Let’s get small, part three

Some of the earliest philosopher/scientists taught that material objects—whether solid, liquid, or gas—are made of atoms. By “atoms,” they meant tiny pieces that could not be divided into smaller pieces Over time, philosopher/scientists convinced themselves that four kinds of atoms exist: water, earth, fire, and air.  For centuries, they conducted chemical experiments based on the assumption that all materials in the world are built from those four kinds of atoms.

Today we teach that water is not an element. Water consists of two elements—hydrogen and oxygen. The hydrogen atom is the simplest of all atoms, containing one proton as its nucleus and one electron somehow related to the nucleus. Oxygen is more complicated. Oxygen has eight protons in its nucleus, as well as eight neutrons (in the most common form of oxygen—other forms, called isotopes, also exist). Oxygen also has eight electrons. When a molecule of water forms, each of the atoms of hydrogen “shares” its electron with the oxygen atom, linking the three atoms into one molecule. And these molecules are so tiny that a huge number of them must be in the same place for them to behave with the properties our senses detect as water.

If the tiny world of molecules and atoms were that simple, scientists and philosophers would be delighted. Further experiments in modern times, though, have shown that the atoms are not unbreakable—they consist of even smaller parts. (One physicist commented on continuing discoveries of subatomic particles by saying that it seems as if God is making up new complications as quickly as researchers unravel the previous complications.) Electrons, for example, are so tiny that they cannot be measured—estimates of the size of an electron vary wildly. This difficulty comes from the apparent fact that electrons are not tiny particles, specks of something solid, but instead are packets of energy. An electrician designs devices that rely on electricity, treating the moving electrons as “currents” as if they flowed like water in a stream. But individual electrons jump around like nothing we experience in our regular lives as larger creatures.

In that difference, electrons resemble photons. Photons are also packets of energy that act like tiny particles in some ways, but they also travel as waves of energy—sometimes as visible light, sometimes as radio waves, X-rays, or other frequencies. Electrons of photons do not follow the rules of physics that were used from the time of Isaac Newton to the time of Albert Einstein. Nor do they seem to exist in the kind of geometric space that has been used since the time of Euclid. Euclid’s geometry and Newton’s physics are not wrong. They merely are unable to describe realities for very tiny things (and also for very big things). Because of our experiences with objects that are neither very tiny nor very big, we tend to think in terms of Euclid’s geometry and Newton’s physics. We imagine the entire universe existing an infinite distance in every dimension—up and down, back and forth, right and left. We imagine time also existing an infinite distance into the past and into the future. Both time and space are more flexible than we generally imagine—which is why Einstein’s theories of relativity are difficult for our minds to grasp. But for the Christian, who describes time and space as created by a God who transcends both time and space, the flexibility of those creations should not be a great surprise.

In a molecule of water, then, we have ten protons and ten electrons and eight neutrons. Beyond that, each proton and each neutron are made of three quarks. Each electron has a negative charge equal to one, and each proton has a positive charge equal to one, but quarks have fractional charges which provide the sum charge of a proton as positive one and the sum charge of a neutron as zero. Although six kinds of quarks exist, only two are commonly found in atoms—two up quarks and a down quark in each proton, and two down quarks and an up quark in each neutron. So a molecule of water consists of sixty-four very tiny mysterious pieces, each of which is as much energy as it is matter—plus some particles called gluons that hold the quarks together in their protons and neutrons.

Immanuel Kant would be pleased to know that today’s scientists describe reality at the tiny level as completely unlike what we experience in our everyday world. Kant insisted that the phenomena we observe are very different than the noumena that really exist and that cause us to observe things. Time and space are nothing like what we generally consider them to be. This comment allows us to transition to consideration of the nature of time—what time really is, and how it relates to the lives that we live. J.

Let’s get small, part two

If you tear a sheet of paper into tiny pieces of paper, you will not be able to determine if you have discovered the smallest possible piece of paper. Therefore, you cannot prove in this way that whether paper is made of nothing but paper. Remember: there are three possibilities: every piece of paper might be divisible into smaller pieces of paper, continuing endlessly to smaller and smaller pieces; or there might be a smallest piece of paper that cannot be divided; or paper might be made out of small pieces of something else, small pieces which together have the properties of paper. We will test the third possibility. Weigh the piece of paper; then set it on fire. When it has burned, weigh the ashes that remain. In this way, you prove that paper consists of at least two ingredients. One ingredient is the ash that is left; the other ingredient somehow disappeared in the fire.

