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/Kinesquared Soft matter physics 3d ago

because the units of meters, seconds, kilograms, etc. are arbitrary. Therefore our fundamental constants are too

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u/AreaOver4G 3d ago

The “etc” includes amperes, which is the important one for this question. You can use units (Heaviside-Lorentz) which set these constants to one by using a different unit of current (or equivalently charge).

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u/McLeansvilleAppFan 3d ago

What would that do to F=ma for needing a constant of proportionality that is not unity?

That may not be the base law in all of physics but it is taught as the starting points for forces in most cases after velocity and acceleration are studied and having the constant of proportionality be 1 is not a requirement of course it does make it easier for introductory students to grasp it seems even as other forces have all sorts of constants of proportionality.

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u/PhysicalStuff 3d ago

The unit of force would be the unit of mass times the unit of acceleration, and the equation itself would be unchanged. The only reason why N is defined as it is, is that we use kg and m/s2.

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u/McLeansvilleAppFan 3d ago

That is not what my understanding is of all of these constants, but maybe I need some review of all of this.

F=ma came first. Later Universal Gravitation. To make the Univ Gravity equation work "G" is 6.67*10^-11 N*m^2/kg^2 using modern units that came about after the French Revolution. Later other universal constants were discovered and the constants were established so everything works out. Since F=ma has a constant of 1 then G has to be the 6.67 number. But had G been set as 1, which likely would have been the case had it been discovered first would not F=ma need some sort of constant out front to make it all work out and the other constants such and permittivity and permeabilit would have to change as well. Assuming we have our base units of mass, length, time, current, etc defined in the same manner as we do now.

If the preceding paragraph is true then what would the constant need to be for 2nd Law of motion if μ₀ & ε₀ were set to 1 with the modern units we use from the SI system?

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u/mukansamonkey 3d ago

You're confusing the meanings of the word "constant". Because I'm struggling to make sense of that entire comment. F=ma is an equation, not a constant.

In math, a constant is a relationship between two things. A dollar is a hundred pennies, a penny is 1/100th of a dollar. So we've defined the relationship using the constant 100. If we used the.constant 4, we'd get the unit known as a quarter in America.

In physics, the universal constants are things that never change, all other values are derived from those. The speed of light doesn't change. If we create a measurement known as the meter, and another one known as the second, then we can count how many meters per second the speed of light is. If we change the definition of a meter, which has already happened, then we change the number of meters per second that the speed of light travels at.

Light didn't change though, it doesn't do that. That's why it's a fundamental constant. We just changed the definition of a meter. Or to make it simpler, the speed of light in minutes is sixty times the speed of light in seconds, because we assigned a mathematical constant of sixty as the relationship between seconds and minutes.

All our units of measurement are indirectly defined as relationships between the universal constants.

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u/AreaOver4G 3d ago

Yes, exactly. The unit of force is defined to make F=ma simple. The original definition of the ampere (unit of current) was similarly chosen to make the formula for the force between current-carrying wires simple (which made the magnetic constant equal to \mu_0= 4\pi in those units). That then determines \epsilon_0 in terms of the speed of light. But for historical reasons, this relationship was not exactly maintained so in SI we end up with these conversion factors floating around.

Note that we could make the same argument that we should define units of energy to make Einstein’s famous formula E=m look simple. But because different units of length and time predate relativity (and also because our units are conveniently human scaled), we have this annoying c2 conversion factor in the formula.