Why is the gravity a fictitious force?

[Mike_bb]

I read about equivalence principle. I tried to understand Einstein's thought experiment with elevator and I can't understand why we compare elevator in the space and elevator on the surface of the Earth and conclude that gravity is fictitious force.

Why?

Thanks!

 

[Ibix]

I can't understand why we compare elevator in the space and elevator on the surface of the Earth and conclude that gravity is fictitious force.

We don't. Newtonian gravity respects the equivalence principle, and that models gravity as a real force.

However, if gravity (in practice) did not respect the equivalence principle then metric theories of gravity, in which "the force of gravity" is a so-called fictitious force, would immediately be ruled out. The elevator thought experiment is simply a way of relating the equivalence principle to a practical situation.

To put it another way, the equivalence principle is necessary for a "fictitious force" model of gravity, but it does not rule out all other models.

 

[A.T.]

I can't understand why we compare elevator in the space and elevator on the surface of the Earth and conclude that gravity is fictitious force.

Do you understand what "fictitious forces" are in the first place?
https://en.wikipedia.org/wiki/Fictitious_force

They are all proportional to the mass of the object they act on, so combined with Newton's 2nd Law (where acceleration is anti-proportional to mass) they all accelerate everything in the same way, regardless of its mass.

Newtoninan Gravity is not a "fictitious force", but it is proportional to the mass of the object it acts on. So you can locally or for a uniform field treat it as such.

 

[Demystifier]

The geodesic equation
$$\frac{d^2x^{\mu}}{d\tau^2} + \Gamma^{\mu}_{\alpha\beta} \frac{dx^{\alpha}}{d\tau} \frac{dx^{\beta}}{d\tau} = 0$$
can be written as
$$m\frac{d^2x^{\mu}}{d\tau^2} = F^{\mu}$$
where
$$F^{\mu} \equiv - m \Gamma^{\mu}_{\alpha\beta} \frac{dx^{\alpha}}{d\tau} \frac{dx^{\beta}}{d\tau}$$
In the second equation, the quantity $F^{\mu}$ can be interpreted as the gravitational force. However, the third equation reveals that it does not transform as a vector, because $\Gamma^{\mu}_{\alpha\beta}$ does not transform as a tensor. At any point in spacetime, one can always choose a local frame of coordinates in which it vanishes. This is the reason why we don't call it a force, but a fictitious force; its existence depends on the choice of frame.

 

[Mike_bb]

Ok.

If gravity was force then mass of object (gravity mass) in elevator on the surface of the Earth differs from inertia mass of object in elevator in the space. Is this statement true?

Could anyone provide easy explanation ? Thx.

 

[FactChecker]

No. But the current understanding explains why the exact same mass is appropriate in both equations. That is one of the strong points of General Relativity. Without that, we would have to come up with some other theory of why those two masses are exactly the same.

 

[Mike_bb]

No.

From $M_i=M_g$ we can conclude that gravity is fictitious force. Right?

 

[FactChecker]

I read about equivalence principle. I tried to understand Einstein's thought experiment with elevator and I can't understand why we compare elevator in the space and elevator on the surface of the Earth and conclude that gravity is fictitious force.

Why?

Thanks!

General Relativity hypothesizes that an object, appearing to accelerate due to gravity, is simply moving in a non-accelerated straight line in its spacetime geometry. To that object, it is not reacting to an external force, it is going in a straight, non-accelerated path. That is why gravity is called a fictitious force -- it looks like an external force to us, but it is not.
The thought experiment with the elevators is just a way of illustrating that basic part of General Relativity.

 

[FactChecker]

From $M_i=M_g$ we can conclude that gravity is fictitious force. Right?

I would call it a satisfying consequence of General Relativity. GR explains the mysterious reason behind $M_i=M_g$, not the other way around.

 

[FactChecker]

From $M_i=M_g$ we can conclude that gravity is fictitious force. Right?

There could have been some reason for $M_i=M_g$ other than GR, but nobody could come up with one. It was a mystery until Einstein explained it with GR.

 

[Mike_bb]

FactChecker,

In Russian sources I read another explanations. It confuse me.

 

[FactChecker]

FactChecker,

In Russian sources I read another explanations. It confuse me.

Give yourself time to think about it. GR is a profound change in our thinking.

 

[FactChecker]

I personally think that GR's explanation of why $M_i=M_g$ is one of the most intellectually satisfying things in physics.