Dear Edwin Klingman,
In nature, everything is interconnected and, of course, time is connected with energy. Besides, time is associated with inertia, momentum, movement and space. The question is what connections are short and direct, and which are indirect? Let us consider these connections on the example of an electron. If the internal energy of an electron is kinetic energy, then any point that is part of the electron has zero rest mass and moves at the speed of light. The zero mass of points in a closed volume forms a nonzero mass of the electron. Here the points are very conditional definition - these can be any structures with nonzero dimensions. The motion of points inside an electron is an internal process of an electron. This motion causes a continuous change in the state of the electron, since each point continuously changes its spatial coordinates. The change in the state of the electron forms the proper time of the electron. Now imagine that the gravitational field has one single property - the action on the speed of light, and the smaller the distance to the central mass, the speed of light is less. Let the electron be placed in a gravitational field. In this case, all processes inside the electron slow down in proportion to the decrease in the local speed of light and this leads to a dilation of the electron proper time. In the case of an electron moving relative to the central mass, the average rate of processes inside the electron is additionally slowed down and this leads to an additional expansion of the electron proper time. Both forms of time dilation are observed in the GPS satellite system. In reality, the gravitational field has not one but two fundamental properties, and the combined action of these properties causes various adventures for the electron, including its gravitational acceleration. More details are shown in the essay.
The length contraction caused by gravity can be discussed in the future. Here I note that the rate of time flow in different frames of reference can differ very much, but any two events that are simultaneous in one reference frame are also simultaneous in any other reference frame. So, I give You a high rating.
Best wishes,
Robert Sadykov