I am really sorry if this question is inappropriate or wrong. But this is something that I can never perfectly agree with, it just keeps on striking my mind when I am studying something new in Physics. So, my question is:
Whenever developing any new theory or formulating any law, why have scientist always considered the constant of proportionality to be constant for every case?
Here is my question in depth:
Lets take the case of resistivity:
- We say: $R \varpropto L$
- And, $R \varpropto 1/A$
- So, $R \varpropto L/A$
- And hence, $R = \rho L/A$
And this works in the real world very well. Now, have a look at this example and my question. Why is the $\rho$ constant considered to be constant for every case? I mean I understand that if $R$ increases, $L/A$ will definitely increase(which is intuitive enough), but the thing which I am not able to understand is why, for every $k$ times increase or reduction in $R$, why does $L/A$ also gets effected by the same $k$? Is this not more guess work or making assumptions instead of precision?
I have another question: Suppose in the above example, we noted that $R \varpropto L$.
So, could we not make another constant, like $R = kL$? Will this constant not help us to determine $L$ without knowing what is $A$? Why do we combine all variables into one equation while formulating laws?
Note: I request the readers to give a more general answer. This was just an example I quoted, as we all know most of the physics laws involve these constants.