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Our future, our universe, and other weighty topics

Saturday, November 23, 2013

Cosmic Fine-Tuning Visualized

The evolution of the cosmos is determined by initial conditions (such as the initial rate of expansion and the initial mass of matter), as well as by fifteen or so numbers called physical constants (such as the speed of the light and the mass of the electron). We have by now measured these physical constants with extremely high precision, but we have failed to come up with any theory explaining why they have their particular values. One of the most surprising discoveries of modern cosmology is the realization that the initial conditions and physical constants of the universe had to be adjusted with exquisite precision if they are to allow the emergence of conscious observers. This realization is referred to as the “anthropic principle”...Change the initial conditions and physical constants ever so slightly, and the universe would be empty and sterile; we would not be around to discuss it. The precision of this fine-tuning is nothing short of stunning. The initial rate of expansion of the universe, to take just one example, had to have been tweaked to a precision comparable to that of an archer trying to land an arrow in a 1-square-centimeter target located on the fringes of the universe, 15 billion light years away!
Chaos and Harmony” by Trinh Xuan Thuan, Professor of Astronomy, University of Virginia, p. 235 

The phrase cosmic fine-tuning is nowadays used in a theologically neutral sense to mean the universe's improbable fitness for life (the term may or may not imply the existence of a fine-tuner). One of the first books on the anthropic principle discussed above was Paul Davies' book The Accidental Universe, which had a cover showing a pair of dice and a galaxy.

But rather than imagining a dice-throwing Las Vegas crapshooter to visualize the idea of cosmic fine-tuning, we should perhaps imagine something else in Las Vegas: a slot machine. The slot machine that we need to imagine is one that has not one row that must consist of matching symbols for a win, but a slot machine with multiple rows, each of which must have matching symbols to win the jackpot. Each row represents one of the conditions for intelligent life that a successful universe must have. The chance of any one row having all matching symbols is very low, only about 1 in 1,000,000. To win the jackpot (which in this case is a universe that has the right conditions for intelligent life), each of the rows must be successful, consisting of all matching symbols. There are multiple possible combinations that allow for success (such as all apples on the first row, all pears on the second row, and all grapes on the other rows, or all 7's on the even rows and all oranges on the odd rows). But still the chance of overall success (each row being successful) is very, very low. The slot machine would look something like the slot machine shown below (click on the image to expand it).

anthropic principle

Now let's take a look at each of the rows on this slot machine, and discuss the habitability condition that the row represents, including a mention of why the chance of the condition being met is roughly as improbable as the chance of getting all matching symbols on the row when you pull the red slot machine lever in the slot machine I have depicted.

cosmic fine tuning

The word gravity in the visual refers to the universal gravitational constant of 6.6 X 10-11 N·(m/kg)2 which defines the degree to which matter attracts other matter through gravitational attraction. The existence of intelligent life in our universe requires the gravitational constant to exist within a narrow range of values. Cosmologists say that if the gravitational constant had been much greater, the expansion of the universe would have been stopped by the gravitational attraction between galaxies, and the universe would have collapsed in on itself before there was time for life to evolve. If the gravitational constant were much weaker, there would not have been enough gravitational attraction for galaxies to form. 

Referring to the short-lived stars known as blue giants (which don't last long enough to support planets where life evolves), and to the type of stars known as red dwarfs (generally regarded as being stars not as suitable for Earth-like planets as yellow stars like our sun), the physicist Paul Davies says on page 73 of The Accidental Universe: “If gravity were very slightly weaker, or electromagnetism very slightly stronger (or the electron slightly less massive relative to the proton), all stars would be red dwarfs. A correspondingly tiny change the other way, and they would all be blue giants.” So apparently our universe lucked out with its gravitational level, and this was at least as lucky or improbable as a row match on the slot machine I have visualized.

In our universe we have the remarkable coincidence that the proton (which has a mass 1836 times greater than an electron) has an electric charge identical to the charge of an electron, the only difference being that the proton charge is positive and the electron charge is negative. The charge of the proton is 1.60217657 ×1019 coulomb, and the charge of the electron is 1.60217657 ×1019 coulomb. This scientific paper is by a scientist who used a molecular beam deflection method to conclude that the proton charge and the electron charge have a magnitude differing by less than 5 parts in 10,000,000,000,000,000,000. 

The chemistry on which life depends could not exist if the magnitude of the charge on the electron did not match the magnitude of the charge on the proton. It would require only a small difference between the two to make planets unstable (not surprising because electromagnetism is a force more than a trillion trillion trillion times greater than the gravity that holds our planet together). 

