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In a peer-reviewed publication, one of the length-contraction effects of a physical object, depicted in the diagram, is used to derive conclusions. It has been referenced by other authors and in Wikipedia. The paper is not identified here intentionally, hopefully, to avoid bias in possible explanations.

Edit summary: The original diagram is modified in response to initial comments, to clarify that what was referred to as 'changes in the y-direction' is not relevant to the main question. Please ignore the ‘old set of drawings’ and kindly consider the same question with reference to the ‘new set of drawings”, as edited.

new diagram

Question: Which of the bottom two diagrams in the edited drawing above shows (descriptively) the effect of length contraction for an object depicted with solid lines in the top diagram?

The old diagram is included below, for reference with the initial comments.

old diagram

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    $\begingroup$ Is y axis height increasing in both images? $\endgroup$ – Razor May 15 at 16:19
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    $\begingroup$ The length of the moving object along the y axis should be the same as when it is stationary since this is perpendicular to the direction of motion. Yet this distance changes in both bottom diagrams ?? $\endgroup$ – gandalf61 May 15 at 16:23
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    $\begingroup$ Since this is a question tagged "special relativity". The axes should be clarified. Is this a diagram in the xy-plane? Or a spacetime diagram? $\endgroup$ – robphy May 15 at 16:54
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    $\begingroup$ I'm not sure what bias you're worried about, but I strongly suggest that you identify the paper you're talking about. People will be able to provide more complete answers if you include the full context behind your question. $\endgroup$ – Carmeister May 16 at 0:59
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    $\begingroup$ @ghogoh Please do not ever edit a question which has received answers in a way that invalidates the answers! That is against the site policy. You should always ask a new question instead. I normally revert such edits but since Math Keeps Me Busy has already updated their good answer I will not revert this one. $\endgroup$ – Dale May 16 at 13:05
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EDIT:

The question has been altered with a new set of diagrams. There are no lengths given in the new (or old diagrams) nor are either the length contraction factor or the velocity given. So the question is slightly ambiguous. However, working with what we have we can say that

  1. The diagram which shows the thickness of the object reduced to about half, but the angle unchanged, is definitely wrong. If the thickness were reduced to about one half, the total extension in the X-axis would be reduced by about one half as well. One would see a very substantial change in the "angle" of the object.

  2. The diagram which shows the angle changed is wrong as well, at least if it is interpreted to show the thickness unchanged, as it seems to. Since the overall X-axis contraction is a smallish fraction of the overall X-axis extension, the change in the thickness of the object will be smallish, and might not be noticeable in the diagram. However, there are two clues that suggest that the thickness was not meant to change. One is the label "length contraction" which seems to suggest the only contraction occurred in the front. The second is the base of the object, which appears unchanged by the contraction. If the thickness of the object is not meant to change in this diagram, then it is wrong as well.

  3. A correct diagram would show both the overall extension (in the X-axis) changed, and consequently the "angle" of the object, and also the thickness of the object. Furthermore, both of those changes would be in the same proportion. If the overall extension (in the X-axis) changed by, say, 10%, the thickness would change by 10% as well.

ORIGINAL ANSWER:

Which of the bottom two diagrams shows (descriptively) the effect of length contraction for an object depicted with solid lines in the top diagram?

Neither.

The dimension in the direction of motion is contracted (the "x" dimension in this case). The other dimensions stay the same, (i.e. the y dimension). Both of the diagrams show a stretching in the y direction, which will not occur.

