Quantum Theory of Gravity - "QTG"

4. The Temporal Uncertainty Principle

                Chapter 3 demonstrated that, due to the relativistic nature of simultaneity, time passes at different rates with respect to points of reference in relative motion. It has also been demonstrated theoretically and experimentally that one of the consequences of the General Theory of Relativity is that time also passes at different rates in locations with different gravitational potentials or subject to different inertias. For the subatomic world, where inertias are also present, we should therefore accept a further phenomenon, which introduces the coexistence of the past and the future in the same environment: temporal uncertainty.

                Given the existence of different rates of time in the atom, we must admit that, when examined in isolation, an atom must have its own temporal system and possess a location, which is in equilibrium with its external time reference. This point of reference is the nucleus, or a location very close to it: it is the geometric center of the atom and concentrates the greater part of its mass, thus connecting the atom with the external time reference.

                In heavier atoms, this point of reference can be well defined, due to the more homogeneous distribution of electrons in the electron cloud and the greater concentration of mass (energy) in the nucleus; in the lighter atoms it oscillates considerably. The double slit experiment thus reveals interference characteristics with light atoms as it does with photons and electrons, as will be seen in chapter 12.

                Figure 1 describes an imaginary experiment, which should be imagined in three dimensions, consisting of a hydrogen atom and two observation systems, A and B, located on opposite sides of it. The observation system is to be understood as an entity consisting of one or more atoms that establish among themselves a local time reference independent of the individual temporal oscillations of the atoms and their parts, within the conditions established by the principles of relativity.

                At a given instant, the components of the hydrogen atom emit some kind of signal, which is propagated at the velocity of light. For observation system A, the signal from the electron arrives at time t_e = (ℓ - radius)/c, while the signal from the nucleus arrives at t_p = ℓ / c. It is clear that t_e < t_p, which is to say that, for observation system A, the electron is in the future, because the signal arrives before the reference signal from the nucleus.

                In this case, the electron is in the future in relation to the local time reference. For observation system B, the signal from the electron arrives after the reference signal, indicating that the electron is in the past in relation to the local time reference.

                Each observation system clearly perceives a different reality for the atom. It can therefore be concluded that the electron oscillates between the past and the future in a manner that can be represented in three dimensions as a spiral and in two dimensions as a sine curve, as shown in figure 2. Each observer will also perceive a different sine curve.

                
                It can be seen that these time differences are very small, and are directly proportional to the size of the atom. For the sake of curiosity, we can calculate the difference:

                It has been confirmed experimentally that when an electron is observed escaping from an atom, it is obliged to do so from the nucleus, even though this is a location where it cannot be. This is practical confirmation that the nucleus is the connection between the atom’s temporal system and the external time reference.