Knowledge Limited: Deep Time, Deep Space

We continue our series of excerpts (and discussion) from the outstanding survey paper by George F. R. Ellis, Issues in the Philosophy of Cosmology.

Thesis A4: The concept of probability is problematic in the context of existence of only one object.
It is useful to distinguish between the experimental sciences—physics, chemistry, microbiology for example—on the one hand, and the historical and geographical sciences—astronomy, geology, evolutionary theory for example, on the other.

In the experimental sciences, one is usually free to both observe and experiment.  For example, we can observe at what temperature water freezes with different concentrations of various salts such as sodium chloride.  But in the historical and geographical sciences, one can observe but we are seldom, if ever, able to experiment.  We can observe the properties of the Sun and other stars, but we cannot create a star nor modify its properties to see how that alters its development.  We must infer how individual stars or classes of stars change with time by observing many stars of different masses at various points along their continuum of existence.  And what of objects that are unique or that happened only once?  The evolution of life on Earth, the Grand Canyon, and the Universe itself?  The greatest challenge in the historical and geographical sciences besides not being able to run experiments is the enormous amount of time it takes for measurable changes to occur.  How can we humans—who seldom live more than a century—begin to comprehend changes that occur over a million, let alone a billion, years?

Thesis B1: Astronomical observations are confined to the past null cone, fading with distance.
Uncertainty grows with distance and time.  The vast scale of the universe implies we can effectively only view it from one spacetime event (“here and now”).

Cosmology is both a geographic and a historical science combined into one: we see distant sources at an earlier epoch, when their properties may have been different.  As we are looking back in the past, source evolution must be taken into account; their properties at the time they emitted the light may be quite different from their properties now.  We can only determine the distances of objects if we understand this evolution; but in practice it is one of the unknowns we have to try to determine.

Distant sources appear very small and very faint, both because of their physical distance, and because their light is highly redshifted (due to the expansion of the universe).  Simply detecting them, let alone determining their characteristics, becomes rapidly more difficult with distance.  Furthermore absorption by intervening matter can interfere with light from distant objects.  The further back we look, the worse these problems become; thus our reliable knowledge of the universe decreases rapidly with distance.

Another name for the “null cone” Ellis mentions above is light cone.  A light cone is a two-dimensional model of our three spatial dimensions, plus time.  We build up the cone using a series of circles along the time dimension.

First, let’s consider that you, the observer, as experimenter, produce an isotropic flash of light sometime this year at a particular location.  The flash of light will move outward in all directions at the speed of light.  The concentric circles below show the location of the wavefront from your flash in the year 2027, 2037, and 2047 when it is 10 light years, 20 light years, and 30 light years from Earth, respectively, and so on.  If we add a time axis that is perpendicular to the plane of our two-dimensional “Flatland” and points away from you, we see that we can build up a cone from the ever-expanding circular wavefront at every instant of time.  This is the future light cone.

Similarly, when you look out into the depths of space on a clear night you are also inexorably looking back in time.  Light from a star 10 light years away left on its journey to Earth in 2007.  If the star is 20 light years away, the light began its journey in 1997.  If 30 light years away, in 1987, and so on.  Again, if we add a time axis perpendicular to our two spatial dimensions, now pointing towards you (coming from the past), we see that we can build up a cone from the incoming wavefront’s location at each moment of time in the past.  This is the past light cone.

Now, if we put the past and future light cones together we get the full view of our location in spacetime, as shown below.  The two cones meet at the “here and now”.  Keep in mind that the diagram below is a two-dimensional representation of a 3D object (two spatial dimensions and one time dimension), but in reality, this should be a four-dimensional object (three spatial dimensions and one time dimension).

So, our view from the “here and now” is small and provincial.  Instead of obtaining a panoramic snapshot of our universe as it currently exists today, we are being served up old photos instead.  But quite useful, nonetheless.

Ellis, G. F. R. 2006, 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.

