Nails in the coffin of dark energy?

 kw: science, cosmology, dark energy, supernovae, supernovas, type ia supernova, metallicity

INTRODUCTION

The ΛCDM model of the Universe was proposed after two research groups (led by Adam G. Reiss and Saul Perlmutter) studied certain supernovae. "Λ" (Greek lambda) refers to the cosmological constant, first proposed by Einstein, that describes the expansion of spacetime. The research teams concluded that spacetime was not just expanding, but expanding at an increasing rate. This is called "cosmic acceleration." Their key observation was that distant Type Ia supernovae are fainter than expected. This soon led to the hypothesis that 75% of the energy content of the Universe is "dark energy", which is driving and accelerating the expansion.

When I first read about "dark energy" more than 25 years ago I thought, "How can they be sure that these supernovae are truly 'standard candles' over the full range of ages represented, more than ten billion years?" I soon considered, "Is the brightness of a Type Ia supernova affected by the metallicity of the exploding star?" and "Is it worth positing a huge increase in the energy of the Universe?" From that day until now I have considered dark energy to be the second-silliest hypothesis in cosmology (I may deal with the silliest one on another occasion).

On December 10, 2025, an article appeared that has me very excited: "99.9999999% Certainty: Astronomers Confirm a Discovery with Far-Reaching Consequences for the Universe’s Fate", written by Arezki Amiri. In the article, this figure demonstrates that I was on the right track. The caption reads, "Correlation between SN Ia Hubble residuals and host-galaxy population age using updated age measurements. Both the low-redshift R19 sample and the broader G11 sample show a consistent trend: older hosts produce brighter SNe Ia after standardization, confirming the universality of the age bias. Credit: Chung et al. 2025"

It reveals a correlation between the brightness of a Type Ia supernova and the age of its host galaxy. Galactic age is related to the average metallicity of the stars that make it up. Thus, more distant Type Ia supernovae can be expected to be fainter than closer ones, because more distant galaxies are seen when they were younger, and consequently had lower metallicity. This all requires a bit of explanation.

WHAT IS METALLICITY?

Eighty percent of the naturally-occurring chemical elements are metals. That means they conduct electricity. Astronomers, for convenience, call all elements other than hydrogen (H) and helium (He) "metals". The very early Universe consisted almost entirely of H and He, with a tiny bit of lithium (Li), element #3, the lightest metal. The first stars to form were not like any of the stars we see in our sky. They were composed of 3/4 hydrogen by weight, and 1/4 helium. The spectral emission lines of H and He are sparse and not strong. Thus, the primary way for such a star to shine is almost strictly thermal radiation from a "surface" that has low emissivity.

[Insert Fig2 and add a caption] By contrast, a star like the Sun, which contains 1.39% "metals", has many, many spectral lines emitted by these elements, even as the same elements in the outer photosphere absorb the same wavelengths. On balance, this increases the effective emissivity of the Sun's "surface" and allows it to radiate light more efficiently. The figure below shows the spectra of several stars. Note in particular the lower three spectra. These are metal-poor stars, and few elemental absorption lines are visible (The M4.5 star's spectrum shows mainly molecular absorption lines and bands). However, even such metal-poor stars, with less than 1/10th or 1/100th as much metals content as the Sun, are very metal-rich compared to the very first stars, which were metal-free.

Spectra of stars of different spectral types. The Sun is a G2 star, with a spectrum similar to the line labeled "G0".

One consequence of this is that a metal-poor star of the same size and temperature as the Sun isn't as bright. It produces less energy. Another consequence, for the first stars, is that they had to be very massive, more than 50-100 times as massive as the Sun, because it was difficult for smaller gas clouds to shed radiant heat and collapse into stars. Such primordial supergiant stars burned out fast and either exploded as supernovae of Type II or collapsed directly into black holes.

THE TWO MAIN TYPES OF SUPERNOVAE

1) Type I, little or no H in the spectrum

A star similar to the Sun cannot become a supernova. It fuses hydrogen into helium until about half of its hydrogen is gone. Then its core shrinks and heats up until helium begins to fuse to carbon. While doing so, it grows to be a red giant and gradually sheds the remaining hydrogen as "red giant stellar wind". When the helium runs out, the fusion engine shuts off and the star shrinks to a white dwarf composed mainly of carbon, a sphere about 1% of the star's original size, containing about half the original mass. For an isolated star like the Sun, that is that.

However, most stars have one or more co-orbital companion stars. For any pair of co-orbiting stars, at some point the heavier star becomes a red giant and then a white dwarf. If the orbit is close enough some of the material shed by the red giant will be added to the companion star, which will increase its mass and shorten its life. When it becomes a red giant in turn, its red giant stellar wind will add material to the white dwarf. The figure shows what this might look like.

White dwarfs are very dense, but are prevented from collapsing further by electron degeneracy pressure. This pressure is capable of resisting collapse for a white dwarf with less than 1.44 solar masses (1.44 Ms). That is almost three times as massive a the white dwarf that our Sun is expected to produce in about six billion more years. It takes a much larger star to produce a white dwarf with a mass greater than 1.4 Ms, one that began with about 8 Ms. Such a star can produce more elements before fusion ceases: C fuses to O (oxygen), O fuses to neon (Ne), and so on through Na (sodium) to Mg (magnesium). The white dwarf thus formed will be composed primarily of oxygen, with significant amounts of Ne and Mg. Such a stellar remnant is called an ONeMg white dwarf. Naturally it has more metals present than the original star did when it was formed, but less than a white dwarf formed from a higher-metallicity star.

Now consider a white dwarf with a mass a little greater than 1.4 Ms, with a companion star that is shedding mass, much of which spirals to the white dwarf, as the figure illustrates. When the white dwarf grows to 1.44 Ms, which is called the Chandrasekhar Limit, it will collapse as a powerful Type Ia supernova.

There are two other subtypes, Ib and Ic, that form by different mechanisms. While they are also no-H supernovae, there are differences in their spectra and light curve that distinguish them from Type Ia, so we don't need to consider them further.

2) Type II, strong H in the spectrum

Type II supernovae are important because they provide most of the metals in the Universe. They occur when a star greater than 10 Ms runs out of fusion fuel. It takes a star with 10 Ms to produce elements beyond Mg, from Si (silicon) to Fe (iron). Fe is the heaviest element that can be produced by fusion. These heavy stars experience direct core collapse to a neutron star, with most of the star rebounding from the core as a Type II supernova. During this blast, the extreme environment produces elements heavier than Fe also. (Stars that are much heavier can collapse directly to become a black hole.)

EVOLUTION OF UNIVERSAL METALLICITY

At the time the first stars formed, the Universe was metal-free. It took a few hundred million years for a few generations of supernovae to add newly-formed metals, such that the first galaxies were formed from very-low-metal stars and low metal stars. Even with very-low to low metallicity, smaller stars could form. Since that time, most stars have been Sun-size and smaller, though stars can still form with masses up to about 50 Ms.

Stars of these early generations smaller than about 0.75 Ms are still with us, having a "main sequence lifetime" exceeding 15 million years. I can't get into the topic of the main sequence here. We're going in a different direction.

Stars of the Sun's mass and heavier have progressively shorter lifetimes. Over time, the metallicity of the Universe has steadily increased. That means that the "young" galaxies discussed in the Daily Galaxy article (and the journal article it references) are more distant, were formed at earlier times in the Universe, and thus tend to have lower metallicity.

LOWER METALLICITY MEANS LOWER BRIGHTNESS

This leads directly to my conclusion. A Type Ia supernova erupts when a white dwarf, whatever its composition, exceeds the Chandrasekhar Limit of 1.44 Ms. This has made them attractive as "standard candles" for probing the distant Universe. However, they are not so "standard" as we have been led to believe.

Consider two white dwarfs that have the same mass, say 1.439 Ms, but different compositions. One is composed of C or C+O, with very low amounts of metallic elements. The other has a composition more like stars in the solar neighborhood, with 1% metals or more. As seen with stars, more metals lead to more brightness, for a star of a given mass. Similarly, when these two white dwarfs reach 1.44 Ms and explode, the one with more metals will be brighter than the other.

The final question to be answered: Is this effect sufficient to eliminate all of the faint-early-supernova trend that led to the hypothesis of dark energy in the first place? The headline to the article indicates that the answer is Yes. A resounding yes, with a probability of 99.9999999%. That's seven nines after the decimal. That corresponds to a 6.5-sigma result, where 5 sigma or larger is termed "near certainty".

The article notes that plans are in the works to use a much larger sample of 20,000 supernovae to test this result. I expect it to confirm it. The author also suggests that perhaps Λ is variable and decreasing. My conclusion is that dark energy does not exist at all. Gravity has free reign in the Universe, and is gradually slowing down the expansion that began with the Big Bang (or perhaps Inflation if that actually occurred).

That's my take. No Dark Energy. Not now, not ever.

Artificial aliens?

 kw: book reviews, nonfiction, science, biology, physics, cosmology, genetics, first contact

To put Sara Imari Walker's last question first, will first contact with a true alien occur in a laboratory? Dr. Walker's book Life as No One Knows It: The Physics of Life's Emergence is a heady brew of ideas. She has a wonderful kind of mind that looks at things from angles others would never imagine existed, and she has managed to find a number of kindred souls with a similar talent.

