Permeability/Permittivity: Any physical significance?

[Battlemage!]

I have had some issues understanding this topic. On two occasions Dale has pointed out to me that they are not really based on physical things, given that their values are completely arbitrarily defined for the purpose of matching certain measurable or defined things, like the ampere and the speed of light.

What I've read about them is that their definitions are, respectfully, how the substance influences the magnetic flux in the region it occupies and how a substance/object holds energy in an electric field.

What I don't understand is, assuming the definitions I've seen are remotely close to correct: aren't those things physical?Now, I get that you can use whatever units you want. You can set the speed of light to 1, for example. The meter, obviously is a defined quantity. As far as I can tell, as far as it goes for units for speed, acceleration, jerk and so forth, only the definition of the second has real physical origins, given that an atom is used to define it.

But isn't the way an object reacts to magnetic or electric fields something physical, regardless of whatever units we make up for it? As far as I can tell, if they aren't really anything to do with reality, then why is the magnetic field or electric field? Are those too merely made up constructs that give us values that match measurements?This is clearly a big point of confusion for me. I'd appreciate any elaboration on this. Or resources with good explanations. Thanks to all!

 

[Dale]

Hi @Battlemage!

This is an essay by Baez that explains the issue. The basic point is that the universal constants that are physically meaningful are the dimensionless ones.

http://math.ucr.edu/home/baez/constants.html

After you have read through the article then we can talk specifically about EM and the fine structure constant.

 

[Battlemage!]

Thanks @Dale ! That actually does shed some light on this. I imagine some things like Pi, which I've read is only the usual value in a flat space, might not fit that mold (the article seems to fit that narrative, as it distinguishes between purely mathematical dimensionless constants and measurable dimensionless constants)?

In any case, since obviously magnets work and electricity is an actual thing, would it be a reasonable assumption that there has to be some sort of dimensionless constant that is in some way related to them? (the link mentions the fine structure constant, aka the electromagnetic coupling constant, per the link) That or I suppose some things just cannot be explained without at least some made up ideas that may not actually have anything to do with reality other than correlating with what we measure.

However the article brought up something kind of disconcerting: it says there are no fundamental dimensionless constants in either general relativity or "pure" quantum mechanics. Granted, while phenomenally accurate there clearly has to be something incomplete about them, but nonetheless it bothers me a bit. Conversely the link mentions that the Standard Model actually has all of these constants, which in that respect seems to be an additional argument for it being on the right path.

Then again maybe I'm getting worked up over nothing important.

Again I appreciate the link and the response!

 

[Dale]

there has to be some sort of dimensionless constant that is in some way related to them? (the link mentions the fine structure constant

Yes, the fine structure constant is the primary dimensionless constant for EM. Basically, it describes in a dimensionless way how strong the EM interaction is.

When people talk about the speed of light "itself" what they are interested in is probably the fine structure constant. The speed of light by itself is just an arbitrary unit, but the fine structure constant governs things like the speed of light compared to the size of atoms and the frequency of atomic transitions. That is the physical content.

 

[Dadface]

I think of permeability and permittivity as representing properties of the medium. For example a capacitor with air between the plates has a certain capacitance but with a different medium of different permittivity between the plates it has a different capacitance.
The difference is related to how the electric field of the medium is affected by the polarisation of the molecules eg polar molecules like water tend to orientate themselves with the field and some molecules can distort such that there is an excess of positive charge at one end and an excess of negative charge at the other end.
Dimensionless constants can be introduced by defining relative permittivity and relative permeability.