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.

References
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.
[http://arxiv.org/abs/astro-ph/0602280]

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.

1824

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

1876

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

1888

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

2000

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

2016

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.

References
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.
[http://arxiv.org/abs/astro-ph/0602280]

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)

Distant Supernovae Evince Accelerating Expansion of our Universe

In 1998, it was discovered by two independent research teams through the study of distant Type Ia supernovae that our expanding universe has an expansion rate that is accelerating.  This was a completely unexpected result.

A Type Ia supernova occurs in a close binary star system where mass from one star accretes onto a white dwarf until it reaches a critical mass and a supernova explosion ensues.  Many of these events, chosen carefully, can be used as “standard candles” for distance determination.  The intrinsic peak luminosity of a typical Type Ia supernova is a function of the light curve decay time.  Type Ia supernovae whose luminosity curves rise and fall more rapidly are less intrinsically luminous at maximum brightness.  Type Ia supernovae whose luminosity curves rise and fall more slowly are more intrinsically luminous at maximum brightness.

If we know the intrinsic luminosity of an object (the absolute magnitude) and can measure the apparent luminosity of that object (the apparent magnitude), we can calculate its distance.  Type Ia supernovae are on the order of a million times brighter than Cepheid variables, and are in fact the brightest of all “normal” supernovae.  They can thus be used to measure the distance to extremely distant objects.

The evidence for an accelerating universe is that these distant supernovae appear fainter than they should be at their measured cosmological redshift, indicating that they are farther away than expected.  A number of possible explanations for the faint supernova phenomenon had to be eliminated before the conclusion that the universe’s expansion is accelerating could be arrived at, including

(1) Do distant supernovae (and therefore supernovae that occurred many billions of years ago) have the same intrinsic brightness as comparable nearby supernovae that occurred in the recent past?

(2) Are the distant supernovae being dimmed by galactic and intergalactic extinction due to dust and gas along our line of sight to the supernova?

As described above, the shape of the supernova light curve indicates the supernova’s intrinsic brightness, analogous in a way to the period of a Cepheid indicating its intrinsic brightness.  Though there is evidence that ancient supernovae may have been a little different than those today because of lower metallicity, the effect is small and doesn’t change the overall conclusion of an accelerating universe.  However, properly characterizing the influence of metallicity will result in less uncertainly in distance and therefore less uncertainty in the acceleration rate of the universe.

Extinction is worse at bluer wavelengths, but how the apparent magnitude changes as a function of distance is independent of wavelength, so the two effects can be disentangled.  2011 Nobel physics laureate Adam Riess in his award-winning 1996 Ph.D. thesis developed a “Multicolor Light Curve Shape Method” to analyze the light curves of a large ensemble of type Ia supernovae, both near and far, allowing him to determine their distances more accurately by removing the effects of extinction.

Separating Observer from Observed

One of the most difficult things to do in observational science is to separate the observer from the observed.  For example, in CCD astronomy, we apply bias, dark, and flat-field corrections as well as utilize median combines of shifted images to yield an image that is, ideally, free of any CCD chip defects including differences in pixel sensitivity and zero-point.

We as observers are constrained by other limitations.  For example, when we look at a particular galaxy, we observe it from a single vantage point in space and time, a vantage point we cannot change due to our great distance from the object and our existence within an exceedingly short interval of time.

Yet another limitation is a phenomenon that astronomers often call “observational selection”.  Put simply, we are most likely to see what is easiest to see.  For example, many of the exoplanets we have discovered thus far are “hot Jupiters”.  Is this because massive planets that orbit very close to a star are common?  Not necessarily.  The radial velocity technique we use to detect many exoplanets is biased towards finding massive planets with short-period orbits because such planets cause the biggest radial velocity fluctuations in their parent star over the shortest period of time.  Planets like the Earth with its relatively small mass and long orbital period (1 year) are much more difficult to detect using the radial velocity technique.  The same holds true for the transit method.  Planets orbiting close to a star will transit more often—and are more likely to transit—than comparable planets further out.  Larger planets will exhibit a larger Δm than smaller planets, regardless of their location.  It may be that Earthlike planets are much more prevalent than hot Jupiters, but we can’t really conclude that looking at the data collected so far (though Kepler has helped recently to make a stronger case for abundant terrestrial planets).

