The Equivalence Principle
Classical Mechanics
Level
1
Which of the following is the most correct statement of the equivalence principle?
The acceleration due to gravity is equivalent to
always.
All kinds of energy are equivalent.
The effects of accelerating a frame are indistinguishable from gravitational forces.
General relativity is equivalent to Newtonian gravity under certain conditions.
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1 solution
While the acceleration due to gravity in Newtonian mechanics is always a = r 2 G M , this is not exactly the statement of the equivalence principle (although it is related, since this acceleration is found by canceling "m"s on either side of Newton's second law). Furthermore, it is no longer true in general relativity: the inverse square law of Newtonian gravity picks up a corrective inverse cube term in the case of spherical symmetry, for instance.
General relativity yields Newtonian gravity under certain limits, but is certainly not generally an equivalent theory under any conditions; in any case, this is not what the equivalence principle is.
The statement that "all kinds of energy are equivalent" is not the equivalence principle, and is also extremely vague: what does it mean for energy to be equivalent? Some kinds of energy (vacuum energy vs. matter vs. radiation) behave differently in an expanding universe, some energy is in the form of solid matter vs. radiation, etc.
The correct answer is that accelerated frames are indistinguishable from (uniform) gravitational forces. This idea was one of the founding principles of general relativity.