Weak and strong equivalence principles

[lalbatros]

Hello,

I would like to see more clearly the differences between the various forms of the equivalence principle.
When reading about it on http://en.wikipedia.org/wiki/Equivalence_principle" I have the strange feeling that the difference is too small and too easily accepted to justify the difference in their names as "weak" and "strong".
In addition, I guess that on the experimental side it make really a difference.

As a side topic, I would also like to understand more clearly where and why which version of the EP has been used and was necessary in building the theory of General Relativity. My background on that is rather naïve: since acceleration changes the metric tensor so should gravity also change it. And for the rest I take GR as a beautiful mathematical construction that expands on the idea that gravity is geometry.

Could you help me clarify this, by your sharp explanations, or by excellent references.

Thanks a lot,

Michel

 

[actionintegral]

Please explain to me your understanding of the two forms of the equivalence principle.

 

[Entropia]

The equivalence principle is a fundamental concept in physics that relates the effects of gravity to the effects of acceleration. It essentially states that the laws of physics should be the same in a uniformly accelerating frame of reference as they are in a stationary gravitational field. This principle has been crucial in the development of Einstein's theory of General Relativity, which is our current understanding of gravity.

There are two main versions of the equivalence principle: the weak equivalence principle and the strong equivalence principle. The weak equivalence principle, also known as the "Einstein equivalence principle," states that the effects of gravity are indistinguishable from the effects of acceleration in a small region of spacetime. This means that for any local experiment, the results should be the same whether the observer is in a stationary gravitational field or in a uniformly accelerating frame of reference. This principle is the foundation of General Relativity and is supported by numerous experiments, such as the famous Eötvös experiment.

On the other hand, the strong equivalence principle, also known as the "Newton equivalence principle," goes a step further and states that the effects of gravity are indistinguishable from the effects of any kind of acceleration, not just uniform acceleration. This means that even in a non-uniform gravitational field, the laws of physics should still be the same as in a non-inertial frame of reference. This principle is more difficult to test experimentally and is not as widely accepted as the weak equivalence principle.

So why do we have these different versions of the equivalence principle? As you mentioned, the differences may seem small, but they have important implications for our understanding of gravity. The strong equivalence principle, for example, has been used to argue against alternative theories of gravity that do not follow the same principles as General Relativity. Additionally, the strong equivalence principle is important for understanding the phenomenon of gravitational time dilation, which is a key aspect of General Relativity.

In terms of the history of the equivalence principle, it was first proposed by Galileo in the 17th century, and then further developed by Newton in his theory of gravity. However, it was not until Einstein's theory of General Relativity that the principle was fully understood and incorporated into a mathematical framework. Since then, the equivalence principle has been confirmed by numerous experiments and continues to be a crucial concept in our understanding of gravity.

I hope this helps clarify the differences between the weak and strong equivalence principles and their importance in the development of General Relativity. If you would like to