In the ancient world, many philosopher/scientists concluded that the material world and everything in it consists of four elements: earth, water, air, and fire. From this experiment, they would say that paper must consist of earth (the ashes left when the paper was burned) and fire (the missing weight that disappeared when the paper was burned). For centuries, philosopher/scientists called alchemists proposed theories and conducted experiments to learn more about the material world and the substances in this world. Often alchemists are portrayed as magicians trying to turn lead into gold. They did, in fact, attempt to make that change. However, they also performed many other investigations which led to the modern discovery of the science called chemistry.

Modern science would determine that most of the ash produced by burning the paper is an element called carbon. Carbon is one of the elements found in paper. Modern science also reports that water is not an element. Each molecule of water contains three atoms—two atoms of hydrogen and one atom of oxygen. Water molecules can be broken. Connect wires to the terminals of a battery and put the wires into a glass of water. Bubbles will form at each wire—hydrogen molecules at the cathode (attached to the negative pole of the battery) and oxygen molecules at the anode (attached to the positive pole).

If you could see a molecule of water, it would look like a Mickey Mouse head—two little atoms of hydrogen set sixty degrees apart on a larger atom of oxygen. Remember that these molecules are very tiny. A large number of them are required for the water to have any properties that our senses can detect. But another interesting fact about a glass of water is that –in addition to chemicals contained in the water—even a full glass of water contains much empty space.

To prove this, try the following experiment. Take a measuring cup and carefully add half a cup (four ounces) of water. Now carefully add a tablespoon of water and notice that the water level is above the half-cup (or four ounce) mark. Add a second tablespoon of water, and you now have five ounces. Add two more tablespoons of water, and you have six ounces, or three-quarters of a cup of water.

Now add a tablespoon of sugar and gently stir until all the sugar is dissolved. Notice that the water level has not increased above the six-ounce mark. Do so again, and you still have only three-quarters of a cup of water. A third time will not have the same results, because all the sugar cannot dissolve. But, even with three tablespoons of sugar in six ounces of water, you will still be far closer to the six ounce line than you are to the full cup of water. The dissolved sugar has found empty spaces between the molecules of water in your cup.

Matter contains atoms, but it also contains much empty space. Empty space exists between electrons and nuclei in each atom (and none of the sugar was able to fit into that empty space in the water). Empty space exists between molecules in even the most seemingly solid substances. Empty space exists beyond the atmosphere of the earth. Except for the brief times when the Moon, Mercury, Venus, or some asteroid crosses between the Earth and the Sun, that distance is more than ninety million miles of empty space. Even with one of those objects in the way, the bulk of that ninety million miles is empty space. More empty space separates the Sun from other stars, and yet more empty space lies between the galaxies. Most of the universe is empty space.

Empty space is not nothing. People who confuse emptiness, or the void, with nothing make the same mistake that the Cyclops named Polyphemus made in Homer’s Odyssey. Clever Odysseus introduced himself to the Cyclops as “No one.” Later, when Odysseus poked a sharpened stick into Polyphemus’ eye, the Cyclops roared out, “No one is attacking me! No one has blinded me!” None of his friends came to help him; they thought that, if no one was attacking him, everything was fine. Likewise, in Lewis Carroll’s Through the Looking Glass, the king asks his messenger who he passed on the road and the messenger answers, “nobody.” The king remarks that nobody is slower than his messenger. Indignant, the messenger says that he believes nobody is faster than he is. “He can’t do that,” the king said, “or he’d have been here first.”

In the same way, even experienced philosophers sometimes confuse themselves, mistaking emptiness or the void with nothing. Earlier philosophers felt that empty space was impossible. For anything to move, they figured, it must displace something else. When you walk into a room, you displace some air. When you lower yourself into a bathtub, you displace some water. (When Archimedes realized the significance of that displacement, he was so invited that he invented streaking.) Those early philosophers were certain that, from the very smallest pieces of the world to the very largest, everything must displace something else as it moved. They were the ones who coined the expression, “Nature abhors a vacuum,” which has nothing to do with housecleaning.

But Nature cannot abhor a vacuum; nature is almost entirely vacuum. From the empty space inside each atom to the empty space between galaxies, most of the universe is empty space. But emptiness, or void, can be measured. The tiny space between electrons of an atom and its nucleus can be measured (and that empty space is much bigger than the nucleus of the atom, let alone the electrons). The empty space between planets and the sun, or between stars, or between galaxies, can be measured. Because it can be measured, it is not nothing.

