The Search for the Fundamental

Motion of gas molecules Español: Animación mos...
Motion of gas molecules Español: Animación mostrando la agitación térmica de un gas. Cinco partículas han sido coloreadas de rojo para facilitar el seguimiento de sus movimientos. Русский: Хаотическое тепловое движение на плоскости частиц газа таких как атомы и молекулы (Photo credit: Wikipedia)

When does it stop? This screen that I am looking at, the keyboard that I am typing on, the invisible air between my eyes and the screen, even my body, all are composed of atoms, I told and believe. Apart from atoms, all there is is radiation, of various sorts.

The ancient Greek philosophers didn’t know about atoms so proposed various theories, which today seem quaint, but eventually they came around to atomism, and abandoned the other theories. In particular the theory of the four classical elements, earth, fire, water and air was dropped.

The four classical elements, after Aristotle. ...
The four classical elements, after Aristotle. Чотири стихії (за Арістотелем) (Photo credit: Wikipedia)

As I said, the theory now sounds quaint, but, given that the ancient Greek philosophers were not of an experimental frame of mind, the four classical elements could explain much of what could be observed. Everything could have been a mixture of these elements in various proportions.

After all, it appeared to work for colours – all colours that can be displayed on a computer screen can be specified in terms of the amount of the three primary colours of red, green and blue that a single pixel or dot on the screen emits. Why shouldn’t this scheme work for other things than light?

Barycentric RGB
Barycentric RGB (Photo credit: Wikipedia)

However Greek philosophers (and of course, philosophers in other cultures) noticed that, while some things could be broken down into component parts – sugar could be melted and burned, water could be driven off to leave the salts behind, and more importantly alcohol could be evaporated off and collected to make spirits, some things could not be broken down.

Gold, sulphur and phosphorus stubbornly refused to separate into earth, air, water or fire. Of course such stubbornness could be explained by the classical element theory – after all some things are easier to break down than others, but the Greeks eventually dropped the theory in favour of atomism. (This and what follows is highly simplified and condensed).

(Click here for rotating model)
(Click here for rotating model) (Photo credit: Wikipedia)

This is the belief that everything is made up of small indivisible particles which differ from element to element. The lump of gold contains billions of gold atoms, while the sulphur block contains sulphur atoms.

From about the start of the scientific revolution, people started to work out the rules of chemistry, and the ‘why’ of chemical reactions. Why did carbon in coal burn away and leave an ash? We know that the carbon in the coal burns using the oxygen in the air and creates oxides of carbon which are gasses and not easily detectable, but the experiments which led to this knowledge were preformed in the era of the scientific revolution.

So, matter is composed of atoms. That seemed to be the end of the story, as the vast majority of chemical experiments could be explained in terms of atoms, but exactly why atom A reacts in fixed proportions with atom B, but won’t have a bar of atom C. These relationships were noted but not really explained.

By the middle of the 19th century scientists began to detect problems with the “atoms as billiard balls” model. Electrons were discovered and soon related to chemistry, answering the above question. The new model, “atoms as small planetary-like systems”, had a small positively charged, and solid nucleus surrounded by a swarm of negatively charged electrons, with the electrons taking a major role in determining the chemistry of the atom.

It was discovered that many elements behaved as if each atoms of the element weighed the same, but some elements broke this rule. The gas Chlorine for example has an atomic weight of 35.45. In other words each atom weighed about 35 and half times as much as a Hydrogen atom.

It was eventually discovered that not all Chlorine atoms weighed the same. Most had an atomic weight of 35 but some (about half) had a weight of 36. To cut a long story short it was discovered that the supposedly solid nucleus was composed of a collection of other particles called protons and neutrons.

English: Liquid Chlorine in flask for analysis.
English: Liquid Chlorine in flask for analysis. (Photo credit: Wikipedia)

While the number of protons and electrons determine the chemistry of an atom almost completely, the number of neutrons contribute mass to the atom and barely affect the chemistry.

While electrons appear to be truly fundamental particles and cannot be broken down further, the protons and neutrons are composed of particles called quarks. For reasons mentioned in the Wikipedia article quarks cannot be found in isolation, but are only found in other particles.

