Why do apples fall rather than lift off the ground?

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On 6/9/2020 at 6:54 AM, Mordred said:

[...] just a side note I've often wondered if the Frenet Serett equations used in R^3 would apply to R^4. However that's just a side note curiosity lol.

8 hours ago, Markus Hanke said:

I know that these relations can be generalised to any number of dimensions on Euclidean manifolds; I also know that they can be generalised to Minkowski spacetime. However, whether one can generalise them to arbitrary pseudo-Riemannian manifolds is a question I don’t know the answer to (probably best posed to a mathematician). I suspect that, if it is possible at all, you’d end up with something very convoluted and awkward, certainly something much more difficult to work with than the comparatively simple geodesic equations.

My guess would be that they wouldn't, because R3 is special in that covectors are isomorphic to vectors. In Minkowski I've seen them used, but that's because you've got spacelike and timelike, and the derivative by the invariant parameter must preserve the genus, so you would have the timelike element plus a Frenet-Serret spacelike triad. Spacelike go their own way, while timelike keep the isomorphy between 3-vectors and 3-covectors, so that Frenet-Serret would still be useful. But that would be just my guess...

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When I finally get this thread sorted out am I going to find that not only does the Apple fall towards the ground, but that somehow amazingly the ground falls towards the Apple?

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2 minutes ago, jajrussel said:

When I finally get this thread sorted out am I going to find that not only does the Apple fall towards the ground, but that somehow amazingly the ground falls towards the Apple?

I would hope so.That is what I always assumed.

"Falling" ,as used colloquially implies a particular (up/down) frame of reference and Relativity says that no frame can be preferred over another.

In this apple/Earth  context it is the centre of gravity of the apple and the centre of gravity of the Earth that "fall towards" each other.

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1 minute ago, geordief said:

I would hope so.That is what I always assumed.

"Falling" ,as used colloquially implies a particular (up/down) frame of reference and Relativity says that no frame can be preferred over another.

In this apple/Earth  context it is the centre of gravity of the apple and the centre of gravity of the Earth that "fall towards" each other.

Good. I was afraid that it might be a trick question, and was afraid that I might fall for it.  I have to admit that the quick read had kinda confused me though.

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