ON THE VERY SMALL

I hope by now you’ve read my article, Scale.  It hints at something odd about the Universe.


Saturn back-lit by the Sun. Earth is the tiny dot inside the artist’s circle to the left of the gas giant. In this pic Earth is 900 million miles or so into the page behind Saturn. Click pic to enlarge in new window.

When looking up into the night sky people sense the vast distances between the objects they see. But when looking down at the ground they experience something different. It seems that objects are solid, without internal structure.

No one can know by looking that solid objects are made of tiny molecules separated from each other by tiny gaps. Even sophisticated instruments like microscopes provide experimenters with no chance of seeing any molecules. Molecules are too small.


This algae is a single cell composed of many billions of molecules.

Think about it. No one has ever seen a molecule. 

No one.

Computers have created pictures based on programming rules and data from sensors to provide an idea of what molecules might look like — if molecules lived in the world at human scales and reacted to sensors and probes the way people do. But, of course, they don’t.


porin molecule occuring in cell membranes
Model of a single porin molecule.  These molecules stack to create tunnels for passage of smaller molecules through cell membranes.  Each molecule is made from hundreds of atoms.

Few professors emphasize to kids in freshman chemistry, as far as I know, that they are learning the rules from models of molecules which have been invented — fabricated — to help make sense of lab experiments done on substances that are able to be touched by hands and seen with unaided eyes.

Worse, visual models can never be realistic when applied to the objects scientists call atoms. Atoms are what molecules are made from. They must be completely fanciful. It’s true. Scanning tunneling microscopes (STMs) have been used since 1981 to “feel” the forces of atoms with “nano” probes. Based on plots of these forces, pictures of atoms that look like stacked billiard balls are generated by computer algorithms.

Whatever it is that atoms are, they aren’t resolvable with light, which is what brains use to view and imagine things. The constituents of atoms are quantum objects that don’t behave like anything familiar to ordinary life. Everything folks think they know about atoms is made-up by scientists who are struggling to make sense of the way substances behave under every set of experimental circumstances imaginable.


pentacene molecule
Atomic Force Microscopy (AFM) provided data to an IBM computer, which constructed this image of a benzene molecule. This technology cannot resolve the structure of the individual atoms, which impart to the molecule its geometric shape and electrical properties.

Scientists have invented models of atoms, which are made from protons, neutrons and electrons (that whirl inside s, p, d,  f & g orbitals) — whatever — to aid their thinking. No one examines an atom to see if it looks like its model, because they can’t.

Whatever it is scientists are modeling can’t be seen by eyes or microscopes. If the model helps scientists predict what will happen in experiments, they are OK with it. Physicist Stephen Hawking calls it model-dependent realism. The models are good enough.


Quarks
Artist rendering of quarks. It is impossible to see quarks or to know what they really are. They were invented by physicists to help make sense of experiments done in particle colliders, which show that protons, for example, cannot be fundamental, but must have (thus far) unobservable internal structures, which in the case of protons are most realistically modeled by two ”up” quarks and one ”down”. Quarks have color as well, to help explain their interactions with gluons — which carry the ”strong force”.  

During the past fifty years or so experiments have revealed new layers of complexity, which older models of the atom don’t address. So scientists have devised new models to help them reason more clearly about the strange events they were observing.

Scientists invented more structures and more “particles” — quarks being the best known — to explain and simplify the fantastic results of recent experiments.

Before the idea of the quark, scientists struggled with the complexity of a theory that included hundreds of particles. Frustrated physicists referred to the complexity as the “particle zoo.” After the theory of quarks was accepted, the number of particles in the “standard model” dropped to seventeen.


molecular and optical physics
Periodic optical lattice potentials for atoms. At a certain ‘magic wavelength’ of the trapping light one finds identical polarizabilities for ground state atoms and Rydberg atoms (see the inset), such that the trapping strength no longer depends on the internal atomic state. (Excuse me, but anyone who understands what they just read is a genius, a mad scientist, or both.)

Some current models of the subatomic world postulate point-size masses immersed in vast volumes of interstitial space. These models reflect the mathematics used to build them, but are probably not helpful for understanding what is really going on.

