This was the old Mach/Einstein debate. One of the two (I can’t remember which!) said no, there could be no rotation because there isn’t anything to rotate relative to. The other said that “empty space” itself had a metric, sort of like a blank piece of paper. You can measure distances and specify points even in perfectly empty space.
I believe the actual solution, as seen today, is slightly more messy than either position. But the equations are so very, very gnarly, they vastly exceed the ability of nearly anyone (hello, anyone here really good at tensors and things?) to explain in commonplace language.
The best thing about frame dragging is that it has been experimentally verified, (or at least supported) by a satellite experiment.
One thing we must always come back to about Relativity: it ain’t just pie-in-the-sky ivory-tower theorizing. It’s absolutely and concretely real, and can be observed by several different kinds of equipment. (I’m not accusing you of being a Relativity denier…but we have had lengthy and uncomfortable discussions with those who were…and who never quite grokked that point.)
What a Wonderful World – where “damn weird” is substituted for “wonderful!”
Mass can’t be converted to energy, because it’s already energy. All mass is energy. But not all energy is mass. Mass is, as Ring correctly stated, that portion of the energy of a system that cannot be transformed away.
The correct form of Einstein’s equation is actually E[sup]2[/sup] = m[sup]2[/sup]c[sup]4[/sup] + p[sup]2[/sup]c[sup]2[/sup]. The familiar E = mc[sup]2[/sup] is just the special case for where momentum is zero: In a reference frame where the momentum of a system is zero, its energy is just its mass. But in any other reference frame, you’ll get some energy from mass, and some from the momentum. This is especially relevant in, for instance, a system consisting of a single photon: Such a system has no reference frame where its momentum is zero, and thus has no mass: All of the energy of such a system is due to its momentum.
Ludovic already posted the xkcd link, but to be less glib about it, what about the centrifugal acceleration do you think is only “apparent”? If I’m in a rotating reference frame and release a ping pong ball at any point but the centre of rotation, will it not fly away as if centrifugal and Coriolis forces are acting on it?
One of my old Newtonian Mechanics profs started the trimester by pointing out that Newton’s first law (the law of inertia) doesn’t actually say very much. It says, that things that are unaffected by anything else stay still or move with uniform velocity, but only in inertial frames. But the definition of an inertial frame is one in which things that are unaffected by anything else stay still or move with uniform velocity. So Newton’s first law is basically, “things have inertia when they do”.
His point was that we like inertial frames, because the equations of motion come out simpler, but they’re not fundamentally “better”. In a rotating reference frame the law of inertia is just, “things that aren’t affected by anything experience a centrifugal and Coriolis acceleration”. You don’t even need to think of them as “forces”, just a change in the way things that aren’t interacting with anything act.
So in a reference frame rotating with the Earth, the equivalent of the law of inertia is, “things accelerate outward from the Earth, unless affected by an outside force (and some crap about the Coriolis effect)”. The geosynchronous satellite just has gravity exactly cancelling the natural acceleration to keep it perfectly still.
As I was dicking around in Wiki following framedragging, the Penrose effect seemed pertinent to a seeming “no-pain energy gain.” How might this apply? Also, does the top (or any spinning item) have an ergosphere, the pertinent concept that I just read about that seems poised to blow my mind were I ever to understand it minimally…
