The Biggest Ideas in the Universe

This is a series of informal videos by the distinguished physicist Sean Carroll with the purpouse "to make our brains active" in these pandemic times. You can find the videos in his blog's page.
The series is growing with a new video every week and a Q&A video for each one main video.
I liked a lot all the videos up to now and in particular the fourth video dedicated to the concept of "Space" (and the following Q&A one). Here you can find a nice explanation of the Lagrangian and the Hamiltonian approach and in particular of the importance of putting position and momentum on equal footin in the Hamiltonian approach. Infact this make possible to ask very deep questions about the world, questions you would'nt have asked following the Newtonian approach such as  "Why do we leave in space? Why not in momentum space?".
I think those videos are an important resource for understanding physics! Thanke you prof Carroll.

An image of the BH at the center of the M87 galaxy, showing a ring of radio waves from a disk of rapidly rotating gas. The image was captured by the Event Horizon Telescope team and presented today to the world.

You can find in this blog of Matt Strassler (here) and in this page of the NASA's Astronomic Picture of the Day interesting explanations.

Relational Quantum Mechanics

Schrödinger's cat

A bit less nervous?

Richard Feynman wrote: “We have always had a great deal of difficulty understanding the world view that quantum mechanics represents. At least I do, because I’m an old enough man that I haven’t got to the point that this stuff is obvious to me. Okay, I still get nervous with it ... You know how it always is, every new idea, it takes a generation or two until it becomes obvious that there’s no real problem. I cannot define the real problem, therefore I suspect there’s no real problem, but I’m not sure there’s no real problem” (Simulating Physics with Computers, 1981).

I'm studying the article "Relational Quantum Mechanics" by Carlo Rovelli (search the internet for: arXiv: quant-ph/9609002). Carlo Rovelli is an Italian theoretical physicist and writer that works in the field of Quantum Gravity, where he is among the founders of the Loop Quantum Gravity theory.

In this article Rovelli provides an interpretation of Quantum Mechanics that I didn't know and it just seems to make sense! This is the first time I see a chance to understand what nature is telling us with the laws of Quantum Mechanics. Rovelli's critics of the physical meaning of the mysterious wave function is in my opinion illuminating. His work is based on the analysis of the famous problem of Wigner's friend (the third person problem) and on the concept of Everett's relative status. The interpretation of the theory makes use of the concept of Shannon information.

The consequences of the relational interpretation is that properties of quantum systems have no absolute meaning but they must be always characterized with respect to other physical systems. It turns out that Relational QM is compatible with realism in the sense that there is a world outside our mind, which exists independently from us, but is incompatible with realism in a stronger sense that it is possible (at last in principle) to list all the features of the world as we can do in classical mechanics.

Work in progress. I’m studying again (starting from The Theoretical Minimum) Quantum Mechanics(*), but I'm a bit less nervous now.

(*) https://theoreticalminimum.com/courses/quantum-mechanics/2012/winter

Stephen Hawking has died.

I like to honor him remembering a passage from his beautiful book “A Brief History of Time”.

“Even if there is only one possible unified theory, it is just a set of rules and equations. What is it that breathes fire into the equations and makes a universe for them to describe? The usual approach of science of constructing a mathematical model cannot answer the questions of why there should be a universe for the model to describe. Why does the universe go to all the bother of existing? Is the unified theory so compelling that it brings about its own existence? Or does it need a Creator, and, if so, does He have any other effect on the universe? And who created Him?”.

When I think of him I hear in my mind his question: ”What is it that breathes fire into the equations and makes a universe for them to describe?”. I believe he now knows.







Here you can get the Discover magazine free download "The Life and Times of Stephen Hawking. Celebrating the life of the brilliant professor":
discovermagazine/the-life-and-times-of-stephen-hawking


Here you can read Roger Penrose on The Guardian:
Mind over matter: Stephen Hawking

