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John Duffield
John Duffield
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Yes, gravitational redshift. See what Einstein said: "an atom absorbs or emits light at a frequency which is dependent on the potential of the gravitational field in which it is situated". When the E=hf photon ascends, its frequency doesn't actually reduce. Conservation of energy appliesapplies*. It appears to have less energy at the higher elevation because that's where the spatial energy density is lower, so we and our clocks go faster. So we measure the photon frequency as reduced.

  • Some say conservation of energy does not apply in general relativity. I do not agree with that.

Yes, gravitational redshift. See what Einstein said: "an atom absorbs or emits light at a frequency which is dependent on the potential of the gravitational field in which it is situated". When the E=hf photon ascends, its frequency doesn't actually reduce. Conservation of energy applies. It appears to have less energy at the higher elevation because that's where the spatial energy density is lower, so we and our clocks go faster. So we measure the photon frequency as reduced.

Yes, gravitational redshift. See what Einstein said: "an atom absorbs or emits light at a frequency which is dependent on the potential of the gravitational field in which it is situated". When the E=hf photon ascends, its frequency doesn't actually reduce. Conservation of energy applies*. It appears to have less energy at the higher elevation because that's where the spatial energy density is lower, so we and our clocks go faster. So we measure the photon frequency as reduced.

  • Some say conservation of energy does not apply in general relativity. I do not agree with that.
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John Duffield
John Duffield
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What is the experimental evidence for the gravitational field having positive energy density?

Clocks go slower when they're lower, all the more so when the gravitating body is more massive.

Recent direct observation of gravitational perturbations attributed to merging black holes and merging neutron stars has reliably confirmed the existence of gravitational waves.

I'm not sure how reliable they are, but I don't have any issue with the existence of gravitational waves.

I understand that the observed fact that the orbits of binary pulsars decay, and the assumption that the decay is due to emission of gravitational waves, has led to a consensus that the energy density of the gravitational field is positive.

I don't think there is a consensus on that. I'm forever saying gravitational field energy is positive. I point to page 185 of the Doc30 Foundation of the General Theory of Relativity and Einstein saying “the energy of the gravitational field shall act gravitatively in the same way as any other kind of energy”. And yet I find there are people who object, and point to physicists and cosmologists who claim the opposite. For example Lawrence Krauss claims gravitational field energy is negative, and that the total energy of the universe is zero.

Here's a relevant quote from Steve Carlip: "To make gravity attractive in such a [vector-like] theory, you must require that the gravitational field has negative energy, which (apart from the obvious instabilities) would drastically disagree with binary pulsar observations".

I'm not clear on the context there. Gravitational attraction works in a particular way, and it doesn't depend on the spatial energy density, it depends on the gradient of the spatial energ density. If there is no gradient, there is no gravity.

It does seem to imply that the energy content of the gravitational waves emitted by the orbiting pulsars is positive, but it's not obvious that this requires the energy density of the gravitational field to be positive.

IMHO it's obvious because a field is a standing wave, or a wave is a dynamical field-variation propagating through space.

For example, suppose the gravitational field energy density is negative, and a gravitational wave is a perturbation in which the field strength is reduced within the wave.

The energy density relates to potential, whilst field strength relates to the gradient in potential. The latter causes you pencil to fall down. It falls towards the place where energy density is greater. If the wave is very large such that there's no discernible local gradient, you might be able to detect distant pulsars speeding up whilst you and your clocks are subjected to gravitational time dilation.

It seems that this would give the gravitational wave net positive energy, but allow the gravitational field energy density to be negative.

I don't see that I'm afraid.

Is there other experimental evidence that can clarify this?

Yes, gravitational redshift. See what Einstein said: "an atom absorbs or emits light at a frequency which is dependent on the potential of the gravitational field in which it is situated". When the E=hf photon ascends, its frequency doesn't actually reduce. Conservation of energy applies. It appears to have less energy at the higher elevation because that's where the spatial energy density is lower, so we and our clocks go faster. So we measure the photon frequency as reduced.

Are there inescapable theoretical arguments against the gravitational field having negative energy density?

IMHO general relativity is fairly inescapable, as is classical electromagnetism, and they both say field energy is positive. I don't know of any theory per se that says field energy is negative.