John Wheeler, the theoretical physicist who coined the terms worm-hole and quantum-foam, said this about the very small:  …every item of the physical world has at bottom — a very deep bottom, in most instances — an immaterial source and explanation…

At the smallest scale anyone can realistically work with — the scale of molecules — the structure of matter is dense. The space between molecules in a lattice is not much larger than the size of the molecules.

The force fields inside the molecular lattice are powerful — powerful enough to make the lattice impermeable. Vast volumes of empty space don’t exist within. Matter and energy seem to be working together in a kind of soup of symbiotic equivalence.


Atlas particle detector at CERN
Atlas particle detector at CERN. See human inside for scale. Are they kidding? This monster machine detects so-called ”particles” that cannot be seen by humans, even with microscopes.

It might be reasonable to expect that at smaller scales, forces and fields take over. Matter, as folks usually think of it, is gone. Fields (whatever they might really be) predominate. When fields interact with detectors, the detectors provide data as if they interacted with massive particles immersed in vast volumes of empty space.

It might be an illusion that leads people to miss an underlying reality of smaller scales — descent into the abyss of small scales reveals regions of disproportionately less space, not more. The stairway to smaller scales may lead to densities of force/energy and limitations of space/time like those found in black holes.  

In a typical black hole — a hundred million may inhabit the Milky Way Galaxy — a typical event horizon might have a circumference of thirty miles. Its diameter could measure millions of miles. Dimensions like these violate the Euclidean rules of geometry everyone expects. According to the rules, a spheroidal event horizon with a thirty mile circumference can’t measure more than ten miles across.

A diameter of millions of miles for an object with a thirty mile circumference seems crazy at first, until the implications of relativity are examined, which demand that the volume of space and span of time within a black hole be densely distorted and wildly warped.

A black hole contains within its volume the energy-equivalent of all the matter of the collapsed and vanished star that formed it plus all the energy-equivalent of any other matter that may have fallen into it. It is a region mostly devoid of matter — it is energy rich but matter impoverished — analogous perhaps to those tiny spaces some think might exist within and between atoms and inside the sub-atomic realms of ordinary matter.

Said plainly, whatever exists at tiny scales is not understood, but maybe knowledge about black holes can provide insights. I think so. The problem: knowledge about black holes is speculation based on mathematics; unless we are already living inside a black hole, no one can experimentally verify the ideas of smart and talented people like Stephen Hawking, for example.

The problem of understanding the very small is serious. The most advanced particle detector humans can afford to build blows up protons to examine their debris field. The detector “looks at” debris that measures about 1/100th the size of the protons it smashes. Accelerators — like the one at CERN — can’t “see” anything smaller.

From these tiny pieces of accelerator-trash theories of nature are fashioned. The inability to resolve the super small stuff is a problem. No one can see quarks, for example. Scientists at the ALICE Lab at CERN hope to fashion a “work around” by using the nuclei of iron atoms to make progress in the coming years.

To examine debris at Planck scales — which would answer everyone’s questions — requires a resolution many trillions of times greater than CERN can deliver. Such a machine would have to be much larger than the one at CERN. It would have to be larger than the solar system. In fact, it would have to be larger than the Milky Way Galaxy. Even then, the uncertainty principle guarantees that such a machine could not remove all the quantum fuzziness from whatever images it might create.


Nema Arkani-Hamed
Nima Arkani-Hamed, theoretical physicist, born April 5, 1972

According to IAS theoretical physicist, Nima Arkani-Hamed, it might be possible to burrow down to an understanding of the very small by using pure thought — as long as it is consistent with the mathematics that is already known for sure about quantum physics and relativity theory. The problem is, no one will ever be able to confirm the new models by doing an experiment.

The good news, Nema says, is that constraints imposed by knowledge already confirmed may so reduce the number of paths to truth that somebody might find a way that is unique, sufficient, and exclusive. If so, folks can have confidence in it, though experimental verification may lie well beyond the reach of technology.

But again, fundamental problems — like trying to observe an intact, whole atom — remain. No technology of any kind exists that will permit anyone to observe an entire atom at once and resolve its parts.