In his book The Symbiotic Universe, astronomer George Greenstein (a professor emeritus at Amherst College) says this about the equality of the proton and electron charges:  "Relatively small things like stones, people, and the like would fly apart if the two charges differed by as little as one part in 100 billion. Large structures like the Earth and the Sun require for their existence a yet more perfect balance of one part in a billion billion." 

In any universe containing life, the electron could have any old charge, as long as the magnitude of the charge exactly matched the magnitude of the charge of the proton. The fact that both match exactly is unexplained by the Standard Model of Physics. So a habitable universe requires a lucky match of the proton and electron charges, which is at least as improbable as the likelihood of a match on the “Particle Charges” row on the slot machine I have depicted.

Entropy can be roughly defined as the amount of waste mass-energy in a system or universe, energy that is unavailable for work. Entropy is increased when the stars burns up their nuclear fuel to radiate energy into space, and it is also increased when matter gets trapped in black holes. It is a fundamental law of nature that entropy gradually increases as time passes, a principle known as the Second Law of Thermodynamics. Scientists say this law will eventually lead in the incredibly distant future to a “heat death” of the universe, in which there is no usable energy. We know roughly how much entropy is now in the universe, and if we “rewind the film” backward all the way back to the time of the Big Bang, we then have a universe that begins with very, very little entropy. The diagram below illustrates the point.

Roger Penrose (one of the most famous cosmologists) has emphasized the fantastic specialness of the low-entropy state of the early universe. In the video clip below, he discusses the issue.

At the end of this brief clip Penrose estimates that the chance of a random universe having entropy as low as the entropy in the early universe is some inconceivably small number such as 1 in 10N, where N is a number greater than the total number of particles in the observable universe. By comparison with such conclusions, the “entropy” slot on our cosmic slot machine is very modest, requiring luck of only about 1 in a million for this condition to be met. This is probably a great underestimation of the luck actually required for the initial entropy of a life-bearing universe, but at least it means we don't have to depict a slot machine with a row stretching on for many miles.

The expansion rate is the rate at which an expanding universe expands. Around 1975 cosmologists said there was a problem called the flatness problem, which is the fact that in order for the universe to be in its current state the initial expansion rate of the universe (at the time of the Big Bang) had to be fine-tuned to about 1 part in 1050. Then the theory of cosmic inflation was developed, which offered a mechanism that might explain why the universe had such a suitable initial expansion rate. But even with such a theory, it is still a very long shot for a universe to start out with an expansion rate suitable for habitability.

For one thing, lots of conditions have to be met for cosmic inflation to occur, and leave us with a universe like ours; so any inflation theory requires its own type of fine-tuning – perhaps not as much as 1 part in 1050 but still something on the order needed to win a huge lottery jackpot. In this paper Cal Tech professor Sean Carroll says, “When perturbations are taken into account, inflation only occurs in a negligibly small fraction of cosmological histories,” and then defines this fraction as a number much less than 1 in 1,000,000,000,000,000,000,000,000. Princeton professor Paul Steinhardt has recently raised many objections to the inflation theory in this paper, claiming that cosmic inflation requires fine-tuning to 15 decimal places (a 1 in 1,000,000,000,000,000 bit of luck). So without discounting the possibility that the theory of cosmic inflation is correct, we can say that with or without inflation, to have a universe begin by chance with an expansion rate suitable for intelligent life we need something to happen at least as lucky as about a 1 in a million long shot, which is about the luck requirement depicted in my slot machine visual for the “Expansion Rate” row.

Dark energy (basically the same as the cosmological constant) is one of the great unsolved mysteries of the universe. It's not simply that we don't know enough about it. The mystery is that dark energy in our universe is so small, even though quantum field theory suggests it should be so much larger. Scientists say that quantum uncertainty should cause an ordinary vacuum to be teeming with short-lived, fleeting particles called virtual particles. Those particles should give an ordinary vacuum a very high energy density. When scientists do the calculations, they come up with a number indicating that ordinary space should be filled with a vacuum energy density more than 10100 times greater (more than a million billion trillion quadrillion quintillion sextillion times greater) than the maximum value consistent with astronomical observations (a problem known as the "vacuum catastrophe"). The simplest explanation is that there is some lucky balancing by which negative contributions to the vacuum energy density cancel out positive contributions, resulting in a net value near zero. But such a lucky balancing is incredibly improbable (far more improbable than the chance that all of the money you earned in a particular decade matches to the penny, by coincidence, all the money that you spent or charged in that decade). Some think it actually required a 1 in 10100 long shot for dark energy to be so small, but in the “Dark Energy” line of my visual I merely imagine a requirement that has about a 1 in a million chance of occurring. 

