S1C1: Particles and Forces

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a) The World of Physics

Physics is the scientific study of matter, its objective is to understand what it consists of and its behaviour, unravelling the underlying processes. In that sense, it can be considered the base of the edifice of our theoretical knowledge. While we may be able to make sense of macro-phenomena such as the conditions necessary for water to boil and how to manufacture a TV screen, if one asks the question ‘why’ at every step, then the iterations will ultimately get us to ask questions about and seek answers from the fundamental laws of physics.

Attempting to truly comprehend a mundane occurrence such as the boiling of water will trigger a cascade of questions about air pressure, temperature and vaporization, which requires awareness about the H₂O molecules, equilibrium vapor pressure and phase transitions, and so on through covalent bonds, electron pairs, etc. So, physics may not be defined as the world of the infinitesimally small, but since it all starts at this scale, in practice it is. And this, even though the interacting range of forces can span interstellar distances, as is the case for gravity.

Granted, one need not master the fundamental physics to grasp the big picture of boiling water. Even so, having a modicum of comprehension will help one appreciate why boiling temperature changes depending on the type of liquid, the altitude one is at and generalize this phenomena to other phase transitions such as freezing or sublimation (the direct transition from solid to gas state we can often observe with dry ice). In short, the deeper our understanding, the wider it can be deployed and the more insightful our observations.

In addition, the continuing quest to elucidate the unexplained aspects of matter and its behaviour through space and time is indispensable in achieving technological breakthroughs in diverse fields such as nanotechnologies and quantum computing, cosmology and the origins of the universe, or even ethics. Indeed, ruling out the need for the soul or an ultimate designer has consequential impacts in terms of the origin and immutability of our moral values.

b) Property emergence

Now, just because physics is akin to the bottom layer of the pyramid of the laws of the natural world, this doesn’t mean having a good handle on it will translate into us easily deducing all macro behaviours and phenomena by progressing one level at a time. In theory, it might be possible, and certainly it appears so with the benefit of hindsight, but in practice it would take a much deeper proficiency, imagination and intellectual modelling capabilities than we humans are capable of to foresee what we term “emerging properties”.

Put simply, emergence refers to the display by a complex entity of properties or behaviours that its constituting parts do not exhibit when taken individually. Famous examples include beehives Vs bees, organs Vs cells, cells Vs proteins, proteins Vs amino acids, amino acids Vs the molecules they are made of, molecules Vs atoms, and so forth down to elementary particles. Or to take another case: a car is made up of an engine, gearbox, tires, etc. and behaves differently from any of those. In turn, a car engine is made of pistons, a flywheel, a crankshaft, a drive belt, etc. and none of those are able on their own to do what an engine does, which is to convert the fuel’s potential chemical energy into mechanical energy.

This should illustrate why learning about physics is only the first step in building a solid understanding of the world around us: each layer up in terms of complexity comes with its own set of explanations and opens a world of possibilities. And by the way, complexity is not the same as hard, it is the opposite of simple. Simple can be hard and complex can be easy.

c) The atom and subatomic particles

We’ll start our journey probably where you may expect, with the atom. The etymology of this almost mythical particle means indivisible or uncuttable and its existence took more than two millennia to be established from the time the name and concept were put forward by Democritus and his teacher Leucippus of Miletus, in the 5^th century BCE. Towards the end of the 19^th century, scientists worked out there were other smaller particles within the atom, which was subsequently split for the first time in 1932. For modelling and convenience’s sake, the atom is still considered the “basic” particle that defines the type of chemical elements one is dealing with and forms the basis of chemical compounds. Hence it feels like a natural place to kick off this first chapter in the series.

By the way, don’t worry when some technical terms such as electric charge, electrons and nucleus are mentioned for the first time, they will be explained sooner rather than later, either incrementally or with the benefit of a dedicated section, but it is often hard to describe physical systems and interactions without using them once or twice before they have been properly introduced. Think of this chapter for what it truly is, a sort of introduction of the main protagonists and key modes of interaction between them.

