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A geon is a bound state of gravitational (GR) or electromagnetic (EM) waves. This section is focused on the gravitational geon composed of GR waves only. It has been shown that parallel EM waves do not attract at all. Even for anti–parallel EM waves, their attractive force is about 80 orders of magnitude smaller than the force between EM and GR waves (Faraoni and Dumse, 1998, Eq. 6.1). Therefore, the attractive forces among EM waves are too weak to form an electromagnetic geon under practical conditions, but a gravitational geon is realistically permitted (Anderson and Brill, 1997; Kermode and Vollick, 2011).
A free GR wave, like a free EM wave, propagates at the speed of light. As discussed in the previous section, the formation of standing waves is a key mechanism to stop propagation. However, it requires simultaneously generated waves traveling in opposite directions, but neuronal activities may radiate GR waves in all directions. If only precisely synchronized waves traveling in exact opposite directions could stop propagation, a large portion of waves would leave the brain at high speed. "Binding by synchrony" is another key mechanism to hold waves in a small region around the brain. Not only is it important for the creation of a geon, but also crucial for the conscious perception of sensory inputs and internal memory.
Synchronization (in phase coherence) facilitates constructive interference of waves (Figure 8-8). For two waves with equal amplitude, their constructive interference will double the amplitude. On the other hand, the energy of a wave is proportional to the square of the wave's amplitude (Google Search). This applies to all kinds of waves, including the GR waves (Kokkotas, 2002, Eq. 2.26). Let E1 be the energy of an individual wave. In the absence of any interaction between two identical waves, the total wave energy, Ew, should be 2E1. Now, the constructive interference will double the amplitude and thus quadruple the energy. Ew becomes 4E1. Since the total energy of an isolated system must be conserved, where does the additional energy come from?
For most types of waves, the additional energy may come from their environment. However, the GR waves have virtually no interaction with surrounding matter. They do not exchange energy with the environment. The most likely energy source is from the GR system itself, which possesses gravitational potential energy, Ep.
Ep exists almost everywhere. Any object near the surface of the Earth should have an Ep, whose value is negative. The more negative Ep is, the stronger the binding (attraction) between an object and the Earth. In Einstein's view, the gravitational binding arises from the distortion of space-time (Section 8.2). Since GR waves are the ripples of space-time, they should have Ep.
Thus, the total energy of a GR system includes both Ew and Ep. As the constructive interference increases Ew, Ep should decrease (more negative) so that the total energy remains constant. This leads to the conclusion that constructive interference will increase the binding energy between GR waves. For a system of N identical GR waves, the binding energy created by their constructive interference is given by
Binding energy = (N2 - N) E1
In the brain, the ion flow through each ion channel will generate a GR wave. A neuron contains more than 10,000 ion channels (Buchholtz et al., 2002). Even if only 1% of channels produce constructive interference of GR waves, their binding energy is already enormously increased (~ 106 times). In addition, a large population of neurons may fire synchronously, creating an even stronger bound state around the brain. Therefore, it is quite possible that the globally synchronized alpha activities may create a gravitational geon.