# Why can we not treat gravity as a force?

• HomogenousCow
In summary, the conversation discusses the interpretation of the geodesic equation and the possibility of treating gravity as a force. It is noted that while the RHS of the geodesic equation can be interpreted as a four-acceleration, it is not a tensor equation and does not transform as a tensor does. However, this non-tensor equation can still be interpreted as an acceleration due to a gravitational force. The conversation also touches on the concept of fictitious forces in relation to gravity and how they are locally indistinguishable.

#### HomogenousCow

If you simply interpret the RHS of the geodesic equation as a four-acceleration, can't we just treat gravity as a force?

A four-vector has certain transformation properties. Those terms involving Christoffel symbols do not. Even in a flat space using spherical coordinates, you would get apparent acceleration for a free particle.

HomogenousCow said:
If you simply interpret the RHS of the geodesic equation as a four-acceleration, can't we just treat gravity as a force?
Murphrid is correct. You can certainly move the term involving Christoffel symbols to the other side from the term involving the coordinate acceleration, but the resulting equation is no longer a tensor equation and does not transform as a tensor does.

However, the non-tensor equation that you have can certainly then be interpreted as an acceleration due to a gravitational force. The gravitational force, however, is clearly a fictitious force and even in this situation cannot be locally distinguished from other fictitious forces such as those due to acceleration or rotation of the coordinate system.

Additionally, how would you split the Einstein field equations into a source providing force equation? The Geodesic equation has enough problems as is, interpreting one side as a force, the Einstein field equations would have just infinitely more problems on that front...

Reading this thread triggered an interest in fictitious forces and I googled to get more information.Some promising stuff seemed to come up but there was something which confused me.Writing about fictitious forces for "Scientific American" David Pollitzer referred to General relativity and amongst other things stated

"The cornerstone of Einsteins theory,however,is the proposition that gravity is itself a fictitious force(or, rather,that it is indistinguishable from a fictitious force)"

So what is it? Is it considered to be a fictitious force or just indistinguishable from a fictitious force or something else? Thanks if anyone answers.

Try googling What is a "fictitious force"
Caltech 2004 Nobel laureate David politzer writing for "Scientific American"

I think that's an unnecessary distinction. If you can't tell a bird apart from a duck, then the bird is a duck, not indistinguishable from a duck.

Locally indistinguishable. When you take their derivative you find that fictitious forces do not have Riemann tensors.

## 1. Why can we not treat gravity as a force?

Gravity cannot be treated as a force because it is not a force in the traditional sense. Instead, it is a curvature of space-time caused by the presence of mass and energy. This curvature affects the motion of objects and gives the illusion of a force pulling them towards each other.

## 2. How does Einstein's theory of relativity explain gravity?

Einstein's theory of relativity explains gravity as a result of the warping of space and time caused by massive objects. This warping creates a gravitational field that affects the motion of other objects around it. This is known as the curvature of space-time.

## 3. Can gravity be explained by Newton's laws of motion?

No, gravity cannot be fully explained by Newton's laws of motion. While Newton's laws can accurately describe the motion of objects under the influence of gravity, they do not explain what causes gravity or how it works on a larger scale. Einstein's theory of relativity provides a more comprehensive explanation of gravity.

## 4. Why is gravity considered a fundamental force?

Gravity is considered a fundamental force because it is one of the four fundamental forces in nature, along with the strong nuclear force, the weak nuclear force, and electromagnetism. These forces cannot be explained by any other fundamental forces and are essential for understanding the behavior of matter and energy in the universe.

## 5. Can gravity be shielded or canceled out?

Gravity cannot be shielded or canceled out because it is not a force that can be blocked or countered. Since gravity is a result of the curvature of space-time, it cannot be shielded like other forces. However, its effects can be counteracted by other forces, such as the centrifugal force, in certain situations.