Dr. Walker and her colleagues propose Assembly Theory, a new view of evolution in which technology has become an agent of evolutionary change, and "selection" takes on a meaning that would mightily bemuse Darwin. Her explanations make sense. I don't yet understand enough about assembly theory to attempt an explanation. I must content myself with a few bullet points gleaned from the third chapter ("Life is what?"; intended to be pronounced with a distinct upward lilt, as, "Life is WHAT??"). These items do not describe life, but rather objects. Objects as the new theory envisions them:

• Objects are finite and distinguishable
• Objects are breakable (I would have said, "can be disassembled")
• Objects exist more than once
• Objects are lineages
• Objects form via selection

Some objects are living things. Some are not. A wooden table of the kind I built long ago to hold my mouse pad next to my desk is an example. I constructed it using nine pieces of wood, eight large wood screws, 24 small nails, and some glue. The top is plywood, which itself was fabricated by someone else before I bought it from a lumberyard and cut it to size. We can inventory the statements. 

• My little mouse-pad table is finite (less than a meter tall) and is distinct from other items of furniture in this room, some purchased (and thus built by someone else) and others built here, by me.
• It can be taken apart, by removing the fasteners and breaking the glue joints (no doubt tearing wood in the process). I don't plan to do so.
• I have made other similar tables, which I suppose qualifies at "exists more than once." Worldwide, there are many tables of many designs, but all related in general shape and function.
• Is it a lineage? The idea of "table", generalized from "supporting platform" is certainly a lineage, going back to the first table or table-like platform built by a human or prehuman creature.
• "Selection" in such a case means that the I selected to make a table rather than a cantilevered shelf hung off my desk, or other possible means of supporting my mouse pad.

Consider a screwdriver. The author writes, "An evolutionary chain of objects is necessary to assemble screwdrivers into existence." In other words, the forebears of screwdrivers include machine shops, mining and metals productions facilities, and creatures like us to think them up. In the case of living things, the "lineage" of everything alive today goes back about 3.9 billion years. All known life comes from life. What came before?

This is the crux of the matter for assembly theory. The theorists use these concepts to imagine life as we don't know it, life as no one knows it.

Side question: Can objects be produced by other objects that are not living? They can, which is apparently where all nonliving and never-previously-living things arose. For example, a planet such as Earth was assembled from dust, rocks, etc., under the influence of gravity and electromagnetism and sundry other possible forces. Also, natural, nonliving actions produce raindrops and snowflakes in clouds, sand and gravel from rocks, and so forth. 

However, the production of objects by nonliving processes yields objects with very few unique parts. Living objects tend to be much more complex, as do many of their products. Thus this conjecture, stated at least a couple of times in the book, "Life is the only thing in the universe that can make objects with many unique parts." The author notes that many kinds of minerals don't form in the absence of life. I recall taking a class in minerology, in which the professor stated, "There are about 1,000 mineral species known in the earliest rocks, before there was much life on Earth. There are now more than 4,000 minerals, and most of them can only form because there is life on Earth." Today the number of catalogued minerals is almost 7,000, and that may grow to more than 10,000 as busy geologists keep finding new stuff.

This principle yields the basis of the author's "assembly index", a measure of the minimum number of steps needed to produce an object. This gets us away from looking for life that is too chemically similar to "Earthlings" (from microbes and viruses to whales and forests, with us in the mid-range). If the assembly index of numerous objects collected on an exoplanet is large enough, we could conclude that life most likely produced them. The critical number is, according to the author, fifteen.

Frankly, I don't know how assembly index is calculated. I read that the assembly index of the molecule ATP is fifteen. This molecule has 47 atoms. Perhaps the calculation allows the synthesis to begin with smaller molecules that natural processes have already produced: water, carbon dioxide, ammonia, phosphorus oxide, and perhaps even small hydrocarbons such as ethane (ethane can result from abiotic, or nonliving, processes, but in the presence of a living biosphere we never observe it).

Therefore, the number 15 seems to be a good "filter" to discern objects produced by life.

A second prong in the approach by proponents of assembly theory is the development of a "chemputer", a semi-automated way to sort of "3d print" molecules, designed to have certain properties, in an attempt to produce a chemical system that takes on the attributes of life: reproduction, ingestion of supplies, elimination of wastes, relationships (very broadly construed), for example. Were such an effort to succeed, using large numbers of chemputers to explore the "assembly space" of small-to-medium sized molecules, there might indeed be alien life produced in the laboratory. It would be as alien as anything we might find on a planet far away, perhaps even more so. 

The key to grasping assembly theory is the claim that all things life can build are historically contingent. We can see this in the visible relatedness between the wide range of animals known as "tetrapods". They all have four limbs. The mythical flying horse Pegasus cannot evolve from a horse, because to do so would require adding two new limbs (to become wings) to a body that already works well with four limbs. The intermediate steps required don't make sense (and let's ignore the physics of wings long enough to support a half-ton animal). In fact, mammalian hexapods in general aren't likely to arise, because the competition from extremely well-adapted tetrapods has already pretty much filled all available ecological niches for critters bigger than a cockroach…on land, at least.

Historical contingency is a key concept. Finger-and-toenails didn't evolve all at once. They descended from claws. Claws came from something else. All living things trace back to a single-celled creature called LUCA, the Last Universal Common Ancestor. LUCA may not be the first cell. At one time other living things could have existed alongside LUCA that may have had quite different chemistry and cellular mechanisms. But only LUCA has descendants: us, and every living thing in the biosphere of Earth.

Our chain of imagined forebears stops with LUCA. Our knowledge is further constrained, because it is extremely unlikely that any creature now living is descended without change from LUCA. When I say "extremely unlikely", that middle E needs to be drawn out, "Extreeeeeeeeeeeemely!" Meaning, utterly impossible unless the universe is truly infinite, with an infinite number, not just of planets, but of biospheres. Even if we somehow track back the chain of biochemical contingency to "show" us a robust model of LUCA, the chain stops there.

I like the idea of the chemputer. But I don't hold out much hope. The assembly space of "small molecules" is too big. For example, if we "restrict" ourselves to the twenty most common elements, all of which are found in known life, and all of which are likely to be in any possible kind of life, and further, we call a molecule "small" if it has fifty or fewer atoms (just a tad bigger than ATP), the number of possible chemical species (most of them quite chemically unstable) is close to ten-to-the-power-of-65. A 66-digit integer. How large is that number? The number of stars in the visible universe is thought to be a 22- or 23-digit number. Could the average number of planets be as great as ten? Even if that were so, the number of planets in all the galaxies in the visible universe is no larger than the largest 24-digit number. It is hard to think about 66-digit numbers in any useful way. 

Dr. Walker dreams of being the researcher in the cartoon above, "meeting" the first true alien in the laboratory. I hope her dream comes true. But I think it more likely that we'll come across something, somewhere, soon, that proves life as we don't yet know it does in fact exist.

Universal FAQ

 kw: book reviews, nonfiction, science, cosmology, ultimate questions, humor

I was thinking of titling this post "The FAQ to end all FAQ's", but realized that's too much hubris. I like answer lists (and many kinds of lists). Frequently Asked Questions About the Universe, by Jorge Cham and Daniel Whiteson, serves up question-answering essays on twenty big questions. One could say they have really put the universe under a microscope.

Both authors are PhD scientists, and Jorge Cham is also a cartoonist (see Piled Higher and Deeper – this links to the archive; it ran 20 years). Nearly every page of the book has at least one of his little illustrations. Here are a couple of them, picked at random.

The first question: "Why Can't I Travel Back in Time?" The answer isn't simple, though the authors simplify things as much as they can, so the essay takes up about 14 pages. It ends with a technical dichotomy, that time reversal doesn't violate any laws of physics, but getting the engineering expertise to carry it off is far, far from us. Put simply, you can't unmake an omelette, a practical expression of the term "entropy".

Another question that is currently on the minds of many is "How Long Will Humanity Survive?" Here the dichotomy is between doomsayers and Pollyanna's, which make up only a few percent of humanity, but between them they make nearly all the noise. Things that might doom us include asteroids, "gray goo" (runaway nanotech), and too much CO₂. I have to quibble about the comparison of Earth and Venus in this chapter. The surface temperature of Venus is 800°+ F, and the description goes into a runaway greenhouse as the oceans boiled off. However, Venus is presently water-free. It is the CO₂ that is keeping it that hot. Furthermore, the amount of CO₂ in its atmosphere is about 2 million times the amount in Earth's atmosphere. Clearly, the relationship between the amount of CO₂ and the temperature isn't a simple straight line, otherwise Venus would be hotter than the hottest known star (I plan to go into this principle in a future post...how far in the future is not settled). Also, something that isn't mentioned, probably because the authors are into robotics and physics, and not biology, is that few species remain unchanged for more than one or two million years. To speculate about what humans might be doing a billion years from now, by which time the Sun will be 40% hotter and our oceans will have long since boiled off, has to include being somewhere else.

By the way, the chapter "Can We Turn Mars into Earth?" mentions that Mars is so cold because there's no greenhouse effect, because its atmosphere is less than 1/100th as dense as Earth's. But I realized that nearly all of that is CO₂. Earth's atmosphere is only 0.04% CO₂. So Mars has 25 times as much greenhouse gas per square meter! What gives? Water, that's what. Nearly all the greenhouse effect on Earth is from water vapor, 60° worth. The CO₂ just adds another couple of degrees. And the amount of water vapor in Earth's atmosphere is 1-2% (up to 3% in the Tropics). It would take a lot of water to bring the temperature of Mars up by 60°, and it would still be colder than winter in Montana. The water would immediately freeze back out, so terraforming Mars is rather out of the question.

