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The case for True Length = Rest Length 
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#37
Mar111, 02:09 PM

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Is your idea of "objective reality" fundamentally incompatible with relative quantities? 


#38
Mar111, 02:36 PM

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If an object is transported from one laboratory to another that is moving relative to the first laboratory, then if its length is measured in that lab, the outcome will be the same as the identical procedure that was carried out earlier in the first lab. So there is some property of the object that was unaffected by being moved between the labs. Sort of like "the laws of physics are the same in all inertial frames". Allowed this premise, I assert that relativistic effects cause miscalibrated measurements to give wrong answers. However if the instruments are made so they can take into account these effects, then all inertial observers will actually be measuring the length, and agreeing. Using miscalibrated measurement procedures, one is not measuring anything. A question for you, if there is no objective reality, what exactly is the nature of thing you call length, and is there any point in measuring it ? I have to leave now, but I'll check in again in about eight hours. 


#39
Mar111, 02:45 PM

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A rocket with rest length of 100 meters is moving by at relativistic speed. I have a pair of super fast barriers I can raise and lower simultaneously (as I see it). I can momentarily contain the rest length 100 meter rocket between my barriers set 10 meters apart. My conclusion that the length is less than 10 meters is miscalibrated, and inferior in some way to the rocket's own perception that what happened is that a barrier went up and down in front of the rocket, then both barriers moved, then the other barrier went up and down behind the rocket. 


#40
Mar111, 02:53 PM

P: 266

The scenario above, though, has an analogy in my Rubik's Cube mentioned a couple of posts back...relative motion is analogous to a differing amount of physical rotation, so your 100m rocket would indeed fit between two barriers set 10m apart if it was twisted to the side. My position is that to say that the twisted rocket is now "truly" less than 10m long is a fallacy. 


#41
Mar111, 04:01 PM

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Just a segment of a circle, with each point having the same distance from the origin. That's what you're representing in your speedometer drawings too. But the argument about what this implies about length contraction is still unclear to me. You say: But it seems to me this is just a happenstance fact about mathematical similarities between length contraction and rotated needles seen at a great distance, it doesn't make sense to me to say that because the numbers work out, that means length contraction "really is" just a consequence of "viewing" some vector in an abstract space of (speed*rest length/c) vs. (moving length) at an angleafter all, we measure length in real space and time, not in this abstract space! Also, wouldn't it be just as much a consequence of your argument that you should say the "true" value of the rate a clock ticks is always 1 second/second, and that any apparent change is an "illusion" caused by the foreshortening of a needle in an abstract space of (speed/c) vs. (rate of ticking in frame where clock is moving)? 


#42
Mar111, 04:34 PM

P: 266

Anyway, I'm asserting a correspondence between Lorentz transforms and foreshortening. When you view SR in the manner that I described, both phenomena involve rotating an invariant between 2 perpendicular dimensions. In the former case we are claiming that something is "actually changing" while in the latter case we all acknowledge that it's simply an illusion. All are welcome to continue to hold their own views, obviously, but I find the analogy to be convincing. Also, consider Wiki's explanation of the barandring paradox: 


#43
Mar111, 04:35 PM

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I am sorry Mentz114, but your stance here is completely contrary to SR. In SR length is a relative quantity, meaning that it depends on the frame of reference. It is not a property of the object itself. The length of an object is the distance between the two ends of an object at the same time in some specified reference frame. I would now appreciate an answer to the question which you have avoided twice now: Is your idea of "objective reality" fundamentally incompatible with relative quantities? 


#44
Mar111, 04:37 PM

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#45
Mar111, 04:43 PM

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#46
Mar111, 05:08 PM

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e.g. I do not consider the length of a shadow to be an illusion; the shadow actually has some length. Also, I would not confuse the length of a shadow with some property of the object casting the shadow, and I would recognize that if the shadow were cast from a different light source that the result could be different without there being any paradox or contradiction. 


#47
Mar111, 05:12 PM

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I think there is an issue here with rigid bodies and how they are, in fact, not allowed in special relativity. Special relativity is violated by rigid bodies since, they transmit cause and effect at infinite speed between 2 end points. We should only consider point particles in special relativity. In this sense, the fact that the space "contracts" between 2 points when you are moving between those 2 points can easily be seen in the following experiment (taking timedilation for granted):
Suppose particle A and particle B is 1 lightsecond apart in my (at rest w.r.t. A and B) frame of reference. There is a spaceship, traveling at velocity = .5c from particle A to particle B. At t=0 me, particle A, and the spaceship all coincide in position and the spaceship and me synchronize our watches. From my POV, the spaceship is traveling at .5c from A to B, from the spaceship's POV, point B is moving towards him at .5c and point A is moving away from him at .5c. So, for me the spaceship will get from A to B in 2 seconds. For the spaceship though, B will arrive at where he is in (I am unprimed, spaceship is primed) [tex]t'=\frac{t}{\gamma} = 1.732s[/tex] (The spaceship is the one measuring proper time) Therefore he will say that the distance that point B has traveled from the time that A coincided with him to be: d'=.5c*t'=.866 lightseconds. Therefore, the spaceship must have measured a contracted distance between A and B than I did because his time has been dilated and I must measure the same velocity that the spaceship has that the spaceship measure me to have (otherwise, we would have some paradox like he is traveling at .5c away from me, but in his perspective, I am traveling at v not equal to .5c away from him). If we then ask "what is the ACTUAL or TRUE distance between A or B", then there is no good answer because if you take the length I measure to be some "true distance", then the spaceship which is moving relative to me can never MEASURE this "true" distance (the people can write some equations and try to figure it out, I suppose). Since there are no rigid bodies in SR, I cannot somehow put a perfectly rigid rod between A and B, and allow the spaceship to measure the distance I would measure by transporting that rod to the spaceship. Whether you really want to call my measurement the "true" distance and the spaceship's measurement somehow an "untrue" distance, I think is more up to philosophy than actual physics. 


#48
Mar111, 05:25 PM

P: 266

1) Turn the foreshortened object squarely with yourself and measure it. 2) Turn your measuring device to match the angle of the foreshortened dimension you're trying to measure. 3) Measure the foreshortened length (or, if you prefer, the length of the shadow), and mathematically calculate what the "true length" of the object is. Each one of these actions has an SR analogue. When you observe a Lorentzcontracted object you (could) do 1 of 3 things: 1) Bring the object under consideration into your rest frame. 2) Send your measuring device into the moving frame of the object. 3) Measure it's contracted length and correct your answer taking into consideration the Lorentz transform determined by your relative velocity. In my opinion it's the SAME THING. By claiming that a shadow has a definite length which is separate from the object's "true length" you are merely reasserting my claim that a lengthcontracted object has a definite length which is separate from that object's "true length". 


#49
Mar111, 05:32 PM

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#50
Mar111, 05:44 PM

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The point is that the distance between two ends of an object at some instant in a given reference frame is some number. That number is named "length". You may not like the fact that that number is called "length" but your opinion is not relevant and does not change the facts. 


#51
Mar111, 05:57 PM

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Since option 1 and 2 that you posted, are not possible, and 3 is just manipulating some formulas, then I would say that there is no better reason to call the distance I measure to be "true" than to call, say, the restenergy of a particle as it's "true" energy. 


#52
Mar111, 05:58 PM

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#53
Mar111, 06:05 PM

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#54
Mar111, 06:05 PM

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