Surprises in Quantum Mechanics (SiQuM) (1.) Introduction

In this short series of my blogs, I like to shed a light on Quantum Mechanics (QM) and in particular Quantum Particles and how their behaviour interferes with our normal word. After month of Corona shutdown, I thought it is beneficial to recall the principles of nature and learn from the facts.

The scope

So let's start! First, lets discuss our scope and where we are: In fig 1 I've tried to summarise the 'global' or even more 'cosmic' scale of the subjects in physics. Here, we have:

  1. The micro cosmos determined by the physical laws of Quantum Mechanics. Of course, this is our primary subject.
  2. Our visible world which is determined by Newton's mechanics; and since mankind is knowledgable about electro-magnetism, we need to consider those, though it rules our daily live by means of chemistry.
  3. The Universe as such, which is still out-of-reach except for exploring our solar system, is ruled be the gravitational forces and at extreme edges by Einstein's General Relativity.

Fig 1: Universe to micro cosmos on one page

Fig 1 makes an attempt to put it all together. We see, that we talk about a scale of 1045 magnitudes of size, starting from the 'size' of an electron and reaching the diameter of the Universe. The forces span almost the same order from gravitation to strong interaction. It is interesting to note, that the stronger the force the more restricted (in terms of spatial dimension) it is, while the - principally - very weak force of gravitation 'rules' the Universe!

However, we see that forces - together with all quantum particles - carry an intrinsic property called 'spin' which rules indeed their behaviour. Let's come to that point later. For now, we me recognise that we - given our experiences and instruments - are sitting 'in between' the scales. Both experience and instruments need to be adjusted in order not only to understand and analyse the given physics but in addition interact with the analysed subjects. In case of the universe, interaction can be neglected; but for the quantum world it is most significant since it impacts the observed behaviour.

Quantum Mechanics tries to cope with this interdependency, because it is formulated as a theory of 'observables': What we do measure is not the quantum 'object' by itself, but rather its behaviour measured at our 'scale'.

Angular momentum

If you take a ride with your bike you've noticed (fig 2 bottom): Your motion is stable unless you stop. The physical source which keeps your bike straight is given by the energy conserved in the motion or your wheels: An energy conversation force is given once the wheels turn; and the amount of energy is proportional to the size (radius) of the wheels and the rotating speed.

In essence, energy can be conserved by a rotating system. Even the quantum world follows this principle introducing the spin of a particle. This spin - and any other angular momentum - in the quantum world is however (though) quantised, thus possessing discrete levels, starting with 1/2.

Actually, the 1/2 is just an artefact of you math describing those particles. However, the rules QM particles follow are strict.

Basically, this is why we have a 'material girl': Quantum exclusion rules forbid spin 1/2 particles to fill up the quantum states regardless. On the other hand, that is the reason why 'Luke Skywalker's' light sober never will work the photons, because they are spin 1 particles and thus infinite photons may exist in the same quantum state and would not interact.

Angular momentum is present in our daily life, since this the reason why the earth is circulating around the sun and why planet systems do exit over a very long period. Even the order (= distance) of planets relative to the sun is determined well defined by a physical theorem, the Titus-Bode law, although we are outside any quantum rules.

However, it shows that a many-body system's energy can be conserved. It is however not clear, whether this is the reasons why fermions have finite mass ... Looking at the other scale, we can say that the long-time existence of objects like galaxies really depends on the bound energy given by their angular momentum. In (fig 1 bottom) this is called the Virial theorem: If you observe some object and you can measure their (radial) velocity and estimate the radius relative to it's center, you can calculate the mass (within the given radius) forcing the objects to circulate around the center.

Particles

The fact, that I can beat on my desk is basically due to the fact that the quantum particles building my desk are spin 1/2 particles. The need to follow the exclusion rule that only 2 particles can be in the same quantum state (at the very same moment). We call these particles Fermions, since they obey the Fermi/Dirac statistics. The entire 'matter' is build from fermions as shown in fig 2. On the opposite; even spin (or zero spin) particles are used as force particles, in particular the photons and gluons.

Fig 2: The known elementary particles; without their anti-particles

The question is now: Is this behaviour exclusive. The answer is: No. We do have mesons which may have integer spin values (among others) and we observe spin 1/2 particles to act as exchange particles. However, the underlying reason is still not clear.

Forces

Within your known world (the middle lane) we experience the following forces:

  • The Gravitational Force being proportional to the product of the masses of two bodies divided the the square of their distance: Newton's Gravity law.
  • Electromagnetic forces; either experienced by an lightning or the at/distraction of a magnet. We are their master now using electricity and electric circuits.
  • Important for us is the stability of proton: This is granted by the ++Strong Interaction.
  • However, this is not for sake: Atoms (and in particular their nucleus) may 'decay' - governed by the Weak Interaction: Radioactivity!
  • Fig 2: Strength of the forces as a function of the (interaction) energy scale

    Interesting to note, that the gravitational and electro-magnetic forces behave almost alike, since observe a dependence of the force given by F ∝ a*b/r2 a and b are the masses of the objects, or their electrical charges respectively, while r2 is the square of their relative distance. Actually, this is due to the vanishing rest-mass of the mediating force, the photon γ and the Graviton g respectively. The short distance reach of the weak force originates from the masses of their respective exchange particles; the W± and the Z0. However, for Gluons - though they are massless them-self - a particular confinement is given for both these particles and the quarks.

    These forces behave differently depending on the scale (fig 3). In particular, physicists assume that all forces can be derived from a primary primeval force, which was split up during the birth of the universe. Assuming that, we my conclude that all the different forces behave identical in case we can 'reconstruct' the primeval circumstances. The unification of the electro-magnetic and the weak force acts here as a blueprint and has been achieved already.

    Outlook

    Let's try to explore this word! I've planned to discuss the following topics: