## Physics, a masterpiece – Classical Mechanics

Classical mechanics is the background of physical theories that explain our daily phenomena; machines running, planes flying, planets orbiting and etc.

Almost everything we know is moving. In fact, it is difficult to find infinitely static or stopped things.

In principle, we can think about allÂ that exists, maybe our first approach to describe the universe is to draw a static infinity and dark space with bodies moving inside it.Â

ToÂ illustrate, you can imagine the universe as a pinball game, there are the rules, there are impossibilities, there is the body moving and interacting with the ambient.

Similarly, is the classical view of mechanics. We suppose the existence ofÂ a static point of reference in the universe (the First Newtons Law). From this static and non-interacting point, the inertial frame, we compare all the bodies movement. Incidentally, it is unnoticedÂ and singular that this static point is arbitrary and inaccessible. BecauseÂ of that, we have the principle of relativity over referenceÂ frames:

If you are stoped in relation to an inertial frame of reference, you are moving in respect to another.

# The mathematical description of mechanics

Mathematics was the main responsible for the growth of physics. Before writing about mathematics, we should talk shortly about space and time. It is important because any object moves in space over the time.

• Space is the place where everything physical is in. On that view, the distance between objects can be described by geometry.
• Time is the flow of events, in each time an object is in a point of the space. Normally, time is quantified throughÂ some clock.

Under those circumstances, if space is a set of points and time is a quantifiable set of numbers, for every time there is a point in space. Mathematically, we call it a function. Then, every single object in the universe has a function that defines its movement.

The task of physics is toÂ find any function, that I will callÂ theÂ trajectoryÂ of a body. In this way, objects in nature appear to interact themselves. For example, every time you throw a ball at the floor, it kicks, rises up, back down, kicks again, and do it repeatedly until it stops. Then, the ball looks to interact with the floor and with something that is responsible for the fall.

# The date with causation

It is intuitive that our universe has a complexity of effects and causes. In order to maintain this principle, there is the Second Newtons Law. According to this law, objects act with forces in one to another, and the action of a force causes a change in the movement of the object that depends on the object mass. Then, we have introduced a property called mass. In mechanics, every object should have a definite mass, it quantifies how the object reacts to an interaction.

The interaction betweenÂ objects can happen throughÂ contact orÂ by distance. Most of the interactionsÂ we fell daily are apparently by contact (really, they are electromagnetic interactions).

Finally, natural phenomenaÂ can be described by the addition of NewtonsÂ Third Law:

If an object acts with a force to another, it received a force with the same intesity and oposity direction.

Nowadays, when using classical mechanics the most interactions can be reduced to gravitational, electromagnetic and strong. I will talk better about those forces in another post.

# A purpose in the universe

Before Newtonian mechanics, there was a principle commonly used in practical optical theories; a principle of minimization. It was used in ancient Greece and Rome. Rigorously, it was developed by Fermat in the XVII century and by Maupertuis and Euler in the early 1700’s.

Especially, it was used to derive Newtonian mechanics and nowadays is responsible for most modern physical theories. In this sense, this principle is a fundamental law of the universe. The universe has the purpose of extremize things.

That is the principle of least action:

The real path of a body is the one which minimize the action.

In classical mechanics, the action can be seen as a propriety of the universe. In all possible universes, the universe where the action is the smallest is the real one.

To be brief, as Newtonian mechanics supposes metaphysical entities like inertial frames, the least action principle supposes a non-interactingÂ finite closed system; the universe.

# A view of possibilities

As a final point, the final view of classical mechanics leads to quantum mechanics. It was the abstract Hamilton mechanics.

By contrast with Newtonian mechanics, the focus of Hamiltonian mechanics was not the path, but the state of a body or system. The state of a system can be defined by two independent coordinates of a phase space for each particle, one is related to its position, another to its energy.

In this way, a system can be described by a set of possibilities involving a six-dimensional space, where three dimensions are spatial and the others are called momentum. Using those possibilities to describe a statistical system leads to controversies in the XIX century. Consequently, those problems lead to the development of quantum mechanics in the XX century.

Things here are much more abstract, and sometimes the beauty of mathematics is needed. But don’t lose hard, optics will be the subject of our next post.

