So, despite Einstein’s hopes, general relativity does not in any way explain or obviate the principle of inertia. Granted, if the field equations didn’t include the trace term (so that the covariant divergence didn’t vanish), the resulting theory would have many problems and be subject to many objections, but this goes without saying. No one disputes that the principle of inertia is extremely well-founded in observation. It is an extremely well-justified postulate – but it is still a postulate. General relativity does not explain inertia, nor does it dispense with the need to organize our spatio-temporal theories on the topology and morphology implicit in the principle of inertia and the associated distinguished coordinate systems.
Furthermore, once we recognize that the inertial and gravitational field are one and the same, the twins paradox becomes even more acute, because we must then acknowledge that within the theory of relativity it's possible to contrive a situation in which two identical clocks in identical local circumstances (i.e., without comparing their positions to any external reference) can nevertheless exhibit different lapses in proper time between two given events. The simplest example is to place the twins in intersecting orbits, one circular and the other highly elliptical. Each twin is in freefall continuously between their periodic meetings, and yet they experience different lapses of proper time. Thus the difference between the twins is not a consequence of local effects; it is a global effect. At any point along those two geodesic paths the local physics is identical, but the paths are embedded differently within the global manifold, and it is the different embedding within the manifold that accounts for the difference in proper length. (The same point can be made by referring to a flat cylindrical spacetime.) This more general form of the twins paradox compels us to abandon the view that physical phenomena are governed solely by locally sensible influences. (Notice, however, that we are forced to this conclusion not by logical contradiction, but only by our philosophical devotion to the principle of sufficient cause, which requires us to assign like physical causes to like physical effects.) Likewise the identification of gravity with local spacetime curvature is untenable, as shown by the fact that a suitable arrangement of gravitating masses can produce an extended region of flat spacetime in which the metrical field is nevertheless accelerating in the global sense, and we surely would not regard such a region as free of gravitation.
Quote from: spacester on 06/05/2009 05:19 amI've always preferred the term "spin-g" when talking about the (sole) method available with today's technology. From my archives:For tons of information on the realities of spin-gravity, see:This discussion about the effects of micro-g and the issues regarding artificial gravity and this for all the math you could ever want (scroll down to the conclusions) and then this for an architect's view of what it would be like.I'd like to see a ship built in LEO to be spun for 0.38 g to simulate Mars gravity, and 0.16 g to simulate Lunar gravity (IIRC)....I agree, an LEO spin gravity lab would be very worthwhile. It could tell us if lunar or Mars gravity is sufficient to maintain health.Human tolerance to angular velocity could also be tested. Some have suggested humans could become acclimated to high angular velocity just as sailors get used to sea motion. As you point out, for a given fraction of G, diameter goes down with the inverse square of angular velocity.If we could endure 3 rpm and lunar gravity is sufficient to maintain health, this would drastically reduce mission requirements for spin gravity habs. This could make orbital settlement and/or long interplanetary trips cheaper.
I've always preferred the term "spin-g" when talking about the (sole) method available with today's technology. From my archives:For tons of information on the realities of spin-gravity, see:This discussion about the effects of micro-g and the issues regarding artificial gravity and this for all the math you could ever want (scroll down to the conclusions) and then this for an architect's view of what it would be like.I'd like to see a ship built in LEO to be spun for 0.38 g to simulate Mars gravity, and 0.16 g to simulate Lunar gravity (IIRC)....
If one accepts that we need to know the answer to the question of the effectiveness for livability and human health of spin-gravity, and one further accepts that building a Mars-bound spin-gravity ship only makes sense if that answer has been found, then shouldn't one be advocating for a spin-g lab in LEO?
But I heard bad things on small diameter centrifuges.
According to current research, 5 RPM can be tolerated by most people, possibly as much as 10 RPM. 4 RPM is considered by many NASA papers as the upper limit for spin-grav design but that's based on old research.
The point is, would you rather spend 6 months going there and 6 months coming back and spend a few weeks on the surface, or go there in a few days and spend a whole year exploring the planet? Which is more valuable? Obviously spending the time on the planet.