Formal definition of the Equivalence Principle(s)

In summary, the conversation discusses the need for formal definitions of the various forms of the Equivalence Principle in order to avoid ambiguity and potential contradictions with General Relativity. The speaker is looking for a clear and precise statement about trajectories and physical variables in the context of the Equivalence Principle. They reference a source on the subject but note that it does not contain a formal definition. The expert summarizer also adds that the Equivalence Principle states that gravity is not a force, but rather the absence of force, and that a freefalling observer experiences flat spacetime.
  • #1
lalbatros
1,256
2
Considering how the various forms of equivalence principle can lead to ambiguous discussions, I would like to know if more formal definitions for the various forms of the Equivalence Principles are available.

I would consider as "formal" all definitions that could be used (formally) to check if a theory satisfies this principle and eventually under which conditions it does.

For example, to avoid useless discussions about alleged contradictions between the EP and GR, a formal definition would make a formal and general proof crystal clear. I would also be interrested to see such a formal proof, although I consider it is rather obvious (WEP + sufficient smoothness of the equations).

Thanks for your help,

Michel
 
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  • #2
One might start here:
http://relativity.livingreviews.org/open?pubNo=lrr-2006-3&page=articlesu1.html
"The Confrontation between General Relativity and Experiment"
by Clifford M. Will
 
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  • #3
Thanks Robphy, this is a very interresting reference.
I also just received a book by the same author on the same subject.
A little more difficult to read.

However, there is no formal definition to be found there.

What I am looking for is not necessarily a big and complicated mathematical formulation.
It could be just a little bit more precise than casual english.
Some statement about trajectories or physical variables in the context of the various forms of EP.

Michel
 
  • #4
The equivalence principle states that what we normally think of as the force of gravity is actually the absence of force: a freely falling observer does not feel his own weight, a freefalling frame is equivalent to an inertial reference frame, flat spacetime.
 

FAQ: Formal definition of the Equivalence Principle(s)

What is the Equivalence Principle?

The Equivalence Principle, also known as the Universality of Free Fall, states that the gravitational mass and the inertial mass of an object are equivalent. This means that the acceleration of an object due to gravity is independent of its mass and composition.

What are the two types of Equivalence Principles?

The two types of Equivalence Principles are the Weak Equivalence Principle and the Strong Equivalence Principle. The Weak Equivalence Principle states that the trajectory of a freely falling object is independent of its composition, while the Strong Equivalence Principle states that the laws of physics are the same in all inertial reference frames.

What is the significance of the Equivalence Principle in physics?

The Equivalence Principle is significant because it led to the development of Einstein's Theory of General Relativity, which revolutionized our understanding of gravity and its effects on the fabric of space-time. It also plays a crucial role in modern cosmology and our understanding of the universe.

How is the Equivalence Principle tested?

The Equivalence Principle is tested through experiments, such as Galileo's Leaning Tower of Pisa experiment, which demonstrated that objects of different masses fall at the same rate. Modern experiments also use advanced technology, such as precision clocks and satellites, to test the Equivalence Principle and its implications.

Are there any exceptions to the Equivalence Principle?

Currently, there are no known exceptions to the Equivalence Principle. However, some theories, such as string theory, propose that there may be deviations from the Equivalence Principle at very small scales. These deviations have not been observed and are still a topic of ongoing research and debate.

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