This example totally confused me. An object spinning in space experiences centripetal acceleration, relative to its own center of mass. For sake of example, let's say that instead of spinning in cartwheels, the one spinning astronaut is spinning like an ice skater. OK, which astronaut feels their arms being pulled outwards due to centripetal force, and which one has their arms hanging limply at their sides? Wouldn't that answer the question?

in the model where inertia is a result of interacting with all the other gravitational fields empty Universe would mean no inertia and thus no centripetal force. (of course there is another model - that of Higgs boson - for which i haven't so far been able to find how it explains equivalence of inertial and gravitational masses and thus it is so far non-starter for me, i mean not the boson itself - that of course exists, i mean the boson's role in inertial mass story until of course the boson happesn to be the main carrier of the "gravitational charge" then all would fall nicely in place)

> would mean no inertia and thus no centripetal force

Wouldn't that allow infinite acceleration?

Without inertia, if two objects collide elastically - what controls the final speeds?

I don't think you can just get rid of inertia in a thought experiment and expect results that correlate with the real world.

Correct me if I'm wrong, but without the Higgs boson and its corresponding scalar field, the concept of mass/inertia does not exist. Without mass, can matter still exist? How would this "matter without mass" behave? My mind is close to exploding.

imagine that there is only gravitational force in the Universe and the matter has only gravitational mass("charge"). Accelerating any given piece of matter with respect to all the other matter would cause propagation of change (ie. wave) in the gravitational field of the whole system (Universe). Wave is energy and to generate wave a work is required, ie. a force has to be applied to the piece of matter being accelerated - the requirement for that force is what we call inertia.

Now of course the question - what is the carrier of that "gravitational charge". It would be great if Higgs boson was the carrier of that charge.

I thought the idea that "the Higgs boson is the field responsible for imparting mass" was the dominant theory, are there reasonable alternative explanations?

I don't think that's right. I think the Higgs creates a large amount of mass (90%-ish), but not 100% of it. (This is from memory of something I read, so I can't point you to a source...)

> An object spinning in space experiences centripetal acceleration, relative to its own center of mass.

In this universe, yes.

But in an otherwise empty universe? We don't know.

I agree - this doesn't make sense. You can detect if you are spinning without looking at the outside world.

In an absolutely empty universe you can still tell if you are rotating.

Wouldn't the spinning one see the other "orbiting" rather than spinning? If gravity is not strong enough to cause that orbit and there's no thrust evident that could explain the delta-V causing the orbit, couldn't you then conclude that you're spinning without an external reference?

I think this thought experiment assumes the astronaut is spinning around an axis orthogonal to their belly. From the cartwheeling astronaut's perspective, the other one is also cartwheeling in their own plane.

But if you tuck in your knees and the other guy spins differently, that's a sign you're the one spinning, no?

Yeah, the choice of a non-inertial reference frame for this example is a little confusing to me too. I also haven't been able to find an independent mention of the spinning astronaut experiment.

No because you technically performed an action which changes the system.

Relativity states that there isn't a measurement you can take if you change the system however it's a different story.