The first thing to note, peering at the atom, is that there is no visible boundary to this particle; no membrane or any other type of matter that delimitates one atom from its neighbours. Rather, the spherical shape it is usually represented with corresponds to the catchment area of the electromagnetic force so that electrons, subatomic particles with a negative electric charge, are bound to the nucleus of the atom and ensure some distance is kept with other atoms. Furthermore, the model of the atom as a perfect sphere with orbiting electrons inside, as proposed by Bohr in the 1910s and on the basis of which we took physics classes, did dramatically evolve during the course of the 20^th century. As for the nucleus, it comprises one or several protons, with positive charges opposite to those of the electrons, and potentially neutrons as well. It is the number of protons that determines the nature of a chemical element so that all carbon atoms have 6 protons and, unless they have been ionized, they will also have 6 electrons – ions will be covered in Section 2.d. On the other hand, the number of neutrons is subject to change; for instance, there are several carbon isotopes, three of which are naturally occurring: Carbon 12 (the most abundant), Carbon 13 and Carbon 14 (the one used to date organic materials) with six, seven and eight neutrons, respectively.

Before turning our attention towards the fundamental interactions, let us talk size for a short while so that one understand why research in this particular domain is tremendously challenging and why, as Richard Feynman famously said during one of his lectures: “there’s plenty of room at the bottom”, at a time when nanotechnology wasn’t yet a thing. The diameter of an atom is in the range of 100 picometers, with a picometer being one trillionth of a metre (1pm = 1×10⁻¹² m). The comparison often cited is that we could fit about 1 million carbon atoms across the width of a human hair. As I write this, the fabs of TSMC fabs, the most advanced microchip manufacturer in the world, are producing transistors with contacted gate pitch of under 50 nanometres (1nm = 1×10⁻⁹ m) as part of their 3nm node process (that last bit is just a marketing name), so one can imagine there are some technical challenges when getting this close to atomic dimensions. For one, an atom’s diameter sits well outside the visible light spectrum of ~400nm (which we perceive as the colour violet) to ~700nm (perceived as red); in fact it corresponds to the X-ray wavelength. As a consequence, it is really hard to imagine what atoms truly look like, especially since they do not truly exist in the material sense of the word.

As mentioned earlier, an atom doesn’t have an envelope of any kind, it consists of a nucleus and a cloud of electrons. Fine, assuming we have the proper equipment we could see them, right? Not so fast. Firstly, their dimensions make an atom look huge in comparison: the diameter of protons and neutrons are both comparable, around 1.6 femtometres (1 fm = 1×10⁻¹⁵ m), that is 60,000 times smaller than a carbon atom. Being so unfathomably small, we would currently be unable to measure them directly, even in theory. Secondly, like the atom, those subatomic particles don’t really exist in practice either since they are made of what we nowadays think are elementary particles so that their estimated size is a function of their charge distribution. So what about those elementary particles, what is their size then, you may well be tempted to ask? Well, as far as we know, and for the purpose of modelling, they have none. They are “point-like”. Same thing for the electrons since they are considered to be elementary particles (from the lepton family). In conclusion, as we zoom in continuously through both theoretical and experimental research, we come to realize there doesn’t seem to be any such thing as “hard matter”; it is all space and energy.

d) Mass, energy and interactions

How can there be no hard matter if the atoms, subatomic particles and elementary particles have weight though? And how come we can see trees, tables and chairs? The second question will be answered in Series 2 covering the topics of the human body and our various senses but, spoiler alert, it is all made up in our mind.

As for weight, that is not made up at all. Nonetheless, it is not what we instinctively think or feel it is. Weight is a function of mass and the force to which it is subjected. At the scale of human beings and other animals or even of planets and galaxies, this force is overwhelmingly gravity – and its unit of measurement is the newton, but it can also be another form of acceleration. Accordingly, if there is no gravity or acceleration, there is no weight, hence the floating astronauts in outer space – although they are still subjected to the pull of the planets and stars around them but we will leave this and the concept of frame of reference for later chapters.

