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and, my terminology is probably off, but, I think I can explain with an example.

Take a Newton, which can be described as a KG*Meter/Second^2 - which frankly, written that way, looks confusing to me, and it makes more sense written in English "it's a force that will accelerate a 1 KG object 1 meter per second per second." - assuming no friction or angular momentum of-course.

Now, here's my question. I read once that there was a physics formula that was purely numerical and didn't have an units (units being, "KG" "Meter" and "Second", etc) - and I remember reading that once, but I've been googling and I can't find it.

Does that ring a bell, that physics formula where the units cancel out and you're just left with a number?

And my 2nd question is, is that relevant to anything or is it just a mathematical quirk?

I don't know if that makes sense and if doesn't, I'm going from remembering something I came across years ago and I might not have it exactly right in my memory.

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closed as unclear what you're asking by John Rennie, ACuriousMind, Kyle Kanos, Martin, JamalS Feb 19 '15 at 14:59

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    $\begingroup$ There are lots of dimensionless constants used in physics. I think the best we can do is point towards the list I've linked so you can look through for the particular constant you remember. $\endgroup$ – John Rennie Feb 19 '15 at 10:51
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    $\begingroup$ There's also non-dimensionalization which is where you divide your equation by a characteristic scale and obtain an equation that has no dimension. $\endgroup$ – Kyle Kanos Feb 19 '15 at 14:01
  • $\begingroup$ As a sidebar, I found what I was looking for. I was posting from memory, not knowing what it was called, which is why my question seems vague. This is what I was asking about: en.wikipedia.org/wiki/Fine-structure_constant $\endgroup$ – userLTK Nov 6 '18 at 7:04
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There are many of such formulas. Start with Snell's law that relates sines of angles (which are just numbers) to refractive incides (which are also just numbers) but obviously has physical content.

What's even more astonishing (but might also be a bit confusing) is that in so-called "natural units" most equations have no units. All you have to do is to measure everything with respect to other physical quantities (preferably those that are fundamentally constant, such as the speed of light or Planck's constant) and then a speed is just a number (basically at how much of the speed of light you go). The whole system of units is man-made in order to measure stuff in numbers that go well with everyday applications but Physics itself can do without them.

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  • $\begingroup$ I found what I was remembering but didn't articulate very well: en.wikipedia.org/wiki/Fine-structure_constant Thanks for your answer. I'm not sure I follow it entirely, so I'll read it again when I have a bit more time. $\endgroup$ – userLTK Nov 6 '18 at 7:05

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