Outdoor Lighting Codes and Ordinances in Wisconsin

Last Updated: 5/22/2017

Here are all the outdoor lighting codes and ordinances in Wisconsin that I am aware of.  A big thank you to Scott Lind, PE, of Hollandale, Wisconsin for initially putting together this list in 2007!

Please post a comment or contact me via email if you have additions or updates to this list.

Blue Moundsmap
http://www.ecode360.com/27010348

Brookfieldmap
http://www.codepublishing.com/WI/Brookfield/html/Brookfield17/Brookfield17120.html#17.120.070

Chenequamap
http://chenequa.org/wp-content/themes/Chenequa/Documents/Ordinances/Chap5.pdf

Cloverlandmap
http://www.townofcloverland.org/Documents/Ordinances/Code%203.01%20Lighting.pdf

Delafieldmap
https://www.municode.com/library/wi/delafield/codes/code_of_ordinances?nodeId=CH17ZOCORERE411_GEPR_17.235OULIAM491

Delavanmap
http://ci.delavan.wi.us/download/departments/building-zoning/zoning-codes/zc_23-7perstand_code.pdf
See Section 23.707 Exterior Lighting Standards

Egg Harbormap
http://www.villageofeggharbor.org/vertical/sites/%7B569578EA-93E6-481F-B733-DF3296C08FEE%7D/uploads/%7B7B55219C-9B97-4628-AEF1-445C51A0BB09%7D.PDF

Fontana-on-Geneva Lakemap
https://www.municode.com/library/wi/fontana-on-geneva_lake/codes/code_of_ordinances?nodeId=PTIIMUCO_CH18ZO_ARTXDEST_S18-165EXLIST

Fox Crossingmap
http://www.town-menasha.com/departments/clerks-office/ordinances/
Click on section Chapter 29 Development Ordinance and search for “lighting”

Fox Pointmap
http://www.ecode360.com/14717677

Genevamap
http://www.townofgenevawi.com/uploads/documents/ORDIN-59%20Regulate%20Outdoor%20Lighting%20&%20Advertising%20Signs.pdf

Green Lake Countymap
http://ecode360.com/9770791

Hollandmap
https://drive.google.com/file/d/0B1qD1hgbbNz-bWRSWmlkN2o0eEU/view

Kenoshamap
https://www.kenosha.org/images/GENORD.pdf
See Section 4.07 Artificial Light and Glare

Koshkonongmap
http://koshkonongwi.com/download/outdoor-lighting-ordinance/

Madisonmap
http://www.cityofmadison.com/attorney/ordinances/documents/chapter%2010%20-%20streets,%20alleys,%20sidewalks,%20and%20gutters.pdf
See Section 10.085 Outdoor Lighting

Mequonmap
https://www.municode.com/library/wi/mequon/codes/code_of_ordinances?nodeId=PTIICOOR_CH58PLDERE_ARTVSISTDECR_DIV2COINPAINMUMIREDE_S58-567OULIIN

Middletonmap
http://www.ci.middleton.wi.us/DocumentCenter/View/43

Mineral Pointmap
http://skythisweek.info/mineralpointlighting.pdf
Is this lighting ordinance still in effect?  I cannot find it on the Mineral Point website.

Mukwonagomap
https://www.municode.com/library/wi/mukwonago/codes/code_of_ordinances?nodeId=PTIICOOR_CH100ZO_ARTIXSIPLRE_S100-601SIPLARRESTALNOMIPR
See Section e Lighting Standards

New Glarusmap
http://www.newglarusvillage.com/__media/pdfs/ordinances/LightingLandscape.pdf
See Article XVIII Exterior Lighting Plans and Standards

Oconomowoc Lakemap
http://www.oconlake.com/Documents/ord178.html

Richfieldmap
http://ecode360.com/16178580

Shorewood Hillsmap
http://www.shorewood-hills.org/vertical/sites/%7B00D5AF3F-ADFE-4173-AF3A-FC0C1A78DA4B%7D/uploads/Ch_22_Dark_Sky.pdf

Springdalemap
http://www.townofspringdale.org/site_files/editor_files/image/file/Ordinance/031714_pdf_Final_Dark_Sky_Lighting_Ordinance.pdf

Springfieldmap
http://www.town.springfield.wi.us/ordinances/chapter-9/
See sections 9.02(7) Exterior Lighting, and 9.04(7) Exterior Lighting Plan

Sturgeon Baymap
https://www.municode.com/library/wi/sturgeon_bay/codes/code_of_ordinances?nodeId=CO_CH20ZOCO_20.12USREDI
See Section 20.12.(1)(b)12

Sussexmap
http://www.villagesussex.org/vertical/sites/%7B1FD3B636-3BF9-4496-900E-EAA7FFADF5E8%7D/uploads/17.0600_Traffic_Loading_Parking_Access_Storage_and_Lighting-01-2016.pdf
See Section 17.0608 Lighting

