As a mathematician, I will inherently be biased against dark matter and dark energy (if you're calculations don't fit, then your mathematics is not suitable, so change the math before you change the physical description). What is the relationship between dark matter and dark energy, and does this have any effect on the r^2 law assumptions and the introduction of dark matter?
For example, does this mean that when we thought that r^2 was not strictly followed that in fact we had the positions of the bodies wrong?
> if you're calculations don't fit, then your mathematics is not suitable, so change the math before you change the physical description
Physics is littered with mathematical formulations predicting new phenomenon (forces and particles).
> What is the relationship between dark matter and dark energy
There is no known relationship between dark matter and dark energy. They could have been called unknown matter and unknown energy! The absence of a good account for each does not infer a relationship between the two.
> Physics is littered with mathematical formulations predicting new phenomenon (forces and particles).
Sorry, I should have clarified: I mean I would spend all my days doubting the mathematics, rather than doubting the physical universe. If that makes sense? Of course all of mathematics can be argued to have a physical sort of root.
You cannot choose your allegiance and stick with it. The reality is that there is always various types of evidence to contend with.
Chances are if you were a physicist/cosmologist you would be of the same opinion as the majority because you would be exposed to just about the same evidence.
> You cannot choose your allegiance and stick with it.
Exactly, yes. In mathematics we are also discoverers rather than inventors. I am just making the point that personality does play a role. Think of Newton's calculus vs. Leibniz's calculus.
They are not related at all. Dark matter is visible on the scale of galaxies, dark energy on the scale of the universe.
Dark matter is currently the best model that can describe the rotational curves of galaxies under the assumption that general relativity is correct. Since GR has so far stood all tests extremely well, this is a very compelling argument for the existence of dark matter. There are also some more direct observations, such as gravitational lensing caused by dark matter.
I understand that r^2 is in many ways already the best thing to do. What I mean is that I would always scratch myself in doubt (sometimes literally) with something as simple as the area of a flat surface. I just mean that physics and mathematics are sometimes in spirit different.
For example, does this mean that when we thought that r^2 was not strictly followed that in fact we had the positions of the bodies wrong?