Imagine a particle moving with non-zero velocity with respect to us. If I keep measuring an observable of the particle, such as position, then does the particle evolve relativistically? For example, if I have a neutrino under measurement since its creation, and if I let it travel at a very high velocity, would the spacetime contract for that neutrino or it would "die" as fast as a stationary neutrino? (i.e. die out simultaneous to the stationary one.)
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1$\begingroup$ Relativity works. are you asking how to transform between inertial frames? $\endgroup$– Cosmas ZachosCommented Feb 7, 2020 at 15:17
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$\begingroup$ No. By "realtivity works" I meant " the evolution of an observable is relativistic ". My question is: does the act of measuring an observable of a moving particle affect the contraction or dilation of spacetime for that particle, such that it no longer behaves relativistically? In fact I wonder if any experiment has ever tested this statement. $\endgroup$– seyed sepehr mousaviCommented Feb 7, 2020 at 19:39
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Yes, relativity is always applicable. Sometimes the relativistic effects are negligible and regular Newtonian physics can be used without any measurable loss in accuracy, but even in such cases you could use the relativistic math to make your analysis if you wanted.
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$\begingroup$ Is there any experiment that either directly or indirectly supports this claim that spacetime contracts even if we are measuring an observable of the particle? $\endgroup$ Commented Feb 7, 2020 at 19:31
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$\begingroup$ The usual terminology is "time dilation" rather than "spacetime contracts". Yes, time dilation is a well established experimental phenomenon. My favorite experiment is the one by Bailey et al., Nature 268 (July 28, 1977) pg 301, but see here for a more complete list: edu-observatory.org/physics-faq/Relativity/SR/… $\endgroup$– DaleCommented Feb 7, 2020 at 20:03
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$\begingroup$ Thank you for your comment! $\endgroup$ Commented Feb 10, 2020 at 10:35