Being somewhere else is taken up in "What's Stopping Us From Traveling to the Stars?" and a later chapter, "Can We Build a Warp Drive?" We have about 200 million years to figure these out...at most. Basic parameters of what the Sun will do to us, if nothing else really bad happens (like a Moon-size asteroid smacking into Central Park):

• A quarter to half a billion years from now, whether CO₂ is under control or not, it's too hot for terrestrial animals and plants to live.
• A billion years from now, the oceans have finished boiling away, so marine life is also caput.
• 4 billion years along, the Sun expands into a red giant. It may or may not reach Earth, but with at least 30% of the sky toasting at a temperature of 5,000°F or more, the planet will be liquified.

There are more stages to the Sun's evolution into a white dwarf, but that's enough to ruin the entire solar system. If we move to Enceladus, under the ice, by that time, the oceans of Enceladus will also boil off. So, how do we "go elsewhere"? Slowly, by galactic standards. If we want to push a 190,000 ton (170,000 metric Tons) spaceship to half the speed of light, its kinetic energy becomes immense. BTW, that is the supposed weight of the Enterprise in Star Trek, which is powered by antimatter-matter annihilation. Each kg of the spaceship has a kinetic energy of 3x10¹⁶ Joules, which you could obtain by annihilating 1/6 of a kg of matter with 1/6 of a kg of antimatter…if the conversion of energy to motion is 100% efficient. To go more like 90% the speed of light more than doubles the energy required. Basically, to send a fleet of spaceships "nearly as fast as light" (NAFAL) would require annihilating the entire mass of, say, Jupiter. And then you have to slow them down when they reach their destination. Thus the question about warp drives. Again, we find the answer is dichotomous: possible in two or three ways according to the laws of physics, but an engineering "challenge."

The last chapter is "Why Do We Ask Questions?" I'm a simpleton; my answer is, "Because we don't know everything yet, and we are driven to do so," some of us, at least. The authors get more philosophical than that. In the end they point out that we can answer questions of What and How, usually, but never Why. It occurs to me that when a little kid asks, "Why is the sky blue?" we should answer, "I can tell you how" (well, I can, but perhaps not every Dad can), and then proceed to do so, at the kid's level.

OK, for those who aren't sure how the sky is blue, it's because light scatters off molecules, but it scatters better and better the closer the size of the molecules are to the wavelength of the light. Molecules are a lot smaller than the wavelength of visible light, so the shorter wavelengths, which look blue, get scattered more. So sunlight is scattered, and more blue scatters than other colors. Bonus point: The light that comes straight to us from the Sun is thus a bit more yellow, because some of the blue has been scattered away. It's the reason the Sun is thought of as a yellow star, when actually, if you get above the atmosphere, it is pure white.

So this is a very enjoyable book, with a great lot of humor in the answers (one author likes banana smoothies and the other likes peach smoothies, so there are digs back and forth, for example). We get multiple answers to a bunch of interesting questions. We may not like all the answers (I'd really like to be able to get to another star system, for example), but we get a better understanding of what's involved in real answers.

Creeping toward the Matrix

 kw: book reviews, nonfiction, cosmology, simulation, modeling

I was for several years, in my career of writing scientific software, the leader of a "Modeling and Simulation Group". One of our products had three sections, simulating first the geochemistry of crude oil generation from organic matter in deep rocks (up to a few kilometers), then the upward migration of the petroleum liquids through porous rocks, and finally their entrapment against nonporous, or less porous, rock layers to form oil and gas reservoirs.

I was sent to a few exploration offices to show off the software. In one instance, after the geologist set up access to a set of grids based on seismic data, I ran the software, which displayed the progress through time of oil and natural gas collecting under the trapping layer some half-kilometer beneath our feet. At the end of the run, he pointed to one green blob on the map, saying, "This is X field," and to another, "This is Y field." Then he pointed to a third one between them, asking, "But what is that?" I answered, "That could represent a lot of money." As it happened, the company had decided to sell that property to another company. That oil company made the money! But the software found the oil before the property was drilled. Later that year I spoke about the experience at a Research Review. My talk was titled, "Finding Oil in a Computer."

It was with great relish that I read The Universe in a Box: Simulations and the Quest to Code the Cosmos by Andrew Pontzen. If you buy the book feel free to download this image to print a bookplate; it's 1024x1024 px. Use Upscayl or something similar if you want it rendered at higher resolution. I produced it using Playground AI; the only prompt was "Cosmology". I tinkered with Samplers and other parameters, looking for something else. Getting this image was a side benefit.

The author could have delved deeply into sundry technical issues—there are many! Instead, he has skirted these, providing just a taste of some of them, in favor of the philosophy and motivations for making computer simulations of natural phenomena.

The terms "simulation" and "modeling" have overlapping meanings. In principle, a Model is the framework and the sets of parameters that define the physical structure and the physics rules to be followed, while a Simulation is the operation of the Model over a chosen span of time, producing a series of output data sets that describe the expected physical state of the modeled "thing" at one or more points in time, whether past or future. Note that a simulation can be done on equipment other than a computer. One story of the book is about a galaxy simulation done with light bulbs and photocells and a glorious tangle of wires.

Weather forecasting is one very visible result of computer simulation, seen daily (or hourly) on newscasts and in the various weather apps on our devices. There are a couple of dozen important models used by weather agencies the world over. One expression of these is the Spaghetti Plot of a hurricane's forecasted track, as produced by several models. The models differ in the importance they place on various aspects of the modeled system, including whether it represents the whole Earth or a hemisphere, or a couple of continents.

All weather models are based on a global General Circulation Model, in which the atmosphere and the land and sea surfaces in contact with it (and sometimes a surface layer of the ocean) are divided up into roughly ¼ to ½ million quasi-rectangular portions. Half a million to a million "cells" is about the most that modern supercomputers can handle. In general, spatial resolution is likely to be as large as 200x200 km! The Earth's surface area is about 127 million km², and the models have between 20 and 40 vertical layers (at present). A 40-layer model would have more than five billion cells of 1x1x0.5 km, so to get the count below one million requires using cells with an area of more than 5,000 km², which is 71x71x0.5 km, and most models are set up for grid squares of about 100x100 to 200x200 (and half a km thick). The physics rules, primarily those relating to pressure and temperature relationships, are applied at the boundaries between grid cells.

To get a "future radar rain" map with finer detail requires using "sub grid" rules, and partial simulations over short times and restricted areas, a subject that Dr. Pontzen discusses. Compared to Earth, the Universe is immensely more complex, and the problems of building an appropriate model and running simulations that may span billions of years, but don't take billions of years of computer time, are truly tough!

For example, consider a galaxy. On the scale of the while Universe, galaxies are tiny and far apart.

This is the Hubble Ultra-Deep Field image, which shows about 10,000 galaxies (only one star is in the field, the really bright point with spikes caused by diffraction). The area of this image on the sky is 0.038°x0.038°, or about 0.15% of a square degree. It is about the size of the smallest thing you can see with your eye.

To a very rough estimate, although galaxies vary a lot in size, the really big ones seen here are a lot closer than the really small ones. The six or eight largest ones in this image are seen to be far from one another. If their intrinsic size is a little smaller than the size of "our" galaxy, the Milky Way, they are about 50,000 light-years across, and the average spacing between them is one or two million light-years. But larger-scale observations reveal that nearly all galaxies are strung out along strands in an immense web, with voids that contain no galaxies at all but span hundreds of millions of light-years.

One problem of computational cosmology that the author dwells on is that it is really hard to produce a cosmological simulation that doesn't result in a much larger number of galaxies. According to most models, this image "should" contain so many galaxies that there would be very little black space seen between them! A conundrum of computational cosmology is, "Why is space so empty?" I suppose all I can say is, "Stay tuned." I await a follow-on book on the subject as more is learned!

The smallness of galaxies compared to the intergalactic web, and the incredible smallness of the stars that make up the galaxies, and even more amazing smallness of planets, moons, and everything "solid" that we are familiar with, produce a huge problem of "stiffness" in any kind of simulation that seeks to span the entire range of sizes. Mathematical equations that drive simulations are called differential equations (DE's). By their nature, DE's produce one or more side effects, which mathematicians deal with using various schemes, and such schemes are embodied in the computer codes that run simulations. However, these schemes are seldom perfect, and runaway effects can swamp the simulation if it is run outside of a carefully chosen range. If a simple simulation includes two processes, and one runs 100 times as fast as the other, it is necessary to cater to the faster process or the results blow up. This time-scale contrast is called "stiffness". One must use time steps shorter than the time scale of the faster process, even though during such short steps, the slower process doesn't do much. Now consider what happens if the time scale varies over a range, not of 100 to one, but millions to one, with numerous processes all across the time spectrum. Not only that, if 99% of the volume is empty, and the remaining 1% has similar ranges of "spatial stiffness", the problem compounds dramatically. A lot of the book deals with such things, but using more accessible language.

The author also discusses dark matter and dark energy. Dark matter is probably quite real. It is needed to keep the stars in their orbits about their galactic centers, because the visible mass is not sufficient. This is not a small effect: the "extra gravity" needed is about five times what would be exerted by all the visible stuff we see. The current theory is that 70+% of the matter in the Universe isn't affected by electromagnetic radiation, so we can't see it. Scientists are working hard to find out what kind of stuff could be so invisible but so heavy.

Side question for the author or other cosmologists who may come across this review: Do black holes consume dark matter that encounters them?

