Basically, in physics, there are 4 fundamental constants of nature.
G-gravitational constant
h-planck constant
e-electron charge
c-speed of light
(one can say that assosiated with h is h-bar, and the 1/3 fractional charge of a quark)
Suppose we set G=c=hbar=quarkcharge=1.
how would this simplify Relativity and/or quantum mechanics?
Everything would come out even, and physics would be so simple, that no one would fund research.
Oh, yeah, the values would not reflect the observations of a thousand years of scientific research, another minor quibble.
The rule of reason: “If no one uses it, there’s a reason.”
This is often done as a device to make one’s equations neater.
Basically, all one is doing is changing the units with which the constants are measured.
Yes, it does make the equations neater and the reason for doing so is sheer laziness. It’s utterly standard in particle physics to take c=hbar=1 and then just forget about them. You occasionally need to work in SI units, but it’s hardly difficult (particularly by the standards of whatever else you might be doing) to use dimensional arguments to put these constants explicitly back into your final equations. While I wouldn’t swear to their typical habits, I believe that general relativity types usually have c=G=1. If you’re particularly anal, you can work out constraints on exactly what systems of such units are possible in general.
As a consequence of this sort of behaviour, I have to confess that, while I have a Ph.D. in quantum field theory, I’d be pushed to quote either h or G to within a good few orders of magnitude in SI units. In practice, they’re both 1. Otherwise, look them up in data tables.
These sorts of issues aren’t entirely trivial: Planck was partially influenced in his black-body research that led to quantum physics by the prospect that a constant with the units of action (i.e h) would give a “natural system” of units. That’d be one in which the fundamental units of length, time and mass could all be defined as 1.
I love this kind of thread. Can you elaborate?
Make that 6:
[list][li] $ - taxes[/li] X - death
Others have noted that it is done all the time.
Two interesting observations: the mass of the Sun is 1.5 kilometers. And, the difference between the electric terms and the magnetic terms in Maxwell’s equations involve a factor of c, the speed of light–by making c=1, the difference disappears, and it is clear that electricity and magnetism are different aspects of the same phenomenon.
If you let c=1, then, for instance, a certain well known equation becomes E=m. If you’ve done this in all your equations, you can continue to merrily do all your manipulations with them as normal. When you derive something, you can put the missing constant back in by looking at the dimensions of the result. Thus, if you’d derived E=m, you know that in SI units energy is kg m[sup]2[/sup] s[sup]-2[/sup], while mass is in kg. You’re missing something of dimensions m[sup]2[/sup] s[sup]-2[/sup]. Since c has units of m/s, you know you’re missing a factor c[sup]2[/sup]. Hey presto, E=mc[sup]2[/sup]. It’s more fiddly when there’s more than one constant that you’ve set to 1, but you can still do (provided you didn’t make the mistake of setting too many to 1 in the first place; you can do it with up to the number of units in the problem.)
It’s one of those little tricks that people quickly pick up when it becomes useful to them. About the only disadvantage to it is that you usually have to think a bit harder when it comes to checking the dimensions in an answer to see if you’ve made a mistake. After all, you’re already exploiting the fact that the dimensions are wrong in the answer to deduce the missing constants.
As jiHymas noted, you can think of it as changing to a different set of units. You still have to remember that, even if c=1, that’s still a dimensionful quantity. In normal units you can say that the length of a 1-metre long rod is 1, but it’s still more correct to say that the length is 1 metre. Alternatively, you can think of it as just being a technical trick.
It only works for dimensionful constants, so you can’t take the fine structure constant and change it from 1/137 to 1. If you’re being particularly pedantic, you can argue that only dimensionless quantities have any meaning. It’s thus not particularly fundamental (though often convenient) to relate the mass of an electron to a lump of metal in Paris. The dimensionless ratio of the mass of the proton to the mass of an electron is interesting and that’s a number which is the same in all possible systems of units. In practice, you usually can calculate an answer as a ratio with some more familiar quantity. That gives you a better feel for the significance of your answer. It also lets you avoid worrying about the likes of SI units much of the time.