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Showing posts with the label physics

### The demons haunting thermodynamics

In a recent Physics Today article [1], Katie Robertson wonders if the philosophical demons that haunt thermodynamics have been exorcised. She begins by stating that thermodynamics is a strange theory because although it is fundamental to our understanding of the world, it differs dramatically from other physical theories. I do not agree. First, thermodynamics is not a theory. Thermodynamics is a scientific discipline and, as in other sciences, we have theoretical, computational, and experimental flavors. Second, I do not know what she mean when she claims that thermodynamic theory differs dramatically from other physical theories. I do not find any fundamental difference with electrodynamics, with mechanics or with general relativity. In this newsletter, I will avoid "the bizarre philosophical implications" and focus on the scientific aspects. The "many oddities" that Robertson assigns to thermodynamics are actually oddities of statistical mechanics and, more speci

### Entropy

Entropy is one of the most misunderstood concepts in physics, usually associated with disorder or ignorance, and often confused with different concepts that have the same name, such as the Jaynes entropy. THERMODYNAMIC ENTROPY The concept of entropy was introduced in physics by Clausius as part of the development of thermodynamics. Its physical meaning is often omitted from textbooks, but we can say it is a measure of the amount of thermal energy per unit of temperature. If we subtract the mechanical, chemical, electrical, magnetic, and other components that make up the internal energy of a system, and divide it by the temperature of the system, we get its entropy $$S$$ $S = \frac{ U + pV - \sum_i \mu_i N_i }{ T } + S_0$ This is the Euler form and I have added a constant $$S_0$$, which is usually set to zero, because most thermodynamic studies only deal with processes and $$\Delta S$$. As you can see, entropy is a physical quantity that depends on physical quantities of

### What Hawking meant when he said "there are no black holes"

During a technical talk, Stephen Hawking made the next bold statement: "there are no black holes". It is quite easy to grasp that Hawking meant that there are no black holes in the Universe, that is, that the popular concept of black hole is an illusion, but some people [1] seems unable to accept that the champion of the black holes finally changed his mind. In August 2013, Hawking gave a talk at The Kavli Institute for Theoretical Physics , the talk was given the uninspiring title "Information Preservation and Weather Forecasting for Black Holes" [2]. This is the relevant quote that has raised dust: The absence of event horizons mean that there are no black holes - in the sense of regimes from which light can’t escape to infinity. There are however apparent horizons which persist for a period of time. This suggests that black holes should be redefined as metastable bound states of the gravitational field. That is to say, Hawking affirms that black holes do not e

### The reason for antiparticles

Why do we need antiparticles in a relativistic quantum theory? I will review the usual arguments based on spacetime symmetries and CPT invariance and show that antiparticles are not particles that travel backwards in time as Feynman claimed. In a recent twitter thread [1], Martin Bauer states that antiparticles are needed in a relativistic quantum theory because if we swap space and time in a quantum scattering process, the particles would travel backward in time and this is a puzzle, forcing us to reinterpret those exotic particles that travel backward in time as antiparticles that travel forward in time. His argument is not valid. First, because applied to classical scattering events it would lead to the conclusion that antiparticles are also necessary in the classical theory, which is not the case. Secondly, because relativity does not establish that space and time are equivalent and can be freely interchanged. It is a common misunderstanding of relativity that space

### The quantum vacuum

We saw in a previous post that the Casimir effect cannot be used to prove the existence of the quantum vacuum. In this post, I will explain why the quantum vacuum is not a true state of emptiness and why it is an artifact of quantum field theory. Reference [1] states: "In the old days of classical mechanics the idea of a vacuum was simple. The vacuum was what remained if you emptied a container of all its particles and lowered the temperature down to absolute zero. The arrival of quantum mechanics, however, completely changed our notion of a vacuum. All fields – in particular electromagnetic fields – have fluctuations." A similar misunderstanding is found in [2] and many other places. Quantum mechanics did not change our notion of a vacuum. The concept of emptyness in quantum mechanics is the same concept that is used in classical mechanics. The modern concept of quantum vacuum was introduced by quantum field theory, but quantum field theory is not the application of quant