Anyway, dark matter and the properties we infer for it must be included in cosmological models for their simulations to make any sense.

Dark energy is the term applied to an odd effect seen when very distant supernovae are studied. They seem too dim. Their distances are determined from the redshift calculated from their spectrum and, if possible, the redshift of their host galaxies. There are distinct "lines" in the spectrum of any astronomical body that allow us to determine its composition and the speed with which it is moving, radially at least. The Hubble Constant (named for Edwin Hubble, not the space telescope which was also named for him) characterizes the velocity-distance relationship.

Determining the actual brightness of a distant object is not straightforward. Dust and gas in and between galaxies absorbs some light. The relationship between distance and "intergalactic extinction" ("extinction" to an astronomer means light is being absorbed) is thought to be well understood. When such calculations are applied to certain supernovae, a discrepancy is found between how bright they are and how bright they "should" be. The farther away they are, the greater the discrepancy. This indicates that they might be farther away than their redshift would indicate; the "Hubble Constant" would then be not so constant! This implies that cosmological expansion is speeding up, not slowing down as we would expect.

I personally look at two matters that need more study before I will seriously consider that dark energy is real. 

Firstly, it is not mentioned in the book that the kind of supernovae one must study to discern dark energy are Type 1a. They are produced by a special mechanism. Most supernovae result when a large star (8-20x the mass of the Sun) runs out of fuel and its core collapses. About a quarter of supernovae result from a white dwarf star being loaded up with matter from a nearby red giant that is shedding mass. The maximum mass of a white dwarf is 1.44 solar masses; at this point it collapses and erupts as a Type 1a supernova. Because of these mechanics, Type 1a supernovae have very similar maximum brightness, making them a "standard candle". However, I have looked in the literature for an indication that the composition of the white dwarf and/or its red giant companion might affect the brightness of a Type 1a supernova. In the very early Universe there was hardly anything except hydrogen and helium. The first supernovae were all Type 2, when large stars, that had been forging hydrogen into more helium, and then forging helium into heavier elements, up to iron, exploded. Over time, the abundance of heavier elements in the Universe increased. To astronomers, all elements from lithium on up are called "metals" for convenience. Metallicity is a measure of the percent of "metals" in a star or galaxy. Our Sun's metallicity, at its visible surface, is 1.3%. Its age is 4.5 billion years, and it has not undergone fusion reactions that could change its metallicity, but an unknown amount of interstellar "stuff" has fallen into it; this is probably quite small in proportion to its total mass. Thus, a little over 1% probably represents the metallicity of this part of the Universe 4.5 billion years ago. The metallicity of the stars in a galaxy varies with distance from the center also, but not over a huge range. The bigger difference is seen between "Population I" stars, that are younger and have higher metallicity, and "Population II" stars, that are older and have something more like the metallicity of the Milky Way when it first formed, perhaps 10-12 billion years ago. This is roughly 1/10 or less of our Sun's metallicity, or less than 0.1%.

Very early galaxies and their stars had very small metallicities, ranging from 0.001% down to nearly zero. Therefore, so do the earliest Type 1a supernovae. A question I have not seen answered:

We know that white dwarf stars are composed primarily of carbon and oxygen. They are known to have some metals, because they are diagnosed by lines of silicon. BUT: Is the peak brightness of a Type 1a supernova significantly affected by the proportion of elements heavier than oxygen?

Secondly, is it possible that dark matter interacts very slightly with electromagnetic radiation? Simply put, the Universe's age is considered to be 13.8 billion years. At an age of 1.38 billion years, its "size" was 1/10 of its present "size", and the concentration of both ordinary matter and dark matter would have been, on average, 1,000 times greater. Somewhere along midway, say at an age of 4.4 billion years (the square root of 1/10 times 13.8), the "size" would have been about 0.32 of the current size, and the concentration of both ordinary matter and dark matter would have been about 32 times greater than at present. If there is even a slight interaction, "dark matter luminous extinction" could be a genuine effect, yet we would be very hard put to determine whether the dark matter that must be all around us has a measurable influence on light.

For the time being I consider that it is much, much more likely that "dark energy" is a phantom, and will eventually be found not to exist.

That is a significant digression from the discussion of the book. The author discusses the utility of cosmological simulations of various kinds. They aren't just a way for us to have a "pocket Universe" to play with, but they help us understand what might have occurred at various stages of the evolution of the Universe, or of groups of galaxies, or of stars and star clusters. Unlike weather forecasting, Universe simulation focuses on retro-casting, trying to reproduce how things worked out over some interesting span of past time, whether measured in centuries, millennia, or billions of years. To know where we really are we need to know what came before. Looking at distant things, as the Ultra Deep Field does, lets us look back in time. Things were different way back then, and computational cosmology is a powerful tool to help us understand it all. We've made a bit of a start; we're just getting going!

The author also asks whether it is plausible that we are living in an über-simulation inside some super-Matrix run by super-beings. He gets into that because he gets asked about it frequently. I'll mention one thing that he does not: one human brain has complexity of the same scale as a good chunk of the non-human Universe, and all of us together are more complex than the whole rest of the Universe (unless there are lots and lots of alien species!). In the Cosmos series by Carl Sagan, decades ago, it was stated that there are probably 100 billion galaxies in the observable Universe, with an average population of 100 billion stars each. The number of galaxies is probably more like a trillion. The number of stars is thus a number with 23 digits.

What's in a brain? The cortex has 16 billion neurons and the cerebellum has 70 billion. Each neuron has about 5,000 connections to other neurons. The 100 billion smaller "glial cells" also contact numerous neurons and large numbers of each other. The number of connections is thus a number with 15 digits. The number of humans is about 8 billion, a 10-digit number. So the "total human connectome" is about 100 times as great as the number of stars in the Universe. Another number of similar size is the number of molecules in 18 grams of water (a quantity known to chemists as a "mole"), which is a 24-digit number starting with the digit 6. If one could somehow use each water molecule in a tablespoon of water as a computer bit, it would take ten tablespoons to have enough molecules to devote just one "bit" to each connection in the sum total of all human brains. That's the bare bones of what's needed to produce The Matrix. And that's just one intelligent species on one planet. I'd say that if Moore's Law gallops along unimpeded long enough (but it won't, it's already faltering), it would take hundreds of doublings, or at least 1,000 years, for a big enough, fast enough computer to be produced (by Someone) that could simulate the entire Universe in real time. Of course, by making the computer's time steps for each second of real time actually take, say, a century, a much smaller computing system could to the work. How could we tell? Dr. Pontzen doesn't know, and neither do I.

A very enjoyable book. You don't have to be a computer geek like me to understand it.

Star stuff 'R' us

 kw: book reviews, nonfiction, science, chemistry, cosmology, biology, philosophy

Let's take powers of ten, in time, looking back to the beginning:

• 13.8 billion years ago, everything began. Starting with the "Big Bang", or whatever it was, in some tiny fraction of a second all energy and matter appeared and sorted themselves out, becoming something like 10⁸⁰ "elementary" particles; either protons, neutrons, and electrons, or electrons plus quarks. Initially something like a thousand times that many particles of both "matter" and "antimatter" formed, and some tiny imbalance resulted in all the matter presently in existence. At least the visible or potentially visible stuff. This is accompanied by a much greater number of bosons such as photons.
• 1.38 billion years ago, we find that our Galaxy has appeared (10 billion years earlier) and then our solar system (just over 3 billion years earlier), and then once Earth settled down, life that either began as bacteria or soon became bacterial and archaean (AKA prokaryotes); and finally eukaryotic cells (larger cells with a nucleus) had arisen, such that almost anything big enough for us to see was composed of them (though they were, as we are, vastly outnumbered by the tinier prokaryotes).
• 138 million years ago it's already getting late in the Age of Dinosaurs: the familiar Tyrannosaurs plus Triceratops, Iguanodon, and sauropods such as Argentinosaurus stalked the land, pterosaurs flew hither and yon, and the seas were filled with ammonites (like an octopus with a big, coiled shell), mosasaurs and plesiosaurs. Flowering plants had recently evolved and were spreading everywhere.
• 13.8 million years ago it's the middle of the Miocene; mountain building is going on, and the continents have formed something similar to their modern configuration. A minor branch of mammals, the primates, has produced a few species larger than a rat, up to the size of a squirrel monkey.
• 1.38 million years ago, it's the middle Pleistocene. The ice ages began a million years earlier, and the Gorilla-Chimp-Hominin divide occurred in the range of 6-9 million years earlier. Homo erectus appeared 2 million years ago and by 1.38 million, was speciating into a few hominid species, although Neanderthals had yet to appear.
• 138,000 years ago, Neanderthals are all over Europe and Asia, while all archaic Homo sapiens are still in Africa.
• 13,800 years ago: It's been about 20,000 years since Neanderthals became extinct (or assimilated with H. sapiens). It's the middle of the Late Glacial Interstadial, a warm period that lasted about 1,800 years, followed by the colder Younger Dryas era. Humans are already on every continent except Antarctica (and maybe there also at times!). 
• 1,380 years ago: As I write this, that would be 643 AD (or CE), almost 160 years before Charlemagne unified the Holy Roman Empire. Anything resembling "science" is a millennium in the future.
• 138 years ago, in 1843, Queen Victoria had recently begun her 63-year reign; Louis Pasteur began to teach; the first Opium War had just ended in China; the first immigrant from Japan arrived in the United States. The germ theory of disease is still 50 years in the future.

