# C and h are not fundamental constants?

1. Sep 16, 2014

### kmm

I was looking through Zee's 'Quantum Field theory in a Nutshell" and he says that $c$ and $\hbar$ are "not so much fundamental constants as conversion factors." I've heard other physicists say this as well. I understand that these constants are used in some equations to give units of energy so in this sense I understand how they are "conversion factors" but we can't we still regard them as fundamental constants? Zee didn't say they absolutely aren't, but I'm not entirely sure what he's trying to get at with his distinction. That is, why is putting more emphasis on them as conversion factors than fundamental constants?

2. Sep 16, 2014

### The_Duck

By selecting the right units in which to measure length, time, and energy you can make both $c$ and $\hbar$ equal to one. Since they can be eliminated by a convenient choice of units, they can't be that fundamental. Furthermore, any significant amount of work in special relativity and quantum mechanics will convince you that those units in which $c$ and $\hbar$ are eliminated are the *right* ones to use when working with the fundamental laws. See here for a nice analogy.

Compare, say, the fine structure constant, which is approximately 1/137 regardless of your choice of units and therefore is a better candidate for a "fundamental" constant.

Last edited: Sep 16, 2014
3. Sep 16, 2014

### kmm

Thanks for clarifying that more. I've never really thought about the physical constants in this way. I can understand why we want to say that a constant is "fundamental" when it is a number that it is independent of the units used.

At the same time I still want to call for example, the speed of light, a fundamental constant. No matter what reference frame or units are used, we come to a number for the speed of light which still describes the same speed. So perhaps it's that the speed of light is itself fundamental but the constant itself isn't. I suppose I'm being a bit semantical about this.

4. Sep 16, 2014

### ChrisVer

how can an energy dependent quantity as the fine structure, be considered fundamental? (just to avoid misconceptions)
I guess you mean that whatever the choice of your units, it is always 1/137 at low energies.

5. Sep 16, 2014

### Staff: Mentor

6. Sep 16, 2014

### The_Duck

Yes, there is a fundamental important thing here, and it is that the laws of physics are invariant under Lorentz transformations. This symmetry means that time and distance ought properly to be measured in the same units. Therefore an object's speed is really a dimensionless number, and the speed 1 (i.e., the speed of light) is indeed special and important.

I knew someone was going to quibble about this. Yes, to be definite pick $\alpha(\mu = 0)$ or $\alpha(\mu = m_Z)$ or something, or better yet the coupling constants of whatever GUT underlies the standard model.

Last edited: Sep 16, 2014
7. Sep 16, 2014

### kmm

Exactly, this is what I expected.

Thanks for that!

8. Sep 16, 2014