Instead of weight, we should use the appropriate technical term of mass, which is probably what you had in mind anyways since the unit of measurement for this is the kilogram – and no, since weight is a force, kilogram is not the relevant unit for it. Mass can be roughly defined as the quantity of matter in a body and, unlike weight, its measure is unaffected by gravity or acceleration. Why do I say ‘roughly’? Because there are different definitions for the concept of mass, depending on context. Nothing too confusing however and all give the same result; they are merely different ways to think about an abstract concept. The more mainstream representation of mass, in our mind’s eye, is “inertial mass”: the resistance of a body to acceleration. The more massive a rock, the more force needs to be applied to push it to reach a given speed. The heavier a cyclist and his bike, the more watts (a measure of power) need to be generated to climb a hill in a specific time. This is captured by Newton’s famous second law of motion, which will be covered properly in Section 6.d and states that the net force on a body is equal to the body’s acceleration multiplied by its mass. This can be expressed as a simple enough formula: F = m.a where “F” is the force, “m” the mass and “a” the acceleration.

The other way to think about mass, especially in the subatomic realm, is as energy. Maybe the formula E=mc² looks familiar? This is known as mass-energy equivalence and was derived by Einstein when he proposed his theory of special relativity. The “E” is for energy expressed in joule, the “m” for mass (measured in kg) and the “c” is the speed of light in a vacuum (in metres per second); again we will revert to this in a subsequent chapter.

So, back to our subatomic particles. The proton’s mass can be expressed either in kilogram: ~1.6×10⁻²⁷ kg, or as energy: ~938 MeV/c² where M is for mega (1 million) and eV is an electronvolt (1 eV is equal to ~1.6×10⁻¹⁹ J). Some of this might get a little confusing so if you must remember only two things, it would be #1 mass and energy can be used interchangeably when it comes to the infinitesimally small and when approaching the speed of light – what is called “relativistic speeds” – and #2 the mass of the nucleons (this refers to both the protons and the neutrons) are tiny, and yet nearly 2000 times greater than that of an electron.

Why go into those details about mass and energy? Because following the comment in the previous section on particles most likely not taking up any volume, we should think of matter not in the traditional sense of material but rather as energy generated by forces. Those forces should partially be familiar to the reader and come under the name of “fundamental interactions”. Our current scientific knowledge has identified and measured four of them: electromagnetism, gravity, the strong interaction and the weak interaction. The first two are long-range, with effect at the macroscopic level, so we can readily observe them as we go about our day, and the last two are no less important but their ranges are subatomic in scale.

Electromagnetism is the dominant force at the level of atoms and molecules, this interaction takes place between electrically charged particles. Charges can be positive or negative with opposite charges attracting each other and similar ones repulsing each other. Electromagnetism is the force preventing electrons from escaping away from the nucleus and is involved in the formation of molecules and even macromolecules. It is also ubiquitous in human technology, think wireless communication and electricity. Even the light we see is actually waves of the electromagnetic field known as electromagnetic radiation (EMR) and wavelength determining the colour we perceive.

Next in line is gravity, which needs no introduction. Or does it? Gravity is behind the attraction between any objects or particles with mass. It makes us land back to the ground after we jump, it keeps the planet together, it gets Earth rotating around the sun and our solar system orbiting around the centre of the Milky Way. Pretty powerful then – yes and no, it is all relative. Its range is seemingly limitless but gravity is by far the weakest of the four fundamental interactions, as in 1×10³⁶ times weaker than electromagnetism (that’s a billion billion billion billion) and 1×10²⁹ times weaker than the weak interaction. The higher the intensity, the shorter the range of the force field it seems. This was the straightforward way to think about this fundamental interaction until Einstein upended our perspective with his “general theory of relativity”. In that framework, gravity is a property of four-dimensional space time and, without getting more technical at this stage since we will expand on the topic in Section 10.a, this is consistent with experimental data, explaining phenomena such as the bending of light around massive bodies and the gravitational time dilation one would experience near a blackhole (this is why some of the characters age much faster than on Earth in the movie Interstellar). And yet, this theory doesn’t sit well with those underpinning quantum mechanics and scientists have so far been unable to unify gravity with the other three forces in a grand “theory of everything”.

Moving on to the strong interaction, this force is what permits elementary particles to come together and form the proton and the neutron as well as bind those subatomic particles to form the nuclei of an atom – a phenomenon known as nuclear force. Indeed, due to the electromagnetic interaction, positively charged protons repulse each other but since the strong interaction is about 100 times more powerful, stable nuclei can form. Those two interactions are also involved in nuclear fusion, which is the combination of two or more atomic nuclei, and the process that powers active stars like the sun. During fusion, when conditions allow for the strong interaction to overcome the electromagnetic one, more nucleons will combine and release binding energy, quite a bit of it in fact. Thermonuclear weapons such as the hydrogen bomb are effectively fusion weapons where the fusion state is enabled by a fission primary stage.

