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Any body in a bound system tends to possess negative total energy, like a satellite in Earth's orbit, according to classical physics. An external agent needs to expend energy in order to bring such a body to infinity, that is, a state of zero energy, this justifying the negative sign. In what way is this negative energy different from the 'negative energy' that physicists are hunting for and whose existence is under question? Is there something in Relativity or Quantum Mechanics that differentiates the two?

Prajwal Muralidharan
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  • It's not true that "Any body in a bound system tends to possess negative total energy". Any two masses connected by a spring form a bound system with positive total energy, and that's just one of many large classes of counterexamples. The reason this is true for inverse-square central forces is mainly because of the way we set the zero point for potential in those systems (and the choice of where to put "zero potential energy" is entirely arbitrary, and cannot affect the actual physics). – probably_someone Mar 23 '20 at 19:55
  • @probably_someone The zero point is not arbitrary. The potential energy contributes to the energy-momentum tensor and thus has gravitational effects in the form of, for example, electrostatic field energy, which really is zero at infinity. – G. Smith Mar 23 '20 at 20:00
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    @G.Smith It is in classical mechanics, that's for sure. If we're going to bring general relativity into this, there are a boatload of more subtle sub-questions about what energy even means in curved space-time (for a primer for this discussion, see e.g. http://math.ucr.edu/home/baez/physics/Relativity/GR/energy_gr.html). – probably_someone Mar 23 '20 at 20:03
  • @G.Smith What do you mean when you say that "electrostatic field energy really is zero at infinity"? The concept of the energy of a field at a distance doesn't really make sense; fields have a energy density that's a function of position, and that quantity is zero for a charge distribution with finite support, but lots of very commonly-studied charge distributions don't have finite support (e.g. the infinite line charge, the infinite charged plane, etc.), and for those, the energy density fails to be nonzero at infinity. – probably_someone Mar 23 '20 at 20:07
  • I meant energy density, and I’m talking about for compact systems. You cannot take this energy density at infinity to be some arbitrary constant. And you cannot take the overall PE to be nonzero at infinite separation, or solar system dynamics don't work under GR. The post-Newtonian formalism makes this clear. – G. Smith Mar 23 '20 at 20:18
  • @G.Smith Who said I was? The potential and the energy density are two completely different things. And if you were talking about compact systems, you should say so. Plenty of misinformation in science is spread by lack of precision in language. – probably_someone Mar 23 '20 at 20:21
  • @G.Smith I'm going to need a proof of the statement "you cannot take the overall PE to be nonzero and infinite separation, or solar system dynamics don't work under GR". – probably_someone Mar 23 '20 at 20:21
  • @probably_someone Look at what $\beta_2$ stands for in the PPN formalism: “How much gravity is produced by unit gravitational potential energy.” – G. Smith Mar 23 '20 at 20:26
  • I’m getting the message to avoid extended discussions in comments, so I’m done. – G. Smith Mar 23 '20 at 20:29
  • @probably_someone Actually, I have to say one more thing. The simplest argument that the zero point of the Newtonian gravitational potential $\varphi$ is no longer arbitrary in GR is that this potential appears in the metric approximation $g_{00}\approx-1-2\varphi$. The metric does not depend on the derivative of the potential but on the actual value of the potential. You cannot add an arbitrary constant to the potential. – G. Smith Mar 23 '20 at 21:02

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When you include the mass-energy of a gravitationally-bound or electrostatically-bound system, its total energy is positive, not negative. It’s just less than the total energy when the system is separated to infinity.

So negative binding energy is not the exotic kind of negative energy that some people like to speculate about.

G. Smith
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