# On the accuracy of “ Freefalling reference frames are equivalent to an inertial reference frame.”

In this Wikipedia article on fictious forces, under the section Gravity as a fictitious force, is stated,

All fictitious forces are proportional to the mass of the object upon which they act, which is also true for gravity. This led Albert Einstein to wonder whether gravity was a fictitious force as well. He noted that a freefalling observer in a closed box would not be able to detect the force of gravity; hence, freefalling reference frames are equivalent to an inertial reference frame.

Is this last statement accurate? As I understood, accelerating reference frames are not inertial because the principle of inertia does not hold in them.

• Your question is tagged newtonian-mechanics, but your question discusses Einstein's idea of gravity in GR (general relativity), which is not Newtonian. Do you want a GR answer, or a Newtonian one? – PM 2Ring Oct 29 '19 at 11:08
• @PM2Ring A Newtonian explanation, if possible. – Hilbert Oct 29 '19 at 11:31
• It's my understanding that inertial frames for Newton are not the same thing as inertial frames for GR. Have you looked into this? – Aaron Stevens Oct 29 '19 at 11:40
• physics.stackexchange.com/q/178417/37364 – mmesser314 Oct 29 '19 at 12:52

In a non inertial system you can recover inertia if you introduce pseudo forces. But because gravity acts on all objects, the pseudoforce on each object will be of the same magnitude and opposite direction than that of gravity, effectively canceling each other. Thus you can work in the accelerated system as if there were neither pseudoforces nor gravity.

• So, If I understood, it is as if we were dealing with two fictitious forces, the first one being gravity and the second force is the one resulting from the fall. And it is the mutual cancellation of these two forces that gives rise to the inertial frame? – Hilbert Oct 29 '19 at 17:44
• gravity would not be a fictitious force, it actually cancel the effect of the fictitious forces. That in Newtonian mechanics. In general relativity gravity is not considered a force – Wolphram jonny Oct 29 '19 at 17:47
• "gravity would not be a fictitious force" Why can't gravity be considered a fictitious force? The article says that, "All fictitious forces are proportional to the mass of the object upon which they act, which is also true for gravity. This led Albert Einstein to wonder whether gravity was a fictitious force as well." – Hilbert Oct 29 '19 at 17:51
• @Hilbert I agree but not in the context of newtonian mechanics. I also said that in GR gravity is not a force – Wolphram jonny Oct 29 '19 at 17:55

"freefalling reference frames are equivalent to an inertial reference frame."

In a accelerated car, from 0 to 100 m/s for example, there is a fictitious force directed backwards inside the car. When it reaches 100 m/s and the speed is constant, that force vanishes. Now the car is an inertial frame of reference.

When we are at rest on earth, the force of gravity is present. Inside a free falling box, that force vanishes.

The symmetry of both situations suggests that gravity could be understood as a kind of fictitious force as well.

Of course a free falling box is not an inertial frame of reference, but is equivalent to it by leading to the same effect of "turning off" the force of gravity.