Is there any experimental evidence of space contraction which theory of spacial relativity predicts? You should bear in mind that GPS & muon detection beyond the distance permitted by its half life are the evidences of time dilation. If not is it justified to accept the theory of special relativity & consequences thereof? The supposedly answer to the similar question is already ruled out in the question.
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$\begingroup$ Do you mean length contraction? Did you read the Wikipedia article? $\endgroup$– ACuriousMind ♦Commented Apr 24, 2015 at 14:44
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$\begingroup$ Yes! length contraction amounts to space contraction. $\endgroup$– Mohammad Shafiq KhanCommented Apr 24, 2015 at 14:45
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1$\begingroup$ Yes, it's been done at the RHIC. See the link I've suggested. $\endgroup$– John RennieCommented Apr 24, 2015 at 14:46
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3$\begingroup$ Both questions ask the wrong question. Length contraction and time dilation are flip sides of the same coin. $\endgroup$– David HammenCommented Apr 24, 2015 at 14:57
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3$\begingroup$ @MohammadShafiqKhan - I don't have the time or inclination to read yet another wrong-headed anti-relativity rant. They are one and the same thing, just from different perspectives. From the perspective of someone on the ground, a relativistic muon created at an altitude of 10 km can reach the ground because of time dilation. This time dilation doesn't exist from the muon's perspective. Instead, the muon sees the ground as being only 2 km away. $\endgroup$– David HammenCommented Apr 24, 2015 at 15:29
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It would be really difficult to get experimental evidence of length contraction of an extended object. A measuring device attached to the object would contract along with it, and even if measurements were recorded and then read after the object stopped (relative to an observer's inertial frame), they would show no contraction.
Thus, length contraction can be measured only from an inertial frame at rest or moving considerably slower than the observed object's inertial frame. It's not possible with present technology to achieve relativistic speeds with a significantly extended object. Although it's possible to achieve relativistic speeds with atomic particles, their small size prevents direct measurement of their relative extension.
Nevertheless, as John Rennie noted in his comment: "Experiments at the RHIC (Brookhaven Relativistic Heavy Ion Collider) have "seen" the nucleons inside gold nuclei contract to a thin disk configuration when moving at close-to-light speed. Gold nuclei, moving in opposite directions, are collided." Reference https://www.physicsforums.com/threads/modern-physics-view-of-length-contraction.575495/page-3
There is indirect experimental evidence of length contraction. Five examples of this are in the Wikipedia article to which @ACuriusMind directed you: http://en.wikipedia.org/wiki/Length_contraction#Experimental_verifications
The paucity of direct experimental evidence has led some to take an extreme position, more suited to philosophy than physics, that length contraction does not occur (Be careful not to swallow it "hook, line & sinker", and note that this view is invalid if the RHIC experiment is considered a direct measurement): http://www.alternativephysics.org/book/LengthContraction.htm
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$\begingroup$ I reproduce the final statement in your last link. "So what do experiments tell us about LC? Here we draw a blank. Several experiments have been either tried or proposed, but they failed to measure that a variation in length occurred [2], [3]. To date no experiment has been able to confirm the existence of LC". $\endgroup$ Commented Apr 25, 2015 at 4:49
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$\begingroup$ I reproduce the problems of LC in the other link en.wikipedia.org/wiki/Length_co..."Due to superficial application of the contraction formula some paradoxes can occur. For examples see the Ladder paradox or Bell's spaceship paradox. However, those paradoxes can simply be solved by a correct application of relativity of simultaneity. Another famous paradox is the Ehrenfest paradox, which proves that the concept of rigid bodies is not compatible with relativity, reducing the applicability of Born rigidity, and showing that for a co-rotating observer the geometry is in fact non-euclidean". $\endgroup$ Commented Apr 25, 2015 at 4:56