I want to deeply understand it on a mathematical level. Unfortunately I’m not quite there yet in school, but looking forward to it makes me feel unconfident. I know the facts, but I don’t “understand them.”FactChecker said:"Understand" at what depth? There is a big difference between developing an intuitive acceptance and being able to do all the calculations. GR is an extreme example of that. Even Einstein had trouble doing specific calculations for examples to support GR. SR is much easier. Intuitive acceptance of SR is very easy if you understand (and consider) the relativity of simultaneity. That is especially true for the well-known "paradoxes" of SR. Even in SR, the calculations can get tricky if the problems introduce unnecessary complications.
Strong disagree on this point. A novice should be meticulous about fully displaying all units and continue to do so until the person intuitively knows the units of everything in the equations being used.robphy said:Advice:
-Work in natural units so that c = (3e8 m/s) doesn't show up in calculations.
You just work in seconds and light seconds (or years/light years or whatever). Then ##c## shows up but the numerical work is easy.ohwilleke said:Strong disagree on this point. A novice should be meticulous about fully displaying all units and continue to do so until the person intuitively knows the units of everything in the equations being used.
ohwilleke said:robphy said:Advice:
-Work in natural units so that c = (3e8 m/s) doesn't show up in calculations.
Strong disagree on this point. A novice should be meticulous about fully displaying all units and continue to do so until the person intuitively knows the units of everything in the equations being used.
As a math and science tutor when I was in college (and afterwards), one of the most common mistakes I saw was confusion about what units a quantity has which leads to stupid mistakes because the student is confused about which dimensions something has and makes assumptions that are dimensionally obviously wrong.
Reserve natural units until finishing a course in graduate school.
robphy said:Advice:
-Work in natural units so that c = (3e8 m/s) doesn't show up in calculations.
-Use seconds and light-seconds, not seconds and meters.
A frequently meaning of "using natural units" is to omit c=h=1 from the notation entirely.robphy said:Take the next sentence in my quote.
A "light-second" is a perfectly good unit of length,
and on the road to truly natural units where (say) length is also measured in "seconds".
My point is: use "4 light-seconds" instead of "1.2e9 m".