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Apologies in advance if this is a naive question. I'm learning the fundamentals of gravity and from what I've understood, it's not particularly meaningful to talk about it as a force, since it induces the same "acceleration" (classically speaking) in everything.

This means that whatever device or accelerometer we use, every component of that too will be accelerated the same way as the observer will, and the observer will not be able to measure (provided they or the measuring device are under no other influence other than gravity) any acceleration whatsoever. This makes it meaningless to talk about gravity-induced "acceleration" since we can't measure it.

One central idea underlying this is the equivalence principle (gravitational mass = inertial mass) that makes sense to me. But I wonder - is the fact that gravity acts on everything also fundamental to this? If there were anything at all that's not acted on by gravity, would the whole "gravity as a force doesn't make sense" premise (or maybe GR itself) break down? Is this question related to Mach's principle in any way?

(I'm not claiming any such thing might or should exist so please don't bash me for it - just trying to clarify my understanding)

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  • $\begingroup$ That type of things exist in a certain way. Distant galaxies repel themselves instead of attract, what is called dark energy. It can be fitted in GR by the cosmological constant. $\endgroup$ – Claudio Saspinski Jun 5 at 23:00
  • $\begingroup$ @ClaudioSaspinski: So then if something exists on which gravity doesn't act (or doesn't act the way it does on ordinary matter), wouldn't it make it possible for an observer to measure a concrete acceleration reading relative to that "something"? $\endgroup$ – Shirish Kulhari Jun 5 at 23:06
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    $\begingroup$ Kepler and Newton had no problem considering gravity as a force that produces an easily measurable acceleration. Anyone who throws a ball up in the air can watch it decelerate and accelerate. Before learning the GR explanation of gravity as a pseudoforce, you should first learn Newton's explanation of it as a real force. $\endgroup$ – G. Smith Jun 5 at 23:07
  • $\begingroup$ @G.Smith: I'm comfortable with the classical notion of gravity as a force though. As far as I'm concerned that was a pre-requisite to wrapping my head around the GR notion of it as a pseudoforce. $\endgroup$ – Shirish Kulhari Jun 5 at 23:10
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    $\begingroup$ I'm amazed this hasn't been brought up, because what you're talking about is exactly what the strong equivalence principle says. Unlike the weak version, the strong one says all laws of physics can be locally rewritten (via a coordinate transformation) so as to look as if there is no gravity (approx to first order around a point). The implication of this is that everything is indeed affected by gravity the same way. If this principle is violated, then GR is violated. $\endgroup$ – Maximal Ideal Jun 5 at 23:49
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That gravity affects all things the same way is not an assumption in general relativity. It is an inevitable result of general relativity. Basically, GR describes the geometry of spacetime in terms of the distribution of mass-energy. Gravitation is just another word for constraints on object trajectories imposed by that geometry.

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  • $\begingroup$ I understand. But doubling down on one aspect of the question, if something exists on which gravity doesn't act (or doesn't act the way it does on ordinary matter), wouldn't it make it possible for an observer to measure a concrete acceleration reading relative to that "something"? Would that spell trouble for GR? $\endgroup$ – Shirish Kulhari Jun 5 at 23:15
  • $\begingroup$ You should think that through and pose it as a new question. $\endgroup$ – S. McGrew Jun 5 at 23:40
  • $\begingroup$ That gravity affects all things the same way is a fundamental assumption in general relativity. General relativity was intentionally formulated to be consistent with Einstein's equivalence principle. $\endgroup$ – David Hammen Jun 6 at 11:25
  • $\begingroup$ The distinction is "assumption"(e.g., an axiom in geometry) vs "consequence" (e.g, a theorem in geometry). World lines are geodesics in GR. The fact that this is consistent with an assumption that all things are affected the same way doesn't mean that the assumption is necessary to derive GR. On the other hand, in derivation of special relativity, constancy of the speed of light for all observers is an explicit assumption that leads (in flat spacetime) directly to the equations of SR . $\endgroup$ – S. McGrew Jun 6 at 14:02
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    $\begingroup$ @ChiralAnomaly: My bad for not being specific enough. What I meant to ask was, if there exists anything on which gravity does not act, would that spell trouble for GR. I think S. McGrew's last comment addresses that. If we were to find something like that, it would be a contradiction to a "consequence" of GR and definitely spell trouble. The assumption vs. consequence point was useful to me. $\endgroup$ – Shirish Kulhari Jun 6 at 14:15

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