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I'm reading that general relativity let's us describe physics from the point of view of both inertial and accelerated observers. What does that actually mean in terms of doing actual physics? For example, say a physicist performed Millikan's oil drop experiment or Young's double slit experiment or decomposed white light with a prism: (1) in deep space, far from any gravitational field, (2) on Earth, (3) near a black hole. I'm assuming she would get different results, and I'm assuming that in some way this is near the heart of what's important regarding GTR, but how exactly? In other words, what are the implications of GTR for understanding these experiments?

Thank you

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You're right that the comparison of real experiments such as Young's experiment or Millikan's experiment in the three situations (deep space, Earth, black hole) goes to the very heart of the general theory of relativity but your conclusion is exactly the opposite of the correct one.

The very basic postulate and fundamental principle of GTR, the equivalence principle, says that the three situations will have an indistinguishable impact on the lab experiments such as Young's or Millikan's experiment. If the labs were freely falling near the Earth; in outer space; or near the black hole horizons, they would see exactly the same thing in the experiments.

In the same way, if the lab isn't freely falling but instead, moves with some acceleration relatively to a freely falling frame, you may again prepare three experiments in the three situations that will proceed identically even though all of the physicists will feel some "gravity" (or "inertia": the same feeling).

In classical physics or special relativity, one talks about inertial and non-inertial frames. Only in the inertial frames (which include all uniformly moving frames relatively to a chosen representative), the laws of physics have a simple form. In general relativity, one may also talk about non-inertial frames, and because both inertial and non-inertial frames must use a generally variable metric tensor to describe gravity in general, the laws of physics actually have the same form in all frames, not just "inertial ones". In fact, in a generic curved spacetime, one can't find any "inertial systems of coordinates" anymore.

According to GTR, it's very helpful to compare not inertial frames with each other; but to compare all frames associated with freely falling observers. And the principle is that they will see the same physics regardless of the position or gravitational fields around them. They will always feel "zero gravity" whether they're in outer space, near the Earth, or near the black hole horizon.

Your basic template that "physics tells us that things should be different in the three situations" is just the opposite of what the important principles in physics tell us. Important principles, e.g. symmetries and their generalizations, are always telling us that certain observations are independent of certain choices.

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Luboš Motl - many thanks. You must admit it takes some talent to draw not only the wrong conclusion but the totally opposite wrong conclusion! I can see how the experiments would proceed identically in a freely falling frame, but surely the observer would make very different measurements in frames in different gravitational fields (eg a ball thrown on the Moon will travel further than one thrown with the same force on the Earth). I can see that the laws of physics are the same on the Earth and Moon, but how does GTR allow us to derive those laws from different sets of measurements? –  Peter4075 Nov 13 '11 at 20:59
    
Dear @Peter4075, I don't quite know how to quantify the talent needed to draw the wrong conclusions. Physics isn't about praising people for their hypothetical or real talents. Physics is about finding the right answers to questions about Nature. The equivalence principle is an important fact of Nature and who has trouble to get it - and appreciate its importance - is probably lacking some essential type of talent needed to do physics, regardless of the excuses for the wrong answers and indefinite rationalizations he may offer. –  Luboš Motl Jun 22 '13 at 9:11
    
Otherwise general relativity isn't enough to derive what will be observed in Millikan's or Young's or another non-gravitational experiment out of nothing. General relativity is not a theory of charged droplets in electric fields; it is not a theory on interference of light. General relativity is a theory of gravity. Among other things, it also predicts the effect of gravity and acceleration on non-gravitational experiments such as Millikan's or Young's, and in particular, its equivalence principle says that local experiments in freely falling frames always proceed in the same way. –  Luboš Motl Jun 22 '13 at 9:14
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