Cognitive Resources for Understanding Energy

The papers "Cognitive Resources for Understanding Energy" and "Making Work Work"  (that you can find on the net) by Gregg Swackhamer,  helped me a lot in my understanding of Energy. Swackhamer describes the "mysterious school science energy concept" in contrast to the scientific energy concept, explaining that is important to understand that energy does not come in different forms and that the distinctive names of Energy arise because of the different systems in which Energy is stored, not because there are different forms of energy (you can find an analogous approach in the Karlsruhe Physics Course, described in a previous blog, "The Karlsruhe Physics Course" 28 july 2017). I also found very usefull his explanation of the so colled Potential Energy (just as real as Energy stored in any other way) in connection with the introduction of the concept of field that is the physical system wich Energy we call "potential" is  stored in. It is very interesting the idea that "thinking that forms of energy really do exist sometimes induces people erroneously to think of energy itself as a physical system. This leads to the claim that light is pure energy rather than just a property of some proper physical system such as a photon or an electromagnetic wave". You can find the misleading term "pure energy" in famous popular books. I think is particularly enlightening the comparison between Energy and Information: looking at your computer you don't think that, for example, hard disk information is transformed into wire information and then into RAM information and then into CD information, and so on. Information is Information wherever it is stored; the same is for Energy.

Gravitational waves

Kip Thorne, Nobel Prize Physics 2017 "for decisive contributions to the LIGO detector and the observation of gravitational waves".

Link to the interview in wich Kip Thorne describes his own role and that of colleagues Rainer Weiss and Barry Barish, in the discovery of gravitational waves.

In his 1994’s book “Black Holes and Time Warps. Einstein’s Outrageous Legacy” he wrote:

“Gravitational-wave detectors will soon bring us observational maps of black holes, and the symphonic sounds of black holes colliding symphonies filled with rich, new information about how warped spacetime behaves when wildly vibrating. Supercomputer simulations will attempt to replicate the symphonies and tell us what they mean, and black holes thereby will become objects of detailed experimental scrutiny. What will that scrutiny teach us? There will be surprises.”

We are now in the surprises hera!

Electromagnetism. E, D, B, H and all that. Part 1

The description of the electromagnetic field with four vectors, E,  D, B and H, has always puzzled me. Why four and not two? The explanation that the two real field are E and B with D  and H being two auxiliary fields helping you taking into consideration the  complications due to the presence of matter, seemed not to be the final word. I think of it from time to time; here is my actual position, my "phase space" about this subject.

1) First you need to introduce differential forms

How and why? It isn't an unnecessary complication?
You introduce differential forms from a logical point of view, as always in mathematics. You extend previous concepts fixing logical rules (for this I like the explanations of Richard Courant and Herbert Robbins in "What Is Mathematics? An Elementary Approach to Ideas and Methods").
The starting point is the concept of differential (I find clear the explanation in Demidovich). For the introduction of differential forms you can see for example "Calculus: a complete course" Adam and Essex, Chapter 17: "Differential Forms and Exterior Calculus". In brief you start considering differentials, and note that they have properties similar to vectors (you can see it for example considering  the differential of the function f(x, y, z) and its gradient ∇f). Than, proceeding step by step, you build new objects (differential forms) and new operations (wedge product and Exterior derivative).

2) Than you understand that electromagnetic field is better described using differential forms

Here we face with one of the argument I love more: the relation beetween physic and mathematics.  As an introduction I can't resist quoting Wigner:

"The miracle of the appropriateness of the language of mathematics for the formulation of the laws of physics is a wonderful gift which we neither understand nor deserve" (Eugene P. Wigner from The Unreasonable Effectiveness of Mathematics in the Natural Sciences,1960).

I think one can see a bit of this in action with the introduction of differential forms in electromagnetism. The best introduction I found is the one of Alain Bossavit (Electricite´ de France) in a series of articles on the geometry of electromagnetism (published in 1998 in  J. Japan Soc. Appl. Electromagn. & Mech. 6) you can find on the net, in wich he focus on the fact that "one can discuss the same physics within widely different mathematical formalisms". He shows that different geometrical objects can serve in describing electromagnetism. In his words:

"The World is, and it certainly has order and structure. But order and structure in our descriptions of the world are something else, even if we try our best towards a close match, in the process of model building. Pure mathematicians try to discover, analyse, and classify all logically possible abstract structures. People who apply mathematics, including physicists and engineers, use them to construct specific abstract structures, which reproduce some of the features of the real world, and thus can help in explaining or predicting the behavior of some definite segment of reality. So mathematical entities by which we thus describe physics are not a priori frames of our thinking. They are our creation, moulded of course by the structures of the world out there, but still abstract things. Therefore, they are more or less adequate as tools with which to deal with the real world, which means one can—and one should—criticize the way they are applied, and question their adequacy".

He introduce the use of differential forms for describing electromagnetic fields and explain concepts I always found a bit obscure such as pseudo vectors,  twisted forms and orientation of space in a very clear manner. (to be continued ...)