Here’s another important observational selection effect to consider in astronomy: the farther away a celestial object is the brighter that object must be for us to even see it.  In other words, many far-away objects cannot be observed because they are too dim.  This means that when we look at a given volume of space, intrinsically bright objects are over-represented.  The average luminosity of objects seems to increase with increasing distance.  This is called the Malmquist bias, named after the Swedish astronomer Gunnar Malmquist (1893-1982).

Dodgeville is Not Bicycle Friendly

Quite a few people living in Dodgeville work at Lands’ End, but there really isn’t a safe bicycle route connecting Lands’ End with most of Dodgeville.  Right now, we basically have two choices—neither of them are very safe.  You can ride down Lehner Rd. to US 18 and then ride along the south shoulder of the highway until you get up to King St., then cross the highway there (no traffic lights and a 55 mph speed limit).  Or, alternatively, you can ride on the busiest street in town, N. Bequette St. (Wisconsin Hwy 23) and then follow rubblized W. Leffler St. up to King St.

There’s a large piece of farm land for sale between W. North St. and US 18, and though most of us would prefer that it remain farm land, chances are that it will someday be developed into Dodgeville’s newest residential subdivision.  If and when that happens, we should put in an asphalt bike path adjacent to the new road that will almost certainly get built to connect W. Chapel St. to King St.  Of course, the W. Chapel / US 18 / King St. intersection will need to have traffic signals.  What a wonderful addition this bike path would be for our community!

In the meantime, it would help if Lands’ End constructed a short connector bike path from the north shoulder of US 18 just east of the Lehner Rd. intersection to Lands’ End Lane as shown below.  Wisconsin DOT would need to review and approve the project, but it is likely they would be supportive of such a project given the unsafe conditions that exist today.

Another option would be to make use of the City of Dodgeville utility access road already in place on the north side of US 18, just a little west of the Lehner Rd. intersection.  A connector bike path could be built to Lands’ End Lane as shown below.

While we’re on the topic of bicycles, has anyone else noticed how much worse condition the streets are in—not just in Dodgeville but everywhere—than they were, say, 40 or 50 years ago?  The transverse cracking and alligator cracking on our city streets is as bad as I have ever seen, and certainly must be a major factor in why there are so few bicycle riders in our town.

Update August 17, 2018

OK, the US 18 sealcoat project from Dodgeville to Edmund gave me an opportunity to revisit a safer way to currently ride from the west side of Dodgeville to and from the Lands’ End campus.

Going to Lands’ End, the first step is to get to the intersection of W. North St. & N. Bequette St.  Ride along the sidewalk on the west side of N. Bequette. down to US 18.

Cross at the crosswalk to the north side of the intersection.  You can do this without getting off your bicycle as there is an easy-to-access crosswalk button and curb ramp on both sides of US 18.  Just a few feet past that intersection, take the unnamed access road to the Lands’ End store (formerly Walmart) parking lot and wend your way over to Joseph St.

Head north on Joseph St. to the left turn lane at the intersection with King St.  Head west on King until you get to the main entrance to the Lands’ End campus, Lands’ End Lane.  You’ve arrived!

One improvement is needed for making a left turn heading home.  The inductance loop underneath the pavement on Lands’ End Lane at the King St. intersection is not clearly marked nor is it able to detect bicycles (believe me, I’ve tried!).  When I lived in Ames, Iowa, most controlled intersections had clearly-marked inductance loops and all you had to do was to position the middle of your bike frame above one of the corners of the loop and you would trigger the traffic light to change just like a car does.  As it is now, I have to cross on a red light unless there is a car behind me that triggers the traffic light.

The most dangerous part of the journey is along the ingress and egress points for Kwik Trip #340.  One improvement that could be made is to clearly mark (with painted lines and possibly signage) the sidewalk/bike route in this area.  Also, the sidewalk sort of “disappears” between the south and north driveways, as you can see in the image below.  Structural improvements could be made to this section to make it safer.

The Language We Use

Much has been said about how television, movies, video games, and the internet contributes to the culture of violence in our uncivilization, and this extends to even the language we use to describe events, activities, and phenomena.  Even astronomy is not immune from pervasive, perverse imagery.  Little things add up.  For example, why do we call THE event 13.8 billion years ago the Big Bang instead of something like the Great Flaring Forth?  And, instead of telling a group of eager young stargazers, “Our next target will be M13” why not say something like “Our next destination will be M13”?  And why do we call a smaller galaxy merging with a larger one “galactic cannibalism”?  You get the idea.

