Crossing the brachistochrone- Prologue

Perhaps the most famous equation in all physics is Albert Einstein’s formula

Specifically, because the relativistic mass m changes, it is

where m₀ is the ‘rest,’ or inertial, mass.

The relativistic factor γ_L is called Lorentz factor, and its value is

The problem here is that if the speed v (of some object) approaches the speed of light c, Lorentz factor goes to infinity, so that the relativistic energy will also be infinite,

A spontaneous thought of mine was to suppose for the energy a formula of the form

Later on I discovered that this energy had better be

where γ is the damping factor (distinct from γ_L).

The comparison between the two factors made me think that motion in spacetime is wave-like, so that spacetime is fundamentally an oscillatory medium.

I found out that a wave can be approximated with a brachistochrone, and I wondered what the connection between motion in spacetime and motion on the brachistochrone could be.

Since the brachistochrone is the path of least action, I assumed that all (accelerated) motions occur on brachistochrones.

Then I made the connection between the energy of the brachistochrone and that of an oscillator, so that motion in spacetime can also be described as motion on the brachistochrone.

I also devised a thought experiment (the spaceship on the brachistochrone) in order to relate an object moving on the brachistochrone to the photons the object emits, and I came up with a condition of simultaneity,

where v is the speed of the object, τ is the period of the photons, c is the speed of photons (the speed of light), and T₀ is the time of the brachistochrone.

The intimate relationship between photons and objects (or material particles) can also be described in the context of wave- particle duality, using the following equations

where p_m and p_μ are the momenta of an object (a particle) and of a wave (a photon), respectively.

Significant is here that the mass m of the object is different from the mass μ of the wave. The deepest meaning is that photons are disturbances in spacetime caused by the moving object. A consequence is that an object can exceed the speed of light.

Then came to my mind the idea of synchronicity as put forward by Carl Jung. According to his description, there is a correspondence between physical and psychic phenomena based on the action of archetypes. Thus I wondered what the relationship between spacetime and Consciousness could be.

At that moment I recalled that in the energy equation of the oscillator, a constant 𝒞 of integration appears,

I identified the constant 𝒞 with Consciousness.

The correspondence between physical phenomena and observation can also be revealed by numerical coincidences between the values of fundamental quantities and according to the anthropic principle.

I also formulated a set of rules, based on the aforementioned condition of simultaneity, including a principle of synchronicity.

From there after I made some thoughts with respect to the notion of information and the holographic principle, so that I came up with the following equation (which appears inscribed in the previous picture),

where I(t) is the available information, and Γ(t) is what I call factor of Free Will.

Explicitly the previous equation can be written as

where the state or harmonic n also represents the degrees of freedom available to Free Will,

Thus Consciousness can be seen as a material object which transforms the total available energy E₀ into its own kinetic energy K(t),

acquiring knowledge in a process which I call displacement of Consciousness,

This way one may integrate the observer with the phenomena he/she observes. In string theory for example each physical property corresponds to the mode or harmonic of a vibrating string, so that a physical object is the collection of those harmonics n.

If we identify such strings with archetypes then each harmonic or state can be related both to a physical property and to a psychic property (emotion).

Consequently Consciousness will be the sum of all the states or harmonics n.