George F. R. Ellis writes in Issues in the Philosophy of Cosmology:

9.2 Issue H: The possible existence of multiverses
If there is a large enough ensemble of numerous universes with varying properties, it may be claimed that it becomes virtually certain that some of them will just happen to get things right, so that life can exist; and this can help explain the fine-tuned nature of many parameters whose values are otherwise unconstrained by physics.  As discussed in the previous section, there are a number of ways in which, theoretically, multiverses could be realized.  They provide a way of applying probability to the universe (because they deny the uniqueness of the universe).  However, there are a number of problems with this concept.  Besides, this proposal is observationally and experimentally untestable; thus its scientific status is debatable.

My 100-year-old uncle—a lifelong teacher and voracious reader who is still intellectually active—recently sent me Max Tegmark’s book Our Mathematical Universe: My Quest for the Ultimate Nature of Reality, published by Vintage Books in 2014. I could not have had a more engaging introduction to the concept of the Multiverse. Tegmark presents four levels of multiverses that might exist. They are

Level I Multiverse: Distant regions of space with the same laws of physics that are currently but not necessarily forever unobservable.

Level II Multiverse: Distant regions of space that may have different laws of physics and are forever unobservable.

Level III Multiverse: Quantum events at any location in space and in time cause reality to split and diverge along parallel storylines.

Level IV Multiverse: Space, time, and the Level I, II, and III multiverses all exist within mathematical structures that describe all physical existence at the most fundamental level.

There seems little question that our universe is very much larger than the part that we can observe. The vast majority of our universe is so far away that light has not yet had time to reach us from those regions. Whether we choose to call the totality of these regions the universe or a Level I multiverse is a matter of semantics.

Is our universe or the Level I multiverse infinite? Most likely not. That infinity is a useful mathematical construct is indisputable. That infinite space or infinite time exists is doubtful. Both Ellis and Tegmark agree on this and present cogent arguments as to why infinity cannot be associated with physical reality. Very, very large, or very, very small, yes, but not infinitely large or infinitely small.

Does a Level II, III, and IV multiverse exist? Tegmark thinks so, but Ellis raises several objections, noted above and elsewhere. The multiverse idea remains quite controversial, but as Tegmark writes,

Even those of my colleagues who dislike the multiverse idea now tend to grudgingly acknowledge that the basic arguments for it are reasonable. The main critique has shifted from “This makes no sense and I hate it” to “I hate it.”

I will not delve into the details of the Level II, III, and IV multiverses here. Read Tegmark’s book as he adroitly takes you through the details of eternal inflation, quantum mechanics and wave functions and the genius and tragic story of Hugh Everett III, the touching tribute to John Archibald Wheeler, and more, leading into a description of each multiverse level in detail.

I’d like to end this article with a quote from Max Tegmark from Mathematical Universe. It’s about when you think you’re the first person ever to discover something, only to find that someone else has made that discovery or had that idea before.

Gradually, I’ve come to totally change my feelings about getting scooped. First of all, the main reason I’m doing science is that I delight in discovering things, and it’s every bit as exciting to rediscover something as it is to be the first to discover it—because at the time of the discovery, you don’t know which is the case. Second, since I believe that there are other more advanced civilizations out there—in parallel universes if not our own—everything we come up with here on our particular planet is a rediscovery, and that fact clearly doesn’t spoil the fun. Third, when you discover something yourself, you probably understand it more deeply and you certainly appreciate it more. From studying history, I’ve also come to realize that a large fraction of all breakthroughs in science were repeatedly rediscovered—when the right questions are floating around and the tools to tackle them are available, many people will naturally find the same answers independently.

Ellis, G.F.R., Issues in the Philosophy of Cosmology, Philosophy of Physics (Handbook of the Philosophy of Science), Ed. J. Butterfield and J. Earman (Elsevier, 2006), 1183-1285.

Tegmark, Max. Our mathematical universe : my quest for the ultimate nature of reality. New York: Alfred A. Knopf, 2014.