That's a good place to stop the timeline, because 13.8 years ago almost anyone who can read this was alive and can remember numerous world events. It's also a useful backdrop to the much different history developed in What's Gotten Into You: The Story of Your Body's Atoms, from the Big Bang Through Last Night's Dinner, by Dan Levitt. 

Note that there is no question mark in the title; it is not a question but a statement, an affirmation. Wind back to 13.8 billion years ago, and the first atoms were produced soon after, very soon. They are nearly all still with us. If we pull back to look at the Universe as a whole, nearly 75% by mass is hydrogen and 25% is helium. About 1% is everything else, all the other 90-odd elements that have been formed since stars began to shine. Subtract that 1%, and you have the composition of the Universe 13.7 (or maybe 13.6) billion years ago.

The core of an atom is its nucleus. For hydrogen, it's almost always a single proton. Two other forms (isotopes) of hydrogen have one and two added neutrons, respectively. Helium almost always has two protons and two neutrons; a rare isotope of helium has one neutron. Nearly all the atoms of hydrogen and helium that were produced in the extremely early universe are still in existence. About 1% of them have been compounded (fused) into other atoms, of almost 100 elements and several hundred isotopes. The book tells about the step-by-step discovery of how the stars "cooked" the other elements. Without that cooking, there would be no carbon, oxygen, nitrogen, and other elements that it takes to make Earth and the other planets, and also all living things including us. Note that the atoms in the stars, in planets, in us, probably don't have their "original" electrons. Those can move from atom to atom, and chemistry is what we call the movements of electrons.

So, what has gotten into you, and into me? Primarily water (60+% of our bodies are water), composed of hydrogen from the early universe and oxygen cooked up in a large star that later blew up as a supernova. In whatever way elements were produced in stars, the way they got back into the universe to become planets and people was by supernova explosions…well, some amount of lighter elements got out of stars in a more gentle way as they shed their outer layers in the late stages of being a red giant. But anything heavier than iron had to come from a supernova, created during the eruption, and most elements heavier than oxygen also were expelled during supernova eruptions.

Chapters in the book detail the discoveries of organic chemicals, and RNA and DNA, and other molecules of life, a story that is still unfolding. The story of all the parts that have to work together for a cell to function is one of the most complex tales there is. Every cell in your body is as complex as Chicago, but operates millions of times faster. Even bacterial cells are only "simpler" by comparison: one cell of the "simple" bacterium E. coli contains 20,000 "factories" called ribosomes, that produce proteins under the direction of bits of RNA copied from the DNA "library". And the same cell contains thousands of other active bits called organelles with sundry functions. A typical cell in our body is 15,000 times as large (in volume; 25x the diameter) as an E. coli cell, and contains dozens of organelles that the bacterium doesn't have (or need). All are made from either primordial hydrogen or from the forty or so other elements, ejected by supernovae, which were brought together on this planet to become living things. THAT is what has gotten into us.

Reading this book was joyful. I hope you read it and will agree.

Beyond solipsism

 kw: book reviews, nonfiction, science, cosmology, theories, biocentrism

Near the end of the book I reviewed last week (here), the possibility that the observer creates the universe was discussed. The next book I read, The Grand Biocentric Design: How Life Creates Reality, by Robert Lanza, MD and Matej Pavšič, PhD, with Bob Berman, presents the theory in detail.

Quite a number of physicists have said things like, "We are the opening through which the universe examines itself." While this is typically uttered as a self-referential metaphor, some, including Drs Lanza and Pavšič, take it more literally, and in this case in particular, attempt to offer proof.

The authors take their time building up to the real meaning of Biocentrism. Things seem to proceed by easy stages, then in mid-book, they get more explicit. On page 145 I find this: "There remains a certain fluidity—a certain degree of uncertainty—to anything that is not actually observed." They go on to explain that whatever has not been observed, such as most of the Earth beneath our feet, exists in "a range of possible states, and it's not until observed that they take on real properties."

At that point, I thought, "As a kid I hunted fossils in a limestone stream bank near our house. Were those fossils 'not there' until I went looking for them?" Later on the authors write of "the consensus world we're aware of during the day" (p 183), discussing the seeming unreality of many dreams, supposedly not constrained by that "consensus world." So now, the world is whatever we all agree it is? Wow! Soon (p 186) I read, "By observing your world, you keep collapsing probability waves, and thus you effortlessly create an ever-more detailed world that includes reinforcing memories," and a few sentences later, with no irony at all: "It is amazing how far we've come by following the implications of quantum mechanics in an unbiased way." At this point, it is clear that their view is so biased there is no meeting of minds with realists like me. They go on in the following chapter to posit this (my paraphrase): All the past, all 14 billion years of it, is brought into existence by observations in the present and near-present.

They have the gall to claim that this is not solipsism. By a strict definition ("The view or theory that the self is all that is known to exist"), they are right. But they turn it on its head, making the universe not just "in our head", but created ex nihilo because of our observations. All of this supposition (and that is all it is) is based on a few experiments that seem to prove that an observation taken now can affect something that happened in the past. Here I must dwell a little.

The starting point for all this is the Copenhagen Interpretation, propounded and promoted by Neils Bohr. Werner Heisenberg had determined the limits of accuracy of measurement, particularly as applied to quanta (elementary particles such as electrons and force-carrier particles such as the photons of light). Thousands, perhaps millions, of versions of the two-slit experiment have made this clear. If one allows a beam of light or of low-energy electrons (electrons with an energy more than about 10 eV have a wavelength too short to be useful here) to pass through a pair of narrow slits, separated by a small distance, ideally between 10x and 100x the wavelength, a suitable detector or screen will show an interference pattern. This experiment shows that not just light but also electrons (and more recently buckyballs and even larger molecules) express a wave nature. Much is made of "collapsing the wave" to get the particle that is finally detected when it strikes the detector.

(An aside: photons act as waves as they enter your eye, being diffracted by the pupil and refracted by the lens, something particles can't do, then within 18-19 millimeters, express particle behavior when they deposit their energy onto the opsin proteins in the retina so they can be "seen".)

The fun comes when we get to Bohr's expression, "Each particle must pass through both slits and interfere with itself." We don't know that. No experiment yet done has shown that, because any attempt to discern where a photon or electron or whatever "is going" between the emitter and the detector, messes up the pattern and there is no interference. Many physicists, including me, would say that the measurement cannot discern where or how fast the particle is moving without disturbing it so much that the measurement's accuracy is limited. In this case, it is limited such that the uncertainty of position is large compared to the separation between the slits.  Bohr claimed that the particle was really "fuzzed out" to be bigger than that, and "really goes through both slits". Baldly put, that is the Copenhagen Interpretation. For photons, maybe; for electrons, I am not so sure. For buckyballs, the idea is ludicrous. I think Bohr was wrong.

Consider this: all matter has an electronic nature, and is always accompanied by electromagnetic (EM) fields. The slits are holes in a material. They disturb the symmetry of the EM field of the otherwise smooth material membrane or plate (frequently a metallic foil or thin ceramic sheet). The moving particle is affected by the EM field. The disturbed EM field in the vicinity of two slits is different from that near a single slit. I haven't seen any attempting to calculate what effect that EM field may have on the moving particle, all by itself.

Do you know what is the Airy disc of a star image in a telescope's focal plane? It is the expression of the diffraction of the telescope's diameter. The wider the mirror or lens, the smaller the Airy disc. That is why one needs a really wide telescope to see small or distant things. Resolution (angular accuracy) is inversely proportional to the diameter of the aperture. That's why the new Webb telescope's mirror is 21 feet (6.5m) in diameter. Big area to gather a lot of light, but even more importantly, big diameter so see tiny things far away. The Airy disc seems to indicate that the incoming photons can sense how big the mirror is. Taken to an extreme, the phenomenon of diffraction indicates that the path a photon takes is affected by the presence of everything in the universe. If you don't mind doing the calculations to a few thousand decimals, you could probably calculate how the shape of the Airy disc of any particular telescope would be modified by the presence of the Moon or any of the other planets, in the general direction the telescope is pointed. That's probably true.

Some physicists get around the Copenhagen view by considering "observer" to be anything that is "close enough" to affect a particular particle. Bohr claimed the observer had to be "intelligent". So what? (Neils, Baby, sayin' it don't make it so.) It is a claim, and a claim only. A huge superstructure of physics calculations has been built upon it, including the nonsense in this book.

I took the trouble to closely read the two articles at the end of the book, in its Appendices. They contain a ton of calculations. It was hard because it's been fifty years since I last worked with Hamiltonians (a type of obtuse mathematical expression, needed to do anything useful with Schrödinger's equation). The articles are intended to prove that an intelligent observer is needed to bring the universe into being. The authors truly believe that, before there was a living mind to think about it, the entire universe, and all its billions of years of history, existed as a great lot of potentiality, a universal wave function (a really complex version of Schrödinger's Equation, with a trillion trillion trillion trillion trillion trillion trillion—I think that's enough trillions—partial differential equations). The first eye with a brain behind it "collapsed the wave function" so that at least a few trillion trillions of particles, making up that animal or person, and its surroundings, could exist in a more concrete form. (By the way, one gram of matter consists of about 1.2 trillion trillion particles).

I eventually saw a pattern in all the math. A few equations would be presented, then there would be a statement such as, "Equation 12a is similar to the Jim-Dandy formula, when expressed thus", and a rather similar equation would follow, numbered 13. Then a little later, a reference to "the formalization of Glock and Winchester", turning Equation 24 into Equation 25. And so forth and so on. There were several such shifts of perspective. I consider each to be a potential disconnect in the logic. I didn't dig deeply enough to discern which ones are true disconnects…but I am sure there are several!

