Physical interpretation of equations

[autodidude]

Can all formulas be thought of intuitively/physically?

For example, average speed is change in distance over change in time, that is intuitive and can easily be derived

But when you have something like v^2 = u^2 + 2ax, or e=mc^2, how do you think of it intuitively? Specifically the squared part, what exactly does velocity and the speed of light squared mean physically?

 

[Naty1]

sure,sooner or later. Sometimes via multiple interpretations...like the Schrodinger Wave equation...it's meaning is STILL debated...

but it may take quite a while to get to that stage (of physical interpretation) since as you suggest some math is so complicated it's physical meaning may take years to determine. And different people may have opposing/contradictory views...like Hawking and Jacob Beckenstein regarding the entropy of black holes...Hawking (as I recall) thought Beckenstein was nutty...until he arrived at the same conclusion via a different mathematical approach.

And typically mathematicians are not all that interested in the physical meaning when they may develop some new math...often they develop math and physicists come along and use it in a physical situation. When some math appears we may not have any theory to go with it.

One example is the Euler beta function which was later seen to be an aspect of the strong nuclear force...and even caused people to stumble intio string theory! String theory started out as one subject and someone later realized the math included gravitons...and so it became what it is today. Another example is some of the mathematics black holes: frames of reference...and the solution(s) to Einstein's equation of General Relativty...Einstein had the equation, Schwarszchild, Kerr, to name two, figured out solutions (for non rotating and rotating black holes) ...and what they meant...what the equation said physically about black holes.

Similar situation regarding