Largest Sunspots

A sunspot is a region of the Sun’s photosphere that is cooled by a very strong magnetic field, ranging between 1 and 4 kilogauss.  The larger the sunspot, the stronger the magnetic field.  In comparison, the Sun’s average photospheric field strength is around 1 gauss, and the Earth’s surface field strength is around 0.5 gauss.  The strength of the magnetic field at any point on the Sun can be accurately determined by measuring the degree that spectral lines are split due to the Zeeman effect.  Under the influence of a strong magnetic field, individual spectral lines in a hot gas will be split into several adjacent lines at slightly different wavelengths.  The greater the distance (in wavelength) between the sublines, the stronger the magnetic field.

A sunspot is magnetically cooled, then, to a temperature that is 2,300 to 5,000° F cooler than the surrounding photosphere.  Since a cooler gas emits less light, the sunspot appears dark against the hotter and brighter photosphere.  It is a contrast effect.  Large sunspots have the “coolest” temperatures.

Every once in a great while, a really large sunspot forms.  The area covered by a sunspot is usually given in units of “millionths of the Sun’s Earth-facing hemisphere”.  Here are the 10 largest sunspots recorded since 1874.

Rank Month Active Region Size (10-6)
1 Apr 1947 14886 6132
2 Feb 1946 14417 5202
3 May 1951 16763 4865
4 Jul 1946 14585 4720
5 Mar 1947 14851 4554
6 Jan 1926 9861 3716
7 Jan 1938 12673 3627
8 Mar 1989 5395 3600
9 Feb 1917 7977 3590
10 Jul 1938 12902 3379

How big would an Earth-sized sunspot be?  Just 84 millionths of the Sun’s area on its Earth-facing hemisphere.  Far smaller than the giant sunspots listed above!

Beginnings, Quantum Gravity, and Inflation

We continue our series on the outstanding survey paper by George F. R. Ellis, Issues in the Philosophy of Cosmology.

2.6  Inflation
Particle horizons in inflationary FL models will be much larger than in the standard models with ordinary matter, allowing causal connection of matter on scales larger than the visual horizon, and inflation also will sweep topological defects outside the visible domain.

The particle horizon is the distance beyond which light would have not yet had time to reach us in all the time since the Big Bang.  The visual horizon is the distance beyond which the universe was still opaque to photons due to high temperature and density.  The visual horizon, therefore, is not as far away as the particle horizon.  FL stands for Friedmann-Lemaître, the standard models of a flat, open, or closed universe.

What is inflation?  At the moment of the Big Bang, the expansion of the universe accelerated exponentially for a very short period of time.  This caused portions of space that had been close enough together to be causally connected to become causally disconnected.  While inflation does a very good job of explaining many observed features of our universe, such as its uniformity in all directions, at this point it is an untestable hypothesis (unlike special and general relativity), and the underlying physical principles are completely unknown.

2.7  The very early universe
Quantum gravity processes are presumed to have dominated the very earliest times, preceding inflation.  There are many theories of the quantum origin of the universe, but none has attained dominance.  The problem is that we do not have a good theory of quantum gravity, so all these attempts are essentially different proposals for extrapolating known physics into the unknown.  A key issue is whether quantum effects can remove the initial singularity and make possible universes without a beginning.  Preliminary results suggest that this may be so.

We currently live in a universe where the density may be too low to observe how gravity behaves at the quantum level.  Though we may never be able to build a particle accelerator with energies high enough to explore quantum gravity, quantum gravity might possibly play a detectable role in high-density stars such as white dwarfs, neutron stars, or black holes.  At the time of the Big Bang, however, the density of the universe was so high that quantum gravity certainly must have played a role in the subsequent development of our universe.

Do we live in the universe that had no beginning and will have no end?  A universe that is supratemporal—existing outside of time—because it has always existed and always will exist?  Admittedly, this is an idea that appeals to me, but at present it is little more than conjecture, or, perhaps, even wishful thinking.

2.7.1  Is there a quantum gravity epoch?
A key issue is whether the start of the universe was very special or generic.

Will science ever be able to answer this question?  I sincerely hope so.

