But the PE of the system in question is 1 kg * 1 G * 1 meter, not the full distance from heaven to hell.
Suppose we had a scale sensitive enough to register a relativistic mass increase due to PE, and then we roll a dice to decide how mach mass to drop, or how far... is the reading on the scale in some kind of superposition until the dice lands? And where would the mass increase actually be manifest - in the mass to be dropped, or the earth, or the net system? (i don't mind if we'd have to weigh the whole Sol system - doesn't have to be practically viable, just in principle) If i have to input 9.81 J to raise 1 kg by 1 meter, but only half that - 4.9 J - to excavate a 1 meter-deep hole, both systems have equal output PE, yet unequal input PE.. So what would our hypothetical Schrodinger's weighing scale have to say about this? E=MC^2 ascribes relativistic mass to KE - which is why C is mechanically unattainable - but not "potential", which, as the name implies, can be conditional and even indeterminate - ie. an unstable system can have a multitude of possible stable configurations it could collapse into, each with a unique energy profile. Because of this, i have difficulty accepting the oft-mentioned example of a loaded spring posessing such a mass increase - it would be selective evidence for a generalisation encompassing indeterminate systems... surely, either all PE has relativistic mass, or none does. However even if i'm mistaken, and a relativistic mass increase CAN be in a superposition of states, in that case it's not a conserved quantity either, and free to come and go with the ebb and flow of potential.. just as it does with KE. Which is just as well, since if an EM drive really could reach C, its wet weight would be infinite.. I can think of one permutation that might be an exception - a nuclear-powered EM drive; supposing perfect efficiency, would the relativistic mass gained from KE equal the mass deficit of the spent fuel? Tricky one, that. Or for a real head-twister, suppose we have a Bessler wheel powering our EM drive - gravity is equivalent to an acceleration, so acceleration of the craft in turn powers the Bessler mechanism, in a positive feedback loop. The harder it accelerates, the more PE it has to accelerate even harder. Fueled by its own acceleration, it's limited only by how much inertial force it can withstand... but in principle it has infinite PE, and again, the corresponding mass increase, as some would have it.. You could knock these out all day - bottom line is that a blanket assumption that relativistic mass applies to potential, implies all manner of absurdities and infinities. Which doesn't necessarily mean it's wrong of course, but should set alarm bells ringing.. On Wed, Mar 16, 2016 at 4:42 AM, H LV <[email protected]> wrote: > On Tue, Mar 15, 2016 at 10:32 PM, Vibrator ! <[email protected]> > wrote: > > That's conflating relativistic mass with rest mass. I know the > conclusion > > that potential energy raises a system's mass is commonly accepted as an > > inevitable implication of GR, but it's one frought with pitfalls: > > > > For instance, i dig a 1 meter-deep hole next to a 1 kg mass, at 1 G the > > system now has 9.81 J of PE. But is there a relativistic mass increase > (i > > don't care how small it'd be - multiply the scale if you wish)? > > > > What if the mass never falls into the hole? > > > > Similarly, a vertical wheel is balanced on a hilltop, with an unequal > drop > > on either side, so the system's PE is indeterminate - could relativistic > > mass also be indeterminate? > > > > The gravitational potential energy has a maximum finite value at an > infinite distance from the earth. > The point at infinity ensures that gravitational potential energy does > not have to be arbitrary. > As one moves closer to Earth the potential energy decreases relative > to this maxium value. > > Harry > >
