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There is a question I asked a physics professor a while ago and I couldn't get a satisfying answer. The question was:

"Is there some orthonormed system in space? If there isn't as we generally suppose, when we observe 2 objects rotating around each other in space, couldn't we consider relatively speaking that they are not actually rotating but rather that the universe is rotating around them with opposite spin?"

I see no violation with that consideration, yet we should therefore see the objects crashing into each other due to their attraction if they were static.

So observing that the earth doesn't crash into the moon, can we safely say that there is no relativity of viewpoint possible? That we can calculate, based on the planets' masses, the actual required and therefore "absolute" angular momentum of both planets?

The professor told me that no you have to look at the most distant stars to know your referent, to get angular momentums that are coherent with the fact that they are in stable orbit (something like that, correct this please it was a long time ago). That suggests to me that there is in fact an absolute orthonormed system in space but he still said no. And that I should read some Mach explanation about this but I never found it. Can anyone help me make sense of this apparent paradox please?

Btw I never did maths in English so please edit the title of my question if orthonormed system is not the correct expression. If you don't understand what I mean by it, it's the set of 3 vectors x,y,z in which we use to study 3D maths and which is the absolute referent for everything studied in it.

Qmechanic
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sinekonata
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    Newtonian mechanics is not Machian. Inertial (non-accelerating, non-rotating) frames are postulated to exist in Newtonian mechanics. Such frames are absolute and universal. General relativity is not Machian, either. However, in GR, there is no such thing as absolute space. – David Hammen Mar 25 '17 at 04:49
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    Related: Is Mach's Principle Wrong? – David Hammen Mar 25 '17 at 04:50
  • You might intend to refer to orthogonal / orthonormed coordinate system in your title . –  Mar 25 '17 at 05:18
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    sinekonata: "Is there some absolute orthonormed system in space?" -- The more immediate question seems to be: "How do we determine which participants constitute an inertial frame?". More or less exactly this question gets asked frequently, e.g. already here (PSE/q/3191), where I also already submitted my answer. "The professor told me that no you have to look at the most distant stars to know your referent" -- To me that's not satisfying, either. – user12262 Mar 25 '17 at 07:14

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