With this second post, I continue my project of sharing quantum mechanics lecture notes on Steemit. Having setup the first part of the context in my previous post, I am now moving on by describing the three basic ingredients of the microscopic world: the interactions, the (stable) particles that I will focus on and some useful conservation laws.
THE FOUR FUNDAMENTAL INTERACTIONS
At the macroscopic scale, there exists a lot of different interactions (or also known as forces). At the microscopic level, the situation is different and we only have four fundamental interactions: electromagnetism, gravity and the weak and strong interactions.
The properties of these interactions are however deduced from investigations of their macroscopic effects, and all interactions are defined by their properties, that include their range a, intensity I and their attractive/repulsive behavior.
In the following, the intensity of the different interactions are taken relatively to the intensity of the strong force (which is thus equal to 1).
The range of an interaction is the distance after which its intensity exponentially decreases by a factor of e (in the limit of large distances). The associated potential V(r) can hence be written, in the asymptotic limit where r is large, as
V(r) ~ exp[ -r / a ] / r.
Potentials will be used a lot in these lectures and consist of another way to describe forces.
Gravity
The first interaction that has been discovered is the gravitational one.
It is way weaker than all other interactions, its intensity being 36 orders of magnitude smaller than the one of the strong interaction (I ~ 0.00….01 with 35 zeros). It is always attractive and its range is infinite. Its effects are thus never screened, which makes this interaction the easiest to observe and to study.
The associated effects are moreover proportional to the involved masses, so that at the level of the microscopic world, gravity is negligible (as already said in some of my another posts) and does not play any role.
Electromagnetism
Electromagnetism is the second interaction that has been discovered by physicists, mainly again thanks to its infinite range. The interaction strength is only about 100 weaker than the one of the strong interaction, which means it is not small at all.
Electromagnetic interactions can be either attractive or repulsive as a function of the involved electric charges. Since at the macroscopic level, matter is generally neutral, electromagnetic effects are then screened away: the effects of the positive charges constituting matter are compensated by those of the electric charges being present in the same number.
In contrast, at the microscopic level, the elementary particles are not neutral (more precisely, at least some of them) and electromagnetism thus plays a key role to explain the properties of the structure of matter.
The strong and weak interactions
Only gravity and electromagnetism suffice to describe all observations of the macroscopic world, and the two other interactions have consequently been discovered much later thanks to radioactivity.
The two other interactions have actually no effects on macroscopic objects, their range being 1 fm and 0.001 fm for the strong and weak forces, respectively.
Strong interactions dictate the dynamics of the elementary quarks and gluons (see my bestiary post), and ensure the cohesion of the protons, the neutrons and of the atomic nuclei. Moreover, they can be either attractive or repulsive.
The weak force is 100.000 times weaker than the strong interaction and has no effect on the structure of matter. Its importance is elsewhere.
Besides its weakness and its small range, it renders decay processes possible. These processes are slow (due to the weakness of the weak interactions), and as a result … there was life: the evolution of the sun is slow enough thanks to the weakness of the weak interactions. And Earth is thus still on board.
THE STABLE PARTICLES
The matter around us is constituted of stable particles. Those are not the only discovered particles, but any particle of another kind is unstable and usually decays within a microsecond or less.
In these lectures, and in contrast to what is going on in particle physics, I will consider as my main matter ingredients the neutrons, protons and electrons and the associated antiparticles (that are the antiproton, the antineutron and the positron).
I will also sometimes refer to photons that are needed to introduce the key results that have lead to quantum mechanics.
Each particle species is defined by its properties, like its electric charge, its mass and its lifetime. By lifetime, I mean the mean lifetime on a statistical ground as there is no way to get the lifetime of a specific particle (and we need to average).
Although I will focus in the next posts on systems of stable particles that can be described by quantum mechanics, it is good to start with the basic ingredients before moving on to more complicated composite systems. Please be patient, atoms and molecules are coming (but not too much, I am too scared by the chemists around the place :p).
