so im studying up on the The theory of relativity. While reading about general relativity, I came across the principle of equivalency. I do not understand why there is no difference between the effects in an accelerating box and a box at "rest" in a gravitational field. I also do not understand how Einstein reasoned this theory. Any help is appreciated!

If you are inside the box can you tell which situation you are in?

In Newtonian gravity you can consider a light test particle m in the static field of a larger mass M. You can then look at the force on the small mass and see that this does not depend on the value of mass m. This means that the motion of the test particle is all encoded in the gravitational field: this is irrespective of the properties of the mass m. This follows from the assumption that the mass in F=ma is the same as the mass in Newton's law of gravity: this is another way of presenting the weak equivalence principle.

 

You can now think about if we can have an electromagnetic equivalence principle. The answer is no...

 

I wrote about this on my blog a while back http://blogs.scienceforums.net/ajb/2014/11/10/why-there-is-no-equivalence-prinicple-for-electromagnetic-theory/

thanks for the explanations, i still do not understand how it ties in with newtonian physics and space-time

The commonly called Principle of Equivalence boild down to an assertion that the m in inertial equations, such as Newtons 2nd Law, is the same as the m in gravitational laws (Newtons included).

This has been repeated demonstrated experimentally to ever greater levels of precision.

Eotvos experiments confirmed it in Einstein's day.

 

The principle has often been quoted as its logical consequence or deduction viz that a blindfolded observer cannot tell the source of a hidden acceleration she experiences.