2.8.1  Some misunderstandings
Two distantly separated fundamental observers in a surface {t = const} can have a relative velocity greater than c if their spatial separation is large enough.  No violation of special relativity is implied, as this is not a local velocity difference, and no information is transferred between distant galaxies moving apart at these speeds.  For example, there is presently a sphere around us of matter receding from us at the speed of light; matter beyond this sphere is moving away from us at a speed greater than the speed of light.  The matter that emitted the CBR was moving away from us at a speed of about 61c when it did so.

Thus, there are (many) places in our universe that are receding from us so fast that light will never have a chance to reach us from there.  Indeed, the cosmic background radiation that pervades our universe today was emitted by matter that was receding from us at 61 times the speed of light at that time.  That matter never was nor ever will be visible to us, but the electromagnetic radiation it emitted then, at the time of decoupling, is everywhere around us.  Think of it as an afterglow.

Ellis, G. F. R. 2006, 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.

Holes in Our Democracy

The Electoral College

There have been 58 presidential elections in the United States.  The first was in 1788, and the most recent in 2016.  Five times (8.6% of the time) the winner of the U.S. presidential election did not receive the most votes, thanks to the Electoral College.


Andrew Jackson 151,271 41.4% Democratic-Republican
John Quincy Adams 113,122 30.9% Democratic-Republican


Samuel J. Tilden 4,286,808 50.9% Democratic
Rutherford B. Hayes
4,034,142 47.9% Republican


Grover Cleveland 5,534,488 48.6% Democratic
Benjamin Harrison
5,443,892 47.8% Republican


Al Gore 51,009,810 48.4% Democratic
George W. Bush
50,462,412 47.9% Republican


Hillary Clinton 65,853,516 48.2% Democratic
Donald Trump
62,984,825 46.1% Republican

The Electoral College needs to change or be abolished, and the national popular vote should determine who is elected president.  Why should “winner takes all” in each state continue to prevail?  This isn’t a ball game.  As it is now, a candidate gets 100% of the electoral votes for a state whether they got 80% of the popular vote or 50.5%.  Each state’s electoral votes should be apportioned based on the number of popular votes each candidate got.  Every vote should count equally, no matter what state you live in.

Proportional Representation

In the U.S. Congress and the state legislatures, if the Green Party, for example, is supported by 10% of the electorate, then they should have 10% of the representation in the legislative body.  Proportional representation ensures that all popular viewpoints in the electorate have representation in our government, and prevents any one political party from ever having too much power.

Ballot Measures

Rather than always voting for people who are supposed to represent you and your interests, but often do not, wouldn’t you rather vote on the issues themselves?  We should all have a chance to vote more often on ballot measures, even if they are only directional in nature.  I have no doubt, for example, that we would have stricter weapons laws in this country if we the people were ever given the opportunity to directly vote on the matter.


Lyrid Meteor Shower

The Lyrid meteor shower peaks this Friday night and Saturday morning, April 21/22, and this year we have the perfect trifecta: a weekend event, a peak favorable for North America, and little to no moon interference.  Now, all we need is clear skies!

The Lyrids are expected to crescendo to a peak somewhere between 11 p.m. Friday evening and 10 a.m. Saturday morning.  One prediction I found even has them peaking at noon on Saturday.

Lyrids – April 21/22 – Local Circumstances for Dodgeville, WI

When to watch?  At a minimum, I’d recommend observing at least two hours, from 2:30 to 4:30 a.m.  You can expect to see maybe 15 fairly fast meteors per hour.

My friend Paul Martsching of Ames, Iowa has been one of the most active and meticulous meteor observers in the world.  In nearly 30 years of observing this shower, he notes that 21% of Lyrid meteors leave persistent trains.  Though few Lyrids reach fireball status, Paul did observe a -8 Lyrid at 1:50 a.m. on April 22, 2014 (his brightest Lyrid ever) that left a train that lasted five and a half minutes!  Paul notes a color distribution of the Lyrid meteors as 73% white, 22% yellow, and 5% orange.

I’m still trying to find a good location within about 10 miles of Dodgeville to watch meteor showers.  Governor Dodge State Park would be ideal, but anyone who isn’t camping has to leave the park by 11:00 p.m.

Meteor watching is most enjoyable in groups of two or more.  I’m planning to observe this shower, so contact me if you’d like to team up!