The electron
The electron is a stable elementary particle (his lifetime is thus infinite). It is light, with a mass of 0.0000….0611 kg with 30 zero. It has a negative electric charge of -e, the unit chosen here being 1e = 1.60e-19 C = 0.000…016 C with 18 zeros. For obvious reasons, it is easier to use the e unit for the charge.
Moreover, it is good to say that the electron is only affected by the electromagnetic and weak interactions.
[image credits: the particle zoo and the particle zoo ]
The nucleons
Protons and neutrons are very similar particles usually seem as two distinct realizations of a given particles species named the nucleon that is sensitive to all fundamental interactions.
The neutron and proton mass is indeed similar, being equal to 1836 times the electron mass (or 0.00…0167 kg with 26 zeros) and the proton has a charge of +e whilst the neutron is neutral (now you know where the names comes from).
The proton is slightly lighter than the neutron so that it is stable and the neutron decays in about 15 minutes into a proton, an electron and a neutrino by virtue of the weak interactions. The neutron is however stable when embedded within an atomic nucleus thanks to the presence of the other nucleons. We are thus safe... matter can get organized and have a structure!
One may note that there is no proof that the proton is stable, and there are experiments trying to show that it could actually decay. So far the results are negative, so that one end up with an upper limit on the proton lifetime, that is roughly one million of billions of times the age of the universe… 'Stable' is thus a pretty good approximation.
Let me recall that protons and neutrons are composite objects made of quarks and gluons, as I mentioned it in this particle physics introduction post. But the story becomes more complicated for as this requires special relativity, quantum field theory and even more.
I therefore focus in these lectures on a non-relativistic context and therefore ignore any nucleon substructure. This gives good results for most of the physics I will be describing.
Photons
The last type of particle I will need consist of photons. They are responsible of the mediation of the electromagnetic interactions, as I have already mentioned it in many of my posts.
Its mass and its electric charge are both vanishing, and the photon is not charged under any of the fundamental interactions. Even if he is the force carrier of electromagnetism. This contrasts with all the other interactions where the corresponding force carriers are sensitive to the interaction they mediate. As any massless particle, the photon travels at the speed of light, c ~ 300.000 km/s.
It can be noted that according to their energy, photons get a different name: gamma ray, X-ray, visible photons, …
As a funny anecdote, there are several experiments trying to show that the photon is actually massive. So far, all results are negative so that we have a upper bound on the photon mass of about 0.000…01 kg with 36 zeros. Yeah, the photon is massless (at least in an incredibly very good approximation).
CONSERVATION LAWS
During an interaction, several quantities are conserved, and do not vary. With each conserved quantity we can associate a conservation law that state that the quantity is always conserved.
These laws are derived from a wealth of experimental data indicating that a given quantity is actually conserved. From Emmy Noether, we now know that conservation laws are linked to symmetry principles: if a theory exhibits some symmetry, there is always a related quantity that is conserved with time.
Very importantly, any process that would violate a conservation law is forbidden and will not happen.
The three main conservation laws that I will refer to are the conservation of the energy, the momentum and the electric charge.
At the microscopic level, energy can only exist under three forms (to be compared to the existing variety in the macroscopic world): mass energy, kinetic energy and potential energy. I will come back to this in future posts.
The momentum is strongly connected to the energy. These two quantities are by the way unified by special relativity. Without any external fields, the momentum of a system is given by the product of its mass and its velocity. When a field (like an electromagnetic field) is switched on, the momentum takes a more complicated expression.
Again, I will come back to this in a far future lecture. Yeah, this paragraph can be seen as an appetizer to the rest..
I will not come back to the electric charge, but one important point is that charge conservation implies that a particle and an antiparticle have an opposite electric charge. Both can indeed be pair-produced from a neutral system. As the electric charge cannot vary, the only explanation is what I stated.
SUMMARY
In this lesson, I have introduced the four fundamental interactions, the basic particles I will need for those lectures and I have briefly discussed conservation laws. For any question, pass by #steemSTEM!
In my next post, I will detail the composite system that quantum mechanics describe.
And then, we will move on with the main meat of these lectures! I know, some may be impatient. But patience is the key! :)