Does required time for free falling bodies is independent of mass?

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ddnath
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In a class at OCW 8.01 Professor Walter Lewin said...

"...there are very prestigious physicists who even nowadays do very fancy
experiments and they try to demonstrate that the time for an apple to fall does depend on its mass even though it probably is only very small, if it's true but they try to prove that. And if any of them succeeds or anyone of you succeeds that's certainly worth a Nobel Prize."

What did he actually mean? Really?! Is it possible to proof that time required for free falling of bodies is not independent of mass?
 
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Is it possible to proof that time required for free falling of bodies is not independent of mass?
We don't know. It has not been observed yet, but it could be observed in the future.
IF there is any deviation (that is a big if), it would mean that General Relativity is wrong.