[Kartazion (OP)]

...
...
3. the pressure

For the pressure it's a bit more complicated than that. We need to relate the energy-density value of y which corresponds to the second vector. Indeed one can determine with exactitude the momentum/pressure of the particle.

[Kartazion (OP)]

1. the exact postion of the particle
2. the velocity
3. the pressure

1.  That in itself has nothing to do with a vector.
...

The vector length between -x or x in relation to x=0 indicates the exact position of the particle. I will draw you a GIF.

[Kartazion (OP)]

Waiting to do something more explicit

[Origin]

The vector length between -x or x in relation to x=0 indicates the exact position of the particle.

Please stop using the term 'vector', you don't know what it means and using the term incorrectly is very confusing.  Length is a scalar not a vector!

Don't say this:
The vector length between -x or x in relation to x=0

Say this:
The distance between -x or x in relation to x=0

[Origin]

The vector length between -x or x in relation to x=0 indicates the exact position of the particle. I will draw you a GIF.

Not that it matters at this point but your gif has the particle at X = 0 for the whole sequence.
The particle is moving on the Y-axis not the X-axis, according to convention.

[Origin]

For the pressure it's a bit more complicated than that. We need to relate the energy-density value of y which corresponds to the second vector.

No, really??  The second vector? 
Without using the word 'vector' and with as few words as possible, describe the "second vector".

[Kartazion (OP)]

The vector length between -x or x in relation to x=0 indicates the exact position of the particle. I will draw you a GIF.

Not that it matters at this point but your gif has the particle at X = 0 for the whole sequence.
The particle is moving on the Y-axis not the X-axis, according to convention.

I chose x-axis because graphically the displacement particle is related to its potential well. But as you know, it doesn't matter which way the particle oscillates:

[Origin]

The second vector points along y-axis and its magnitude represents the momentum by a density-energy value.

Sorry I didn't see this post.
You really, really need to stop using the term vector!  You just said here that the [second] vector's magnitude is momentum, so you are saying that the magnitude of a vector is a vector.  That is nonsense.

[Origin]

I see this thread is descending into your oscillation nonsense so I will depart the conversation, have a nice weekend.

[Kartazion (OP)]

The second vector points along y-axis and its magnitude represents the momentum by a density-energy value.

You really, really need to stop using the term vector! ...

So I'm going to use the matrix one.

[Kartazion (OP)]

I see this thread is descending into your oscillation nonsense so I will depart the conversation, have a nice weekend.

Have a nice weekend too.

Cordially

[Kartazion (OP)]

Without using the word 'vector' and with as few words as possible, describe the "second vector".

For the pressure it's a bit more complicated than that. We need to relate the energy-density value of y which corresponds to the second vector. Indeed one can determine with exactitude the momentum/pressure of the particle.

Y determines the amount of energy density in relation to the velocity of the particle. Y remains that of an energy of the potential well.

Pressure in a fluid may be considered to be a measure of energy per unit volume or energy density. For a force exerted on a fluid, this can be seen from the definition of pressure: source: http://hyperphysics.phy-astr.gsu.edu/hbase/press.html

[Kartazion (OP)]

Y determines the amount of energy density in relation to the velocity of the particle.

The momentum is the energy-density in relation to the velocity of the particle.

But I wish and for the understanding of all to stick to the uncertainty principle rather than to have spoken of perssure [1]. The uncertainty principle which does not have to be, because through the exactness of the position and the momentum which represents the vectors according to x(t) for x-axis and the density-energy for y-axis becomes possible.

Reference [1] Matter confined to a small volume generates quantum pressure and this pressure acts as a source of gravity according to general relativity, in which mass, energy, stress and pressure are all sources of gravity. https://www.worldscientific.com/doi/10.1142/S0218271808012486

In the model that I am developing, it is a question of an exclusively gravitational oscillator whose source of potential energy is that of a gravitational singularity.

To be continued for the pressure part...

[Kartazion (OP)]

Here is an overview of the scalar quantities through an an.harmonic oscillator:

[Kartazion (OP)]

For the reader:

...,  so you are saying that the magnitude of a vector is a vector.  That is nonsense.

Yes. Why do you say it's nonsense? In the convential interprétation "The magnitude of a vector is the length of the vector, and is derived from the Pythagorean theorem."

[Kartazion (OP)]

This graph demonstrates and within the framework of an an.harmonic oscillator the amount of energy density is in relation to the position of the particle between Kinetic and Potential energy. This experience occurs in a vacuum. This oscillator is a gravitational oscillator where its point of origin is a gravitational source.



Have you ever studied this? And in this graphical representation/configuration?

[Origin]

You just said here that the [second] vector's magnitude is momentum, so you are saying that the magnitude of a vector is a vector.  That is nonsense.

A vector is a quantity that has a magnitude and a direction.  Velocity is a vector.  That means velocity will have a magnitude, which is the speed and it will have direction.  For example if I was in a car I might say my velocity (a vector quantity) is 100 km/hr heading east.  Both a magnitude (100 km/hr) and a direction (east).

Why do you say it's nonsense?

The magnitude of a vector CANNOT be a vector.  A vector has a magnitude AND direction.  Magnitude does not have a direction so it cannot be a vector.

If this does not make sense to you then remove the word 'vector' from your vocabulary to keep from misleading people reading your posts.

[Kartazion (OP)]

If this does not make sense to you then remove the word 'vector' from your vocabulary to keep from misleading people reading your posts.

Ok. So I'm going to call it arrows. Here, then, on the following graph, are the arrows which give the information relating to a "table/database" (I guess it is not a matrix) the position of the particle in ratio of its quantity of energy.



Thanks to its arrows in relation to its database, the position of the particle is determined with precision at time t. For this and to make the distinction between kinetic energy and potential energy, it is necessary to know the direction of the arrow in relation to 0 as well as its length in terms of evolution.

[Origin]

This is the way that the KE and PE relationship in simple harmonic motion is usually presented:

Graph is from:  phys.libretexts.org

I think this typical presentation is more intuitive than your graph, but your graph looks correct, except that the axis should be just PE or KE not density.

[Kartazion (OP)]

Yes, the one you are presenting to me is that of the energy of the potential well. While the one I present is that of density. I think that the problem with the one you present to me, and I know it's conventional, is that the total energy in relation to y-axis does not take into account the negative energy which would be that of potential energy. In addition, with the conventional presentation, the rotation of my arrow in radians is only done from pi to 2pi, or an angle of 180° max, while my presentation allows a complete turn.


Small image attached to click: