- #1

em3ry

Gold Member

- 63

- 18

I have been thinking about the physical significance of Planck's constant.

The effect of increasing Planck's constant on blackbody radiation is the red line below. Y-axis is frequency

Apparently if Planck's constant were infinite then there would be no blackbody radiation. But we know that as long as the speed of light is finite then accelerating charges will emit light.

Wikipedia says:

So that got me thinking. The speed of light is $$\sqrt{\frac{1}{μ0 ϵ0}}$$. So that means that if you increase μ0 and decrease ϵ0 by the same amount then the speed of light would be the same but surely something in the universe would change.

My question is about μ0 and ϵ0 but if you have any insight into Planck's constant then I will be glad to hear it too.

edit: I see that the Larmor formula depends on

$$P = {2 \over 3} \frac{q^2 a^2}{ 4 \pi \varepsilon_0 c^3}$$

edit2: Dale mentioned the Fine structure constant in post 1 below. It is:

$$\alpha = \frac{1}{4 \pi \varepsilon_0} \frac{e^2}{\hbar c} = \frac{\mu_0}{4 \pi} \frac{e^2 c}{\hbar}$$

edit3: The force between two separated electric charges with spherical symmetry (in the vacuum of classical electromagnetism) is given by Coulomb's law:

$$F_\text{C} = \frac{1} {4 \pi \varepsilon_0} \frac{q_1 q_2} {r^2}$$

comparing to the equation for the Fine structure constant we get:

$$F_\text{C} r^2 = constant = \alpha \hbar c$$

edit4: As Dale explains in post 65 his point about alpha is that given an equation like 1=abcxyz if you change z then you must change at least one other variable but more importantly the equation doesn't tell you which one to change. You must decide that on your own. Dale's point went under my radar and I apologize.

The effect of increasing Planck's constant on blackbody radiation is the red line below. Y-axis is frequency

Apparently if Planck's constant were infinite then there would be no blackbody radiation. But we know that as long as the speed of light is finite then accelerating charges will emit light.

Wikipedia says:

So that got me thinking. The speed of light is $$\sqrt{\frac{1}{μ0 ϵ0}}$$. So that means that if you increase μ0 and decrease ϵ0 by the same amount then the speed of light would be the same but surely something in the universe would change.

**So what would change if you increased μ0 and decreased ϵ0 by the same amount so that the speed of light was the same as before?**Surely this would have some effect on the universe.My question is about μ0 and ϵ0 but if you have any insight into Planck's constant then I will be glad to hear it too.

edit: I see that the Larmor formula depends on

**ϵ0**and c but not**μ0**. Decreasing**ϵ0**increases the energy radiated by an accelerating charge.$$P = {2 \over 3} \frac{q^2 a^2}{ 4 \pi \varepsilon_0 c^3}$$

edit2: Dale mentioned the Fine structure constant in post 1 below. It is:

$$\alpha = \frac{1}{4 \pi \varepsilon_0} \frac{e^2}{\hbar c} = \frac{\mu_0}{4 \pi} \frac{e^2 c}{\hbar}$$

edit3: The force between two separated electric charges with spherical symmetry (in the vacuum of classical electromagnetism) is given by Coulomb's law:

$$F_\text{C} = \frac{1} {4 \pi \varepsilon_0} \frac{q_1 q_2} {r^2}$$

comparing to the equation for the Fine structure constant we get:

$$F_\text{C} r^2 = constant = \alpha \hbar c$$

edit4: As Dale explains in post 65 his point about alpha is that given an equation like 1=abcxyz if you change z then you must change at least one other variable but more importantly the equation doesn't tell you which one to change. You must decide that on your own. Dale's point went under my radar and I apologize.

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