Change and continuity

Human understanding of light has wavered over the centuries. Some famous philosopher/scientists, including Rene Descartes, insisted that light consists of waves; others, including Isaac Newton were convinced that light consists of particles. In the twentieth and twenty-first centuries, most scientists who deal with the physics of light acknowledge that light is both wave and particle. The particles, called photons, also have wave-like qualities. Moreover, electrons also possess the same paradoxical wave-particle duality. Even protons and neutrons, consisting of quarks, appear to have wave-particle duality. Therefore, everything in the material world rests upon the paradox that the component parts of every item are, at the same time, tiny particles of matter and also waves of energy.

One result of this paradox is that knowledge is limited about each particle. For example, no one can know the precise position of a particle and also how it is moving. This principle was first enunciated by a scientist named Heisenberg and is called the “Heisenberg uncertainty principle.” One famous scientific joke involves a police officer pulling over a car driven by Dr. Heisenberg. When the officer asks the doctor the standard question, “Sir, do you know how fast you were going?” Dr. Heisenberg replies, “Please don’t tell me, because if you do, I’ll never figure out where I am.”

By the way, there is also a Salvageable uncertainty principle. Ask me what that principle says, and I will answer, “I’m not sure.”

Larger material items, made out of enormous quantities of protons and neutrons and electrons, generally follow rules of geometry and physics that make sense to the average human mind. A police officer’s radar gun accurately measures the speed of a moving car. That car might be shown, by the radar gun, to be traveling seventy miles an hour. That measurement does not prove that an hour ago the car was seventy miles away. Until a few minutes ago, the car might have been sitting in a parking lot only a few miles away. But, for large material objects, we can account for both the speed and the location of that object and can accurately report both statistics at any given moment.

Philosophically, though, the motion of a material object and its location remain a puzzle. Greek philosophers more than twenty-four centuries ago were already asking how any object could move through an infinite number of points in a finite time. Dividing time into an infinite number of punctiliar moments does not solve the philosophical quandary. We can observe an object at rest and can measure its size and describe its location. We can observe an object in motion and determine its speed and direction. Trying to gather all that information at the same time seems as though it should be easy, but problems remain. As we begin measuring size and location and speed in appropriate units, we are forced to make statements that are philosophically untenable. The car that is moving seventy miles an hour does not disappear from the highway this instant and reappear seventy miles away an hour later. Assuming that its speed and direction do not change, it will be present on every bit of paved highway between here and its destination at some point during the next hour. Chopping the highway into miles, feet, inches, or any other unit—while also chopping time into hours, minutes, and seconds, or any other unit—leaves the location of the car between those identified units a mystery. If, for example, we film the car at a rate of twenty-four frames per second, each frame will show the car at a different location on the highway without any explanation of how the car traveled from one point to the next point, since an infinite number of points exists between those two points.

Aside from that problem, the car in each frame of the film is not the same car. The car constantly changes. From instant to instant, it burns a tiny bit of gasoline. Its tires rotate, and tiny bits of rubber from the tires (perhaps mere molecules) separate from the tires. From time to time, dirt and insects are added to the windshield and other parts of the front surface of the car. Take the same car at any two points along its journey and compare its description; one will see that it is not the same car. Tiny changes have occurred to make the car slightly different as it travels down the highway and also travels through time from past into present and on into the future.

We are all like that car. We change continually. None of us is the same person who woke up this morning. We have breathed air in and out of our lungs, and some of that air has been taken into our body to be used by our cells; other air that was in our bodies has left our bodies. We eat, we drink, and we use the bathroom. We wash, removing dead skin cells from the surface of our bodies. Sometimes we cut our hair or trim our nails. Even our minds change as we experience and remember new events every instant of our waking lives (and also while we sleep). You are not the same person you were when you were a child. You are not the same person you were ten years ago. You are not the same person you will be ten years from now.

On an atomic and molecular level, we change constantly. On a cellular level, we change constantly. In other ways, we continually change while we travel the timeline of our lives. Yet, as we view that timeline from outside of time, we also perceive continuity. Because that timeline is unbroken, we are able to describe ourselves as the same person through the years and over the course of a lifetime. In the same way, a car remains the same car in spite of the many changes that happen to it—a new tank of gas, an oil change, new tires, replacement of damaged body parts, replacement of damaged engine parts. Over twenty years, every piece of a car could be replaced, but legally and philosophically it remains the same car. The philosophic implications of continuity as we change are enormous. J.

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.

The oxymoron of subatomic particles

Science, like money, is a human invention that is very useful when used properly and very dangerous when misused. Both money and science can be very useful; on the other hand, a lack of either can be very problematic. Neither science nor money has the strength and significance to be the foundation of a person’s life. A human life based only on science, like a human life based only on money, is sadly crippled and unable to handle the crises that can strike a life emotionally, intellectually, and spiritually.

One of the strengths of science is also one of its weakness: science continually changes. The more effort people put into studying the world, observing the world, experimenting with things in the world, and making predictions based on those experiments and observations, the more likely it becomes that new theories will shape science and direct scientific inquiry on paths that, until that time, were unexpected.

Science was practiced in ancient Egypt, Babylon, India, and China, developing differently in different places. Western science (which drew upon scientific observations and theories from Egypt, Babylon, and India) began roughly twenty-four centuries ago with the philosophers of ancient Greece. Among their efforts was an attempt to determine the basic building blocks of the physical, or observable, world. One early philosopher suggested that everything material is made of water—a reasonable guess, since water can assume so many forms, from ice and snow to liquid water to vapor. Others suggested different basic materials rather than water. Pythagoras and his followers proposed that everything observable consists of numbers. Greek philosophers tended to seek internally consistent explanations of the world, even when those explanations seemed contrary to observation. One group, for example, insisted that motion is logically impossible and is only an illusion—that the true universe is stable and unchanging. Until the invention of calculus many centuries later, scientists and philosophers were not equipped to refute the logic that suggested that motion cannot happen in the world.