English: The quark structure of the proton. Th...
English: The quark structure of the proton. There are two up quarks in it and one down quark. The strong force is mediated by gluons (wavey). The strong force has three types of charges, the so-called red, green and the blue. Note that the choice of green for the down quark is arbitrary; the “color charge” is thought of as circulating among the three quarks. (Photo credit: Wikipedia)

In addition to protons and neutrons, quarks make up other sub-atomic particles such as mesons. Scientists have discovered or postulated bosons which are particles that bind quarks and other fundamental particles together. From then on, things get complicated!

I haven’t mentioned the photon, which is bosonic, or the neutrino which is a fermion. All fundamental particles fit into one of these two families, and all sub-atomic interactions are the result of the rather incestuous exchange of these particles in their various groups and a strict set of rules. So far so good.

English: Enrico Fermi
English: Enrico Fermi (Photo credit: Wikipedia)

However, there are still questions to be answered. Are these particles truly fundamental or do they have components, which may or may not be particles in the classical sense? What are the sizes of these particles, if such a concept is appropriate at this level? Have we found them all? What about dark matter?

Scientists have abandoned the first question. They don’t generally refer to particles as fundamental. They have seen a long list of fundamental particles turn out to be not so fundamental after all.

Sizes of the particles may not make sense at the particle level, but the various theories may indicate sizes for some of them. There are difficulties over the size of the electron for instance. If it were a point object rather than having something that equates to size, then that causes difficulties with some theories.

As for the third and fourth questions, it appears that scientists may have found all the particles that explain ordinary matter, but naturally cautious, they don’t rule out other forms of matter such as the so called “dark matter” and “dark energy“. Dark matter and dark energy apparently interact with gravity and (from the Wikipedia article) and the Weak Nuclear Interaction.

pie chart of dark matter and normal energy rat...
pie chart of dark matter and normal energy ratio taken from en.wikipedia (Photo credit: Wikipedia)

My original question was “When does it stop?” By this I meant, which particles are truly fundamental and which have components that determine their properties? This question remains open, but if you have followed through my exposition, you will probably see that this is a question without an easy answer.

 

Dis-Continuum

English: The Clump looking from the Redhouse
English: The Clump looking from the Redhouse (Photo credit: Wikipedia)

Where ever one looks, things mostly seem to be in lumps or clumps of matter. We live on a lump of matter, one of a number of lumps of matter orbiting an even bigger lump of matter. We look into the sky when the bigger lump of matter is conveniently on the other side of our lump of matter and we see evidence of other lumps of matter similar to the lump of matter that our lump of matter orbits.

We see stars, in short, which poetically speaking float in a void empty of matter. We can see that these stars are not evenly distributed and that they gather together in clumps which we call galaxies. Actually stars seem to clump together in smaller clumps such as the Local Cluster of a dozen or so stars, and most galaxies have arms or other features that show structure at all levels.

Ancient Galaxy Cluster Still Producing Stars
Ancient Galaxy Cluster Still Producing Stars (Photo credit: Wikipedia)

The galaxies, which we can see between the much closer stars of our own galaxy, also appear to be clustered together in clumps, and the clumps seem to be clumped together. Of course, the ultimate clump is the Universe itself, but at all levels the Universe appears to have structure, to be organised, to be formed of lumps and clumps, variously shaped into loops, whorls, sheets, arms, rings, bubbles, and so on.

OK, but in the other direction, towards the smaller rather than the larger, our planet has various systems, weather, orogenic, natural, social and evolutionary. All sorts of systems at all levels, from global scope to the scope of the smallest element.


Embed from Getty Images

In other personal worlds, below the level our interactions with our families, we have all the systems that make up our own bodies. The system that circulates our blood, the system that processes our food, the system that maintains our multiple systems in a state homeostasis.

That is, not a steady state, but a state where all the individual systems self-adjust so that the larger system does not descend into a state of chaos, leading to a disruption of the larger whole. Death.

The main pathways of metabolism in humans, sho...
The main pathways of metabolism in humans, showing all metabolites that account for >1% of an excreted dose. ;Legend PNU-142300, accounts for ~10% of excreted dose at PNU-142586, accounts for ~45% of excreted dose at steady state PNU-173558, accounts for ~3.3% of excreted dose at steady state (Photo credit: Wikipedia)

By and large most systems in our environment are made up of molecules, which are in turn made up of atoms. Atoms are a convenient stopping point on the scale from very large to very small. They are pretty “well defined”, in that they are a very strong concept.

