Into the Unknown, page 30
Another interesting concept arises from a set of space and time dimensions that are hyperbolic; an alternate universe that had three time-like dimensions and only one space-like dimension might be OK. In this case you might try to think about this intuitively as time behaving like space as we know it, and space behaving like time as we know it.
If, on the other hand, we had only space-like (or only time-like) dimensions—Space1, Space2, Space3, Space4, and so forth—the equation would be classified as elliptic. Pretty much the only thing these types of PDEs are good for is describing equilibrium states, which makes sense, because without a parameter in there for something like time, nothing is going to happen.
The rubber hits the road when we allow for more than a single parameter of the same type. For example, what if our universe had Space1, Space2, and Time1, Time2? We find ourselves dealing with what are called “ultrahyperbolic equations,” and these are pathological. In general, they do not have well-defined stable solutions. Another way to say this is that nothing would be predictable. The resulting chaos may not be too far off from what you envisioned intuitively when you thought about being able to turn left in time. Once again, we are faced with asking whether life could evolve under such circumstances, and once again, the answer is probably not life-as-we-know-it.
We have now effectively ruled out all the pixels in the space-time graph except for two. If we want a universe that can host life-as-we-know-it (which I am in favor of), then we either need three macroscopic dimensions of space and one of time, or three of time and one of space.
Chart inspired by Tegmark. Credit: M. Tegmark, “On the Dimensionality of Spacetime,” Classical and Quantum Gravity 14, no. 4 (1997).
Not all the parameters in the universe that appear fine-tuned are specific values like masses of particles or numbers of dimensions. A prime example of this is a characteristic of the universe just after the Big Bang that has had an enormous impact on its habitability today—the primordial density fluctuations.
Even the very early universe couldn’t escape from quantum mechanics and the reality that nothing can be precisely located in space and time, which meant no fields could be precisely flat. Instead, because the laws of physics said so, quantum fluctuations were imprinted on the mass-energy of the universe from the very first moment. These exceedingly minor fluctuations then proceeded to self-amplify with a positive feedback loop; little patches with more mass-energy had correspondingly more gravity and were better able to attract more mass-energy. When they attracted more mass-energy, they had even more gravity, and a snowball effect ensued. Apparently “the rich get richer” has been a theme in the universe since the Big Bang. Then the cosmological inflation kicks in, and all of these “small-scale” perturbations get dramatically stretched out to macroscopic scales.
In a classic coupling between the smallest and largest scales, the amplitude of these teeny tiny initial quantum perturbations determined the fate of structures that have formed over the course of cosmic history. In the recent literature these perturbations are commonly referred to with the parameter σ8.16 The value of σ8 can be measured using observations of the cosmic microwave background, from which we have a current best value of σ8 = 0.82 ± 0.02.17
If σ8 had been significantly smaller, the universe would be largely devoid of structure (which includes things like our own galaxy); the formation of stars would have been significantly inhibited; and consequently very few, if any, heavy elements would be available.18 On the other hand, if σ8 had been significantly larger, massive structures would have coalesced early in the universe, and much of the matter in the universe would have quickly collapsed into black holes. For any galaxies that did manage to form (and survive), they would have such high stellar densities that planetary systems would likely be unstable—any passing star that got a little too close would disrupt orbits and send planets off into the galaxy.
Let’s not forget the very small anti-matter–matter asymmetry that came up in Chapter 7, which gifted us with something like 1/1,000,000,000 of normal matter particles surviving annihilation. This one-in-a-billion difference is known as the “baryon asymmetry” (typically denoted with the symbol ηB). A “natural” number for this asymmetry would have been 0, but if it isn’t 0 it could (in principle) be anything between 0 and 1.
We’ve already established that if the baryon asymmetry were exactly 0, you wouldn’t be reading this book and there wouldn’t be paper for the book to be written upon. But what if this asymmetry were even larger? At the most basic level, if we crank up ηB, less matter is annihilated (and turned into light), which has a host of downstream effects, starting with primordial nucleosynthesis and structure formation.