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    $\begingroup$ Please do not substantially change a question after it has been answered, as it makes the answer look foolish. Instead, ask a new question. $\endgroup$ – Math Keeps Me Busy May 16 at 10:22
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    $\begingroup$ The modification to your question was substantial enough to require rather significant modification to the answer. $\endgroup$ – Math Keeps Me Busy May 16 at 10:53
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    $\begingroup$ @ghogoh No, your edits required revision to the answer, therefore they were substantial edits. You should never make such edits that invalidate already received answers. Doing so is a violation of the site policies. You should not be arguing with Math Keeps Me Busy, you should be apologizing and expressing gratitude for the “above and beyond” assistance that they have provided for you. Their response was very generous, most people would simply revert your edits. Your comments here are both wrong and ungrateful. $\endgroup$ – Dale May 16 at 13:44
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    $\begingroup$ @Dale, What happens, if, due to a misunderstanding, an answer is inaccurate and the edit improves the likelihood of fewer misunderstandings and inaccuracies occurring? However, if my comments are deemed unreasonable, please anyone affected accept my apology. I also express unreserved thanks to everyone, who made an effort and took time to respond. $\endgroup$ – ghogoh May 16 at 14:53
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    $\begingroup$ @ghogoh especially in that case the edit should not be made. If you wrote an unclear question and someone answered your unclear question as it was written instead of as you intended then it is a valid answer and the question must not be edited. Instead, a new question should be asked, linking to the first, and clarifying the distinction. Clearly asking a question is difficult $\endgroup$ – Dale May 16 at 14:58
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The effect of length contraction will be to make the object appear narrower in the x direction (ie more slender) and to reduce the apparent angle of tilt away from the y axis. None of the drawings you have supplied seems to depict that, although if you were to combine the reduced tilt from the left hand drawing with the more slender effect in the right hand drawing, you would capture the overall effect.

If you find it hard to convince yourself, imagine that you replace the object with a large square. You will find it easy to convince yourself that the effect of length contraction on the square will be to make it contract in the x direction so that it becomes a rectangle, taller than it is wide. For extreme length contraction the square will reduce to a tall and narrow rectangle. Now imagine that your slanting object was in fact just a shape painted on the square. You should now find it easy to appreciate that as the square condenses in one direction to become a tall narrow rectangle, the painted section will become both more upright and more slender.

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  • $\begingroup$ Please accept my apology in advance, if I have misunderstood your answer, but the effects of length contraction you describe are both shown in the diagrams: "narrower in the x direction" - in both diagrams; "reduce the apparent angle of tilt away from the y axis" - in the left hand side diagram. $\endgroup$ – ghogoh May 16 at 12:10
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    $\begingroup$ Yes, but neither diagram shows the combined effect properly. The object should appear more slender, as it does in the right hand diagram, and less tilted as it does in the left hand diagram. $\endgroup$ – Marco Ocram May 16 at 12:15
  • $\begingroup$ @ghogoh. If you look at the base of the object in the lower left corner, you see in one figure it is shorter, but in the other figure it appears unchanged. $\endgroup$ – Math Keeps Me Busy May 16 at 12:34
  • $\begingroup$ @Marco, thanks for the clarification - hopefully you would not mind if I entertain your answer as ‘both diagrams combined’ ;-) Could you, please, elaborate why you think length contraction manifests itself in both effects simultaneously, rather than only one or the other? $\endgroup$ – ghogoh May 16 at 12:56
  • $\begingroup$ I will edit my answer to that effect. $\endgroup$ – Marco Ocram May 16 at 13:13
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Both are incorrect. That is, if the "top length" in the left picture equals that of the top picture. Both the angle with the y-axis as "top length" change.

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    $\begingroup$ I don't know why someone down voted this answer. It is correct. $\endgroup$ – Math Keeps Me Busy May 16 at 11:11
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    $\begingroup$ I agree with the comment above. $\endgroup$ – Marco Ocram May 16 at 11:55
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    $\begingroup$ Indeed, I am the writer of the book. My real name is Denis Shaughnessy- Marco Ocram is my pseudonym. You might like the books- their twisted logic should appeal to physicists and mathematicians! $\endgroup$ – Marco Ocram May 16 at 13:20
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    $\begingroup$ @MarcoOcram I notice you pseudonym is a palindrome. :-) $\endgroup$ – Math Keeps Me Busy May 16 at 13:21
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    $\begingroup$ @MathKeepsMeBusy yes, the books are full of puns and wordplay. There is a rumour that you need an IQ of 183 to get all the jokes in the books, but that was started by Marco and I don't believe a word he says. $\endgroup$ – Marco Ocram May 16 at 14:36

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