What happens if you increase μ0 and decrease ϵ0? Or vice versa

[em3ry]

I asked what would change if the value of mu change. You people have spent 3 pages hammering away at me to get me to say "ok let's change the value of alpha too" as though that were somehow the most important thing in the universe. I don't care about alpha. If need to change alpha to change mu then change alpha. If you need to change the price of yoyos in china to change the value of mu then change the price of yo-yo's in china. I don't care. I just want to know the answer to my question. Lol.

Since the equation for alpha contains mu I would have thought it rather trivial that we must change alpha too. You people are the ones making a big deal out of nothing. You are clearly continuing some bizarre argument that you have been having between yourselves.

 

[Ibix]

So did you read the list of things that the fine structure constant controls?

 

[em3ry]

A very interesting list indeed

Alpha is related to the probability that an electron will emit or absorb a photon

the fine-structure constant is one fourth the product of the characteristic impedance of free space, Z0 = μ0c, and the conductance quantum

 

[em3ry]

I tend to think of $\epsilon$ and $\mu$ as defining the strength of the electromagnetic force. Alpha then relates that to various other things

$$\\ \alpha = \frac{1}{4 \pi \varepsilon_0} \frac{e^2}{\hbar c} = \frac{\mu_0}{4 \pi} \frac{e^2 c}{\hbar} = \frac{k_e e^2}{\hbar c} = \frac{e^2}{2\varepsilon_0 c h} = \frac{c \mu_0}{2 R_K} = \frac{e^2 Z_0}{2h} = \frac{e^2 Z_0}{4\pi \hbar}$$

I tend to think of Alpha as the speed of the electron in the Bohr model. But since Planck's constant exists outside of the Bohr model then perhaps alpha does too.

 

[Dale]

I tend to think of ϵ and μ as defining the strength of the electromagnetic force.

That is actually a better way to think of $\alpha$.

So I dug up my old table. If $\alpha$ increases then material objects will get longer when measured in meters. In other words, the length of a metal bar of a certain number of atomic lengths as measured using an atomic clock and a pulse of light will increase with increasing $\alpha$. Similarly, the duration of a pendulum tick will increase when measured by an atomic clock if $\alpha$ increases.

I asked what would change if the value of mu change. You people have spent 3 pages hammering away at me to get me to say "ok let's change the value of alpha too" as though that were somehow the most important thing in the universe. I don't care about alpha. If need to change alpha to change mu then change alpha.

Then you have indeed missed the point. Only changing $\alpha$ changes the physics.

If you change only $\mu_0$ and $\hbar$ leaving everything else constant then there is no physical impact at all. You have merely changed your units away from SI. If you change only $\mu_0$ and $c$ you have again only changed units with no physical changes.

If you change only $\alpha$ and $\mu_0$ then you have kept your SI units the same but you have made real physical changes as I described above. If you change only $\alpha$ and $\hbar$ then you have both changed the physics and your units. Furthermore, if the change in $\alpha$ is the same as before then the physical changes will be the same. The physical changes are purely determined by $\alpha$, not by $\mu_0$.

You people aren't even discussing my thread anymore. ...
I don't care. I just want to know the answer to my question. Lol.

I am a little unclear why you are saying this. I have answered your question. I have talked about how the change you asked about would alter nuclear stability, fusion, length measurements, and time measurements. It is certainly not an exhaustive list, but it is a good start.

Your question required some clarification. I think that you still are missing the importance of that point and that you don’t really see why it was important to clarify. But once it was clarified we have indeed answered your question too.

 

[em3ry]

I asked what changes when you change mu. You keep asking me over and over what else I want to change.

If something depends on mu then I want to change it.
If something doesn't depend on mu then I don't want to change it.

If alpha depends on mu then change it too.
If alpha doesn't depend on mu then don't change it.

If nothing in the universe changes then the answer to my question is "nothing changes"

You want to make this a philosophical discussion about dimensionless constants.
I DONT CARE

I just want to know what changes if you change mu. Why is this so hard for you to understant?

 

[hutchphd]

You want to make this a philosophical discussion about dimensionless constants.
I DONT CARE

I will now retract my previous statement about your questions not being foolish

 

[Dale]

You keep asking me over and over what else I want to change.

Yes, because something else must change. And the result of changing $\mu_0$ depends entirely on what else changes.

If something depends on mu then I want to change it.
If something doesn't depend on mu then I don't want to change it.

Unfortunately the universe doesn’t work the way you want it to. None of these things depend on $\mu_0$.

You can change $\mu_0$ without changing $\alpha$. You can change $\mu_0$ without changing $\hbar$. You can change $\mu_0$ without changing $c$. You can change $\mu_0$ without changing $e$. So none of these quantities actually depend on $\mu_0$.

But you cannot change $\mu_0$ without changing at least one of $\alpha$, $\hbar$, $c$, or $e$. So you must specify what else changes. Nothing else automatically changes but something else must change. This is not a part of the question that can be avoided.

You have chosen to also change only $\alpha$, which is a good choice since it is the simplest choice with some physical consequences. And I have described the result of that. So I have indeed answered your question fully.

You want to make this a philosophical discussion about dimensionless constants.
I DONT CARE

You entirely misunderstand. I dislike philosophical discussions. This is not philosophical at all, it is purely physical. You want the physical world to behave in a way that it simply does not, and no amount of all-caps complaints will change that.

Your question requires a specification of what else happens. If you are unwilling to make that specification then you simply do not have a well-formed question. Such a question cannot be answered, not even with “nothing happens”. This is not a philosophical issue, it is a physical requirement.

“What happens if $\mu_0$ increases?” is not a well formed physical question. It has no answer at all because it is incomplete.

“What happens if $\alpha$ and $\mu_0$ both increase together and no other constants change?” is a well formed physical question with the answer I have given. As near as I can tell this is the question you have asked, and I have answered.

 

[em3ry]

Ok. I agree with that. I guess I owe you an apology then.