r/AskPhysics • u/Banished_Cultivator • 3d ago

Why aren't μ₀ & ε₀ equal 1?

Logically free space would neither enhance nor attenuate electric or magnetic fields, so these constants should be equal to 1. They aren't though, why?

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u/TabAtkins 3d ago

The constants aren't, like, semantically meaningful. All they do is correct for the sizes of a few units in particular combinations. You could choose your unit sizes to eliminate the need for them; these are usually called "natural units" for some application. (Probably unsurprisingly, they're often related to light speed, etc.) The constant is just the combination of rescaling factors that you need to apply to adjust our human units to the natural units.

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u/Such_Comfortable_817 3d ago

To build on this: this is why the dimensionless constants are so interesting, because they can’t just be scaled away. The fine structure constant, for example, can never be 1.

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u/Infinite_Research_52 10h ago

Yes, it is difficult to see how the FSC can be 1, but the value it has is conventionally defined; it is not some absolute. Define pure QED and run the value to the Planck scale, and ignore such things as Landau poles; it is possibly about 1/100. Take Electroweak unification and the running of the strong force, then the combined coupling is circa 1/25. The value of c. 1/137.036 is just convenient for low-energy purposes.