If the person in the train somehow feels that he is in an inclined plane , that would do . However I don't think he can differentiate by seeing the plumb line only. I currently don't find any way. Please suggest some methods?
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Einstein's equivalence principle says no. You can't tell the difference between a gravity field and an acceleration field. – John Alexiou Dec 23 '16 at 16:28
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This question is strange. How can he tell? Certainly he can't tell! In fact Einstein's General relativity is based on the fact that gravity cannot be distinguished from acceleration, and he went on to assume gravity is in fact kind of another "pseudo-force".
Violapterin
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It is a fundamental principle in general relativity, the equivalence principle, that acceleration and gravity are locally indistinguishable so the person in the train cannot tell the difference using a local measurement.
However note the stress on the work local. The Earth's gravitational field decreases with distance from the centre of the Earth, while a force due to acceleration does not change with distance, and this can be used to tell the difference.
Suppose the passenger uses two plumb bobs, one near the floor and one near the ceiling. If th train is on an inline then both plumb lines point towards the centre of the Earth so they will be parallel. However if the train is accelerating then the angle of the plumb lines will be:
$$ \theta = \arctan\left(\frac{a}{g}\right) $$
Since $a$ is the same for both plumb lines but $g$ is slightly smaller for the upper plumb line the two two plumb lines will not be parallel - the upper line will have a slightly greater angle to the vertical.
John Rennie
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Please remove the duplicate on my previous question Question As its not duplicate , Please read the post carefully ! – InquisitiveMind Dec 23 '16 at 17:01
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@InquisitiveMind: I'm in the chat room now if you want to discuss it. – John Rennie Dec 23 '16 at 17:27