Common sense thoughts about geometry

The month April has nearly come to an end and I haven't posted any line to my blog! These past two months, I used all my spare time to ponder over famous geometric problems like the angle trisection or the doubling of the cube. These are "proven" to be impossible to solve with the classical "euclidean tools" that are the compass and the unmarked straightedge. The more I digg into it, the more I feel that such impossibility proofs are just ways to reassure ourselves about our advanced scientific tools.

If an angle exists, the third of an angle also exists. A simple solution hides somewhere beyond scholar hindrances. The same for the double of a cube. If a cube of unit volume exists, a cube with double volume is determined. Or take the squaring of a circle. If a circle has some physical meaning, any other figure may be constructed departing from the area of the circle. Impossibility "proofs" just obstruct the road to a solution. Solutions may be found by playing, playing with real objects, following our intuition.

For an intuitive solution of the squaring of the circle, have a look at the tools of dakhiometry originated by Nguyen Tan Tai.

What if the LHC won't reveal the Higgs boson?

Next sunday, there is an open day at the Large Hadron Collider. If you are in the proximity of Geneva don't miss the chance to visit that pharaonic work! The main goal of that particle collider is to reveal the Higgs boson, the particle that's supposed to give mass to all other massive particles. Hereby an instructive video:



But what if we discover no Higgs boson? How do we proceed? What are the plans? I guess we'll find plethora of other particles at those unexperimented energies. We'll need to set up new supermodels, supertheories. That will generate decennies, if not centuries of theoretical work and speculations, which will call for Xtra LHC's, and so on.

Before heading enthusiastically towards Xtra LHC's - because an XLHC will not cost billions of dollars, but hundreds of billions of dollars - I vote for a quiet time. Let all theorists and experimentalists take a paid sabbatical year and develop independently their own vision on quantum reality, the simpler the better. Because there are a lot of other mechanisms that make particles gain inertia, especially when you think of particles as having concrete reality, like little rotating needles or hooks or any structured non circular extension. Let us first work out all those alternative paths before taking the XLHC highway, if we'll still be there ;-) Wink at what's awaiting us according to the LHC lawsuit at Honolulu.

Classical Mechanics vs. Quantum Mechanics

In order to illustrate the analogy I presented in my preceding post between Newton's laws and QM laws, I composed the following images (you may view them better at wikiversity).

Newtonian mechanics consider relative motions (translational motions or rotational motions with respect to a reference point). Uniform motion takes place when no net forces exert on the body.

The dynamical laws of Quantum mechanics concern an absolute motion: the spinning of an object represented by an arrow. Such an object has uniform spinning motion when no force exerts on it.

It is often said that Quantum Mechanics comes into play when the scale of the elements of the system is microscopic. This restricted view hides the fact that the fundamental difference between CM and QM is not a difference of scale but a difference of describing the objects and their motions. CM focuses on objects that are located at points and on their relative motions. QM focuses on objects whose orientations evolve absolutely. This allows us to approach QM intuitively, reasoning on how arrow-like objects would behave in real life.

SPQR - Simplify Physics's Quantum Rules

In my introduction post, I qualified quantum physics as being nearer to intuition than classical physics. As this is not a widespread opinion, this needs some explanation. Understand me well, I don't say that quantum physics is better understood than classical physics. I merely infer that, because quantum physics deals with elementary particles, its principles should be easier to grasp than the classical principles. But as our reasoning has been formatted since our first physics classes into a classical mould, we are not trained to analyse the ordinary world quantum-mechanically.

The framework of classical physics did not emerge easily during the course of history. It took many efforts from men like Newton (represented by Gotlib in the image), Lagrange or Hamilton to formulate classical principles. Newton had the exceptional capacity to put the classical laws into a few comprehensive sentences. Let us remind his three laws:

1. Every body continues in its state of rest, or of uniform motion in a right line, unless it is compelled to change that state by forces impressed upon it.
2. The change of motion is proportional to the motive force impressed; and is made in the direction of the right line in which that force is impressed.
3. To every action there is always opposed an equal reaction: or, the mutual actions of two bodies upon each other are always equal, and directed to contrary parts.

