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I was considering this xkcd comic from 5/10/14, with the alt-text "Trains rotate the Earth around various axes while elevators shift its position in space." I'm wondering about its accuracy.

http://xkcd.com/1366/

I first considered the elevator scenario. As the elevator accelerates (to start or stop its motion), the occupants feel a fictitious force, demonstrating conclusively that it is the elevator and not the planet which is in motion. By this argument, an elevator is fundamentally different from a device which physically displaces the planet. Similarly, I suspect that a train doesn't "rotate the Earth," since such a rotation would be felt by occupants on Earth as an angular or centripetal acceleration. Any observer can conclude definitively that it is the train which is in motion around the Earth, not the Earth rotating under the train.

For this reason, is the comic is not strictly correct?

(Note that there is a minimal motion of the Earth resulting from the action-reaction force pair between the train and the planet, but it's safe to say that this motion is negligible relative to the distance traveled by the train, since $I_{earth} \gg I_{train}$.)

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The comic is making a joke out of reference frames, it is making no such remark about the accuracy of the physical statement that "trains rotate earth."

If trains did rotate earth, then two trains coming at each other at the same time would cause earth to stop rotating. However, in your own personal reference frame, the train appears to rotate earth as you travel from point A to point B (because you are always the stationary observer). And that is the joke the comic is making.

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  • $\begingroup$ My question then becomes: is the physical statement accurate? Naturally, there's a willing suspension of disbelief required for interpreting most creative works (including this one). $\endgroup$ May 11 '14 at 1:01
  • $\begingroup$ There's no suspension of disbelief required here, it's entirely dependent on you getting that the joke isn't about trains but about relativity. $\endgroup$
    – Kyle Kanos
    May 11 '14 at 1:14
  • $\begingroup$ But, to answer your question, I'll ask you one: if trains rotate earth, what happens to earth when two trains are head towards each other? $\endgroup$
    – Kyle Kanos
    May 11 '14 at 1:14
  • $\begingroup$ I don't think that trains rotate earth. (That's what I believe the comic is claiming, though, which is why I disagree.) It's very possible that I'm misunderstanding something. $\endgroup$ May 11 '14 at 1:27
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    $\begingroup$ Correct, the trains don't actually rotate earth. However, in your personal reference frame, the earth moves while you are on the train going from point A to point B. This is the joke. $\endgroup$
    – Kyle Kanos
    May 11 '14 at 1:28
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While I don't disagree with either of the two existing posters the comic can be interpreted literaly and be correct. However, the motions are ...

  1. Very small as they are of relative size $\frac{m_\text{mode of transport}}{m_\text{Earth}}$.

  2. Taken relative the subjunctive Earth centered frame in which the train or elevator does not move.


To figure out how small do something like

Take an elevator full of people to mass 6 metric tons and allow that it has moved 100 meters (about 30 stories) vertically. The above gives us $$ d_\text{Earth} \approx \frac{6 \times 10^3 \,\mathrm{kg}}{6 \times 10^{24} \,\mathrm{kg}} (100 \,\mathrm{m}) = 10^{-19}\,\mathrm{m} \,,$$ which is about 1/10000 times the size of a proton. Similar calculations can be done with the angular position of the Earth as a large freight train tools across a continent and while the results are not quite as tiny they are still trivial.

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You answered your own question. In order for the comic to be correct, $I_{train} >> I_{earth}$.

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  • $\begingroup$ I suspect the comic primarily alludes to motion from the reference frame of the train rather than the action-reaction force pair in my parenthetical comment. $\endgroup$ May 11 '14 at 1:00
  • $\begingroup$ A (probably untrue) story has Albert Einstein asking a train conductor,"Excuse me, does New York stop at this train?" $\endgroup$
    – DJohnM
    May 11 '14 at 1:22
  • $\begingroup$ This does not provide an answer to the question. To critique or request clarification from an author, leave a comment below their post. $\endgroup$
    – Hunter
    May 11 '14 at 1:35
  • $\begingroup$ @Hunter The last statement does answer his question about whether the comic is accurate. It will only be accurate when $I_{train}>>I_{earth}$. $\endgroup$
    – LDC3
    May 11 '14 at 2:08
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    $\begingroup$ Maybe you are right, but in my opinion this could have been a comment because you are not really explaining anything. $\endgroup$
    – Hunter
    May 11 '14 at 2:13

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