## The Sticky Bead Argument - Part 2

Posted by on Wednesday, July 8, 2020

In the previous article we reviewed the

Let me also state from the start that I am not arguing for one side or the other in this debate, and also make it clear that there are a number of assumptions and unproven claims in this counter-argument. It should certainly not be taken as a proven scientific fact, but rather should be viewed as a possible starting point for proper research and calculations in the future. With that disclaimer out of the way, let us begin.

Suppose that I have ten electrons stored on one side of my laboratory, and no electrons stored on the other side. The exact nature of the storage is unimportant, just that both contain a vacuum and are capable of storing electrons. between the two regions I place an electron detector that can record every single electron that passes from one region to the other.

I come back to the lab later in the day, and discover that there are now nine electrons on one side and one on the other. However my detector has not recorded any electrons passing between the two regions. How can it be so?

The answer is actually quite simple. While I was away, a stray positron entered my electron cloud and annihilated one of the electrons, converting it to a high energy photon. This photon crossed the laboratory, and because it contains no electric charge it was not detected by my particle detector. When it reached the other side of the lab, the photon converted back into an electron-positron pair, and the positron left the lab without leaving a trace.

And so electric charge decreased in one region, and increased in the other region, and yet the photon most certainly did not carry any electric charge.

Gravitational fields are much more difficult to study and understand than electromagnetic fields and high energy photons, and yet it is possible that a similar argument disproves the sticky bead though experiment.

For the sake of argument, suppose that gravitational fields can carry negative energy. There are arguments in both the general theory of relativity and in quantum field theory that support this assumption, but it has not yet been proven either way. The binary black hole system that I discussed in the previous article then contains positive energy in the form of the kinetic energy of each black hole, and negative energy contained in the gravitational field of the system.

When a gravitational wave is generated, the black holes lose some of their positive kinetic energy and potential energy to the wave. According to Einstein's field equations, this reduction in energy also reduces the gravitational field slightly. According to our assumption, the reduced gravitational field then will have a slightly less negative energy, or a slightly more positive energy. The loss of energy by the black hole is a gain in energy for the gravitational field.

The gravitational wave then travels through spacetime, carrying both positive and negative energy components which cancel out. (Or alternatively you could say that the gravitational wave simply contains no energy). When it hits the sticky bead, the gravitational wave causes the bead to heat up, increasing its positive thermal energy. This then generates a larger gravitational field, and this larger gravitational field has a more negative energy than before. The more negative energy of the gravitational field balances the more positive thermal energy of the sticky bead, and we find that the total energy has not changed at all.

And thus if gravitational fields can indeed carry negative energy, which I must make clear is still unproven and debated, then the sticky bead argument actually proves nothing. The binary black hole system can lose energy to the sticky bead, but without requiring the gravitational wave to carry any energy at all.

And so the debate about the energy of gravitational fields continues on.

*sticky bead argument,*which is often used to prove that gravitational fields must carry energy. We also stated without proof that the argument is wrong. In this article we will show an analogous thought experiment which is known to be false, and demonstrate how it applies to the issue of gravitational fields.Let me also state from the start that I am not arguing for one side or the other in this debate, and also make it clear that there are a number of assumptions and unproven claims in this counter-argument. It should certainly not be taken as a proven scientific fact, but rather should be viewed as a possible starting point for proper research and calculations in the future. With that disclaimer out of the way, let us begin.

Suppose that I have ten electrons stored on one side of my laboratory, and no electrons stored on the other side. The exact nature of the storage is unimportant, just that both contain a vacuum and are capable of storing electrons. between the two regions I place an electron detector that can record every single electron that passes from one region to the other.

I come back to the lab later in the day, and discover that there are now nine electrons on one side and one on the other. However my detector has not recorded any electrons passing between the two regions. How can it be so?

The answer is actually quite simple. While I was away, a stray positron entered my electron cloud and annihilated one of the electrons, converting it to a high energy photon. This photon crossed the laboratory, and because it contains no electric charge it was not detected by my particle detector. When it reached the other side of the lab, the photon converted back into an electron-positron pair, and the positron left the lab without leaving a trace.

And so electric charge decreased in one region, and increased in the other region, and yet the photon most certainly did not carry any electric charge.

Gravitational fields are much more difficult to study and understand than electromagnetic fields and high energy photons, and yet it is possible that a similar argument disproves the sticky bead though experiment.

For the sake of argument, suppose that gravitational fields can carry negative energy. There are arguments in both the general theory of relativity and in quantum field theory that support this assumption, but it has not yet been proven either way. The binary black hole system that I discussed in the previous article then contains positive energy in the form of the kinetic energy of each black hole, and negative energy contained in the gravitational field of the system.

When a gravitational wave is generated, the black holes lose some of their positive kinetic energy and potential energy to the wave. According to Einstein's field equations, this reduction in energy also reduces the gravitational field slightly. According to our assumption, the reduced gravitational field then will have a slightly less negative energy, or a slightly more positive energy. The loss of energy by the black hole is a gain in energy for the gravitational field.

The gravitational wave then travels through spacetime, carrying both positive and negative energy components which cancel out. (Or alternatively you could say that the gravitational wave simply contains no energy). When it hits the sticky bead, the gravitational wave causes the bead to heat up, increasing its positive thermal energy. This then generates a larger gravitational field, and this larger gravitational field has a more negative energy than before. The more negative energy of the gravitational field balances the more positive thermal energy of the sticky bead, and we find that the total energy has not changed at all.

And thus if gravitational fields can indeed carry negative energy, which I must make clear is still unproven and debated, then the sticky bead argument actually proves nothing. The binary black hole system can lose energy to the sticky bead, but without requiring the gravitational wave to carry any energy at all.

And so the debate about the energy of gravitational fields continues on.