A Small, Big, or Really Big Universe?

George F. R. Ellis writes in section 2.4.2 of his outstanding survey paper, Issues in the Philosophy of Cosmology:

Clearly we cannot obtain any observational data on what is happening beyond the particle horizon; indeed we cannot even see that far because the universe was opaque before decoupling.  Our view of the universe is limited by the visual horizon, comprised of the worldlines of furthest matter we can observe—namely, the matter that emitted the CBR at the time of last scattering.

The picture we obtain of the LSS by measuring the CBR from satellites such as COBE and WMAP is just a view of the matter comprising the visual horizon, viewed by us at the time in the far distant past when it decoupled from radiation.

Visual horizons do indeed exist, unless we live in a small universe, spatially closed with the closure scale so small that we can have seen right around the universe since decoupling.

The major consequence of the existence of visual horizons is that many present-day speculations about the super-horizon structure of the universe—e.g. the chaotic inflationary theory—are not observationally testable, because one can obtain no definite information whatever about what lies beyond the visual horizon.  This is one of the major limits to be taken into account in our attempts to test the veracity of cosmological models.

Let’s start by defining a few of the terms that Ellis uses above.

particle horizon – the distance beyond which light has not yet had time to reach us in all the time since the Big Bang

decoupling – the time after the Big Bang when the Universe had expanded and cooled enough that it was no longer a completely ionized opaque plasma; atoms could form and photons began traveling great distances without being absorbed

worldlines – the path of a photon (or any particle or object) in 4-dimensional spacetime: its location at each and every moment in time

CBRcosmic background radiation

LSS – last scattering surface

COBECosmic Background Explorer

WMAPWilkinson Microwave Anisotropy Probe

(And, Planck should be added now, too)

Now the question.  Do we live in a small, big, or really big universe?  The best answer we can give now (or, perhaps, even in the future) is that we live in a really big universe, though it is unlikely to be infinite.  Ellis himself provides a cogent argument in section 9.3.2 of the paper referenced here that infinity, while a very useful mathematical tool, does not ever exist in physical reality.  We shall investigate this topic in a future posting.

Even though general relativity shows us how matter defines the geometry of our observable universe, it tells us nothing about the topology of our universe, in other words, its global properties.  Do we live in a wrap-around universe where if we set off in one direction and traveled long enough, we’d eventually return to the same point in spacetime?  Is the topology of our universe finite or infinite?  At the moment it appears that we are not able to observe enough of the universe to discern its topology.  If that is true, we may never be able to understand what type of universe we live in.  But observational cosmologists will continue to search for the imprint of topology on our visible universe at the largest scales.

Ellis, G. F. R. 2006, 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.

Liddle, A.R. 2015, An Introduction to Modern Cosmology, 3rd ed., Wiley, ISBN: 978-1-118-50214-3.

In Praise of the Observatory

Observatories come in all shapes and sizes: you can build your own, or purchase one ready-made from a growing number of companies.  And you can build an observatory for not much more than the cost of a good telescope.  There is even one company, Backyard Observatories, that travels around the country building absolutely first-rate observatories at very reasonable prices.

The advantages of having an observatory are many:

  1. An accurately polar-aligned telescope ready to use on a moment’s notice (an equatorially-mounted telescope still has many advantages over the alt-azimuth variety)
  2. Minimal pre-observing and post-observing chores
  3. A telescope that is already at or near the ambient air temperature (resulting in better images)
  4. A shelter from wind and the glare of nearby lights
  5. An organized very special place to do productive astronomical observing, astroimaging, and research with all the tools you need at hand

As an added measure of protection, keep a heavy ply plastic bag over your telescope when not in use (I recommend Warp’s Original Banana Bags®), cinched up around the pier with a bungee cord, with desiccant inside to keep the telescope optics dry (I recommend the Eva-Dry 333) so that mildew doesn’t form on the optical surfaces.  Here in the Midwest, humidity is almost always a problem, so unless it is really windy, I use an Astrozap FlexiHeat Dew Shield on the telescope during every observing session as an added measure of protection.

Never sleep more than 90 feet from your telescope.
– Clinton B. Ford (1913-1992)