“You passed your exam in many parallel universes—but not in this one.”

Scintillating Stars But Not Planets

Aristotle (384 BC – 322 BC) may have been the first person to write that stars twinkle but planets don’t, though our understanding of twinkling has evolved since he explained that “The planets are near, so that the visual ray reaches them in its full vigour, but when it comes to the fixed stars it is quivering because of the distance and its excessive extension.”

John Stedman (1744-1797), a controversial and complicated figure to be sure, writes the following dialog between teacher and student in The Study of Astronomy, Adapted to the capacities of youth (1796):

PUPIL.  How is the twinkling of the stars in a clear night accounted for?

TUTOR.   It arises from the continual agitation of the air or atmosphere through which we view them; the particles of air being always in motion, will cause a twinkling in any distant luminous body, which shines with a strong light.

PUPIL.  Then, I suppose, the planets not being luminous, is the reason why they do not twinkle.

TUTOR.   Most certainly.  The feeble light with which they shine is not sufficient to cause such an appearance.

Still not quite right, but closer to our current understanding. Our modern term for “twinkling” is atmospheric scintillation, which is changes in a star’s brightness caused by curved wavefronts focusing or defocusing starlight.

Scintillation is caused by refractive index variations (due to differences in pressure, temperature, and humidity) of “pockets” of air passing in front of the light path between star and observer at a typical height of about 5 miles. These pockets are typically about 3 inches across, so from the naked eye observer’s standpoint, they subtend an angle of about 2 arcseconds.

The largest angular diameters of stars are on the order of 50 milliarcseconds1 (R Doradus, Betelgeuse, and Mira), and only seventeen stars have an an angular diameter larger than 1 milliarcsecond. So, it is easy to see how cells of air on the order of 2 arcseconds across moving across the light path could cause the stars to flicker and flash as seen with the unaided eye.

The five planets that are easily visible to the unaided eye (Mercury, Venus, Mars, Jupiter, and Saturn) have angular diameters that range from 3.5 arcseconds (Mars, at its most distant) up to 66 arcseconds (Venus, at its closest). Since the disk of a planet subtends multiple air cells, the different refractive indexes tend to cancel each other out, and the planet shines with a steady light.

From my own experience watching meteors many nights with my friend Paul Martsching, our reclining lawn chairs just a few feet apart, I have sometimes seen a principal star briefly brighten by two magnitudes or more, with Paul seeing no change in the star’s brightness, and vice versa.

Stedman’s dialogue next turns to the distances to the nearest stars.

PUPIL.  Have the stars then light in themselves?

TUTOR.   They undoubtedly shine with their own native light, or we should not see even the nearest of them: the distance being so immensely great, that if a cannon-ball were to travel from it to the sun, with the same velocity with which it left the cannon, it would be more than 1 million, 868 thousand years, before it reached it.

He adds a footnote:

The distance of Syrius is 18,717,442,690,526 miles.  A cannon-ball going at the rate of 1143 miles an hour, would only reach the sun in about 1,868,307 years, 88 days.

Where Stedman comes up with the velocity of a cannon-ball is unclear, but the Earth’s rotational speed at the equator is 1,040 mph, close to Stedman’s cannon-ball velocity of 1,143 mph. He states the distance to the brightest star Sirius—probably then thought to be the nearest star—is 18,717,442,690,526 miles or 3.18 light years, a bit short of the actual value of 8.60 light years. The first measurements of stellar parallax lie 42 years in the future when Stedman’s book was published.

1 1 milliarcsecond (1 mas) = 0.001 arcsecond

Aristotle, De Caelo, Book 2, chap.8, par. 290a, 18
Crumey, A., 2014, MNRAS, 442, 2600
Dravins, D., Lindegren, L., Mezey, E., Young, A. T., 1997a, PASP, 109, 173
Ellison, M. A., & Seddon, H., 1952, MNRAS, 112, 73
Stedman, J., 1796, The Study of Astronomy, Adapted to the capacities of youth