Atoms are rarely found solo. They are sociable critters. They form relationships with other atoms, but some atoms are more sociable than others, forming multiple bonds with other atoms. Some are more promiscuous than others, changing partners frequently.


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These relationships are called molecules, and range from simple to complex, containing from two or three atoms, to millions of atoms. The really large molecules can be broken down to smaller sub-molecules which are linked repeatedly to make up the complex molecules.

To rise higher up the scale for a moment, these molecules, large and small are organised into cells, which are essentially factories for making identical or nearly identical copies of themselves. The differences are necessary to make cells into muscles or organs and other functional features, and cells that make bones and sinews and other structural parts of a body.

A section of DNA; the sequence of the plate-li...
A section of DNA; the sequence of the plate-like units (nucleotides) in the center carries information. (Photo credit: Wikipedia)

As I said, atoms are a convenient stopping point. Every atom of an element is identical at least in its base state. It may lose or gain electrons in a “relationship” or molecule, but basically it is the same as any other element of the same sort.

Each atom consists of a nucleus and surrounding electrons, a model which some people liken to a solar system. There are similarities, but there are also differences (which I won’t go into in this post). The nucleus consists a mix of protons and neutrons. While the number neutrons may vary, they don’t significantly affect the chemical properties of the atom, which makes all atoms of an element effectively the same.

An early, outdated representation of an atom, ...
An early, outdated representation of an atom, with nucleus and electrons described as well-localized particles on well-localized orbits. (Photo credit: Wikipedia)

Each component of an atom is made up of smaller particles called “elementary” particles, although they may not be fundamentally elementary. At this level we reach the blurry level of quantum physics where a particle has an imprecise definition and an imprecise location in macroscopic terms.

Having travelled from the largest to the smallest, I’m now going to talk mathematics. I’ll link back to physics at the end.

Nucleus
Nucleus (Photo credit: Wikipedia)

We are all familiar with counting. One, two, three and so on. These concepts are the atoms of the mathematical world. They can be built up into complex structures, much like atoms can be built into molecules, organelles, cells, tissues and organs. (The analogy is far from perfect. I can think of several ways that it breaks down).

Below the “atomic” level of the integers is the “elementary” level of the rational numbers, what most people would recognise as fractions. Interestingly between any two rational numbers, you can find other rational numbers. These are very roughly equivalent to the elementary particles. Very roughly.

Half of the Hadron Calorimeter
Half of the Hadron Calorimeter (Photo credit: Wikipedia)

One might think that these would exhaust the list of types of numbers, but below (in a sense) the rational numbers is the level of the real numbers. While many of the real numbers are also rational numbers, the majority of the real numbers ate not rational numbers.

The level of the real numbers is also known as the level of the continuum. A continuum implies a line has no gaps, as in a line drawn with a pencil. If the line is made up of dots, no matter how small, it doesn’t represent a continuum.

Qunatum dots delivered by ccp
Qunatum dots delivered by ccp (Photo credit: Wikipedia)

A line made up of atoms is not a continuum, nor is a line of elementary particles. While scientists have found ever more fundamental particles, the line has apparently ended with quarks. Quantum physics seems to indicate that nature, at the lowest level, is discrete, or, to loop back to the start of this post, lumpy. There doesn’t seem to be a level of the continuum in nature.

That leaves us with two options. Either there is no level of the continuum in nature and nature is fundamentally lumpy, or the apparent indication of quantum physics that nature is lumpy is wrong.

Pineapple Lumps (240g size)
Pineapple Lumps (240g size) (Photo credit: Wikipedia)

It’s hard to believe that a lumpy universe would permit the concept of the continuum. If the nature of things is discrete, it’s hard to see how one could consider a smooth continuous thing. It’s like considering chess, which fundamentally defines a discontinuous world, where a playing piece is in a particular square and a square contains a playing piece or not.

It’s a weak argument, but the fact that we can conceive the concept of a continuum hints that the universe may be fundamentally continuous, in spite of quantum physics’ indications that it is not continuous.


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