In his book The Particle at the End of the Universe (page 145 to 146), Cal Tech physicist Sean Carroll says the following:

The size of atoms...is determined by...the mass of the electron. If that mass were less, atoms would be a lot larger. .. If the mass of the electron changed just a little bit, we would have things like 'molecules' and 'chemistry', but the specific rules that we know in the real world would change in important ways...Complicated molecules like DNA or proteins or living cells would be messed up beyond repair. To bring it home: Change the mass of the electron just a little bit, and all life would instantly end.

Besides the luck involved in the electron mass having a suitable value, our universe also had great luck in regard to the neutron mass having a suitable value. Physicist Paul Davies says that if the neutron mass were .998 of its actual value, protons would decay into neutrons, and there would be no atoms at all (The Accidental Universe, page 65). Conversely, if the neutron mass were slightly greater, it would mean there could be no long-lived stars like the sun.

So we can conclude that having electron and neutron masses with values compatible with life requires good luck on the same order as the luck needed for a match on the “Particle Masses” row of the slot machine I have visualized.

After the Big Bang, there was only hydrogen, helium, and a little lithium. All of the other elements were produced inside of stars. Advanced life requires lots of carbon, oxygen, and nitrogen. Having a civilization requires additional elements such as iron. Astronomers say that some of the elements originated in stars that did not blow up, and others originated in stars that did blow up in supernova explosions. A universe must meet many requirements to get all the needed elements in abundant amounts. For one thing, there has to be something like the weak nuclear force that exists in our universe, because that is needed for supernova explosions. Another thing needed are just the right nuclear resonances, which have to exist in the right way to assure the abundant production of carbon and oxygen by stars. In this paper  scientists conclude, “Thus, even with a minimal change of 0.4% in the strength of the N-N force, carbon-based life appears to be impossible, since all the stars then would produce either almost solely carbon or oxygen, but could not produce both elements.” So the total luck needed for you to have a universe with a distribution of elements suitable for the evolution of life (with abundant carbon and oxygen) would seem to be something like the luck required to get a match on the “Element Abundances” row of the slot machine I have visualized.

The two fundamental nuclear forces in our universe are the weak nuclear force (involved in radioactivity) and the strong nuclear force (which holds together the nucleus of an atom). The nucleus of atoms such as carbon consists of neutrons with no charge and protons with a positive charge. All particles with the same charge repel each other, particularly when they are very close together. So if it were not for the strong nuclear force, the nucleus of an atom such as carbon and oxygen could not exist for more than a second; the electromagnetic repulsion of the protons would cause the nucleus to fly apart.

In his book The Accidental Universe physicist Paul Davies says that if the strong nuclear force were 5 percent weaker, the deuteron (a nucleus consisting of a proton and a neutron) could not exist, making it “doubtful if stable, long-lived stars could exist at all.” He also notes that if the strong nuclear force were 2 percent stronger, a nucleus called a diproton (consisting of only two protons and no neutrons) would exist, making it doubtful that “any hydrogen would have survived beyond the hot primeval phase” near the time of the Big Bang (and also causing all kinds of problems for the existence of stars like the sun). So it seems that the strong nuclear force had to exist within a very small range of values. Since the strong nuclear force is roughly a million billion trillion trillion times stronger than gravitation, we can conclude that having the strong nuclear force fall within this narrow range required luck at least as great as the luck needed for a match on the “Nuclear Forces” row of the slot machine I have depicted.


By now I have discussed each of the requirements depicted on my slot machine visual, and how each one represents a very unlikely long shot or coincidence. What is the overall probability of all of these eight long shots occurring? The conditions are all independent requirements, without any causal relation to each other. If one requirement is met, it does not make it more likely that another requirement will be met. The rules of probability indicate that to calculate the likelihood of a set of independent events occurring, you multiply together the likelihood of each separate event or condition occurring. The likelihood of success for each condition is no greater than 1 in a million, so to roughly calculate the chance of all of the conditions being met, we multiply 1 in a million by itself eight times. This gives us a probability of 1 chance in 1,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000. That is the probability mentioned near the top of my slot machine visual, where it says, “1 winner every 1,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000 tries!”

If we imagine someone pulling the lever on this cosmic slot machine, we must imagine him pulling the lever over and over again for many, many centuries before success is finally reached, and each row on the machine consists of all the same symbols. A person pulling the red lever over and over again 24 hours a day would see one successful row every few days, a row consisting of all matching symbols (such as all apples). But that would only be one of the eight successful rows needed to win the jackpot, and it would be overwhelmingly probable that the same row would be unsuccessful the next time the person pulled the red lever. The person pulling the red lever over and over would probably need to pull the lever for many centuries before he saw that each of the rows consisted of all matching symbols, and the grand jackpot (a habitable universe) was won. 

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