Physicists are reduced to using what they learn from observing atomic-scale debris to help fashion, in their imaginations, what such an entity might “look” like. No one will ever have the holistic satisfaction of holding an atom in their experimental hands, observing it, and pushing on its quantum-endowed components to see what happens.


alchemy
Artist rendering of an alchemy research laboratory.

Where does it all lead? At this stage in its history, science is struggling to figure out what’s happening. 

In the USA, (where the big money is) science seems to serve the military and companies struggling to create products that capture the imagination and pocketbooks of a buying public. For the moment at least, science is preoccupied with serving better those who pay for its services.

But someday — hopefully soon — scientists may refocus their considerable talents on the questions that really matter most to people:

Where are we?  What, exactly, is this place? Is anyone in charge?  

Billy Lee

SCALE

The visible universe is big. Most scientists believe the invisible universe — the universe no one can see — is really big.

If the Universe shrunk down to where Earth became the size of a period at the end of a sentence, how big would it be?

When I was a kid, questions like these fascinated me; what harm is there to revisit a few?

About 100 dots the size of the period at the end of this sentence must be strung together to make an inch. We can imagine shrinking Earth to the size of one of these dots, then plugging-in the numbers to calculate the scale of everything else. It turns out that the observable universe shrinks to a diameter of about two light years.

Since a light year is nearly six-trillion miles, the universe is fantastically big. At this reduced scale, the size of the universe remains pretty much incomprehensible.


In this pic, the Sun sits directly behind Saturn, which is backlit by it. Earth is the tiny dot inside the illustrator’s circle to Saturn’s left. Earth is hundreds-of-millions of miles into the page—behind the gas-giant and its rings. Click pic to enlarge in new window.  

When Earth becomes a period (or dot), the Sun shrinks to close to an inch in diameter — or 2/3 the diameter of a ping-pong ball. [regulation ping-pong balls are 1.575″ in diameter] The dot-sized Earth orbits 10 feet away. Neptune, the farthest planet, is smaller than a BB — a tiny ball of methane ice almost one football field distant (97 yards).

The distance light travels in a year shrinks to 120 miles — a speed approaching  ¼  inch-per-second. The distance to Alpha Centauri, the nearest Sun-like star, shrinks to 500 miles. The star Alpha Centauri shrinks to a ball that is only slightly larger than our under-sized ping-pong ball-sized Sun.

Think about two 1″ diameter ping-pong balls separated by 500 miles. Imagine trying to commute between these balls when the top speed is less than  ¼ inch-per-second. Of course, nothing travels at the speed of light. At speeds typical of spacecraft today, it takes 100,000 years to reach Alpha Centauri.

At the scale where Earth is a dot, one might wonder what is the size variation of stars. It turns out that most suns (stars) in the universe range in size from a grapefruit to a pea. 

Of course, outliers exist like Deneb, the blue-white supergiant visible in the Summer Triangle. At 203 times the size of the Sun, it shrinks to 17 feet or so in diameter depending on how accurately anyone cares to scale things. Rare super-giants are larger; some are 75 feet or more in diameter at this scale. But in the Milky Way Galaxy, our undersized ping-pong Sun is one of the larger stars. 

Is there another way to grasp how large the universe is?

The Milky Way Galaxy — the Sun orbits its center in the space between two of its outermost spiral-arms — is 100,000 light-years across. If the Milky Way was reduced to the dimensions of a coin the size of a quarter, the visible universe (the universe that can be seen with telescopes) would collapse into a sphere of space 15 miles in diameter.

In such a reduced sphere of space, large galaxies become the size of Frisbees but outliers like the mammoth IC1101 are the size of truck tires. The smallest galaxies shrivel into mere grains of sand. Distances between galaxies diminish to 100 feet or so but variations are huge because galaxies tend to cluster together to form groups, which are separated from one another by vast distances.

At this scale, astrophysicists say that the presence of galaxies that cannot be seen (because the distances between our Milky Way Galaxy and the farthest-away galaxies recede faster than the speed-of-light) makes the entire universe, visible and beyond, a minimum of 50 miles in diameter. Light, believe it or not, stands still at this scale. No human observer during their lifetime would notice any movement at all of light or any other phenomenon.

Even the faster-than-light expansion of the universe would be unobservable.