Here is my analogy: A friend asked her neighbor for the recipe for her wonderful German chocolate cake. It required many ingredients, and numerous steps. Later she invited the friend over to taste it. The new cake tasted very good, but the neighbor said, "It's not quite the same, is it?" "Oh, no!" my friend said, "Of course, I substituted <brand D> chocolate for <brand A>, and I boiled some milk and added a little brown sugar in place of the evaporated milk, but it's really the same cake." The neighbor was diplomatic and didn't complain further. We all could tell, it wasn't the same. When you get down to it, with enough substitutions, you can start with the recipe for cherry pie and wind up with pineapple upside-down cake.

What we have in this book and the carefully crafted documents it contains is upside-down physics.

Sadly, the godlike powers that lie behind the authors' supposition are useless without volition. If the universe has to be created by us, why did we have to create one so full of frustration? If I create the universe by observing it, why is my wife always late? If you want to be a god, be prepared for theodicy: "if God is good, why is there pain?"

I'll be careful not to use the term "believe" here, because of its religious overtones. Here is my view of the universe. The fossils I found as a child were there millions of years before I was. Could a Trilobite be an "observer" in terms satisfactory to Bohr, or to these authors? Could a coral, or a sponge? The universe existed for at least nine billion years before the Sun and Earth and the rest of the Solar system came into being. They were as real then as they are now. Their existence was not affected, either then or since, by the "observing" animals that arose on Earth about one billion years ago, or by the "observing" humans that arose perhaps a million years ago, or at the very latest, 200,000 years ago. Nor were they affected by supposed aliens that may have arisen five or ten billion years ago.

Every article I have read that describes an experiment on a photon or electron or whatever, being "entangled" with another, and somehow "deciding" to point its spin axis "up" because a scientist forced its entangled partner to point "down", is flawed by circular reasoning. From their creation (emission), the pair of particles had opposed spins, which may have been detected at different times and places, but were there already. Period. Oh, and speaking of time: the authors claim that time is a construct of our perception, and doesn't otherwise exist. It's interesting that so many of the equations in their articles are time-dependent!

I've exhausted my interest in pursuing this matter. I'll read about real stuff in the future.

Errata: 

• On page 39, in a footnote, we read of the size of an atom, "It's 0.0529 nanometer, or about 1/200th of an angstrom in width." There are three errors in this statement:
• A nanometer is 10 angstroms, so the fraction should be 1/2.
• The Bohr radius of neutral Hydrogen is 0.0529 nm; the Bohr radius is the mean distance of the electron from the proton. This isn't just "any atom".
• The word "width" implies diameter, not radius.
• Bonus error (because this should have been specified): every neutral atom has a different radius, and hydrogen is one of the smallest; only atomic oxygen, fluorine and neon are smaller. The radius of a neutral, isolated carbon atom (this rarely occurs!) is 0.067 nm, and that of gold is 0.174 nm. Gold atoms are by no means the largest.
• On page 50 it is stated, "Longitudinal (vertical) waves can pass through liquids and gasses while transverse (sideways) waves require the material to be solid." Remove the parentheses, and this is a correct statement. However, "longitudinal" is not "vertical"; it is a compression-rarefaction wave that varies in the direction of travel, while "vertical" is just transverse on the vertical axis as compared to the horizontal axis.
• On page 128 we read, "…unlike all the other major moons in the solar system—our moon doesn't orbit around its planet's equator." (The point of the paragraph is that the moon's off-equator orbit helps stabilize Earth's axis of rotation.) A more accurate way to state this is that most (not all) other natural satellites orbit nearer their planet's equator, as compared to the Moon. Most of the major satellites' orbits are inclined within a degree of the host planet's equator. However, Triton and Nereid, satellites of Neptune, are inclined 130° (or -50° retrograde) and 27.6°. The inclination of the Moon's orbit is 5.1°. The real issue here is the Moon's large size relative to Earth; 1/80th of the Earth's mass. A tiny satellite, whatever its orbital inclination, would have little effect on the axial direction of Earth.

As the universe darkens

 kw: book reviews, nonfiction, cosmology, dark energy, dark matter

I had one expectation when I saw the title: Fear of a Black Universe: An Outsider's Guide to the Future of Physics by Stephon Alexander. I surmised that it was literal, though metaphor is always possible. As it happens, Dr. Alexander means it both ways. He is black, and in the physics community, that makes him an outsider. Sad to say, institutional racism is more entrenched in academia than it is in most of suburbia, where I dwell.

I will not dwell on the author's reports of prejudice. Being white (or, having no more than about 1/16th African ancestry), I've seen such things from a different perspective than he has. Some aspects of what he is, he has been forced to become. Whether in spite of such handicaps or because of them, he is an excellent scientist (Neil deGrasse Tyson, another black scientist I admire, freely admits he "over-achieved" in reaction to being discriminated against). Suffice it to say, it was clear that the colleagues who denigrated him did so out of fear, thus the book's title. His significant achievements indicate that their fear was well-based, though ill-conceived.

This illustration explains why the universe is becoming darker, tending toward a future of infinite, unending blackness.

According to the cosmology accepted by a great many, something, dubbed "dark energy", is causing the expansion of the universe to accelerate. Some conjecture that at a time between one and 10 billion years in the future, the acceleration will increase rapidly, leading to a "big rip", eventually even dragging atoms apart, leaving nothing material remaining. Others expect something more sedate, but still leading to the "nearest" galaxies being too far away to see, and resulting in the dissolution of galaxies. If living beings remain on any planets in such a universe, there won't be a starry sky. The "sun" will be the only star visible.

Much of the book describes in laymans' terms the observations and hypotheses behind the understanding of "dark matter" (stuff that gravitates but doesn't shine) and "dark energy" (something about space that pushes it apart, ever more rapidly).

Cosmology is a difficult science. If you were to study chemistry, you could do experiments that take place in minutes or hours or days, typically…although I do recall a reaction that required about a month's exposure to the UV light in sunlight. The second term of my Organic Chemistry course, we performed a synthesis that began with the usual "measure carefully, mix thoroughly" stuff, and then we stoppered our flasks and set them on a windowsill until halfway through the term.

There's no such alacrity possible if your subject is the history of the universe. Tons of interesting stuff happened billions of years ago, that doesn't happen now, so astrophysicists have to infer what it was by looking for subtle signals in the light (loosely construed: wavelengths from gamma rays to radio waves) arriving from space. No "experiments" are possible. How can you repeat something that took 12 billion years to happen?

Modern supercomputers can simulate really huge systems at incredibly high speed. That's not enough (yet?) to permit a useful model of the whole universe to be built and run in a useful amount of time. So a lot of theorizing goes on. A LOT!

Dr. Alexander likes string theory. After reading his explanations, however, I was no closer to understanding string theories than before. "Theories": there are a lot of them; the most recent estimate is upwards of 10⁵⁰⁰ of them (that's a number with at least 500 digits. The number of atoms in the universe can be counted with 80-85 digits).

In the last chapter or two the author writes of the theory that, based on the Copenhagen Interpretation of Quantum Physics, nothing exists until it is observed. The Copenhagen Interpretation was the brainchild of Niels Bohr. Quite frankly, I disagree, but I'll get into that when I review another book on that subject in particular, which I've just begun to read.

I am also skeptical of the existence of dark energy, or the cosmological constant, or whatever it is currently called. I have read a number of journal articles challenging the premises on which it is based. It posits a kind of "vacuum energy" that, if it exists, should be 10¹²⁰ times as large as it is claimed to be. To me, that's the largest error so far to be found in any theory I know of. Dr. Alexander has a humorous possible solution to that dilemma: Aliens, great multitudes of them, who can harness dark energy for their own uses, using a "gravitonic computer". The amount of dark energy we observe is the trickle that is left over, leakage from their technology. If that were so, there's a lot of waste heat that has to go somewhere, enough to boil every planet and star in the known universe trillions of times. Second-biggest error? Maybe!

So, the book was enjoyable to read, but I am afraid I didn't gain much enlightenment. Dr. Alexander is a brilliant physicist. I'll have to read more, multiple times, to grasp where he is going.

If you don't like errata, you can stop here. I noticed a couple of things that slipped past the proofreader or copy editor:

• On page 184, discussing the gravitonic computer, two numbers are presented, shown as 10,120 and 10,100. These should have been represented as 10¹²⁰ and 10¹⁰⁰. These are just typos.
• On page 197, two theories of gravitational wave spectra are discussed. One is said to be more "red", the other more "blue": "In inflation the power spectrum is said to be red. This simply means that the longer wavelength perturbations have slightly less power than the shorter wavelength ones." No, "red" means longer wavelengths are stronger, while "blue" means shorter wavelengths are stronger.
• On page 205, John von Neumann is said to have "proved that when a quantum system exists in a superposition of states, a chain of measurements ultimately leading to the consciousness of an observer is what collapses the wave function into one definite state." This is based on the Copenhagen Interpretation, and it is a claim, that so far has not been proved. It cannot be proved. All experiments that purport to prove it, and I have read about many of them, ultimately depend on circular reasoning.
• Two things on page 206: Firstly, Erwin Schrödinger is said to have predicted the basic helical structure of DNA. He actually predicted a regular, aperiodic structure, akin to a crystal but with variable items at each node, so it could carry information. Language is a useful analogy. The helix was posited later, by others. 
• Secondly, Schrödinger "argued that living things fight against entropy, otherwise known as negentropy." He did indeed, but better reasoning has overtaken that theory: living things take advantage of the flow of energy in non-equilibrium environments, and thus they take advantage of the flow of entropy as well, producing small, local reductions in entropy at the expense of larger increases in entropy in their surroundings. That's not "negentropy", it is redirected entropy.

