On Wed, Mar 16, 2016 at 9:15 PM, Vibrator ! <[email protected]> wrote: > But the PE of the system in question is 1 kg * 1 G * 1 meter, not the full > distance from heaven to hell. >
Measure PE relative to the place where the force of gravity is zero inside the Earth. That place has an objective existence even if it is impossible for a body to fall there in practice. > 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. You are confusing possibility with potentiality. Possibility is conditional and indeterminate. A seed has the potential to become a tree, but the condition of the environment may make it impossible for the seed to realize its potential. I would say as long as the environment is sufficiently determined then a body can have an objective PE and extra mass. ( I don't like term relativistic mass because that implies motion which is not required for a body to have PE) > 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.. Harry > > 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 >> >