### The Heisenberg uncertainty principle

The Heisenberg uncertainty principle is one of the most famous elements of quantum theory, not only mentioned in academic papers and described in quantum mechanics textbooks, but also present in popular treatises. Well, the fact is that " Heisenberg uncertainty principle " is a misnomer because it is neither a principle nor about uncertainties. Brian Randolph Greene, a leading theoretical physicist, mathematician, and string theorist, often mentions the Heisenberg uncertainty principle. He does so in his popular books and he did again in a recent tweet . The " Heisenberg uncertainty principle " is usually abbreviated as HUP and the first thing to clarify about it is that it is not a principle, but a theorem derived from the postulates of quantum mechanics. A derivation of this theorem can be found in book [1]. The result for two arbitrary quantum operators $$\hat{A}$$ and $$\hat{B}$$ associated to the observables $$A$$ and $$B$$ is \[ \sigma(A) \cdot \si

### Steven Weinberg's mistakes

Experience shows that some people likes to rewrite history and make heroes, and when Steven Weinberg died in 2021, some obituaries could not resist the temptation. In 2005, Weinberg wrote an article titled "Einstein's Mistakes". I am not Weinberg and he was not Einstein, but I will write about Weinberg's mistakes in this post. Weinberg justified his review [1] of Einstein's mistakes in the following terms: "Perhaps most important, by showing that we are aware of mistakes made by even the greatest scientists, we set a good example to those who follow other supposed paths to truth. We recognize that our most important scientific forerunners were not prophets whose writings must be studied as infallible guides—they were simply great men and women who prepared the ground for the better understandings we have now achieved". I will not review all of Weinberg's mistakes, but only those which appear in the obituary written by Nima Arkani-Hamed: "How St

### General relativity is not a field theory

There is a myth, perpetuated in physics textbooks and popular treatises, that states that general relativity is the theory of a gravitational field. The myth was started by Einstein, who often used the term gravitational field during the development of the theory. The pioneers make a lot of mistakes because the territory is unknown, but there is no reason to continue perpetuating myths a century after Albert Einstein, Marcel Grossmann, and David Hilbert developed the theory of general relativity. Let me quote a recent tweet from cosmologist Will Kinney: in general relativity, the gravitational field doesn’t really exist . Understanding that general relativity is not a field theory is not only desirable for reasons of rigor and consistency, but has profound implications for research. For example, the sad status of quantum gravity research is partially because some physicists such as Feynman and Weinberg have tried to apply quantum field theoretic methods to a theory in which there is

### The modern second law of thermodynamics

The second law is one of the most popular laws of nature, because it is often discussed in popular science treatises and educative videos, but what is the more correct and general formulation of this law? According to P. W. Bridgman (1946 Nobel Prize in Physics) " There have been nearly as many formulations of the second law as there have been discussions of it ". We can find many historical verbal statements of the law, from when the science of thermodynamics was developing in the 19th century. Some examples: " A transformation whose only final result is to transfer heat from a body at a given temperature to a body at a higher temperature is impossible. " " It is impossible, by means of inanimate material agency, to derive mechanical effect from any portion of matter by cooling it below the temperature of the coldest of the surrounding objects. " " It is impossible to construct an engine which will work in a complete cycle, and produce no effect

### Comments on symmetric monoidal categories by John Baez

I recently watched a talk by John Baez titled " Symmetric Monoidal Categories " [1]. Baez presents new mathematical material that he considers provides a common foundation for the description of different scientific and engineering topics, material that he considers to be a kind of " Rosetta stone ". Baez is correct that scientists and engineers like to describe processes or composite systems using diagrams: flow charts, Petri nets, electrical circuit diagrams, signal-flow graphs, chemical reaction networks, Feynman diagrams, etc. He claims that many of these diagrams fit into a common framework, the mathematics of symmetric monoidal categories, and that when we accept this achievement, we begin to see connections between seemingly different topics. Baez also claims that this new viewpoint introduces a paradigm shift in science. Let us go over all those interesting claims. My comments will focus on the scientific side of his talk. To get started, Baez says that s