# Plank units

#### PhiJ

Why do they use newton's universal gravitational constant, when that is a low gravity approximation and general reletivity is what it used to work things out?

#### robphy

##### timelike observer
Homework Helper
Gold Member
PhiJ said:
Why do they use newton's universal gravitational constant, when that is a low gravity approximation and general reletivity is what it used to work things out?
It says "The gravitational constant is a fundamental physical constant which appears in Newton's law of universal gravitation and in Einstein's theory of general relativity."

This constant appears in the Einstein Field Equations (scroll down about 25% on your Planck_units reference).

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#### PhiJ

OK, thanks, I should read more thoroughly next time.

#### PhiJ

Wait a sec (or maybe a plank time :P), if the speed of light is a dimensionless constant, then shouldn't it be -i, as according to SR, time is distance*i, and speed = distance/time = x/ix = 1/i = -i.
Unless, of course I misunderstood my SR text, (v. likely) or GR changes it.

#### robphy

##### timelike observer
Homework Helper
Gold Member
The speed of light is not dimensionless... It's a speed... with SI units of m/s.

#### yogi

You can also arrive at a different set of so called fundamental units of time, space and mass by combining G and c with the electron charge rather than h. All of which leads one to wonder if this process is little more than cosmic numerology with no real physical significance

#### PhiJ

But time is a dimension, and so is distance. I got the impression from the SR sheet I was reading, that time*i*c=a spacial dimetsion. I assumed that the reason why you were mutiplying by c was not to multiply by metres and divide by time to get distance, but because we measure distance and time using a different 'stick', we use a shorter stick for distance than time, and we must convert. If we used the same stick, then t*i=x, and thus the speed of light is t*i/t=i (oops, I put -i earlier).

Somebody tell me I'm being stupid...

#### dextercioby

Homework Helper
You're not. Misinterpreted the old-fashioned $ict=x^{0}=x_{0}$ prescript for making the flat Minkowski metric $\eta_{\mu\nu}\rightarrow \delta_{\mu\nu}$.

In today's physics, we only encounter such anomalies when we do a Wick rotation, but that's another story...

Daniel.

#### PhiJ

So the speed of light is i?
I was reading http://en.wikipedia.org/wiki/Wick_rotated. Why do you model all space times with squared dimensions. I see why in Minkowski, but not in Euclidian.
Also, what's the s on this page (in the formula with ds)

Thanks

#### rbj

yogi said:
You can also arrive at a different set of so called fundamental units of time, space and mass by combining G and c with the electron charge rather than h. All of which leads one to wonder if this process is little more than cosmic numerology with no real physical significance
i think those are called "Stoney units" and had been defined before Planck. i think they had to also include the electron mass. you need 4 independent quantities to base 4 unit definitions on (length, time, mass, and charge). perhaps, now that i think of it, Stoney units normalize $G$, $c$, $e$, and $4 \pi \epsilon_0$ and the electron mass is not in the mix.

my feeling is that Planck units (or a small adjusment to them, i think that normalizing $4 \pi G$ and $\epsilon_0$ makes more natural sense than normalizing $G$ and $4 \pi \epsilon_0$ as is done in Planck units) is more natural than any system that is based on properties of any object or particle or "thing". Planck units are defined based on the properties of the vacuum of space and not of any "thing" in that space. i don't think it's an accident of Nature that there are 3 fundamental dimensions of quantity (length, mass, time) of which 3 fundamental base units had been defined completely anthropocentrically (meter, kilogram, second) which are used to measure three fundamental dimensionful constants ($G$, $c$, $\hbar$) that are not properties of any "thing" in the universe only of the space of the universe itself.

then, given a natural unit of charge, you can ask what is the Fundamental charge in terms of that natural unit and the answer is the square root of the Fine-structure constant. and that actually makes a lot of sense since, in a physical system shorn of all dependence on anthropocentric units, $\alpha$ is the strength of the E&M interaction of fundamental particles. double the charge of the electron, proton, positron (or the quarks that make up these particles) and you quadruple their relative EM force on each other. and likewise quadruple $\alpha$.

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