Free-falling object: When should we consider General Relativity?

Question

My question is related to a statement:

If a pendulum is experiencing free fall, then it will not oscillate.

The statement is true in the sense that its acceleration is (approaching to) zero, then according to the period equation $T$ would be infinity.

I think this sense comes from General Relativity. However, I'm not sure exactly where this result is coming from, and why we should consider General Relativity for this pendulum, rather than considering it to be a pure Newtonian scenario.

Free-falling object: When should we consider General Relativity? Definitely when the object is very expensive :-) — magma, Oct 17 '20 at 13:03

score 2 · Accepted Answer · answered Oct 15 '20 at 23:24

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why we should consider general relativity for this pendulum, rather than a pure Newtonian senario

There is no need to consider general relativity at all for this scenario. Newtonian gravity clearly replicates this behavior.

In a Newtonian context we would consider a free falling frame to be non-inertial. As such there would be a fictitious force that is the same magnitude as gravity but opposite direction (but not a 3rd law pair). This force would cancel out gravity for no net force. Thus there would be no oscillation

answered Oct 15 '20 at 23:24

Dale

99,825

Thanks for the answer! Could you explain a bit more about how the fictitious force coming from? – ZR- Oct 15 '20 at 23:43
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If gravity were a “real” force, then how would I be able to tell if I'm falling or accelerating in space or on Earth? – mmesser314 Oct 15 '20 at 23:47
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@Zhengrong it comes from the non-inertial reference frame. That is the standard behavior of non-inertial frames. In fact, it is their defining characteristic in Newtonian physics. – Dale Oct 16 '20 at 00:21
@Dale Thanks :) – ZR- Oct 16 '20 at 00:26

score 1 · Answer 2 · answered Oct 16 '20 at 00:14

Indeed you don't need GR here as was clarified by the previous answer. But if we look at the situation from the GR point of view, then according to the equivalence principle, a small enough non-rotating freely falling frame, which is falling for a short enough amount of time, is the closest thing we have to an inertial frame, i.e., a frame were the laws of SR hold. And this frame will not detect the external gravitational field, thus will see the pendulum as not oscillating.

Free-falling object: When should we consider General Relativity?

2 Answers2