According to physicist, Stephen Hawking, it takes a billion years for the universe to expand by 10%.  Five miles (10% of 50) during a period of one billion years is 7 billionths-of-an-inch per day. During a human lifetime the expansion adds to 2 thousandths-of-an-inch (.002″) — less than half the width of a strand of hair.

At the scale where the Milky Way Galaxy is the size of a quarter, the entire universe would appear to be frozen solid during the span of a human lifetime.


molecules 3
Artist’s view of water molecules. Molecules are the smallest structures that can be directly observed (with the help of special sensing instruments and computer generated enhancements). Molecules are the building blocks of all things.

What about tiny things?

To examine the scale of the very small we can imagine enlarging molecules, the building blocks of all things, to the size of the same period-sized dots.

How tall might an average person be? After again plugging in the numbers and calculating, it turns out that a human stretches to a height of 1,000 miles. The eye expands to an orb 15 miles across.

Molecules are small. But at this imagined scale — a scale that requires  sophisticated instruments to discern — individual molecules become visible. They grow to look like little dots separated by distances only a bit larger than the dots themselves. Sadly, no one can see the individual atoms that make up the molecules. Even at this enlarged scale, they are too small.

No instruments or microscopes can be constructed to enable anyone to “see” atoms. Physicists believe atoms are real because they see the evidence left behind as their debris moves through the detection mediums of cyclotrons, colliders, and other sensors.

Since 1981 physicists have used scanning tunneling microscopes (STMs) to “feel” the forces of atoms with “nano” probes. A computer algorithm plots the forces and creates pictures of atoms, which with this method look like stacked billiard balls.

Billiard balls is not what quantum objects “look” like because quantum objects can’t be seen using human vision but at least scientists can prove that lumps of energy exist and are arranged in patterns that can be analyzed. It’s a start. It’s something.

Models of atoms studied in science class at universities around the world are contrived to help make sense of the results of many experiments. They are somewhat fanciful. 

As for living cells — the basic building blocks of all biology — people are able to observe them under magnification because every cell is built-up from many billions of molecules. Some human cells have trillions. The size of a typical cell at the scale where molecules are expanded to about the size of three-dimensional dots is about 60 feet across.


scale fabric of universe
Artist’s large scale view of the universe.

The gulf between the very large and the very small strains credulity but science says it’s real. When thinking about it, I am overcome by wonder and the despair of not knowing why or how.

Theoretical physicist Nima Arkani-Hamed has said that the gulf between the very large and the very small is required to balance the force of gravity against electrical forces in celestial objects like planets. He has pointed out that the ratio of the surface area of a typical atom and the surface area of a typical planet mirrors the difference between the two forces.


Nima Arkani-Hamed, one of the world’s top theoretical physicists, makes a point.

The huge difference between the force of gravity and the force of electricity makes the gap between the very large and the very small essential in a universe that works like ours; the difference in scale is necessary and inevitable, Nima has said. 

If the ratio moves too far from this balance — if the surface area of an object gets too big — gravity will overwhelm the electrical forces that hold the atoms apart to cause the object to light up from a process called fusion, which can leave behind a shining star. A much larger object will collapse to become a black hole

Why is the gap between the force of gravity and the electrical force as vast as the difference in surface area between a typical planet and a hydrogen atom? How did the ratio get that way?

No one knows. The values of the forces seem as finely tuned as they are arbitrary. Nima Arkani-Hamed and others are working to understand why. 

Another mystery: Why is the universe so big?

Even Nima Arkani-Hamed admits he doesn’t have the answer — not yet, anyway. Perhaps the answer lies in the geometry of spheres, which is the basis of the Billy Lee Conjecture discussed in the essay Conscious Life.



Speaking of spheres, everyone knows that billiard balls are polished smooth, right?  Earth, after being shrunk to the size of a pool ball, is smoother and less blemished; more perfectly round. Exhale on a pool-ball to create a mist that is 10 times deeper at scale than the deepest ocean on Earth.

Do the math.

It’s true.

As a child my nightmare was of an enormous whale crushing a tiny flower. A psychologist told me that the whale was a parent; I was the flower. 

Maybe.

But the universe captures my nightmare. It’s really big and I am so very small, helpless, and lost within its vast expanse. 

Billy Lee