Axioms [LWN.net]

Axioms

Posted Feb 23, 2021 1:06 UTC (Tue) by mpr22 (subscriber, #60784)
In reply to: Axioms by Wol
Parent article: An introduction to lockless algorithms

It is not possible to calculate the speed of light by pure logic, because the numerical value of the speed of light is a consequence of your units of measurement.

There is one particular physical constant, µ_0 (the permeability of free space) which was historically defined (as a consequence of the relationship between electrical current and induced magnetic fields) as exactly 4π × 10^-7 H/m ... but that value is no longer strictly valid (although it's close enough for the vast majority of practical purposes), because the ampere has been redefined in terms of the elementary charge and the second.

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Axioms

Posted Feb 24, 2021 1:00 UTC (Wed) by SiB (subscriber, #4048) [Link] (2 responses)

Physical constants that carry units do not carry any physics. The universe does not care about the value of the speed of light.

Some years ago in our coffee room at the institute there was a discussion about the possibility that the fine-structure constant α may not have been constant in the past after all. The question was raised, which of the constituents of α=e²/(4πε₀ħc) may be the reason. Well, the answer is e, if at all. α is a constant without units. It is pure physics. It defines the strength of electromagnetic interactions. The universe cares a lot about the value of the fine-structure constant α. In our experimental units it is the charge of the electron e that represents that strength, but in the end, it also just defines units of measure.

Theoretical physics defines the units differently than experimental physics. They mostly use c=4πε₀=ħ=k=1. Everything is measured in eV or eV¯¹.

From a theoretical point I am a bit unhappy about the new definition of the SI units. They fixed the value of e, although it indirectly represents a quantity the universe cares about. The cost is that µ₀ and ε₀ are now _not_ fixed by definition in the SI, as they were before, like Wol said.

Ideally, all units were defined by fixing the value of some fundamental constant. We are now almost there. The second is still defined by an artifact. At least it is an atom, so it can be reproduced everywhere in the universe. To fix that we need to fix the gravitational constant. But metrology defines units by what they can measure with the best precision. The gravitational constant does not apply, it has to catch up at least eight orders of magnitude in precision.

Axioms

Posted Feb 24, 2021 1:16 UTC (Wed) by SiB (subscriber, #4048) [Link]

s/Wol/mpr22/

Axioms

Posted Feb 25, 2021 3:46 UTC (Thu) by NYKevin (subscriber, #129325) [Link]

> Physical constants that carry units do not carry any physics. The universe does not care about the value of the speed of light.

The universe may not care about the speed of light, but the stuff in the universe surely does. To borrow from your "theoretical physics normalizes everything to 1" example, the mass of the proton is much, much (numerically) smaller than the charge of the proton, and surely there's some physical significance of that? Or, alternatively, we can say that there's nothing wrong with the proton, and instead it's gravity which is too weak, but that's just reframing the same question in different units. I'm not sure you can ask that question without using units at all.

Ultimately, I suppose the "proper" framing of this question is some nonsensically complicated question about why the relevant quantum fields happen to interfere in exactly the way that they do to give the proton the properties that it has. But you can't even ask that question until you know what gravity is, at a quantum level, and to the best of my knowledge, nobody does.