as soon as he realized his goose was cooked and that scenario is self-contradictory.

Doesn't matter, the rod needs to be kept horizontal through some device.

<skip some irrelevant , desperate attempt to twist the problem>

Not all thought experiments, yours, certainly.

 

Your response is almost identical to mine, Fednis. May I suggest starting a new thread with the thought experiment simplified even further, with corrected math in the OP? If you do this, you should also invoke "alpha rules" (by putting that phrase in the thread title, which I believe are still applicable here); they basically require extremely concise and professional responses at all times. NO ad hominems, and all questions directed at responders MUST be answered; and the mods are more likely to reign in on BS responses (some of which are mine in this thread I will readily admit). If Tach chooses to join that thread he will be forced to address things in a more sincere manner, and if he doesn't then the rest of us can work it out in peace.