References for laymen: an experiment to verify the law of falling bodies

The first observational measurements on the law of falling bodies were made by Galileo Galilei (1564-1642).
The famous law, considering the distance d traveled during the fall, is:
[1]    d = g t² / 2
where  g  is a constant representing the local gravitational acceleration (on Earth a mean value is  g = 9.8 m/s² ), and  t  is the time elapsed. In more easily observable terms, the fall time can be measured reversing the relationship  [1] :
[2]    t = √(2d/g)  .
Galileo predicted (inspired by what Domingo de Soto had already conceived in 1551) that all bodies follow this law regardless of their mass, studying rolling balls (rather than dropping them from the famous Tower of Pisa). However, everyday experience tells us that light bodies fall more slowly: this is simply due to the friction of the fluid in which they are immersed (e.g., air).

A rather expensive experiment was reported to have been carried out on the Moon, when a hammer and a feather were dropped and touched the ground at the same time (astronaut David Scott on August 2, 1971).
I propose the following more economical experiment: drop a coin that is not too small, for example a 2 euro coin, flat on its face, placing a small piece of paper, e.g. 5 mm in diameter, on top of it. A good height would be half a meter. You can observe that the piece of paper reaches the ground at the same time as the coin, which prevents the air from slowing it down.
You could also place the piece of paper in a transparent container that you then drop, but this would make it less clear to observe.

As a side note, it can be observed that a body in free fall accelerates until this acceleration equals the acceleration of gravity, due to the mass of the body (tipically the Earth) on which it is falling (possibly slowed down by air resistance, known as drag force). Once this is reached, the speed of fall, known as terminal velocity, remains constant. On contrary, a body falling in a vacuum never reaches terminal velocity because there is no drag force; it accelerates indefinitely as long as it is falling.

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Note for laymen – what is the dark matter?

Let’s consider a disc galaxy with billions of stars forming the disc, which rotates (the Andromeda galaxy in the photo, to give a well-known example). We can consider for each of these stars that the centripetal acceleration
[1]    a’ = v²/R
is equal to the gravitational acceleration
[2]    a” = G M/R²
therefore from  [1] = [2]  we obtain:
[3]    v = √(G M/R)
where  v  is the local velocity of the source considered,  R  is its distance from the galactic center,  G  is the gravitational constant,  M  is the total mass contained within the radius  R  (which determines the gravitational attraction).
Measuring the rotational velocities of galaxies is relatively easy, if they are not seen face on, and it is generally observed that throughout the disk the rotational velocities of the sources (stars but also gas clouds) are almost constant. Therefore, from relation  [3]  it follows that the mass  M  must increase in proportion to the radius  R , since  G  is a constant. Indeed, the mass contained within the radius  R  increases as  R  increases, but what is observed is not sufficient to justify the constant value of  v . These considerations leads to the hypothesis that there is a substance that is invisible and non-baryonic in nature (i.e., not made up of protons and neutrons, which are not detected) that manifests itself only through gravitational behavior, which is called dark matter.


Processed photograph of M31, Andromeda. It was not possible to obtain the author of this beautiful photograph.


Andromeda

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Here I am

After a hiatus from 2021, I’m resuming my online presence with this small collection of suggestions, seeking intellectual dialogue. Let me know what you think in the comments or via email.
Thanks

p.s. I posted with the dates of the original documents

 

 

That's me

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My thesis work

My thesis work (written in italian) is published in the University of Padova archive:
pdf_ita  Brussi 2025_Epistemology of time and cosmological interpretations

As an appendix to the same thesis I put a first development draft of the non-standard framework, which, after significant revisions, later became my work
link  The URD Framework.