A modern physicist says that the universe is expanding. Ask, “into what is it expanding?” and the physicist answers, “Nothing.” They physicist does not mean empty space or a void; the nothing that surrounds the known universe is not measurable empty space or void. Christians say that God created the universe out of nothing. They do not mean that He created out of void or empty space. Before God created, according to Christian teachings, nothing but God existed—not even empty space, not even a void. The difference is very important to Christian teachers and to modern physicists. J.

Let’s get small, part one

You have before you a piece of paper. Being a philosopher and a scientist (for the present, we will take those words to be synonyms), you use your senses to analyze this piece of paper. You see that it is white. You see that it is flat. Seeing a measuring device, you use it to determine that the paper is eight and one half inches long and eleven inches wide—or, if you prefer, 261 mm (millimeters) x 279 mm. Measuring the thickness of the paper is not so easy, but you are a clever philosopher and scientist. You stack one hundred sheets of paper and find that the stack is one-half inch tall, or 1.2 mm. Therefore, you know that one sheet of paper is one-two-hundredth of an inch thick, or 0.012 mm—about the smallest size your eyes can see or your fingers can feel.

Scent and taste do not reveal useful information about the paper, but your hands tell you that the paper is smooth, but the edges and corners feel sharp. Left alone, the paper makes no noise. With your hands, though, you can cause it to make noises when you flap it in the air, when you crumple it, or when you tear it.

Tearing the piece of paper gives you a new thought. You now have two pieces of paper, both remaining white and flat, with the same thickness and width, but neither as long as the original. How long can this process continue? Can you continue to tear the paper into smaller and smaller pieces? And will each piece remain a piece of paper? Modern science teaches us about molecules and atoms while we are young, but for centuries philosophers and scientists were lacking that information. For centuries they wondered how small a piece of paper could remain paper, and what it might be if it was no longer paper.

With a microscope, you can see that paper consists of fibers. Perhaps with tiny, delicate tools, you could isolate one fiber from the paper and chop it into shorter and shorter lengths. Even this experiment will not answer the age-old question about what tiny parts might make up a piece of paper. Logically, three possibilities exist. Perhaps the process can continue forever—however small a piece of paper you have, you can divide it into two smaller pieces. Perhaps the process reaches a limit—a small particle of paper exists that cannot be divided into smaller pieces. Or perhaps at some point we will find tiny pieces that are no longer paper, but are something else, ingredients, elements of which paper is made. By tearing and shredding the paper, we will never determine which of these results is real.

We set the paper aside for a little while, and instead we consider a drop of water. How big is a drop? For convenience, we will define one drop as one twentieth of a milliliter (0.2 mL) or one one-hundredth of a teaspoon. Modern science tells us that one drop of water contains 1.5 sextillion molecules of water. Sextillion is a real number, unlike jillion or zillion. It is written as a one followed by twenty-one zeroes. When dealing with huge numbers or tiny numbers, scientists prefer to use “scientific notation”—in the case of one sextillion, writing the number as 1 x 10²¹. Another shortcut is to use special measurements, such as nanometers or Angstroms. To try to put this number into perspective, though, let’s take that drop of water and divide it in half. Then divide the half-drop in half again, and do so a third time, a fourth time, a fifth time, and on to a tenth time. Now we have a speck of water that is about as high and wide and thick as the thickness of one piece of paper—and it still contains 1.5 quintillion molecules of water.

With special instruments, we continue dividing that one speck of water—slightly less than one thousandth the original drop—in half, and divide that half in half, until we have done that process another ten times. The invisible bit of water we have now is one millionth the size of the original drop, and it contains 1.5 quadrillion molecules of water. Repeat the process another ten times, and what we have is one billionth the size of the original drop and contains 1.5 trillion molecules of water. Now we are getting to numbers we recognize—at least if we pay attention to the national budget. Billions and trillions are somewhat familiar. Along the way, we may begin to appreciate just how tiny one molecule of water happens to be.

But another thing has happened. By the eleventh or twelfth division of that drop of water, what we had left was not really water. It still contained water molecules—an unimaginarily huge number of molecules—but that water was no longer wet. Drop it on your skin, and you would not feel it. Drop it into a glass of water, and you would not hear it land or see the ripples. It takes an enormous number of molecules of water to be sensed as water, just as it takes an enormous number of molecules of chlorophyl before we can see any green in a leaf.

We will return to the water again and will look at its molecules and consider even smaller parts of the molecule. But, first, we will experiment again with the paper. J.