Why can we not treat gravity as a force?

  • Context: Graduate 
  • Thread starter Thread starter HomogenousCow
  • Start date Start date
  • Tags Tags
    Force Gravity
Click For Summary

Discussion Overview

The discussion revolves around the interpretation of gravity within the framework of general relativity, particularly whether gravity can be treated as a force. Participants explore the implications of the geodesic equation, fictitious forces, and the nature of gravitational effects in different coordinate systems.

Discussion Character

  • Debate/contested
  • Conceptual clarification
  • Technical explanation

Main Points Raised

  • Some participants suggest that interpreting the right-hand side of the geodesic equation as a four-acceleration allows for treating gravity as a force.
  • Others argue that terms involving Christoffel symbols do not have the same transformation properties as four-vectors, complicating the interpretation of gravity as a force.
  • A participant notes that while one can move the term involving Christoffel symbols to the other side, the resulting equation is no longer a tensor equation and thus does not transform as a tensor does.
  • There is a discussion about the challenges of splitting the Einstein field equations into a source providing force equation, with concerns that this would introduce even more problems than the geodesic equation.
  • A participant raises a question about the classification of gravity as a fictitious force, referencing David Politzer's statement that gravity is indistinguishable from a fictitious force.
  • Another participant challenges the necessity of distinguishing between gravity and fictitious forces, suggesting that if they are indistinguishable, gravity could be considered a fictitious force.
  • One participant emphasizes that fictitious forces do not have Riemann tensors when their derivatives are taken, reinforcing the distinction in a local context.

Areas of Agreement / Disagreement

Participants express differing views on whether gravity can be treated as a force, with some supporting the idea and others contesting it. The discussion remains unresolved, with multiple competing interpretations of gravity's nature and its relationship to fictitious forces.

Contextual Notes

There are limitations in the discussion regarding the assumptions made about the geodesic equation and the definitions of fictitious forces. The implications of these interpretations are not fully resolved, and the mathematical steps involved in the arguments are not detailed.

HomogenousCow
Messages
736
Reaction score
213
If you simply interpret the RHS of the geodesic equation as a four-acceleration, can't we just treat gravity as a force?
 
Physics news on Phys.org
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.
 

Similar threads

Undergrad Gravity: Force or Acceleration?
  • · Replies 69 ·
3
Replies
69
Views
8K
Undergrad Why is gravity a fictitious force?
  • · Replies 124 ·
5
Replies
124
Views
6K
High School Is Gravity Really a Force Like the Other Fundamental Forces?
  • · Replies 12 ·
Replies
12
Views
2K
High School Gravity and speed of information for orbiting planets
  • · Replies 22 ·
Replies
22
Views
1K
High School Is Gravity an illusion of a force but really a curvature of spacetime?
  • · Replies 26 ·
Replies
26
Views
2K
High School Is Time a Fundamental Force in Physics?
  • · Replies 15 ·
Replies
15
Views
4K
Undergrad Reconciling smooth spacetime with variable, rotating, earth gravity
  • · Replies 4 ·
Replies
4
Views
1K
Insights Is Pressure A Source Of Gravity?
  • · Replies 27 ·
Replies
27
Views
4K
Undergrad Understanding Gravity with GR: Beginner's Guide by Aerodyn
  • · Replies 10 ·
Replies
10
Views
2K
Undergrad Why do objects follow a geodesic?
  • · Replies 7 ·
Replies
7
Views
2K