Abstract
The aims of this study on time are first to explore its ontological meaning in the historical developments that have accompanied its interpretative evolution, and then to examine some theoretical critical issues raised by recent literature. With some original theses, some alternative explanations for the expansion of the universe are then analyzed, which the current interpretation claims to be observed experimentally, by means of a model based on the ‘specific time’ of photons as an alternative to the ‘universal time’. Furthermore, it is hypothesized a model that considers the presence of an energy density in the cosmic fluid (called aether) that interacts with the incident radiation, thus determining a redshift effect in the wavelength, or an even longer time for the same radiation to diffuse. The consistency of ‘specific time’ has been verified with Minkowski spacetime, with Einstein’s principles of special relativity, and with Friedman’s equations of cosmic dynamics. Having demonstrated the fallacy of this ‘specific time’ hypothesis, the positive conclusion is that there is no need to postulate a universal time. Once one is defined, its uniqueness or universality can be demonstrated (within the limits of the adopted models). To complement the study, possible causes of the redshift, alternative to the standard cosmological model, were analyzed. It has been taken in consideration the hypothesis that the same universe behaves like a black body, emitting a radiation (the cosmic microwave radiation) that can interact with the observed photons coming from remote sources, attenuating their energy and determining their redshift. A cross section for photons, and a model for photon-photon interactions that respects the law of conservation of energy have therefore been hypothesized. As a basis for the conjectures, direct observational evidence was considered, not interpreted by means of theories, obtaining (from the comparison with other standard candles) better distance estimates than the official ones based on Hubble’s law. This addendum is included as an Annex, believing that the same conjectures and some original models can represent a reference for future in-depth studies.

The work is written in Italian (1.8 MB):

pdf_ita  Brussi 2025_Epistemologia del tempo e interpretazioni cosmologiche

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What’s wrong with scientific research according to Sabine Hossenfelder

An interesting speech by Sabine Hossenfelder: “A few words on some well-known and perhaps lesser-known problems in scientific research and what others have said about them.”

In essence: “Scientific research has big problems, and it’s getting worse”.

 

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A historical photo

Solvay Conference on Quantum Mechanics, 1927

Solvay Conference on Quantum Mechanics, 1927 (photo by Benjamin Couprie, Institut International de Physique Solvay, Bruxelles, Belgium; I have slightly restored this photo, usually available in a lower detail level).

From behind, left to right: Auguste Piccard, Émile Henriot, Paul Ehrenfest, Édouard Herzen, Théophile de Donder, Erwin Schrödinger, Jules-Émile Verschaffelt, Wolfgang Pauli, Werner Heisenberg, Ralph Howard Fowler, Léon Brillouin, Peter Debye, Martin Knudsen, William Lawrence Bragg, Hendrik Anthony Kramers, Paul Dirac, Arthur Compton, Louis de Broglie, Max Born, Niels Bohr, Irving Langmuir, Max Planck, Marie Skłodowska Curie, Hendrik Lorentz, Albert Einstein, Paul Langevin, Charles-Eugène Guye, Charles Thomson Rees Wilson, Owen Willans Richardson

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Einstein 1916: Emission and Absorption of Radiation in the Quantum Theory

This work is a further study of Albert Einstein’s article, “Emission and Absorption of Radiation in the Quantum Theory” (Strahlungs Emission und Absorption nach der Quantentheorie). A brilliant work published in 1916.
This work of mine is written in Italian.

pdf_ita  Brussi 2023_Einstein 1916 Emissione e assorbimento di radiazione

ABSTRACT
Albert Einstein’s study, “Emission and Absorption of Radiation According to Quantum Theory,” [Einstein, 1916], proposed an original interpretation for the probabilities of exchanges between atomic energy levels, predicting spontaneous emissions, as well as absorption and radiation-stimulated emissions, from molecules in thermodynamic equilibrium. This study made the coefficient associated with spontaneous emissions Aji, the absorption coefficient Bij, and the coefficient associated with stimulated emissions Bji famous; it also laid the theoretical foundation for the development of lasers.
In-depth analysis: a paraphrase of the conjectures in Einstein’s original publication, an in-depth analysis of the parameter associated with the coefficients called the oscillator strength (derived with different procedures for both spontaneous emission and absorption of radiation), and some examples of the use of Einstein’s coefficient Aji in astronomical spectroscopy.

 

Brussi 2023_Einstein 1916 Emissione e assorbimento di radiazione

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An in-depth look at the postulate of the unidirectional speed of light

An in-depth analysis of the relativistic and mathematical consequences of a modified special theory of relativity, without taking Einstein’s postulate about the constancy of the speed of light in a round trip for granted.
It’s a work developed to complement another on the epistemology of time and it’s written in italian.

pdf_ita  Brussi 2023_Sul postulato della velocità unidirezionale della luce

 

Brussi 2022_Sul postulato della velocità unidirezionale della luce

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