Monday 16 December 2019

special relativity - "Reality" of length contraction in SR


I was in argument with someone who claims that length contraction is not "real" but only "apparent", that the measurement of a solid rod in its rest reference frame is the "real length" of the rod and all other measurements are somehow just "artificial" and "apparent". Seemed to me like a bad conversation about poorly defined words and not really relevant to physics, but then some quotes were offered:



...so that the back appears closer to the front. But of course nothing has happened to the rod itself.



(Rindler)



The effects are apparent (that is, caused by the motion) in the same sense that proper quantities have not changed.




(Resnick & Halliday)


At the same time, the IEP entry on SR insists that length contraction and time dilation are "real", with observable consequences:



Time and space dilation are often referred to as ‘perspective effects’ in discussions of STR. Objects and processes are said to ‘look’ shorter or longer when viewed in one inertial frame rather than in another. It is common to regard this effect as a purely ‘conventional’ feature, which merely reflects a conventional choice of reference frame. But this is rather misleading, because time and space dilation are very real physical effects, and they lead to completely different types of physical predictions than classical physics.


[...] However, this does not mean that time and space dilation are not real effects. They are displayed in other situations where there is no ambiguity. One example is the twins' paradox, where proper time slows down in an absolute way for a moving twin. And there are equally real physical effects resulting from space dilation. It is just that these effects cannot be used to determine an absolute frame of rest.



I went through a lot of Einstein, Minkowski and Lorentz original material, and didn't find anything about what is "real" and what is not. Finally, I know about muons, where the effects of SR seem to be very real (from Wikipedia, but I had seen it in a physics class before):



When a cosmic ray proton impacts atomic nuclei in the upper atmosphere, pions are created. These decay within a relatively short distance (meters) into muons (their preferred decay product), and muon neutrinos. The muons from these high energy cosmic rays generally continue in about the same direction as the original proton, at a velocity near the speed of light. Although their lifetime without relativistic effects would allow a half-survival distance of only about 456 m (2,197 µs×ln(2) × 0,9997×c) at most (as seen from Earth) the time dilation effect of special relativity (from the viewpoint of the Earth) allows cosmic ray secondary muons to survive the flight to the Earth's surface, since in the Earth frame, the muons have a longer half life due to their velocity. From the viewpoint (inertial frame) of the muon, on the other hand, it is the length contraction effect of special relativity which allows this penetration, since in the muon frame, its lifetime is unaffected, but the length contraction causes distances through the atmosphere and Earth to be far shorter than these distances in the Earth rest-frame. Both effects are equally valid ways of explaining the fast muon's unusual survival over distances.




So which is which? Why do Rindler, Resnick & Halliday use the word "apparent"?



Answer




The laws of physics have the same form for all, but there are different measurements which are equally "real"?



Correct. Having said that, it is often sensible to differentiate between 'apparent' and 'proper' (or 'intrinsic') values, the latter normally measured in the rest frame of the object in question and giving an upper or lower bound for an observable that varies continuously from frame to frame.


However, this does not imply that 'apparent' values are less real: For example, arguably all massive objects have zero proper (3-)momentum, but if you get hit by a train, its apparent momentum will feel quite real to you ;)


Also, proper values need not always exist, in particular in case of light. Eg, there's no way to decide on physical grounds which wavelength should be considered the intrinsic one of a photon: The one at time of emission, or the Doppler-shifted one at time of absorption? The process is time-symmetric and as there is no rest frame for light-like particles, basically the whole continuum of wavelengths is equally (im)proper.


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