Classical potential energy has the property that you describe. You can make it whatever value you want. Often 0 is used for the maximum and all potential energies are then negative. I believe that kinetic energy is always positive so if you consider a moving particle it will have positive kinetic energy and then positive energy unless you put it into a potential well whose escape velocity energy is greater than the particles kinetic energy (although even there you could define the energy at infinity to be arbitrarily negative).
With respect to relativity I think that the relativistic mass is always greater than the rest mass and so you can't decrease energy that way. You can in a sense transform kinetic energy away by just considering the situation from the rest frame but not the rest energy - it stays when you transform to the rest frame. I was amazed to find a statement by Wald in his book General Relativity in which he said that energy was not conserved globally. I guess the idea of energy breaks down when you consider the possible topologies. I am pretty sure that in relativity rest mass is positive and kinetic energy increases it but potential energy does not correspond to mass increase. So if you were to throw two balls up onto two shelves in the potential field of an attractive force between them then the mass would not show up in the balls (as they are now at rest) but I think that you would need some elastic pole between the shelves holding them apart and supporting the fixed separation and when the balls came to rest the pole would be compressed so the stress energy mass tensor of the whole thing would not change and if you weighed the aparatus before and after the balls came to rest you would have the same weight and energy. With respect to quantum mechanics I think that you cannot define the energy of the universe unless you mean the energy for all time. Otherwise the value has some uncertainty. So you cannot get a discreet number for the frequency of a wave (and hence its energy) unless you consider all time. Once you limit the wave to a period of time that is finite you end up with a wave packet that has a distribution of frequencies and hence a distribution of possible energies. If you ask about the value for all time however, then you can have some defined number for its frequency which can be converted to energy by multiplying times Plank's constant. Perhaps that is what is meant by "for all time" just a way of evading Heisenburg. I think it would then be arbitrary what energy number you assigned to it as only interactions or changes in energy have physical meaning. The standard way of refering to the units however what is in the wiki. On Jan 14, 6:38 pm, Twirlip <[email protected]> wrote: > On Jan 13, 11:31 pm, archytas <[email protected]> wrote: > > > The sum of energy in the universe is often considered as zero. > > I haven't studied physics since I was at school, but this looks odd, > especially in view of relativistic mass-energy equivalence. > > In support of it, all I can recall is that a potential energy field is > only defined up to an arbitrary constant, which can therefore be > chosen to make the integral of potential energy equal to zero. > > However, even supposing that to be correct (it leaves undefined what > the potential energy field is, and over what manifold it is being > integrated, e.g. is it mass-energy being integrated over all space- > time, or what?), it doesn't seem to imply that energy (or mass-energy) > has no absolute physical reality, any more than the use of an > arbitrary (Fahrenheit or Centigrade) scale for temperature proves that > there is no absolute zero. > > Against it, a quick Google yields this assertion: > > http://www.advancedphysics.org/forum/showthread.php?t=6997 > > "To give a partial answer, the current best estimate of the total mass- > energy (just the energy due to mass) of the universe is around 2 x > 10^69 Joules (seehttp://www.answers.com/topic/orders-of-magnitude-energy > for example). " > > This reference (obtained from that last URL) would appear > authoritative, at least to me: > > http://imagine.gsfc.nasa.gov/docs/ask_astro/answers/980211b.html
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