Westportmap
http://www.townofwestport.org/Ordinances/Title%209/Title%209%20Chapter%207.pdf

Whitefish Baymap
http://www.wfbvillage.org/DocumentCenter/Home/View/99
See Section 16.31 III A2

Williams Baymap
http://www.williamsbay.org/images/doc/Chapter%2015.pdf
See Section 15.03 Outdoor Lighting and Advertising Signs

Winneconnemap
http://ecode360.com/14487227?highlight=260#14487227

The Wisconsin State Law Library maintains a comprehensive list of Wisconsin Ordinances and Codes.  This will be a good resource for us to find additional outdoor lighting codes and ordinances to be added to this list, as well as to check your local government’s codes and ordinances in general.

It is interesting to note that nearly two-thirds of these ordinances are for suburban communities in very light-polluted metro areas.  Another four ordinances are no doubt in place to help protect the Yerkes Observatory (Williams Bay, Geneva, Fontana-on-Geneva Lake, and Delavan).  Where are the rural ordinances and dark sky preserves?  Since there are very few remaining locations in Wisconsin where the night sky is truly dark, shouldn’t we be aggressively protecting those areas?  Wouldn’t it be easier to save a pristine area than to restore an almost hopelessly polluted one? Another interesting point is that upscale suburban communities are much more likely to have a lighting ordinance than more affordable communities.  Some subdivisions even exclude streetlights, but these are almost never places where most of us can afford to live.

The Hidden Universe

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 B6: Observational horizons limit our ability to observationally determine the very large scale geometry of the universe.
We can only see back to the time of decoupling of matter and radiation, and so have no direct information about earlier times; and unless we live in a “small universe”, most of the matter in the universe is hidden behind the visual horizon.  Conjectures as to its geometry on larger scales cannot be observationally tested.  The situation is completely different in the small universe case: then we can see everything there is in the universe, including our own galaxy at earlier times.

What an intriguing idea.  If the entire universe (or the self-contained section we find ourselves in) is substantially smaller than the distance light has traveled since the universe became transparent to radiation (“decoupling”, about 380,000 years after the Big Bang), we might be able to see our Milky Way galaxy (and other galaxies) at various points in the past.

The key point here is that unless we live in a small universe, the universe itself is much bigger than the observable universe.  There are many galaxies—perhaps an infinite number—at a greater distance than the horizon, that we cannot observe by any electromagnetic radiation.  Furthermore, no causal influence can reach us from matter more distant than our particle horizon—the distance light can have travelled since the creation of the universe, so this is the furthest matter with which we can have had any causal connection.  We can hope to obtain information on matter lying between the visual horizon and the particle horizon by neutrino or gravitational radiation observatories; but we can obtain no reliable information whatever about what lies beyond the particle horizon.  We can in principle feel the gravitational effect of matter beyond the horizon because of the force it exerts (for example, matter beyond the horizon may influence velocities of matter within the horizon, even though we cannot see it).  This is possible because of the constraint equations of general relativity theory, which are in effect instantaneous equations valid on spacelike surfaces.  However we cannot uniquely decode that signal to determine what matter distribution outside the horizon caused it: a particular velocity field might be caused by a relatively small mass near the horizon, or a much larger mass much further away.  Claims about what conditions are like on very large scales—that is, much bigger than the Hubble scale—are unverifiable, for we have no observational evidence as to what conditions are like far beyond the visual horizon.  The situation is like that of an ant surveying the world from the top of a sand dune in the Sahara desert.  Her world model will be a world composed only of sand dunes—despite the existence of cities, oceans, forests, tundra, mountains, and so on beyond her horizon.

Let us now define some terms that Ellis uses above.

visual horizon – the distance beyond which the universe was still opaque to photons due to high temperature and density

particle horizon – the distance beyond which light has not yet had time to reach us in all the time since the Big Bang; our particle horizon is, therefore, farther away than our visual horizon

spacelike surface – a three-dimensional surface in four-dimensional space-time where no event on the surface lies in the past or future of any other event on that surface; every point on the surface as it exists at one instant of time

Hubble scale – a cosmological distance unit equal to the reciprocal of the Hubble constant times the speed of light; see derivation below

A reasonable value for the Hubble constant H0 is 70 km/s/Mpc.  A galaxy one megaparsec distant has a cosmological recession velocity of 70 km/s, two megaparsecs distant 140 km/s, and so on.

You may notice that there are two units of distance in H0: kilometers and megaparsecs.  We can thus rewrite H0 in units of s-1 (reciprocal seconds of time) as follows:

The Hubble time is defined as the inverse of the Hubble constant:

Converting this into more convenient units of years, we get

The Hubble scale is now simply the Hubble time multiplied by the speed of light.

