Let us begin by taking the conservation of total energy seriously. In order to be conserved, it must first exist. So we must have a field of potential energy, with an upper bound of 1 and a lower bound of 0. (You can’t have more than everything, and you can’t have less than nothing.) Any energy usage, from any cause, will subtract from this field to conserve total energy. Our field deforms, with an elasticity such that the deformation represents the inverse square law. Because this is what the equal spread of energy in all directions does. This deformation travels at the speed of causality, also known as the speed of light, c.
Well, now, that creates a gradient. Gradients are represented by vectors. In this case, the vectors will point down slope, towards the energy sink, which we will, for convenience, call mass. E = mc2, after all. (Yes, I know this is a first approximation. We’ll get there.)
So we now have a 4-field with a scalar and a vector. (That sounds suspiciously like the electromagnetic field. As we shall see, they are related, but orthogonal.)
What is this scalar? It is potential energy. What is potential energy? It is the integral of time. Time is imaginary, as it is orthogonal to every dimension of space. That means that potential energy is a negative number.
What is the vector? Given that the magnitude of the vector is equivalent to the amount of lost potential energy, it must be kinetic energy, the integral of momentum. After all, we learn in first semester physics that kinetic energy plus potential energy is a constant. And that is precisely what we have here.
If momentum is mv, then kinetic energy is: ½ mv2
If time is it, then potential energy is: -½ t2
(This is quite possibly the cause of spin 1/2 particles.)
So, where does this vector (or rather, field of vectors) point toward? Since they all point down slope, they must point toward the mass. Congratulations, we just discovered gravity. All hail the gradient!
So, with a motionless point mass, we have a classical gravitational field.
But what happens if the mass is moving? What does it even mean to be in motion?
Motion is obviously an imbalance in the kinetic energy portion of the field, which is equivalent to the instantaneous gradient in the potential energy. Instantaneous gradient - where have we heard that term before? Oh, yes - it is the differential. Which is time for potential energy, and momentum for kinetic energy.
So mass is identical for momentum, kinetic energy, and gravity, because they all have the same cause. Gravity, momentum, and kinetic energy are all effects.
In order to change the potential energy field, we must either withdraw or add energy to it. In either case, this requires a separate energy source or sink. Congratulations, we just discovered inertia.
What does our moving particle look like? We must take the speed of causation, which is the rate at which deformations propagate in our field, as a constant. That means that a moving mass will act as a longitudinal wave. The deformations before it must contract, and those behind it expand. This is another energy gradient in and of itself, even though the contractions and extensions themselves cancel out. (Never forget principle zero - everything adds up to nothing.) The induced kinetic energy subtracts from the potential energy field, increasing the total energy of the moving mass.
Congratulations, we just discovered special relativity. (I told you we’d get there.) We also just discovered redshift as a side effect of these directional gradients. After all, a photon being emitted from our moving body will gain energy from the downward gradient ahead, or lose energy from the upward gradient behind. Note that this applies equally to the emitter and receiver, so two bodies traveling with equal momentum will see no shift at all, because the gradients exactly cancel out.
How do we accelerate a particle? Acceleration is a gradient in the gradient, so the potential energy (and time) are continuously changing. The field must be increasingly squeezed before and stretched behind the accelerating particle. Therefore, so are the kinetic energy and momentum vectors. Congratulations, we just discovered general relativity.
We can even take these basic principles and apply them to the electromagnetic field, keeping in mind these propagate as transverse waves. (The orthogonality of the EM and PK fields keeps arising in surprising ways.) The magnetic moment of the electron can be viewed as the EM equivalent to the gravity of a motionless mass.
So, as we can see, everything flows from taking the conservation of energy seriously.
Cross posted from my Substack. Like and subscribe!
Addendum 1: The Higgs field would seem to be superfluous, since the potential energy field can supply the missing mass with much less complication. I need to research and ponder this some more.
Addendum 2: Time spin or chrono charge? Chrono charge seems simpler, and aligns better with positive and negative electric charges. It also makes a neutral position make more intuitive sense. Positive = matter, negative = antimatter, neutral = doesn't matter. I think I like this better. It leaves the concept of spin open for mass, which doesn't seem to care if it's matter or antimatter.
