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 ...)

The Karlsruhe Physics Course.

This is the course for secondary school I would have attended when I first met physics. The books and the related material are free (http://www.physikdidaktik.uni-karlsruhe.de). I think the Karlsruhe Physics Course (KPK) is very enlightening and that it can really improve the understanding of physic. I found particularly remarkable the aspects listed below:    

• to present different energy carriers instead of different forms of energy (energy is energy is energy! Think of information: you don’t think of different forms of information depending on what medium carries it);

• to describe Newton’s laws in term of momentum current (from the viewpoint of modern physics the three laws are expression of the conservation of momentum);

•  to introduce the concept of entropy from the very beginning;

•  to point out that electric and magnetic fields are physical systems and not mathematical constructions.

KPK is the only course I know of that teachs physics with the aim of not to “reproduce historical errors ... to learn inappropriate concepts and employ outdated methods" (Historical Burdens on Physics).

The theoretical minimum

The eminent Stanford's physicist Leonard Susskind has taught a series of courses in Continuing Studies program, in which he covers the essential foundations of modern physics. “Theoretical minimum” means just what you need to know in order to proceed to the next level. You can find the lectures and related materials online (http://theoreticalminimum.com). I found it extremely useful as a guide and I use Susskind’s Teheoretical Minimum as the reference frame in my study.