Answer by M. Winter for What justifies dimensional analysis?
In my opinion, you can very well add 10 meters and 5 seconds. The answer then is just "10m + 5s". If that is the answer to your computation of how long a metal rod should be, then that is okay.If you...
View ArticleAnswer by Vincent Fraticelli for What justifies dimensional analysis?
Sorry for my english !Above all, I want to say that I totally share everything that has been said before about dimensional analysis and homogeneity of equations. But as often in physics, things can be...
View ArticleAnswer by user5174 for What justifies dimensional analysis?
I'll add a mathematical companion to the existing answers.We are often interested in one-dimensional real vector spaces. While every such thing is just isomorphic to $\mathbb{R}$, there is practical...
View ArticleAnswer by Count Iblis for What justifies dimensional analysis?
Fundamentally there are no units in physics. The result if all measurements is always a dimensionless number. If you say that you measured the length of some object to be one meter, then the outcome of...
View ArticleAnswer by KCd for What justifies dimensional analysis?
Jack, I will explain the problem here first in a mathematical rather than physical way. The mathematical issue at play here is that the operation you are proposing is not well-defined at the level of...
View ArticleAnswer by user300 for What justifies dimensional analysis?
Most of the answers seem to be reiterating that you're not allowed to add lengths and times just because it doesn't make sense. Here's why it doesn't make sense.If two objects have the same temperature...
View ArticleAnswer by jpmc26 for What justifies dimensional analysis?
Physics is concerned with finding a mathematical model to describe and predict reality. Units are a convenient and useful way for us to distinguish between quantities that describe different facets of...
View ArticleAnswer by PotatoEngineer for What justifies dimensional analysis?
In physics, you're not allowed to ignore the units; they come along for the ride on every sub-step of every calculation. From a mathematics perspective, consider the units to be variables, so instead...
View ArticleAnswer by jwimberley for What justifies dimensional analysis?
Physics is independent of our choice of unitsAnd for something like a length plus a time, there is no way to uniquely specify a result that does not depend on the units you choose for the length or for...
View ArticleAnswer by chase for What justifies dimensional analysis?
All right, I'm cashing in my comments to provide an answer:Let's start with an example that doesn't invoke dimensions, units, or physics at all. How do we evaulate the following expression?$$1 +...
View ArticleAnswer by Kyle Kanos for What justifies dimensional analysis?
Surely you can add or multiply any two numbers, those are indeed simple mathematical operations. But physics is not math, it is physics. We attach units to values to represent something physical and...
View ArticleWhat justifies dimensional analysis?
Dimensional analysis, and the notion that quantities with different units cannot be equal, is often used to justify very specific arguments, for example, you might use it to argue that a particular...
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