B Einstein's Equivalence Principle: What's New?

[davidge]

The equivalence principle states that the laws of physics are the same in any inertial frame. Translating this into mathematics language, the equivalence principle states that a given equation should retain its form when one transform between the coordinates of two intertial frames, correct?

But isn't that exactly what Newtonian mechanics state? I mean, if we have two inertial frames, Newton's laws will hold in both of them. Furthermore, the equations of motion will have the same form in both of them.

So what's new in the discovery by Einstein?

 

[vanhees71]

This is not the equivalence principle but the principle of special relativity.

The usual way, special relativity is almost always presented in undergrad textbooks by simply copying Einstein's ingenious approach of his famous paper of 1905 is fine, because you come pretty quickly to the important physics, finally summarized in the Lorentz transformation, which substitutes the Galileo transformation of Newtonian physics.

There's, however, an approach that's a bit more cumbersome but provides great a great insight. You just take the principle of special relativity and some other symmetry principles about space and time (homogeneity of time and space; each inertial observer should find a spatial geometry obeying the laws of Euclidean geometry, implying also isotropy of space), and ask how the corresponding transformation laws between space-time coordinates of inertial observers might look like. The result of a somewhat lengthy analysis is that there are indeed only two possibilities, namely Galilei-Newton or Einstein-Minkowski spacetime, and as empirical evidence shows, the latter is a more comprehensive desription of spacetime.

The equivalence principle goes further and includes gravity into the game. In short, Einstein's "strong equivalence principle" says that at any point in spacetime there's only a local inertial reference frame, where gravity is approximately absent. These local inertial frames are realized by sufficiently small freely falling reference frames like the International Space Station. With some more mathematical precision this leads quite immediately to Einstein's General Relativity.

 

[russ_watters]

The equivalence principle states that the laws of physics are the same in any inertial frame...

That's the principle of relativity and it is the same for Newton and Einstein's Special Relativity (it's the first postulate).

So what's new in the discovery by Einstein?

The second postulate: the speed of light is the same in all non-accelerating frames.

 

[davidge]

These responses were really helpful. Thanks.

 

[Vitro]

The equivalence principle states that the laws of physics are the same in any inertial frame. Translating this into mathematics language, the equivalence principle states that a given equation should retain its form when one transform between the coordinates of two intertial frames, correct?

But isn't that exactly what Newtonian mechanics state?

It isn't. What you described above is in fact Einstein's principle of relativity.

I mean, if we have two inertial frames, Newton's laws will hold in both of them. Furthermore, the equations of motion will have the same form in both of them.

So what's new in the discovery by Einstein?

Right. Pay attention to what you wrote, you said "Newton's laws" and "equations of motion", but those are not the only laws of physics. There were other laws, such as electromagnetism (Maxwell's equations), which were known not to be invariant under Galilean transformations. By replacing the Galilean transformation with the Lorentz transformation Einstein expanded the principle of relativity to include the laws of electromagnetism in addition to the laws of motion.

 

[davidge]

Pay attention to what you wrote, you said "Newton's laws" and "equations of motion", but those are not the only laws of physics. There were other laws, such as electromagnetism (Maxwell's equations), which were known not to be invariant under Galilean transformations. By replacing the Galilean transformation with the Lorentz transformation Einstein expanded the principle of relativity to include the laws of electromagnetism in addition to the laws of motion.

Oh yea. I think I should have made clear that I was talking about the laws of nature being the same in all inertial frames, not concerning on what kind of transformation one has to do in order to get the equations form invariant.

 

[davidge]

By the way, is it correct to say that "the laws of nature being the same in all inertial frames", when translated to mathematics, is to say that the equations expressing the laws of nature should be vectorial?