# B Derive Vacuum permeability and permeability...

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1. Mar 18, 2016

### Younghun park

Derive Vacuum permittivity and permeability using Quantum Field theory or String theory!

If QFT or String theory is real fundamental theory, it can be derived the permittivity and permeability
of vacuum.

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Last edited by a moderator: Mar 18, 2016
2. Mar 18, 2016

### Staff: Mentor

Vacuum permeability is an arbitrary constant that depends on your choice of units. You can choose units where it is 1. In the SI it is chosen to be $\mu_0 = 4 \pi \cdot 10^{-7} \frac{N}{A^2}$ which defines the unit Ampere. There is nothing to derive.

3. Mar 18, 2016

### Younghun park

No! Vacuum permeability and permittivity must have perfect value!
Light speed c is caculated with that according to electro-magnetic theory.

If vacuum permeability and permittivity has no value, light velocity has no perfect value.

4. Mar 18, 2016

### Staff: Mentor

What is a "perfect value"?
The speed of light is another arbitrary constant. In natural units it is just 1. There is nothing to derive.

Only dimensionless physical constants are really fundamental, as they do not depend on the unit system. No current theory predicts them, they are free parameters in the theories. While it would certainly be nice to find some theory that predicts them, there is nothing fundamentally wrong with free parameters in theories.

5. Mar 18, 2016

### Younghun park

mfb
I can't agree with your thought.
Einstein supposed that speed of light has the same value in all the coordinate systems in his special relativity theory.
It was proved through the some precise experiments.

The speed of light is another arbitrary constant ?
Well, I think it is not true..

In electro-magnetism, speed of light is the value which can be derived.
It depends on vacuum permeability and permittivity.
It is not arbitrary constant but the value which depends on vacuum permeability and permittivity.

Last edited: Mar 18, 2016
6. Mar 18, 2016

### Staff: Mentor

Yes. The numerical value of that speed is the same in all reference frames, but it depends on your choice of units. The numerical value is completely arbitrary.

In meters per second, the speed is 299 792 458.
In miles per minute, the speed is about $1.12\cdot 10^7$.
In lightseconds per seconds, the speed is 1.

Actually, we use the speed of light to define the length of a meter. The speed of light is exactly 299 792 458 m/s by definition. Does this number have any physical relevance? Of course not, and anyone else not using our arbitrary meter scale won't recognize that number at all.

There is a relation between vacuum permeability, permittivity and speed of light, yes. This relation is true in all systems, and this has a physical relevance. You can derive it from the Maxwell equations which can be derived from quantum field theory (in very lengthy ways, but it is possible). The individual numbers in various unit systems are meaningless.

7. Mar 18, 2016

### Staff: Mentor

You should pay attention to what mfb is trying to teach you. He is 100% correct on this. Dimensionful fundamental constants are defined by your arbitrary choice of units. It is common practice to use units where they are arbitrarily set to 1.

In the SI system c is arbitrarily defined as exactly 299792458 m/s, and the permeability of free space is defined as $4\pi 10^{-7} H/m$. From those it follows that the permittivity of free space also has an exactly defined value in SI.

Here is a page that explains this concept some more: http://math.ucr.edu/home/baez/constants.html

Last edited: Mar 18, 2016
8. Mar 19, 2016

### Orodruin

Staff Emeritus
Let me just add that the speed of light is defined the way it is because it makes the definition of a meter define a length similar to the original meter definition. It is just a matter if convenience.

Also, I have changed the level tag of this thread - "A" level implies that your understanding is at the level of a graduate student in physics and want an answer directed at that level.

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