6 ms·
Mostly because we (humans) made up physical units (i.e. meters) while we were inventing physics. There's nothing keeping you from re-deriving physics equations
by lscharen 15y ago
Mostly because we (humans) made up physical units (i.e. meters) while we were inventing physics. There's nothing keeping you from re-deriving physics equations without the messy constants.
http://en.wikipedia.org/wiki/Natural_units http://en.wikipedia.org/wiki/Natural_units
- neutronicus 15y agoEven then there are some dimensionless numbers that you can't get rid of (the ratio between the strength of the gravitational and coulomb forces being one obvious example).
- waqf 15y agoPi being another.
- arethuza 15y agoI wouldn't have said Pi was a physical constant - it's not like we actually measure circles to derive it empirically.
- waqf 15y agoTrue, but it certainly is a dimensionless number that you can't get rid of (and that actually shows up in physical formulae, such as http://en.wikipedia.org/wiki/Coulomb%27s_law http://en.wikipedia.org/wiki/Coulomb%27s_law). Come to think of it, so is 2. I guess if you tried to measure π by constructing circles, you'd actually be measuring the curvature tensor of space (which is an experimental observation), not π (which is just π).
- derefr 15y agoπ being, simply, the measurement of the curvature tensor of an ideal Euclidean plane. If we lived in a universe that was non-Euclidean at macro-scale, π would be just another irrational number, and some other quantity would be exalted as "fundamental."
- gjm11 15y agoPi would still be fundamental in mathematics whatever the geometry of our universe. (Examples of where it would turn up: consider the differential equation f''=-f; all its solutions are periodic with period 2pi. The series 1-1/3+1/5-1/7... has sum pi/4. The series 1+1/4+1/9+1/16+... has sum pi^2/6. exp(pi sqrt(163)) is ridiculously close to being an integer. There are deep reasons for all these things, and they wouldn't go away if the universe were very far from spatially flat.)
- schmittz 15y agoNatural units are nice, but they are completely impractical for dealing with normal Mirkowskian space. I.e., how do I explain to someone who cannot view me how tall I am? Our normal unit system is nice because it's phenomenological, and maybe inconvenient.
- lscharen 15y agoAgreed, but the universe is under no obligation to express itself in units that are convenient on a human scale. I like to think of this as an anti-anthropomorphic principle.
- schmittz 15y agoI up-voted this comment, because I liked it, but honestly, I first looked for the "like" button. Facebook's got a serious hold on me.