A basic teaching of western science since Greek times has been the assumption that all physical items consist of tiny unbreakable pieces. These were named “atoms” from the Greek word for “unbreakable.” For many centuries, most western scientists considered four elements to be represented among the atoms: water, earth, air, and fire. Alchemy—the predecessor to modern chemistry—observed and experimented with physical items with the assumption that all such items consist of tiny unbreakable pieces of water, earth, air, and fire. Modern western science would never have developed without the alchemists of medieval Europe. Far from living in “the dark ages,” the medieval alchemists were at the forefront of science, culture, and civilization.

Chemists eventually demonstrated the existence of far more than four elements—for example, that water is not a basic building block, but water can be divided into hydrogen and oxygen. As they continued to experiment and observe, chemists developed a series of mathematical relationships among the elements, re-suggesting the possibility that number is the most fundamental building block of the universe. Modern physics grew out of modern chemistry; roughly one hundred years ago, western scientists began to find particles that seemed to be building blocks even of atoms.

Understand that subatomic particles are an oxymoron. Atoms are supposed to be unbreakable—the word “atom” was created to communicate that important idea. Finding that atoms contained protons, neutrons, and electrons changed the rules of science; evidence of quarks and other subatomic particles continued the process of demonstrating that atoms, though important, are among the worst-named ideas in all of science.

Huge powerful machines have been built to study the tiny pieces of atoms. Smashing atoms to observe their particles has been compared to smashing an old-fashioned watch to try to guess how it functions. One scientist, Leon Lederer, joked that God “seems to be making it up as we go along,” since every layer of discoveries suggests a new layer of tiny pieces even smaller than those already demonstrated.

Scientists continue to study the world, to try to understand how things work. They observe and experiment, not only with subatomic particles, but with viruses and other disease-causing agents, medicines, genetics, and the climate of the planet. Sometimes most scientists agree with each other about how things work; other times their research seems to contradict the research of their peers. We are all familiar with the constant revision of nutritional studies—first eggs are good for us, then they are bad for us, then they are good for us again. The old tradition of individual scientists plugging away in their laboratories to manage great discoveries has long been supplanted by teams of scientists funded by government grants and by corporate investments. Political agendas and the hope to generate a financial profit inevitably shape the work of today’s scientists. Their work is important and should not be curtailed; but every scientific discovery must also be accepted with the proverbial grain of salt. That salt is as important an ingredient as any other contribution to scientific investigation. J.

A little bit of science on the occasion of a college graduation

This weekend I was out of town to attend a graduation. The night before the ceremony the family was gathered, visiting, and the graduate shared a recent event from her physics class. The professor described a scenario, asked the members of the class to make a prediction of the outcome, told them that they were all wrong, but was unable to explain why they were wrong.

Here is a scenario: a container of water has an ice cube floating in it, and a pebble sits on the ice cube. The ice cube melts. The pebble drops to the bottom of the container. Does the water level in the container rise, fall, or remain the same?

Along with most of the other family members, I predicted that the water level would rise. I had pictures of Archimedes running through the streets shouting “Eureka!” after realizing that the volume of a solid object could be measured by dropping it into a container of water and measuring the displacement of the water. Moreover, it seems that the water level should rise because of the melting of the ice. The graduate said all the members of the class had made the same prediction and it was wrong, but she still did not understand why.

One family member, an engineer, said that the professor was correct, and he explained why. The explanation puzzled most of the family members, although I caught on after a couple times through the scenario. The engineer wanted to produce a mathematical explanation with paper and pencil, but the rest of the family assured him that would not be necessary. We did try to experiment by creating the scenario with a measuring cup, an ice cube, and a pebble, but we could not find the right size ice cube or pebble to conduct the experiment.

The next day there was a party in the same house after the graduation ceremony. In addition to family members, several fellow graduates and other college students were present. To fill a lull in the conversation, I reintroduced the scenario from the physics class. One of the college students, a mathematician, insisted that the water level would rise. The engineer again countered that it would drop. This time the two of them did resort to pencil, paper, a laptop computer, and information from the internet, including the density of water and ice. The engineer was able to convince the mathematician that the water level would indeed drop.

It happens that the classic form of this scenario involves a boat and an anchor rather than an ice cube and a pebble. When the anchor is removed from the boat and dropped into the water, the water level drops, even though it seems that it should rise. The reason for the counterintuitive answer is that the boat with the anchor in it displaces some of the water in the pond. When the anchor is removed from the boat, the boat rises and the water level falls. When the anchor is dropped into the water, some water is displaced and the water level rises, but not to the height that it had been when the anchor was in the boat. The reason this happens is that the anchor sinks because it is denser than the water. (If the anchor floated and did not sink, it would not be an anchor, said the engineer.) Because of its density, the anchor displaces less water than its weight alone displaced when it was in the boat, being supported by the water.

By the same token, ice floats because it is less dense than water. As it floats, it displaces some of the water. When it melts, the volume of the water that was previously frozen is less than the volume of water displaced by the floating ice. Therefore, the pebble-ice cube combination displaced more water when the ice was frozen and floating, supporting the pebble, than the pebble displaced after the ice melted; even the melted ice did not add enough water to raise the water level to the height it had been when the ice was still frozen.

The rest of the weekend, including the graduation, was also nice. J.