Having a higher density of elementary particles available for nucleosynthesis enables more reactions to happen in those first few moments after the Big Bang, which results in a lower relative abundance of hydrogen and higher abundance of helium (there is a classic paper on this from Robert Wagoner in 1973 that is full of interesting tidbits on what happens).19
Why do we care if there is less hydrogen and more helium?20 If the abundance of hydrogen is significantly reduced, then nuclear fusion in stars gets much harder, and consequently the duration of time that stars undergo nuclear fusion is decreased. As we saw in the chapter on ET life, longish stellar lifetimes may be important for life to have time to emerge, so if we dial up the helium too much we are in trouble.
Increasing the mass-to-light ratio also impacts the structures that can form in the universe, which also places limits on potential habitability. For example, if ηB were too high, stellar densities would be much higher, and as a result the likelihood of supernova exploding in the vicinity and destroying life (and everything else in its path) would go up. Recent work places an upper boundary on values of ηB that could be tolerated of 10−4.21 On the other hand, if ηB were too low, there would not be enough self-gravitation for stars to fragment out of galactic disks, which gives us a lower limit of 10−11.22 So based on our current models, we have wiggle room in the range of 10−11 < ηB < 10−4. Whether we consider this range small or large depends on the full range that might have been possible (which is possibly 0 < ηB < 1).
Before we move on from examples of possible fine-tuning, I want to dwell on an exquisite property of our universe that I don’t think gets nearly enough attention, but is critically important for life-as-we-know-it. Specifically, at the physical and temporal scales we live, our universe appears to be in a delicate balance between order and chaos. How complex patterns (e.g., life) arise from simple rules is a profound question (and takes us back to the Game of Life in Chapter 9).
To put a finer point on this, I want to borrow from work done in the field of information theory, and, in particular, blatantly usurp two terms that are central to this topic: “algorithmic compressibility” and “logical depth.”23 In the most basic terms, you can think of algorithmic compressibility as the extent to which an object has redundant patterns that could be made more concise. For example, a checkerboard pattern is highly algorithmically compressible; if you were to write a computer program to reproduce the board, it would only take a few lines of code. On the other end of this spectrum is logical depth. If you have ever accidentally deleted a term paper that you spent days writing, you have a visceral understanding of logical depth—the paper you lost will not be easy to reproduce, and a computer program would require an extensive amount of coding to reproduce it.
Our universe appears to be a delicate balance between algorithmic compressibility and logical depth. To see this, all you need to do is look at the nearest tree—symmetries and patterns are embedded in the leaves, bark, wood, and branches. However, at the same time, the patterns are not perfect, no two leaves are the same, and there are random deviations at every scale.
Of the many astounding facts about the universe, to me the balance of the two extremes of algorithmic compressibility and logical depth might be the most simultaneously profound and overlooked. The universe need not be so. If the universe were entirely algorithmically compressible, everything would follow perfect patterns and symmetries, and nothing interesting (a category in which I include life-as-we-know-it) would ever happen. On the other hand, if the universe were dominated by logical depth, there would be little (if any) law and order to reality, with the universe bordering on chaos. Yet, in the universe in which we live, we seem to have some tidy physical laws that govern reality hand in hand with chaotic behavior and random fluctuations imprinted by quantum mechanics.
Turning to information theory as an analogy, the most economical computing programs are the shortest necessary for the required outcome, and hence, the most economical programs are most likely to have resulted from a universal computer.24 In a similar way, this philosophy sits at the root of physicists seeking symmetry and unified laws. Building a system that is both simultaneously deterministic and random requires a careful design—there needs to be enough randomness injected to break perfect symmetries, but not so much that it devolves into chaos. To be fair, this analogy starts to invoke a bit of teleology—that a thing exists for a purpose, with which I am not entirely comfortable, but I also don’t deny the possibility that our universe is essentially a computer in the literal sense—taking input, running a program, and producing output.
