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- Thread starter Stephen Brackin
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PAllen

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Note that in Newtonian mechanics, where you set the zero point for potential energy has no effect whatsoever on observed phenomena. Only changes in potential matter.

Similarly, in GR, arranging that total energy of the universe is zero is just a convention; and this convention is not used by most GR experts.

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PAllen

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Not sure the level of your courses, but the common convention in Newtonian physics is that a body with KE insufficient to escape to infinity has total energy (KE + potential) negative; if its KE is just sufficient to escape to infinity, it total energy is zero; else it is positive. But all of these are just conventions (as is also true in GR). Total energy is both conventional and observer dependent in both. All that matters are conservation laws (within one frame or coordinates), and transfers of energy, not whether the absolute amount is positive or negative (when including potential energy). It is certainly true that KE and rest energy are always non-negative.

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Drakkith

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This link may interest you: http://math.ucr.edu/home/baez/physics/Relativity/GR/energy_gr.html

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Nugatory

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Set the zero point to be the floor and there is no negative energy to understand: We start with potential energy while the cat is on the table; we have positive kinetic energy as the cat is moving towards the floor, and eventually the cat lands and the temperature of the floor increases slightly as the kinetic energy is dissipated as thermal energy. The energy is positive at every step.

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Any object's potential energy from gravity is the kinetic energy the object would acquire if it could fall, only under the influence of gravity to the point where the gravity is zero. For the earth, that point is the center of the earth, and it's always positive. For computational purposes, what we usually call potential energy is the CHANGE in potential energy from some convenient reference point. For a pendulum, the potential energy from gravity is at its lowest (zero) and the kinetic energy is at its highest when the pendulum is at its lowest point and the potential energy is highest and the kinetic energy lowest (zero) when the pendulum is at the highest points in its arc. For a cat on a table, the reference point is the floor, and the cat's potential energy falls from positive to zero as it jumps from the table and falls to the floor -- hitting the floor harder the higher the table. I know of no cases in which it's convenient to take the reference point at infinity -- where the gravitational potential energy is maximum -- and call the potential energy there zero and the potential energy everywhere else negative.

Mentioning reference points was an attempt to evade my question by defining it away, not an attempt to answer my question. Any real form of negative energy will be able to cancel out regular energy -- make hot things colder, moving things slower, or bright things dimmer. And for Hawking's claim, we need enough of it to cancel out all the energy in the universe.

[Mentors' note: some gratuitous invective in violation of the PF rules has been removed]

Mentioning reference points was an attempt to evade my question by defining it away, not an attempt to answer my question. Any real form of negative energy will be able to cancel out regular energy -- make hot things colder, moving things slower, or bright things dimmer. And for Hawking's claim, we need enough of it to cancel out all the energy in the universe.

[Mentors' note: some gratuitous invective in violation of the PF rules has been removed]

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PAllen

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I am not evading your question but trying to explain why it is ill formed, in both GR and Newtonian physics. I believe the negative energy Hawking refers to is equivalent to the rudimentary Newtonian fact that some distribution of bodies has less potential energy than if those bodies were moved infinitely far apart. Given that infinite separation is conventionally given PE=0, all other configurations have negative PE. In Hawking's methodology, this simple fact is being named negative energy of gravity. This is all related to a particular way to talk about total energy of the universe within the formalism of GR that makes it come out identically zero. Precisely for this reason, this way of talking about total energy is not considered meaningful by most GR experts, but (for example) a vocal advocate of this approach is Philip Gibbs. Taking you at your word in the Hawking quote, at least in some source, he was apparently referring to this GR approach.Any object's potential energy from gravity is the kinetic energy the object would acquire if it could fall, only under the influence of gravity to the point where the gravity is zero. For the earth, that point is the center of the earth, and it's always positive. For computational purposes, what we usually call potential energy is the CHANGE in potential energy from some convenient reference point. For a pendulum, the potential energy from gravity is at its lowest (zero) and the kinetic energy is at its highest when the pendulum is at its lowest point and the potential energy is highest and the kinetic energy lowest (zero) when the pendulum is at the highest points in its arc. For a cat on a table, the reference point is the floor, and the cat's potential energy falls from positive to zero as it jumps from the table and falls to the floor -- hitting the floor harder the higher the table. I know of no cases in which it's convenient to take the reference point at infinity -- where the gravitational potential energy is maximum -- and call the potential energy there zero and the potential energy everywhere else negative.

Mentioning reference points was an attempt to evade my question by defining it away, not an attempt to answer my question. Any real form of negative energy will be able to cancel out regular energy -- make hot things colder, moving things slower, or bright things dimmer. And for Hawking's claim, we need enough of it to cancel out all the energy in the universe.

[Mentors' note: some gratuitous invective in violation of the PF rules has been removed]

I emphasize the Newtonian analog to get across the idea that you can add any constant you want to potential energy everywhere without changing the physics. In particular, you can choose the constant to make total energy of the universe zero. Most GR physicists believes the approach advocated by Gibbs (and Hawking?) has precisely as much (or as little) meaning as adopting such a convention.

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Any object's potential energy from gravity is the kinetic energy the object would acquire if it could fall, only under the influence of gravity to the point where the gravity is zero. For the earth, that point is the center of the earth, and it's always positive.

Steve, I don't think that anyone uses the center of the Earth as the zero for potential energy. I don't know where you got that idea from. You certainly can use it, but nobody does, as far as I know. The two conventions that I've seen are:

- [itex]PE = mgh[/itex] where [itex]h[/itex] is the height above the ground. This convention is only useful over a range that is small enough that you can approximate the acceleration due to gravity by a constant, [itex]g[/itex] (approximately 9.8 meters per second
^{2}). - [itex]PE = -\frac{GMm}{r}[/itex] where [itex]G[/itex] is Newton's gravitational constant, and [itex]M[/itex] is the mass of the Earth, and [itex]r[/itex] is the distance from the center of the Earth.

(This is all from the point of view of Newtonian gravity. General Relativity doesn't actually have a notion of "gravitational potential energy".)

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Set the zero point to be the floor and there is no negative energy to understand: We start with potential energy while the cat is on the table; we have positive kinetic energy as the cat is moving towards the floor, and eventually the cat lands and the temperature of the floor increases slightly as the kinetic energy is dissipated as thermal energy. The energy is positive at every step.

For most problems, you can get rid of the negative potential energy by redefining the zero point. But as I said to Steve, if you're considering the potential energy for a configuration of matter, then there is no zero you can pick that will guarantee that the potential energy is always non-negative, because the gravitational potential energy can always be lowered by compressing the matter.

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Astrophysics might be a case where taking the gravitational potential energy reference point as infinity might be convenient, since astronomical distances are so large that infinity is a good approximation. This will make all the potential energies discussed negative and relatively small.For most problems, you can get rid of the negative potential energy by redefining the zero point. But as I said to Steve, if you're considering the potential energy for a configuration of matter, then there is no zero you can pick that will guarantee that the potential energy is always non-negative, because the gravitational potential energy can always be lowered by compressing the matter.

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