Compatability of physics equations

[General_Relativity19]

I've recently been researching Einstein's Theory of Relativity and the compatability with other physics equations i.e Lorentz Transformations, Schrodingers Equation etc. How do physicists famous or not know that each equation they invent are compatabile with one another? Because some of the equations I've seen have used Einsteins equation E=MC^2 in some way. Is it because their equations involved an element of Einstein's equation that their equation would be tested and accepted by other people? I know there are two versions of some equations, one dimension and the third dimension. Aint there a two dimensional version of an equation? if so, which is it? just curious. I do not know physics that well as I am still learning, it was just a question which came into my mind. I've come across a lot of equations, some which look very complex, but i know it will take me along time to understand but i will get there eventually.

thanks

 

[Kurdt]

The reason most physics euations are compatible is that all physicists use a common set of units which describe such things as velocity and energy and time. For example time is measured in seconds and energy is measured in Joules, then any equation relating time in seconds and energy in Joules will be compatible.

 

[jdavel]

The reason most physics euations are compatible is that all physicists use a common set of units which describe such things as velocity and energy and time. For example time is measured in seconds and energy is measured in Joules, then any equation relating time in seconds and energy in Joules will be compatible.

Whoa! There's more to the compability between two equations in physics than their units. The two equations x' = x-vt and x' = gamma(x-vt) are about as incompatible as you can get, but the units are fine.

 

[Kurdt]

Ok there's the context they're taken in as well but essentially you wouldn't try to use galilean transforms in a relativistic situation.

 

[Integral]

The endeavor of Physics is to apply Mathematics to our observations of the world. So underlying all of modern Physics is mathematics, this provides a consistent basis for all physics equations. Now since we are attempting to developer mathematics which model the universe we can expect correct models to conform to the universe we are modeling. Thus the consistency of Physics is based on the consistency of the universe. Mathematical models based on physical observation and sound mathematics are consistent and useful.

I disagree that the Galilean transform is inconsistent with Relativity, simply let v<<c and drop higher order terms, what is left is Newtonian physics with Galilean transforms. Also there are 2 models of Thermodynamics, one the microscopic view the other the Macroscopic view, but once again when viewed in the appropriate limits they make the same predictions.

Currently GR and QM do not agree in the limit so each must be applied carefully and with full understanding of the limits of application.

Consistency of Physical theories come from carefully derivation from 1st principles and mathematics.

 

[Kurdt]

Well if we agree to say that at least it has something to do with how you apply the equations, as in when they are relevant. For example Galilean trasforms are fine when you have v<<c and relativity is more useful for high energy particles, and that we can always determine a constant to interpret results in different units.

The maths then is the underlying cause of conformity, but personally I always hate converting units.