Second video sequence: Schrödinger equation

I just uploaded the second Common Sense Quantum Physics video sequence on youtube, presenting how the Schrödinger equation may be applied to ordinary macroscopic arrows. I have personnally had some difficulties to grasp the physical meaning of the evolution equations of QM when I studied it back in the eighties. I wish someone had tought me QM this way, so I hope it'll help some students.

First video sequence of Common Sense Quantum Physics

Today I published my first video sequence presenting Quantum Physics intuitively. I hope to have another six or seven sequences mixing theoretical and experimental analogies.



Here is the videoscript:

Hello, I'm Arjen, the Common Sense Quantum Physicist. My goal is to bring Quantum Mechanics nearer to intuition. As an introduction, we'll look at a characteristic property of light : the polarization. Light may be polarized in some cases, that means that it can take a characteristic orientation.

For example, the sunlight reflected from this surface is polarized in such a way that it is filtered by these sunglasses if I wear them horizontally on my nose. If I turn my head, I am dazzled by the reflected light.

So, how could we explain this ?

Firstly, we need to know that a polaroid film is deposited on these sunglasses. A polaroid film is in fact a bunch of molecules that are arranged parallelly on the glass of the spectacles.

Secondly, we take advantage of a scientific representation of light. Light is composed of tiny particles, that we call photons. In quantum physics, a photon is represented by a little spinning arrow. One way to understand light is then to visualize it as a flux of little spinning arrows guided by a wave. When an arrow bounces from a reflecting surface, it affects its spinning direction. Before the reflection, the arrow is spinning in a random direction. The reflecting surface then rearranges that in a definite spinning direction and the polaroid film filters the photons depending on their spinning direction.

Let us simulate this polaroid filtering with ordinary objects.

Firstly, we have this safety barrier representing the polaroid film on the sunglasses.

Secondly, we have this rotating rod that represents the spinning arrow. If the rod is spinning perpendicularly to the rails of this barrier, it will nearly never pass the grid... If the rod is spinning parallelly to the grid, the probability is much higher. If it is spinning in any other direction, it is just a matter of probability.

So this experiment learns us two important things about the behaviour of the particles composing light.

Firstly, a photon is represented by a rotating arrow. The photon is a prototype of all quantum particles, in fact it is the simplest of all quantum particles. While in ordinary classical mechanics, particles are represented by points or spherical objects, like bullets or tennis balls, in Quantum Mechanics, the objects are represented by rotating arrows or rods or baseball bats, scientists say vectors. This constitutes the core of Quantum Mechanics. A very famous physicist, Richard Feynman, once presented Quantum Mechanics as the science of drawing arrows. You'll find that in this very clear presentation of Quantum ElectroDynamics : " All we do is draw arrows, that's all ".

The second important thing that we learn through this experiment is that quantum measurements are a matter of probability. The quantum rules do not give certainty about the result of an experiment. Quantum Mechanics only give odds about measurements under given conditions.

So remember these two important facts when dealing with light...

[1] photons are best represented by little arrows and

[2] measurement on these arrows is a matter of probability.

Next time, we'll look at how we may characterize the physics of quantum particles.

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.

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.