## What is beauty?

The concept of beauty is present in all human being. Hume, an XVI century philosopher, remark:

â€œBeauty is no quality in things themselves: It exists merely in the mind which contemplates them; and each mind perceives a different beauty. One person may even perceive deformity, where another is sensible of beauty; and every individual ought to acquiesce in his own sentiment, without pretending to regulate those of others. (Hume 1757, 136)

Humeâ€™s quote highlights the possibility of a subjective perspective in beauty, that is, beauty is essentially dependent on the person that taste it. This view is in opposition to the one accepted by philosophers up to the eighty century; in this sense, beauty is an objective quality, it is independent of people. Overlooking this discussion, there is an agreement between both sides; the tasting of beauty is followed by satisfaction and pleasure.

The branch of philosophy that studies the beauty is called aesthetics. Aesthetics and arts are correlated fields, in some way, they mix together. In fact, arts can be seen as a way that an artist can share its own emotional soup and singular feelings. Under those circumstances, art is totally related to the beauty of the object. That is the basis for this blog, in which it will be structured.

In brief, the purpose of this project is to express the beauty of physics using texts of a blog.

## Modern science

Before an introductory talk about physics, I would like to present physics as a modern science.

The history of humanity is characterized by the development of the knowledge of natural phenomena. The capacity to learning, conduct experiments and dominate the nature could be the one that gives to humans, advantage from usual animals.Â The mastery of cultivation techniques,Â turn possible to humans dominate wherever they were. We were always at the top of any ecosystem. Consequently, the development of this form of manipulating aspects of nature led human societies to what we now call modern science.

Modern science is the way by which knowledge, theories, and new results are generated. Modern science is totally dependent upon a particular community of people, those last are called scientists. Scientists produce theories and experiments that are shared through scientific journals. The own scientific community select among all theories, which ones are the good and the bad theories, discarding a lot of hypothesis over the years. That dynamics, of generating new hypothesis and discards through the community is what we call the modern science. It is interesting to observe; the people are creating modern science, however, people made ethical andÂ aesthetic judgments. Then it is possible that a big part of the scientific hypothesis has an etic and aesthetic influence.

Dirac and Einstein, for example, considered the beauty and simplicity of a physical theory.

## Physics, a beautiful masterpiece

In the last two centuries, to explain the nature around us, great physical theories emerge. We can mention:

• The classical mechanics is used to explain daily moving objects and the solar system orbits. It was the responsible for some planet discoveries.
• The thermodynamics is used to explain pressure and temperature dynamics. Together with classical mechanics, we can predict some atmospheric dynamics.
• Optics, it was used to explain light phenomena in our scale.
• Electromagnetism, it is used to explain electrical and magnetical phenomena.

Later we will see, those classifications mix in some way. Their mixing was provided by theories that emerged at the beginning of the XX century. Some complex theories were the responsible for the emergence of new areas of physics, they are:

• Quantum mechanics.
• General and restrict relativity.
• Particle physics and Quantum Field Theory.

In this context, we can observe physical theories as a painting of an artist, in our case the scientist. Each theory or concept can cause an emotional cocktail, that will be expressed along the next posts. Therefore, in this first post, I would like to introduce slightly the second group of theories.

In fact, the theories created in the XXI century destroy totally the common sense of how nature is.

## Some 21st-century physics

### Relativity

Initially, there is the general and restrict relativity. They are the responsible for the destruction our natural concepts of what time and space are. Through the special relativity, we can conclude absurd things about simultaneity, about the duration of time and the length of things. Likely, through general theory, we conclude that the universe had a beginning, that it expands and that85% of the universe matter is made by dark matter, a kind of matter that is as anything that we know.

### Quantum mechanics

Then, there is the quantum mechanics, it confuses totally our concept of how is the reality. Quantum mechanics is a totally functional theory, I mean, nobody doubts about its predictions. Although, since its creation, a lot of discussions about how to interpret the theory emerged. Nowadays, the majority of physicists accepts the standard interpretation, called orthodox interpretation. Because of such debates, a new study area emerged, called the philosophy of quantum mechanics.

## TheÂ dawn of a new blog

In this blog, I will talk in more details about those areas, point its surprises and beautiful things that arise from them.

We will see how a black hole can appear, how it affects the time flow. We will see how particles can be created and destroyed, how an electron can’t sometimes have a definite position and a lot of that stuff.

I hope you enjoy it!

[1] For more about aesthetics, visitÂ https://plato.stanford.edu/entries/beauty/.

[2] For an understanding of modern science, I recommend: Kuhn, Thomas S.Â The structure of scientific revolutions. University of Chicago press, 2012.