As far as I know, an analogous clear and simple formulation of quantum physics does not exist. There are some tries of physicists like Feynman that are on the good path, see for example his 3 general principles concerning probability amplitudes (in chapter 3 of his Quantum Lectures on Physics) or his explanation of path integrals with rotating arrows (in QED). But we have not yet succeeded to express the quantum laws in an ordinary way like Newton expressed the classical laws. We are very much in need of Simplifying Physics's Quantum Rules, in order to make it more accessible to populusque. Why not take our inspiration from Newton? Let me have a try. Newton considered translational motion. Quantum evolution is about the phase change of arrows, i.e. self-rotational (spinning) motion of arrows. So we could put it in this way:

1. Every arrow-like body continues in its state of rest, or of uniform spinning motion, unless it is compelled to change that state by forces impressed upon it.
2. The change of spinning motion is proportional to the perturbative force impressed.
3. The mutual actions of two spinning arrow-like bodies upon each other are always equal, and directed to contrary parts.

That's nearly all about the fundamental laws of quantum physics. The first two laws may be formulated as evolution laws with a constant angular velocity and a position dependent force potential. The complex factor i merely expresses that the orientation of the vector difference between two subsequent orientations of the spinning vector AB is perpendicular to AB. The main difference between quantum and classical mechanics appears then to be that QM addresses spinning (absolute) motion while CM addresses translational (relative) motion.

If quantum physics is introduced in such a way to beginners, I guess they would gain faster insight into quantum behaviour without being hindered by classical reasoning.

More about it at the related wikiversity project.

Why 'Common Sense' Quantum Physics?

Quantum Physics is generally presented as a weird, non intuitive field of Physics. The domain of application is however that of the simplest systems: discrete particles evolving in a carefully controlled environment. Such systems therefore obey the most fundamental laws of physics. And who says "fundamental" says: simple, intuitive, common sense, natural... My conviction is that quantum laws are the simplest way to express how nature behaves. Or said otherwise: quantum physics is intuitive, with respect to classical physics that is artificially constructed. In order to see this, we must however approach Quantum Physics in a perspective that remains unexplored. Rather than to try to link it to classical and relativistic physics, we ought to take a more direct way.

I love the way Feynman presents Quantum Physics. In his renowned public lecture QED: The Stange Theory of Light and Matter (1985), he says: You will have to brace yourselves for this - not because it is difficult to understand, but because it is absolutely ridiculous: All we do is draw little arrows on a piece of paper - that’s all! That's the essence of Quantum Physics: arrows. Mathematicians call arrows vectors, and there are very advanced, abstract ways to describe operations on such objects. But the mathematical artillery must not hide the fact that physically, we are handling with very simple objects: objects that are alike arrows, or rods, or needles, or ballpens, or baseball bats.

A child knows intuitively how such objects behave. Tintin's cartoon "Ottocar's scepter" shows a comic situation, in which the clue consists in correctly inferring how such an object could pass through a grid. In order to make sense of Quantum Physics, we'll have to brace ourselves for this: all we do is draw little arrows. So how could arrows help us to grasp the essence of Quantum Physics? The first thing is maybe to re-read Feynman's QED, or just visioning its 4 QED public lectures: http://vega.org.uk/video/subseries/8. Than just think about it.

There is not simpler a particle than a photon (apart maybe of a neutrino which is experimentally equivalent to a photon with zero frequency):

• it has no inertia, its departing velocity with respect to the emitter is always the same (provided it does not find obstacles on its way),
• it has a very simple polarization, when correctly oriented, it passes through a wire grid,
• when constrained between two limits, its frequency may take only discrete values,
• many photons with the same polarization may be beamed together,
• in the quantum ocean of other quantum particles (essentially other photons or neutrinos), one photon creates and interacts with (we say interfers with) the wave it generates in that ocean (physicists speak of a field).

Such a particle may be represented by a rotating arrow whose rotational plane has a constant orientation between two obstacles.

This common sense way of interpreting Quantum Mechanics is explored at Wikiversity/Making_Sense_of_Quantum_Mechanics.