Fred Rogers (1928-2003) had it right: “Of course, I get angry.  Of course, I get sad.  I have a full range of emotions.  I also have a whole smorgasbord of ways of dealing with my feelings.  That is what we should give children.  Give them ways to express their rage without hurting themselves or somebody else.  That’s what the world needs.”

Think about it.  Then do something about it.

Cosmologically Distant Objects Appear Magnified

George F. R. Ellis writes in section 2.3.3 of his outstanding survey paper, Issues in the Philosophy of Cosmology:

…there is a minimum apparent size for objects of fixed physical size at some redshift zc = z depending on the density parameter and the cosmological constant.  The past light cone of the observer attains a maximum area at z; the entire universe acts as a gravitational lens for further off objects, magnifying their apparent size so that very distant objects can appear to have the same angular size as nearby ones.  For the Einstein-de Sitter universe, the minimum angular diameter is at z = 1.25; in low density universes, it occurs at higher redshifts.

Electromagnetic radiation such as visible light that we observe from a source that is in motion relative to us (the observer) experiences a change in wavelength that is given by

This is called redshift and is positive for a source that is moving away from us and negative for a source that is moving towards us.  The higher the relative speed toward or away from us, the greater the magnitude of the redshift.  Superimposed upon the kinematic velocities of individual galaxies relative to our Milky Way galaxy, since 1929 we have known that there is a cosmological redshift (called the Hubble flow) that is always positive and increasing in magnitude with increasing distance between any two galaxies.  In the nearby universe, the redshift (or blueshift) from kinematic velocities (often referred to as “peculiar velocities”) swamp the contribution from the Hubble flow, so some galaxies are actually approaching each other.  A good example of this is M31 and the Milky Way galaxy.  For more distant galaxies, however, the cosmological redshift swamps any contribution from the kinematic velocities.  Thus, redshift becomes a useful proxy for distance at cosmological distances.

From our everyday experience, we know that the further away an object is, the smaller is its angular size.  However, there comes a point where the angular size of an object reaches a minimum, and at even greater distances, its angular size increases!  As George Ellis states above, the entire universe acts as a gravitational lens to magnify distant objects.

Michael Richmond presents an equation for angular size as a function of redshift (based on some classical assumptions about the structure of the universe).  In his equation, the angular size of an object also depends upon the value we choose for H0, the Hubble constant, the matter density parameter, ΩM, and, of course, the physical size of the object of interest.

Let’s work through an example using this equation.  The visible part of the Andromeda Galaxy is estimated to be about 220,000 light years across.  In megaparsecs, that is 0.0675.  This is the value we will use for S.

For the Hubble constant, H0, let use a recent result: 71.9 km/s/Mpc.

And, for the matter density parameter, ΩM, let’s use 1.0.  This indicates that we live in a universe that has just enough matter for the universe to eventually recollapse, were it not for dark energy.  Though Richmond’s equation above only applies to a matter-dominated universe where the dark energy density parameter ΩΛ is zero, as George Ellis indicates above, a minimum angular diameter is still reached in a universe with dark-energy (i.e. low density universe), only this occurs at a higher redshift than that presented here.

I have not been able to find or derive a more general equation for angular size as a function of redshift that will work for a dark-energy-dominated universe (perhaps a knowledgeable reader will post a comment here providing some insight into this issue), but it will be a useful exercise to continue with the calculation assuming the matter-dominated Einstein-de Sitter universe.

Casting Michael Richmond’s equation into the following SAS program, I was able to find that the Andromeda galaxy would reach a minimum angular size of 11.3 arcseconds at z = 1.25, as shown below.

In principle, measuring the angular size of a “standard” object at various redshifts could allow us to determine what kind of universe we live in.  But there’s a problem.  As we look further out into space we are also looking further back in time, so there is no guarantee that a “standard” object in today’s universe (say, a spiral galaxy such as M31) would have looked the same or even existed billions of years ago.

References
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.
[http://arxiv.org/abs/astro-ph/0602280]

Richmond, Michael, Two classic cosmological tests
[http://spiff.rit.edu/classes/phys443/lectures/classic/classic.html]