Finally, the weak force is the least talked about fundamental interaction outside of particle physics; its range is subatomic (much smaller than the atomic scale) and it affects elementary particles and composite ones (such as protons and neutrons) with W and Z bosons as the force carriers (more info in next section). The weak interaction is behind radioactive beta decay which has a proton transforming into a neutron by the emission of a positron plus a neutrino (a positron is an antielectron), so the charge of the atom remains unaltered, or the converse, i.e. a neutron being converted into a proton through the emission of an electron and antineutrino. This plays a critical role in the nuclear fusion process inside of stars by permitting the formation of deuterium, an indispensable step to the formation of helium and more generally of elements with heavier nuclei.

e) Elementary particles and Standard Model

We have now reached the bottom rung of matter, or so does our current experimental capabilities and theories suggest. There are a lot of elementary particles in the dominant theory, called the Standard Model, which currently makes sense of all known fundamental forces except for gravity (some physicists are still looking for an elusive graviton). These can be grouped into three categories: the bosons as force carriers, the leptons such as the electrons that are not sensitive to the strong force (and therefore do not club into composite particles), and the quarks that do combine to form composite particles called hadrons such as the familiar neutron and proton. By the way, this is the same “hadron” as in the Large Hadron Collider (LHC), the highest-energy particle accelerator in the world located underground near Geneva, measuring 26.6km and achieving a record beam energy of 6.8 TeV (double that for collision energy). The LHC tries to provide answers to questions around the existence of new elementary particles, the nature of dark matter, or validate predictions of the Standard Model theory (which it did successfully when the Higgs boson was discovered in 2012).

It gets very complex so I have attached an organised table of the elementary particles, at this moment in time, but there is a lot about it which many people (including I) find very speculative and dissatisfying for two reasons: the inability to account for gravity, and the fact that there are too many types of elementary particles. This suggests there might still be at least another layer down with less “true elementary particles” and some of the particles dubbed elementary in the Standard Model could in fact be composite. So, as it stands, there is currently no accepted theory of everything.

Figure 1: Grouping of Elementary Particles according to the Standard Model

Credit: Wikipedia Commons

f) Trivia – base units of measurement

There are only seven base units of measurement in the International System of Units (SI), the most widely used system of measurement in the world:

second for time (time is a very complex concept to define, it links the past with the future in an apparently irreversible direction);
metre for length, a measure of distance;
kilogram for mass (we already introduced mass);
ampere for electric current, a flow of charged particles such as electrons;
kelvin for thermodynamic temperature, related to the energy embedded in the motion of particles such as the atom;
mol to express an amount of substance such as the number of molecules in a given volume; and
the candela for luminous intensity, a measure of how bright a light source is perceived to be by humans from a specific angle, not overall.

All other units you are familiar with are defined as a function or combination of those seven units. For example:

the watt, a measure of power, is expressed as 1 joule per second (1 J/s) or as 1 kg⋅m²⋅s⁻³
the Pascal (pressure) can be defined either as one newton per square meter (n.m^-2 or as 1 kg⋅m⁻¹⋅s⁻²; and
weight is not expressed in kilogram (that would be mass) but in newton, or to use SI base units, in kg⋅m⋅s⁻².

These base units are benchmarked on the basis of seven “SI defining constants”: the speed of light (c), the Planck constant (h), the elementary charge (e), the Boltzmann constant (k), the Avogadro constant (N_A), the luminous efficacy of 540 THz radiation (Kcd, a measure of how well a light source produces visible light, being the ratio of luminous flow to power), and the hyperfine transition frequency of Cs (ΔνCs, where Cs stands for the element Caesium, which is used for atomic clocks).

The SI as well as Coordinated Universal Time used to officially align clocks around the world are set and managed by the International Bureau of Weights and Measures (BIPM in French). You may be surprised to know that not everything is frozen and some redefinitions occur from time to time after long consultations and debate. They are right now looking into possibly redefining the second around the year 2030. I have included the link to the roadmap below.