The last item may not be a copy error, but a conceptual error on the part of the author. He goes on to discuss the "observation creates reality" theory, based on the assertion by von Neumann, which has been developed by many others. This isn't physics any more, it is metaphysics, and ought to stand on its own two feet and proclaim so. That's enough at the moment.

The billion-decade pie recipe

 kw: book reviews, nonfiction, geology, cosmology, astronomy, nucleosynthesis, cooking

This chart was mentioned in How to Make an Apple Pie From Scratch: In Search of the Recipe for Our Universe, From the Origins of Atoms to the Big Bang, by Harry Cliff. The book's title, indeed its raison d'être, is a humorous aside by Carl Sagan on an episode of Cosmos: "If you wish to make an apple pie from scratch, you must first invent the universe."

Harry Cliff is a particle physicist and researcher on the Large Hadron Collider, specifically the experiment/detector called LHCb. The "b" means "beauty", for the Beauty Quark, which most physicists now call the Bottom Quark (the "t" and "b" quarks were initially called "truth" and "beauty"). The short answer to "What is 'scratch'?" would be, "Something smaller than a quark." Quarks are what we call the (possibly) indivisible bits that make up protons and neutrons, which with electrons, form atoms.

I think of the book as a microscope that uses higher and higher powers to probe the makeup of the universe. Dr. Cliff actually began his investigation by obtaining an apple pie and pyrolizing a few grams. That gave him a rough estimate of the phases present, gas/vapor, liquid, and solid. The final product of pyrolysis is charcoal, although he found later that he didn't cook it hot enough; his charcoal still had some volatile stuff in it. It matters little: the end product was mainly carbon, the "gateway element" to producing the entire suite of elements from hydrogen and helium. The chart above shows the various "ovens" in which the elements were made.

Much of the book is history, the history of the discovery of the chemical elements during the Enlightenment, then the discovery of subatomic particles a bit more than a century ago. Although I've read the stories again and again (because writers seem compelled to cover it all every time), I find it enjoyable to rehearse the way alchemy became chemistry, and experiments with "cathode rays" and pitchblende came together to discover that atoms (from "a-tomos", "un-cuttable") are actually cuttable, and the "easy" sub-parts are further cuttable.

The book skips over the range of magnification available to a light microscope. There is nothing about the plant cells in the apples, or the microstructure of a perfectly baked crust. We go from some burnt pie right to atoms, which can only be distinguished when the magnification exceeds 10,000,000X, the magnification of this STM image. The best electron microscopes are hard pressed to deliver magnifications greater than 1,000,000X. Thus STM, or Scanning Tunneling Microscopy, has to be used. The white spheres here are atoms of lead, on a silicon surface.

The reason for this omission is soon apparent. The author's quarry is smaller compared to an atom of lead than that atom is to a sports arena.

An ordinary light microscope "maxes out" when viewing items smaller than half a micrometer (or micron, or µ). An E. coli bacterium is about 2µx6µ. The photons of green light, with a wavelength of 0.55µ, have an energy of 2.25 eV. One eV, or one electron volt, is the energy of an electron that has "fallen" across the gap between an anode and a cathode when the voltage is 1V. Photon energies in the range 1.75 eV to 3.1 eV are used by the retinas of our eyes to detect "light". Things smaller than about 0.5µ, or 500 nm (nanometers), can only be studied using "light" of a shorter wavelength. And here is the important principle: shorter wavelength means higher energy per photon (or other particle).

Why is it hard to "see" an atom? It is because they are so much smaller than the wavelength of visible light. The lead atoms in the image above are about 0.35 nm across. That's 0.00035µ. The silicon atoms in the surface below them are much smaller, with an interatomic spacing of 0.078nm. An electron microscope with beam voltage of a million volts uses electrons with energy of 1 MeV (million eV), and a wavelength of 0.0012 nm. However, such an electron beam simply blows off most of the electrons from the atoms you want to look at, while a more "modest" beam of about 16,000 volts, and a useful magnification of a million, can produce images without causing total disruption. The STM technique sidesteps this by using atomic forces to get higher-resolution information, with a limit in the range of 10 to 20 million X magnification.

When the biggest constituents of atoms were discovered, electrons, protons, and neutrons, they were soon found to be a whole lot smaller than the atoms. One analogy states that an atom of hydrogen magnified to the size of a stadium (a magnification of two trillion) would be "seen" to be an electron cloud with a speck at its center the size of a small pea, perhaps 6mm diameter: the proton.

How do you "see" a proton? Since it is about 50,000 times smaller than the atom, you would need 50,000 times the energy. At a minimum, 16,000 eV x 50,000 or 800,000,000 eV, just under a billion eV (GeV). Now, let's think a minute. A million-volt power supply needs a lot of insulation. In radio, the rule of thumb is that in dry air a spark will jump about a centimeter per 10,000V. So a million-volt potential can jump at least a meter. I remember seeing a picture of an early million-volt electron microscope. It was eight feet high. What do you do with a billion volts? Such a voltage can jump a few miles. Indeed, lightning has voltages in the billion-to-ten-billion-volt range.

Here it gets fun. Particle accelerators finesse the situation by using magnets and rhythmic pulses to take a bunch (that's the scientific term) of electrons or other charged particles from an "easy" energy of 10,000 eV to higher and higher energies. It's sort of like swatting a tetherball again and again to make it go around faster and faster, except these "tetherballs" are soon going 99% of the speed of light, or more.

When I worked at Cal Tech (as a machinist), I worked part of the time in a room with a dismantled synchrotron about 30 feet in diameter. Energetic electrons or protons lose energy when you turn them to go around in a circle, so the more energy you want, the bigger the circle has to be. The LHC, where Dr. Cliff works, is about 8.5 miles in diameter. It produces beams of protons with energies that exceed 10 trillion eV. It also runs them in both directions, and steers them into head-on collisions, so you get enormous penetration. All that to "see" the insides of particles a few thousand times smaller than protons, which is what it took to prove the existence of the Higgs Boson (but not see into its insides…if it has any).

Chapters and chapters earlier, the author discussed where the atoms came from. The chart that begins this article shows where. Things we can eat, and we ourselves, are primarily CHON, that is, Carbon, Hydrogen, Oxygen, and Nitrogen. Hydrogen makes up 75% of the weight of the matter in the universe. Or, at least, of the matter that is either visible or potentially visible because it can respond to electromagnetic energy ("light"). We need to ignore dark matter and dark energy here, because we still have no idea how to interact with them. Most carbon and nitrogen are made in "dwarf" stars, main sequence stars smaller than 1.25 times the mass of the Sun. The jury is still out on whether the white dwarf stars that result from the demise of a main sequence dwarf star have to be blasted apart to release carbon and nitrogen, or if the red giant phase releases enough to amount for what we see in the sky. Most oxygen, at least most of it that gets into the interstellar medium, is forged during supernova explosions. So at an atomic level, that's where the basic ingredients of the apple pie arise.

The reason for using big atom smashers like LHC to dig into the protons for their smaller bits (quarks and gluons, mainly), and into the quantum fields that modulate (or create) their properties such as mass, is that we aren't really back to "scratch" yet. By the end of the book, if we have understood it all (I am not quite there yet), we have the beginnings of matter traced back to the end of the first one-trillionth of a second after the Big Bang. 

Does that sound pretty good? Not to a cosmologist! The Big Bang is thought to have begun with everything we might call space and time located within a radius of about the Planck Length, which is about 1.6x10^-35 meters. The initial "Bang" got rolling in Planck Time, or about 5.4x10^-44 seconds. Let's just call it 10^-45 sec., and compare it to a trillionth, or 10^-12 sec. There are about 10³³ Planck Times in a trillionth of a second; a little matter of a billion trillion trillion of them. A lot happened that we will be hard pressed to probe. The author describes the ultimate particle accelerator, wrapped around the center of the galaxy (where it has a chance of being gravitationally stable), with a diameter of several thousand light years. The biggest we have a chance of building might wrap the Earth at the equator. The particle bunches would circle the planet seven times per second, so we have long enough lives to do experiments with it, with energies as high as perhaps 50,000 TeV. That's still a long way from the Planck Energy, but it might be close enough to be "interesting".

Future beings with very long lifetimes—because each experiment takes a million years or more—might probe the Planck Length using the Galactic Collider. But beyond a certain level of energy, the only output of the experiment will be tiny black holes. According to Hawking's principle, such a black hole would soon explode into a shower of energetic particles, but they would carry no information about what was going on inside, so the fancy machine would simply be a huge fireworks generator.

The book ends with a description for beginning from scratch, to the point where matter exists, including a middling size planet with apple trees and wheat fields and such. Then it ends with a pretty good recipe for making an apple pie. There ain't a quark anywhere that can explain the great taste of fresh apple pie.

Universes by the quintillions

kw: book reviews, nonfiction, cosmology, multiverse, history

There is a corner of science in which I have much interest, cosmology. I usually avoid peeking into one corner of that corner. The various attempts to go onward from "What happened?" to "How did it happen?" and even "Why?" have been getting more and more strange for most of my adult life (50+ years). But I could not pass up the new book by Tom Siegfried, The Number of the Universe: A History of the Multiverse and the Quest to Understand the Cosmos.

