Follow-up of my FQXi essay: Ordinary analogues for Quantum Mechanics

Today I had the good surprise to discover the article "Quantum mechanics writ large" written by John W. M. Bush, Professor of Applied Mathematics at MIT, promoting the work of Couder, Fort et al. on the bouncing droplets. John Bush writes: "At the time that pilot wave theory was developed and then overtaken by the Copenhagen interpretation as the standard view of quantum mechanics, there was no macroscopic pilot wave analog to draw upon. Now there is."

I'm totally in line with this opinion. Quantum mechanics has macroscopic analogues which have so far nearly never been discussed and from which we would learn a lot. There has already been some discussion along with my 2009 FQXi essay. In the abstract, I wrote something similar to John Bush: "Classical physics was not sufficiently advanced to deal with macroscopic particle-wave systems at the birth of quantum mechanics. Physicists therefore lacked references to compare quantum with analogous macroscopic behaviour. After consideration of some recent experiments with droplets steered by waves, we examine possibilities to give some intuitive meaning to the rules governing the quantum world."

So, I hope this new article will gain much attention and foster discussion about macroscopic analogues for quantum behavior.

Quantum mechanics is best understood when you're blind

Occasionally I go through some threads of newsgroup sci.physics.foundations. This moderated newsgroup is dedicated to my main subject of interest and one is bothered neither by flames or spam as in sci.physics nor with biased moderation. So for everyone with an interest in physics foundations, this is a good place to be.

Recently there have been discussions on the difference between classical and quantum. I appreciate the description given by Charles Francis, which I quote hereafter:

Classical mechanics is the mechanics of bodies whose position can be continuously known up to the limit of experimental accuracy.

Quantum mechanics is the mechanics of particles whose position cannot be known between observations even in principle.

I like the fact that this definition goes beyond the historical bias that ordinary objects behave classically and submicroscopic particles behave quantum-mechanically. Charles Francis's definition focuses on the way we describe the behavior of objects, not on the way the objects behave. In other words, this definition doesn't assume a boundary between classical vs. quantum bodies. It merely assumes that we may choose between two descriptions. It assumes we have bodies and particles and we can choose to describe them either classically or quantum-mechanically. This point is very important: it empowers us to go beyond the historical bias. We just have to set up a suitable experimental procedure where:

• positions cannot be known between observations even in principle --> use quantum mechanics.
• positions can continuously be known --> use classical mechanics.

So a body is neither classical nor quantum, it just is. Depending on our purpose, we choose to describe it classically or quantum-mechanically.

As an illustration, we may refer to the perception of blind people. A blind man relies on his blind stick to analyze the behavior of objects surrounding him. He cannot know the position of objects between two "blind stick observations" even in principle. His blind stick "scans" the objects quantum-mechanically, with intrinsic uncertainties, intrinsic probabilities. At each hit of his stick against an object, the "state" of that object collapses at the location of interaction. It had some probability to be detected at any other place depending on the environment, on the boundary conditions and on the respective angles (phases) of the stick and the geometry of the detected object, but the fact of detecting the object collapsed the body at a specific location. It instantly pops up at that location.

I guess a blind man will intuitively choose a quantum-mechanical description with states whose phase varies with time and location, with probabilities, with uncertainties, with interference patterns, etc. Teaching him to describe the world classically would be counter-intuitive because he cannot continuously know the position of the objects. He has to infer it with square state (blind stick projected on detected object) probabilities.

Paradoxically, we could say that quantum mechanics is best understood when you're blind...

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.