If we think we can observe that the same quantum particle can be simultaneously in different places, so maybe that made these places are only one: a track for a holographic theory of Universe?
A quantum particle isn’t simultaneously in different places-that statement is, simply, wrong. Its position has a probability distribution, that’s more complicated than that of its classical limit, that’s all.
So, no, this, mistaken impression doesn’t have anything to do with holography. What does, is that the quantum dynamics of a particle, evolving in flat spacetime, is related to that of a quantum particle that explores a curved spacetime, in a way that takes into account how spacetime is affected by the quantum properties of the particle. While this can't, yet, be done in full generality, what's interesting is that a part of it can be done at all. How to take into account the quantum properties of matter is what can’t be described by general relativity, since the RHS of Einstein's equation, that contains the contribution of matter, only takes its classical properties into account.
What is, also, fascinating is that it is possible to map the properties of the solutions of Einstein’s equations, i.e. general relativity, that describe classical gravitational effects of spacetime, to properties of quantum systems, that can be defined on the boundary of the spacetime. This has allowed the calculation of transport properties of solid state systems.
Indeed and they are subject to verification, for instance in comparing the transport coefficients computed this way to experiment. For example: http://www.birs.ca/workshops/2016/16w5067/files/Landsteiner.pdf
In molecules, the covalent electrons are indeed simultaneously in several different places (in 2 atoms at the same time for example) otherwise there would be no bonds between the atoms, they could not remain "hooked" between them.
Once more, the covalent electrons aren't in several places at once-for some reason this mistake is being perpetuated. The fact that the probability for finding the electron somewhere isn't the delta function, that corresponds to the classical limit, does not mean that it is or can be in more than one places at once. (It's the property that the probability distribution isn't a delta-function, that implies that the chemical bonds have the properties that they do; but this just means that there are more quantum states than exist in the classical limit. And what holography implies is that these quantum properties can be mapped to properties of a classical spacetime geometry. But the correspondence implies much more than that.)
There is a field of research now called ``holographic entanglement chemistry', cf. https://arxiv.org/pdf/1605.00595.pdf
Another related topic is Article Measuring Holographic Entanglement Entropy on a Quantum Simulator
The holographic model can be theoretically (math) representative of the position and contents of an enclosed volume IF the relative density of matter outside the volume is small And if the matter inside is obeying the spherical principle at all points of the enclosing surface. The first can be relaxed if the matter on the outside is also counted and obeying the spherical principle on the surface. One difficulty is when a significant amount of matter is flowing thru the surface.
Do you think everyone understands the Holographic theory?
The spherical principle is seen in Newtonian mechanics as the force exerted on a sphere as proportional to its mass and inversely with radius squared. This derives from the physics that the total force (or energy thru a spherical surface remains the same but the energy per unit surface area declines with the square of the radius. This is the example of the holographic theory for 1 mass particle. It also yields the Newtonian idea that the mass of a body may be represented for calculation purposes outside the body as concentrated at the center of mass of the body.
Now do the same calculation for all bodies in a region and determine the function representing the gross value of the sum of all bodies throughout the body over the entire closed surface. This is the Newtonian derivation of the center of mass. But note that is a surface is inside a body, the force calculation changes.
Be a bit mode complex such as in considering black holes and other considerations than just the Newtonian should be accounted.
Thank you, Sydney Ernest Grimm , for this rich discussion which demonstrates the complexity of an understanding of the universe. We (humanity) are far from having completed the vast puzzle ... of knowledge!
Also, thank you for highlighting the essence of my thought profile.
Nastasenko, V. (2020) Analysis of the Processes of Gravity in the Framework of Curvature of Space and the Substantiation of the New Model. Journal of Applied Mathematics and Physics, 8, 2732-2743. https://doi.org/10.4236/jamp.2020.812202