# Weak and strong equivalence- what is the difference really?

• trelek2
In summary, the difference between weak and strong equivalence is that weak equivalence only applies to test bodies and states that their trajectory is independent of internal structure and composition. Strong equivalence, on the other hand, applies to both self-gravitating and test bodies and states that the outcome of any local experiment is independent of the velocity and location in the universe. The Wikipedia article on equivalence principle is also flawed, as the strong and weak equivalence principles are essentially the same. The Einstein equivalence principle encompasses both WEP and the universality of free fall, and can be summarized as stating that the outcome of any local non-gravitational experiment is independent of the reference frame and location in the universe.
trelek2
Hi!

My lecture notes make me really confused as to what is the difference between weak and strong equivalence. I also read about it on wikipedia, but I'm still not sure. Can anyone give an example how in real life (thought experiment?) of what weak and strong equivalence is.

The Wikipedia article http://en.wikipedia.org/wiki/Equivalence_principle seems messed up. Its statement of the strong and weak equivalence principles are basically identical. I think what they call the Einstein equivalence principle is what most people call the strong equivalence principle.

http://relativity.livingreviews.org/Articles/lrr-2006-3/

"One elementary equivalence principle is the kind Newton had in mind when he stated that the property of a body called “mass” is proportional to the “weight”, and is known as the weak equivalence principle (WEP). An alternative statement of WEP is that the trajectory of a freely falling “test” body (one not acted upon by such forces as electromagnetism and too small to be affected by tidal gravitational forces) is independent of its internal structure and composition. In the simplest case of dropping two different bodies in a gravitational field, WEP states that the bodies fall with the same acceleration (this is often termed the Universality of Free Fall, or UFF)."

"The Einstein equivalence principle (EEP) is a more powerful and far-reaching concept; it states that:
1. WEP is valid.
2. The outcome of any local non-gravitational experiment is independent of the velocity of the freely-falling reference frame in which it is performed.
3. The outcome of any local non-gravitational experiment is independent of where and when in the universe it is performed."

"These ideas can be summarized in the strong equivalence principle (SEP), which states that:
1. WEP is valid for self-gravitating bodies as well as for test bodies.
2. The outcome of any local test experiment is independent of the velocity of the (freely falling) apparatus.
3. The outcome of any local test experiment is independent of where and when in the universe it is performed."

Last edited by a moderator:

## What is the concept of weak and strong equivalence?

Weak and strong equivalence are two terms used to describe the relationship between two scientific theories or models. They refer to the degree of similarity or agreement between the predictions or outcomes of the two theories.

## What is the difference between weak and strong equivalence?

The main difference between weak and strong equivalence is the level of agreement that is required between the two theories. Weak equivalence means that the two theories produce similar results, while strong equivalence means that the two theories produce identical results.

## How do weak and strong equivalence impact scientific research?

Weak and strong equivalence are important concepts in scientific research as they help scientists evaluate the validity and reliability of different theories. They also allow scientists to compare and contrast different theories and determine which one is more accurate or useful.

## What are some examples of weak and strong equivalence in science?

An example of weak equivalence is the Big Bang and Steady State theories of the origin of the universe. While they both explain the expansion of the universe, they differ in their predictions about the age and structure of the universe. An example of strong equivalence is the theory of general relativity and the theory of special relativity, which produce identical results in certain conditions.

## Can weak and strong equivalence coexist?

Yes, it is possible for weak and strong equivalence to coexist. This means that two theories can be considered weakly equivalent in some aspects and strongly equivalent in others. For example, two theories may produce similar results in one set of experiments but produce identical results in another set of experiments.

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