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seen Apr 16 at 21:26

Apr
10
awarded  Notable Question
Mar
22
awarded  Good Question
Feb
17
awarded  Notable Question
Feb
16
awarded  Quorum
Feb
10
comment What justifies dimensional analysis?
@jwimberley I actually didn't even read the math (sorry! It seemed overkill). It was that you explicitly explained that "such a formula would necessarily stop being true if you used different units, and we assume physical laws don't depend on units" that did it for me.
Feb
10
comment What justifies dimensional analysis?
@CarlWitthoft The non-triviality of the question is evidenced by the fact that only 1 answer out of 9 produced a conclusive argument that wasn't just a restatement of "it obviously wouldn't make sense". You should read the accepted answer (and Rahul Narain's which is basically a summary of it) and see if the question still seems so silly.
Feb
9
accepted What justifies dimensional analysis?
Feb
8
awarded  Popular Question
Feb
8
comment What justifies dimensional analysis?
I have to say this does make sense to me. Although, if I wanted to be stubborn I could question why we're so sure there couldn't be a formula that only happens to work in one set of units, but I admit that would be an unusual situation.
Feb
8
awarded  Nice Question
Feb
7
awarded  Yearling
Feb
7
comment What justifies dimensional analysis?
The fact that it wouldn't work for other comets is surely what we're trying to establish through dimensional analysis in the first place, so your reasoning seems circular to me.
Feb
7
awarded  Commentator
Feb
7
comment What justifies dimensional analysis?
But I don't see how you did show that (your last sentence). My claim would be that that equation will always be numerically true, which is meaningful.
Feb
7
comment What justifies dimensional analysis?
@chase No, I didn't concede that. I said that adding matrices of different dimensions was undefined.
Feb
7
comment What justifies dimensional analysis?
@chase But that's wrong because it's undefined. I did define what I meant in the comet example - I meant that I was claiming that that procedure would get you the correct value.
Feb
7
comment What justifies dimensional analysis?
Honestly now, who would use a phrase like that seriously when talking about something like dimensional analysis?
Feb
7
comment What justifies dimensional analysis?
There is no accusatory tone. What there is is a humorous tone (which I'm honestly a bit surprised has gone so completely lost, but sorry about that). In any case, your argument still just seems to boil down to "it wouldn't make sense", which doesn't seem conclusive to me.
Feb
7
asked What justifies dimensional analysis?
Nov
20
answered Physics Paradox about Newtons Second Law $F=ma$