I conjecture the apparent balance between algorithmic compressibility and logical depth is a requirement for life-as-we-know-it. If we were observing the universe at a significantly different time or spatial scale, we might not infer the same balance. For example, the physics of the early universe after inflation was very simple and uniform. Likewise, in the distant future when dark energy has taken over, the observable universe will also be simple and uniform. Or on physical scales approaching the Planck length, it might be hard to infer any rhyme or reason to anything that happened. Similarly, when modeling entire galaxies, there are large-scale patterns that dominate behavior. I’m left to tenuously conclude that there is something very special about the intermediate parameter regime we inhabit in the universe.
Given all these parameters that appear to require very specific values for us to be here, one could understandably feel that the universe must surely be a set-up job. However, before we can jump to that conclusion, we ought to take stock of lessons we have learned over the course of humanity that should have bearing on our thinking here. You know that saying about people who forget history being doomed to repeat it? This is that part of the text. Before we get to possible explanations for the apparent fine-tuning, it is important to take a step back and think about other times and situations that have played out for humans and the lessons learned.
Lesson 1: The solar system. The solar system itself was quite a source of consternation not too long ago. We have all these planets going around the Sun in nice “perfect” circles25 in very nearly the same plane of the sky. These perfect orbits can’t possibly have happened randomly! It’s too ordered! Too perfect! As Newton wrote:
For while comets move in very eccentric orbs in all manner of positions, blind fate could never make all the planets move one and the same way in orbs concentric, some inconsiderable irregularities excepted which may have arisen from the mutual actions of comets and planets on one another, and which will be apt to increase, till this system wants a reformation.26
In other words, the brilliant Newton thought the solar system was a set-up job. But surprise! At that time, we didn’t know all the physics that go into forming a solar system. In model solar systems that we make today using advanced (well, advanced to us today) computational techniques and all the physics that we currently know, it is virtually impossible to make a solar system that does not have properties broadly similar to our own, with planets going around on nice, near-perfect circles in the same direction and in very nearly the same plane. It turns out that blind fate, once in the hands of physics, had little choice but to “make all the planets move one and the same way in orbs concentric.” While the geometry and dynamics of the solar system might have seemed fine-tuned a couple hundred years ago, today we understand that physics made it so. Lesson learned: Don’t assume we humans know all the physics involved.
To be clear, just because we now understand the physics that naturally led to solar systems like ours, that doesn’t mean that the broader universe and the laws that govern it are not fine-tuned. Rather, that the creation of the solar system out of the maelstrom of the universe did not require the existing rules to be tweaked or bent for our system of nice concentric orbits to come about. More generally, we need to be mindful of the logic we talked about way back in Chapter 2 and denying the antecedent.
“If the solar system is fine-tuned then the universe is fine-tuned.”
If P then Q. Valid.
“If the solar system is not fine-tuned then the universe is not fine-tuned.”
Not P therefore not Q. Not valid.
Lesson 2: The habitability of Earth. Earth is a pretty darn good planet as far as life-as-we-know-it is concerned. With fewer planets in the solar system than you can count on two hands, what are the chances that there would be such a downright perfect planet for us to live on? In every respect, the Earth seemed pretty darned special. Only a couple decades ago, we didn’t even know for sure if there were other planetary systems out there. The first confirmed detection of an extrasolar planet (commonly shortened to “exoplanet”) was in 1992, which demonstrated the existence of planets orbiting a pulsar (just FYI, that would not be a good place for life-as-we-know-it).
In the intervening decades, the search for planets in other star systems has exploded, and there are now literally thousands of confirmed exoplanets orbiting other stars in our galaxy. In the observations obtained to date, over half of these exoplanets are part of multiple planet systems, and roughly one in five Sun-like stars has a nearly Earth-sized planet orbiting at a distance that falls in the Habitable Zone.
