Why is gravity a fictitious force?

[Dale]

As Einstein said, it is theory which determines what is measurable.

Where did Einstein say this? Since many things were measured prior to the development of the corresponding theory, that seems like a pretty difficult claim to justify. Even if Einstein did say it.

According to the Newtonian theory of gravity, the gravitational force can be measured.

How?

 

[Demystifier]

How?

E.g. by weighing scale.

 

[Dale]

E.g. by weighing scale.

That doesn’t measure the gravitational force, even in Newtonian physics. In the ISS the Newtonian gravitational force is almost the same as it is on the ground, but a weighing scale reads 0.

In Newtonian theory there is no way to measure the gravitational force. All you can do is infer it from the motion. Just like a fictitious force.

 

[Herman Trivilino]

I can't understand why we compare elevator in the space and elevator on the surface of the Earth

The elevator in space is being accelerated by an external force. For example a rope is tied to the roof of the elevator and pulls on the elevator with a constant force.

As long as the elevator is small enough there is no way to distinguish between being in the elevator in space and the elevator on Earth.

 

[haushofer]

My 2 cents: a fictitious force is due to your (accelerating) frame of reference; there is no interaction involved (if you don't subscribe to Mach's principle, that is). Gravity, although having the mentioned properties of fictitious forces (proportional to mass and frame-dependent), does involve an interaction we call "spacetime curvature". That's why we usually don't call gravity a fictitious force.

 

[A.T.]

Gravity, although having the mentioned properties of fictitious forces (proportional to mass and frame-dependent), does involvevan interaction we call "spacetime curvature".

Spacetime curvature is not an interaction, but a property of spacetime. And it's related to tidal gravity, not gravity itself, which can also arise in flat spacetime in an accelerating frame.

 

[Demystifier]

That doesn’t measure the gravitational force, even in Newtonian physics. In the ISS the Newtonian gravitational force is almost the same as it is on the ground, but a weighing scale reads 0.

In Newtonian theory there is no way to measure the gravitational force. All you can do is infer it from the motion. Just like a fictitious force.

I think we disagree on what does it mean to measure something. In my view, to measure something means to infer it from observing something else, which is correlated with the thing one wants to measure. So inferring the force from the motion, or from the position of a static object, is measuring the force.

 

[Dale]

I think we disagree on what does it mean to measure something. In my view, to measure something means to infer it from observing something else, which is correlated with the thing one wants to measure. So inferring the force from the motion, or from the position of a static object, is measuring the force.

That is reasonable. However, any quantity that is inferred from motion is relative to the reference frame that defines the motion. Its value can be changed at a whim by changing the reference frame, before or after the experiment. For such quantities it is required to explicitly state the frame when describing the quantity.

So we don’t say that “we measured the velocity” but instead we say “we measured the velocity relative to the ground”. Or we don’t say “the duration of the process” but rather “the duration of the process in Bob’s frame”.

Similarly with gravity under your approach. You cannot say that some experiment “measures gravity”, but that it “measures gravity relative to some frame”. The statement is incomplete without the specification of the frame.

Other forces do not require this specification.

 

[Demystifier]

Other forces do not require this specification.

How would you measure the electric force, without a reference to a frame? Note that the Coulomb theory of electric force is almost identical to the Newton theory of gravitational force.

 

[A.T.]

Note that the Coulomb theory of electric force is almost identical to the Newton theory of gravitational force.

Except that the electric force cannot be always locally transformed away by a frame change, because it's not proportional to mass like Newton's force gravity.

 

[Dale]

How would you measure the electric force, without a reference to a frame?

The electromagnetic force on an otherwise isolated charge can be measured with an accelerometer. This measurement is frame-independent.

Note that the Coulomb theory of electric force is almost identical to the Newton theory of gravitational force.

Which is one reason that the Coulomb force is not actually a force, but just a component of a force. The actual force is the Lorentz force.

 

[Demystifier]

The electromagnetic force on an otherwise isolated charge can be measured with an accelerometer.

That works for a macroscopic body, but not for a microscopic particle.

 

[Dale]

That works for a macroscopic body, but not for a microscopic particle.

Why not? It just means that you have to redesign your accelerometer.

In any case, it doesn’t change the fact that the gravitational force is relative to a specified reference frame (like fictitious forces) and real forces are not.

 

[Demystifier]

In any case, it doesn’t change the fact that the gravitational force is relative to a specified reference frame (like fictitious forces) and real forces are not.

I still disagree to some level. If we define force as mass times acceleration, the acceleration is always relative to a specified reference frame, so even the electric force is relative in this sense.

Of course, you are right if by acceleration you mean proper acceleration, which is not relative. The proper acceleration along a geodesic is zero, which is a more precise way to say that the gravitational force is not a proper force. But this point of view is only valid in the context of Einstein relativity theory. I don't see how to make this argument precise in a wider context, including the context of the 19th century physics.

 

[haushofer]

Spacetime curvature is not an interaction, but a property of spacetime. And it's related to tidal gravity, not gravity itself, which can also arise in flat spacetime in an accelerating frame.

I don't see that clear distinction between "interactions" and "spacetime curvature"; Fierz-Pauli is an interactive description of GR, and Newton-Cartan theory describes Newtonian gravity as spacetime curvature.

 

[Mike_bb]

I don't see that clear distinction between "interactions" and "spacetime curvature"; Fierz-Pauli is an interactive description of GR, and Newton-Cartan theory describes Newtonian gravity as spacetime curvature.

Spacetime curvature is geometric property.

 

[Dale]

you are right if by acceleration you mean proper acceleration, which is not relative.

Yes, that is what I mean.

this point of view is only valid in the context of Einstein relativity theory. I don't see how to make this argument precise in a wider context, including the context of the 19th century physics.

I will point out that we are having this conversation in the Special and General Relativity subforum, so relativity is clearly assumed. However, this point of view is valid in any theory which uses a manifold for spacetime. All extant physics can be cast in that framework, including Newtonian gravity (which is the Newton-Cartan gravity that @haushofer mentioned).

 

[PeterDonis]

If we define force as mass times acceleration, the acceleration is always relative to a specified reference frame

Not if you define it as invariant mass times proper acceleration--which is how relativity defines it. Both of those are invariants.

 

[PeterDonis]

this point of view is only valid in the context of Einstein relativity theory.

I don't agree. What an accelerometer measures is not theory dependent. Newtonian gravity agrees that an accelerometer attached to a body moving solely under the influence of gravity (for example, in a free-fall orbit around a planet) will read zero. So even Newtonian gravity recognizes that gravity is in a different category from forces like electromagnetism.

The difference between Newtonian gravity and GR is that the former draws a distinction between gravity. considered as a force, and "fictitious" forces like Centrifugal and Coriolis, whereas GR draws no such distinction; all such "forces" are artifacts of using a non-inertial frame.

 

[Demystifier]

@Dale and @PeterDonis I'm still somewhat confused, so I will ask a slightly more general question. Consider a Newton-like theory of gravity, but with inertial mass different from the gravitational mass. In such a theory, is the "gravitational" force a true force or a fictitious force? Can such a theory be written in the Newton-Cartan form?

 

[Dale]

Consider a Newton-like theory of gravity, but with inertial mass different from the gravitational mass. In such a theory, is the "gravitational" force a true force or a fictitious force?

I haven’t studied such theories, so I am not able to answer this. I am sure there is some scientific literature on the topic, but I don’t know it.