I was quite entertained, and my history itch was well scratched by the author's thorough coverage of how the meanings of "world" and "universe" have morphed through the ages, at least since Aristotle. The early atomists were at odds with Aristotle, who embraced the Continuum. The atomists pointed to things like the hand of a bronze statue that had gradually become quite worn because people always touched or rubbed the fingers on their way by it.

Considering that this could equally be taken as evidence that the statue's material was continuous and thus could be removed in quantities as minute as one liked, their contentions held little water. They didn't convince Aristotle, who also declared that there could be no more than one world. The world as he understood it was equivalent to the universe, and consisted of a series of nested spheres; the outermost held the "fixed stars", the innermost consisted of the Earth, and those between carried the Sun, Moon and five planets in their pathways around the sky.

For reasons that escape me, the atomists also considered that there could be, and should be, something "outside" the outermost sphere. Perhaps other worlds like ours. Camille Flammarion in 1888 published a wood engraving that illustrated one such idea, but it is based on a flat earth, not the sphere that the Greeks understood for the earth's shape. It isn't known whether the original illustrator was displaying a true belief, or lampooning it.

Sixteen centuries were to pass until a clerical edict in 1277 threatened "natural philosophers" with excommunication if they continued to take Aristotle's anti-atomist and anti-multi-world pronouncements as truth. It is odd that, 350 years still later, Galileo was placed under house arrest for writings that contradicted Aristotle.

Mr. Siegfried takes us through the various twists and turns of the various meanings "world" and "universe" have taken on, from Aristotle onward. The "universe/world" of Ptolemy, complete with epicycles, was not far removed from the Aristotelian model. The "revolution" by Copernicus mainly caused the Sun and Earth to switch places, allowing only the Moon to keep orbiting Earth. We call it the solar system, but Copernicus called it the World.

After the telescope was invented, and rather large ones were produced, the Milky Way, or the Galaxy (from γάλα, or gala, for "milk"), was thought to be the whole universe, and the solar system including Earth was just a tiny part of that; the Earth was now "the world" and the rest was "the universe". Still later other galaxies, some found to be larger than the Milky Way, were called "island universes", but now "universe" means "everything". Now there are those who say the universe is "everything we can observe," and posit multiple universes, the multiverse.

The author points out several times that the arguments being put forth now against modern hypotheses of a multiverse are the same as those advanced time and again over the millennia. While reading the book I came to understand these comparisons as political framing. The point of the book is to defend the concept of Multiverse, even though there are between six and nine versions thereof being bandied about.

I will discuss only two of these. Firstly, what we can observe with our instruments reaches to 13.8 billion years ago, and a naïve concept of its radius is 13.8 billion light-years (Gly). However, back-calculating relativistic effects allows us to estimate that the "edge" of what we observe is actually now at a distance of about 75 Gly. That's how far cosmological expansion has carried things. But how big is the "rest of the universe"? We still have no way to know. Ignoring accelerated expansion (the dissension against this idea continues to increase, so I discount it), let's first guess that Alan Guth's inflation popped things open to such an extent that we can observe at most a percent of the whole. Even "inflation" didn't produce an infinite bubble of spacetime. One hundred times the volume is a little over 4.5 times the radius. Let's round that up to a radius of 350 Gly. That's the size of "our bubble universe".

The number of baryons (protons, neutrons and their kin) in the observable universe is thought to be about 10¹⁰⁰ (one Googol), and their number in "our everything", this bubble, may be 10¹⁰² (100 Googol).

One version of the multiverse hypothesizes that there are multiple bubbles, perhaps with differing values of the "natural constants" such as the ratio of mass of the proton/electron. In our universe, or at least on our lab benches, that ratio is 1,836 and change. If the ensuing multiverse is truly infinite, containing an infinite number of such bubbles (200-400 Gly across on average), it is thought that any particular configuration of particles and their motions will be repeated exactly an infinite number of times. Well, that's a lot of infinity. And all of it quite beyond the reach of any possible instrument.

I don't know how big the number of permutations and combinations each bubble consists of, but we can tinker with a few numbers:

• The coordinates of each particle and its velocity consist of six numbers. The position must be known with a precision of about the Planck length (1.6x10^-35 m), and similar precision for the velocity, to obtain a functional match.
• A complete specification for the state of a bubble at any point in time consists then of 6x10¹⁰²  numbers. Call this Nu, the "state number of a universe".
• The permutations of Nu are roughly its factorial: (Nu)!, a number with about 600 times as many zeroes as there are particles in "our" bubble. That's a very rough estimate based on Stirling's Approximation.

If there are at least that many universe-bubbles out there, then at least one pair of them will match exactly, at least at some point in time. Quantum effects may result in immediate divergence. It's a bit like the statement that the formulas for Earth's atmospheric interactions require that, at any one point in time, there are two antipodal points at which the temperature and barometric pressure and wind velocity and direction are exactly matched. But where those points may be, nobody can determine, and where they are a few milliseconds later, is anyone's guess. However, this hypothesis of a multiverse is one I can consider is at least possible. Highly unlikely—perhaps one chance in some number with a Googleplex of zeroes—but possible.

The other multiverse worth considering, if only as a straw man, is the one formulated by Hugh Everett III. Rather than accept quantum randomness, his model states that for every quantum "choice", both or all possible paths are taken, just in different universes. If I understand Dr. Everett correctly, every quantum event causes the splitting of the universe into two or more universes, each one holding one of those outcomes. He is quoted as stating that a "stupendous number" of parallel universes are thus produced every second, separated from one another by unknown mechanisms or materials. "Stupendous" is the understatement of the century.

Let's consider a very simple quantum event, the interaction of a photon with the surface of a sheet of glass. If the refractive index of window glass is taken as 1.5 at some wavelength of choice, then, for normal or near-normal incidence, the photon has a 4% chance of reflecting. Otherwise it passes into the glass. The Everett Multiverse works this way. Each such photon-glass interaction splits the universe into two. In one, the photon reflects, and in the other, it passes through. Or maybe there has to be a split into 25 universes; one of them gets the reflected photon and the rest get the transmitted photon. Let's go with the simple version.

I have a laser pointer with a beam that is nominally "less than 5mW", so I'll call it 4mW. I'll point it straight at my window. What happens? Here are the numbers:

• 0.004 W beam power
• 670 nm beam wavelength
• 6.242x10¹⁸ eV (electron Volts) per Joule (J); 1 W = 1 J/sec
• photon energy at 670 nm = 1.85 eV (proportionality constant 1240 eV-nm)
• 1.35x10¹⁶ photons/sec in the beam

The number of photons striking the near surface of the glass is 13.5 quadrillion per second. (In American units, a quadrillion is a million times a billion.) A slightly smaller number, 96% of 13.5 quadrillion, strike the far surface of the glass. Most of those that reflect inside the glass (about 54 trillion) pass through back upward, but a few are reflected downward again, and so forth. We can say that 27 quadrillion quantum interactions are happening, every second. That is not counting the quantum events that go into creating the laser beam photons in the first place.

I don't know how many universes were being created each second beforehand, but during the time I shined my 4mW beam at the glass, 27 quadrillion new universes were created, that would not have been had I kept the beam off. About every 37 seconds, I "create" a quintillion universes.

And some people think it incredible that God created one universe! Is it any surprise that I consider the Everett hypothesis of the multiverse as the sheerest nonsense? It violates Occam's Razor by the hugest, most incredible amount I have ever encountered.

Do I have an alternative? Indeed I do (and not the theological one)! Keeping my physicist hat on, I'll point out that I find superstring theory less incredible than the Everett hypothesis. These curious entities, if they exist, are something like a Planck length in size (see above) and vibrate at furious rates, at least as great as the frequency of the most powerful gamma rays. The "fundamental particles" that we call quanta, including protons and photons, would then be vibrational modes of one or more superstrings.

If the above is true, quanta have "fuzzy boundaries" with a lot of "buzzing" going on inside, and quantum randomness is then something related to Brownian motion caused by molecules striking tiny items such as pollen grains, in random clusters that don't quite balance out.

Consider the interaction of a photon with a piece of glass. The glass, volume-wise, consists mainly of oxygen atoms held together by covalent bonding with much smaller atoms of silicon, sodium, and a few other elements. The oxygen atoms are slightly ill-defined spheres or spheroids with a diameter of about 0.3 nm. A photon from my laser has a wavelength about 2,000 times as large. I don't know how "wide" a photon is, but the "wavicle" model indicates its "physical" length is probably 2-3 wavelengths. Suffice it to say that the photon interacts with a large number of oxygen atoms, or at least the electrons in their outer orbitals, while taking some fraction of a nanosecond "deciding" whether to turn tail (reflect) or slip past the surface (refract). During that interaction the vibrations of the superstrings involved cause a few trillion (or trillion trillion) jitters of this or that "part" of the photon against various numbers of electrons. Predicting which way a casino die will roll would be infinitely easier than determining beforehand what the photon will do (just bet the odds: 24 out of 25 times, it'll go through).

That is my superstring-Brownian-motion hypothesis for quantum randomness. I ought to copyright it (and I did, just by publishing it in this blog post).

P.S. This shows one concept of a wavicle that I found on zazzle.com. To this scale, the oxygen atoms in window glass would appear about 0.012 mm across, about three times the size of E. coli cells.