Just came across this question and am very confused.
"Which fundamental quantity required that its unit of measurement be redefined following acceptance of the theory of special relativity?
(A) Luminous intensity
(B) Length
(C) Mass
(D) Time "
Any help would be very much appreciated!
I believe the answer is B, though I don't think any of them are right tbh. Luminosity intensity is clearly not related. The other variables (mass, length, and time) do not change within an inertial frame of reference: a meter is still a meter, a second is still a second, and a kilogram is still a kilogram.
Context: the previous definitions of a meter and kilogram were based off arbitrary objects stored in an arbitrary vacuum chamber in France. Every year, scientific institutes around the world would send their copies of a meter and kilogram to France to calibrate them against the official one in France. Cleaning the objects etc would often cause small layers to shed off, and thus the definition of a kilogram and meter changed every year. As a result, there needed to be a more robust way of defining the meter and the kilogram. I don't know the original definition of a second but you could look that up (it was also probably arbitrary).
1 second was redefined as the period it took for electrons to bounce a certain number of times between energy levels of the Caesium atom.
1 meter was redefined as a fraction of the distance that light travels in one second.
1 kg was only redefined up until very recently in the last year or two from what I recall (I'm not clear on the specifics).
The reason I believe the answer to your question is B is because the redefined unit of length is the only one whose definition directly depends on the speed of light. However, I don't know if it was necessarily REQUIRED its unit of measurement to be redefined. I guess one could argue that the meter ruler will contract according to observers in other inertial frames. However, in your frame it doesn't change and you could always use the meter ruler in your reference frame to measure lengths, so the old definition of the meter would still work in your inertial frame. Scientists just wanted a new definition of a meter that wasn't depended on some arbitrary object stored in a vacuum chamber in France. The constancy of the speed of light provided this solution, as it meant that the meter could now have its definition redefined in terms of universal constants.