All of that means that Earth is probably not really all that unique. When you consider the sheer number of Earth-like planets orbiting at Earth-like distances around Sun-like stars—just in our galaxy alone—our sense of importance gets knocked down a notch. Observations from the Kepler mission indicate that in the Milky Way, there are roughly 11 billion of these Earth analogs. If you could visit a different one of these Earth analogs every year, it would take you nearly the age of the universe to see them all.
Once you know that Earth is only one of billions of similar planets in the Milky Way, it no longer seems quite so special and fine-tuned for life. Lesson learned: Be wary of assuming yours is the only example and not part of a much larger ensemble.
Lesson 3: The human body. Even the human body provides lessons for us to consider, and they have long been used as evidence for fine-tuning. How could such complex systems have come about by random chance? A prime example is the human eye; our eyes are downright amazing. In many ways the human eye even dramatically surpasses astronomical detectors that we can make (at least for now). Consider the following:
• The eye has a huge field of view, nearly 180 degrees. With your peripheral vision you can see light from nearly the entire space in front of your head. In large part, this field of view is due to there being a curved “focal plane” and detector (aka the “retina”) on the back of the eye that allows light coming in from different angles to still be in focus.
• Speaking of light detection, the human eye has approximately 125 million light-detection cells. You can think of these as akin to pixels in your camera. How many pixels does your camera have? Technology is advancing quickly, but at the time of this writing, the best cameras on the market have on the order of 50 million pixels and cost a pretty penny.
• With this many pixels, our eyes also have an astonishingly rapid readout, which is the time it takes for the light the cells have detected to be registered by the brain. The cells in the human eye read out at roughly 30 times each second (or 30 hertz). By comparison, that 50 megapixel camera that is on the market now has a maximum readout rate of 5 frames per second.
• The range of faint to bright light the human eye can process is also astounding. This ratio of the brightest light detectable to the faintest light detectable is called the “dynamic range.” The human eye has a dynamic range of roughly 1 to 10 billion, rivaling even astronomical detectors.
Given the capabilities of the human eye, it is hard to blame folks who see it as evidence of fine-tuning. The crux of the issue here is the power of natural selection to shape evolution over millions of years. Because we don’t see significant changes over the course of a human lifetime, extrapolating from our own experience, it is hard to conceive of such amazing things as the human eye arising from evolution. Even Darwin has a quote in The Origin of Species that would seem to support this position:
To suppose that the eye with all its inimitable contrivances for adjusting the focus to different distances, for admitting different amounts of light, and for the correction of spherical and chromatic aberration, could have been formed by natural selection, seems, I freely confess, absurd in the highest degree.
But once again, be careful. That particular quote is frequently taken out of context. Compare the previous excerpt with the full quote from Chapter 4 of The Origin of Species:
To suppose that the eye with all its inimitable contrivances for adjusting the focus to different distances, for admitting different amounts of light, and for the correction of spherical and chromatic aberration, could have been formed by natural selection, seems, I freely confess, absurd in the highest degree. When it was first said that the sun stood still and the world turned round, the common sense of mankind declared the doctrine false; but the old saying of Vox populi, vox Dei, as every philosopher knows, cannot be trusted in science. Reason tells me, that if numerous gradations from a simple and imperfect eye to one complex and perfect can be shown to exist, each grade being useful to its possessor, as is certainly the case; if further, the eye ever varies and the variations be inherited, as is likewise certainly the case; and if such variations should be useful to any animal under changing conditions of life, then the difficulty of believing that a perfect and complex eye could be formed by natural selection, though insuperable by our imagination, should not be considered as subversive of the theory. How a nerve comes to be sensitive to light, hardly concerns us more than how life itself originated; but I may remark that, as some of the lowest organisms, in which nerves cannot be detected, are capable of perceiving light, it does not seem impossible that certain sensitive elements in their sarcode should become aggregated and developed into nerves, endowed with this special sensibility.27
