An Intuitive Free Fall🍏

Free fall was one of the pillars of mechanics and provided the basis for the development of Classical Physics, with Galileo as its main architect. Following him was Isaac Newton, who left a work describing the essence of this phenomenon: the law of universal gravitation.

The analysis of free fall is usually carried out in the local form, that is, the analyzed system is generally located in reference to a horizontal plane, but this model is solidary to the principle that all bodies make a vertical free fall towards the center of the planet Earth.

Given the limitations of common sense, we will present here the interpretation of the question of free fall as a consequence of the mathematical articulation of the lived reality.

🍏The Formula of Perception

Usually when it’s raining, it’s reasonable for people not to question themselves about the direction in which the water is moving, as it is something that is part of common sense. The same happens when throwing a soccer ball in the air, the ball will descend towards the ground.

This is partly reminiscent of what is observed when using a funnel, no matter the point in its internal region where the liquid is poured, it will naturally lead it in the direction it should be.

But there are cases of falling that happen without being noticed, an example is that of the Moon in relation to planet Earth, it is always falling towards the planet.

This characteristic can be the object of mathematical description if we conceive a time scale, where the term “always” will be represented with infinity, that is,

And what would this enigmatic scale make us think of something different from what we already know?

Our mind is always instinctively trying to classify things. So you can do it by naming two categories:

• category 0: those cases that are in the “funnel” state;
• category 1: what is not within reach of the “funnel” effect, that is, it is “always” falling.

Of course we are talking about a mental process, but how about adopting a simple formalism to articulate the unfolding of this conjecture?

Let us then associate category 1 with the figure of a single point and category 0 with a set of congruent points. Point is a nomenclature of Euclidean geometry, and here it is borrowed to start a pseudo geometry.

What would physical reality be like as a result of the geometric construction of pseudo points. And what could be the connection between such points? What meaning would there be?

Analytical thinking suggests that we now define two sets, namely,

Let’s call the Cartesian product

as being a representation associated with the set of realities.

Let’s take an example: two observers A and B. A traveled in a spaceship to the planet Mars and B remained on the planet Earth. We then have this as a possible reality, say, R₁. When A arrived he found B on Mars, second reality, R₂. R₂ at first cannot be observed, due to the time factor. It is then suggested that time is what allows the perception of realities.

Comment: But what makes you think that Mars would be falling on Earth, such as the Earth-Moon system situation? How would this be categorized?

In this case Mars and Earth would be falling on the Sun star, which is pure reality and scenario that falls on set 1.

🍏The Prevalence

Referring to the previous example where the interaction between Mars and Earth is raised as well as Moon and Earth, let’s say that they are not equivalent situations, this due to what in physics is called configuration of potentials. Even so, here, we can say that there is a sense of prevalence.

The elements of set ​​1 are associated with points (pseudo points) and thus we can interpret them as the description of positions in a pseudo geometric space.

It is necessary to adjust the logic in such a way that given a point in 1 this does not belong to my local reality (I do not touch the surface of the Moon, for example), but I cannot ignore the effects that appear (tidal system, for example).

Let us observe that in Nature there are constant processes of accumulation, for example seas and oceans, mountains, riches, populations of beings, etc. So it is intrinsic that the substrate of the pseudo-geometric Universe follows this “natural methodology” and each point becomes an accumulator with prevalence property, such that correspondingly, a planet will be in a certain position given its prevalence over the others. Such prevalence presents itself to us as the constituent matter of bodies and their corresponding substances.