Converting this into more convenient distance units of light years, and then parsecs, we get

As Ellis says, we are like ants in the Sahara desert that cannot see their Earth-universe beyond the sand dunes.  Like the ant, is there a limit to our intellect as well?

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]

Evening Planets

The most convenient time for most of us to observe the planets is in the early evening.  With that in mind, I’ve prepared an ephemeris of favorable evening times to view each of the eight major planets of the solar system over the next ten years.  Some interesting patterns emerge, which I will comment on.

With the exception of Mercury, what follows is a range of dates when each planet is at least 10° above the horizon at the end of evening twilight at latitude 43° N.  Mercury, however, is never even above the horizon at the end of evening twilight.

Mercury’s Maximum
Altitude at 43° N
Solar Depression
Angle
End of
Twilight
13°
Civil
12°
Nautical
below horizon
18°
Astronomical

Here is a list of dates when Mercury is highest above the western horizon at the end of evening civil twilight.

Mercury

Dates – Highest Above
Evening Horizon
Altitude
Constellation
July 18, 2017
Leo
November 28, 2017
Sgr
March 15, 2018
12°
Psc
July 2, 2018
Cnc
November 10, 2018
Oph
February 27, 2019
11°
Psc
June 16, 2019
10°
Gem
October 20, 2019
Lib
February 11, 2020
11°
Aqr
May 30, 2020
12°
Gem
September 25, 2020
Vir
January 25, 2021
10°
Cap
May 14, 2021
13°
Tau
September 2, 2021
Vir
January 9, 2022
Cap
April 28, 2022
13°
Tau
August 14, 2022
Leo
December 24, 2022
Sgr
April 11, 2023
13°
Ari
July 28, 2023
Leo
December 8, 2023
Sgr
March 24, 2024
12°
Psc
July 11, 2024
Cnc
November 20, 2024
Oph
March 8, 2025
12°
Psc
June 25, 2025
Cnc
November 1, 2025
Sco
February 20, 2026
11°
Psc
June 9, 2026
11°
Gem
October 10, 2026
Lib
February 4, 2027
11°
Aqr
May 24, 2027
13°
Tau
September 15, 2027
Vir

Mercury, the innermost planet, whips around the Sun every 88 days (116 days relative to the Earth—its synodic period).  It never strays more than 28° from the Sun.

As you can see in the graph below, Mercury is presently highest above our evening twilight horizon when it reaches greatest eastern elongation in April, and lowest in October.

Similarly, greatest eastern elongations that occur in the constellations Taurus and Aries present Mercury highest above our evening twilight horizon, and Libra, the lowest.

Now, let us turn to Venus.  Unlike Mercury, Venus usually spends a considerable number of days well above the horizon near greatest elongation.  This occurs because Venus orbits further from the Sun—reaching a maximum angular separation of 47°— and because its orbital period is only 140.6 days shorter than the Earth’s: the Earth “keeps up” with Venus reasonably well as the two planets orbit the Sun (the synodic period of Venus is 583.9 days), so it is a long time between successive elongations.  In the next ten years, we will see Venus high above the evening horizon during only three intervals, though for a generous three or four months each time.

Venus

Dates – At Least 10° Above the Horizon
at the End of Evening Twilight
Constellation
January 2, 2020 – May 7, 2020
Cap – Tau
February 26, 2023 – June 3, 2023
Cet – Cnc
November 30, 2024 – March 2, 2025
Sgr – Psc

Now, we turn to the superior planets: Mars, Jupiter, Saturn, Uranus, and Neptune.  These planets are visible in our evening sky during and after opposition.

Mars has the longest synodic period of all the major planets—780 days—so it takes an unusually long period of time for the orbital positions of Mars and the Earth to change relative to one another.  Approximately every two years we get the opportunity to see Mars at least 10° above the horizon at the end of evening twilight.  The number of evenings Mars is visible varies quite a lot (due to its significant orbital eccentricity): 293 evenings during the 2018 perihelic opposition of Mars, down to 145 evenings during the aphelic opposition of Mars in 2027.  In any event, Mars spends a considerable amount of time during these intervals very far away from Earth and therefore disappointingly small in our telescopes.  The best time to observe Mars is during the early weeks of the intervals listed below when Mars is at or near opposition.

Mars

Dates – At Least 10° Above the Horizon
at the End of Evening Twilight
Constellation
July 21, 2018 – May 10, 2019
Cap – Tau
October 5, 2020 – May 27, 2021
Psc – Gem
November 28, 2022 – June 11, 2023
Tau – Cnc
January 7, 2025 – June 22, 2025
Cnc – Leo
February 12, 2027 – July 7, 2027
Leo – Vir

Jupiter orbits the Sun every 11.9 years, so it is easy to see why it is in a different constellation along the zodiac each year.

Jupiter

Dates – At Least 10° Above the Horizon
at the End of Evening Twilight
Constellation
March 30, 2017 – July 24, 2017
Vir
April 29, 2018 – August 29, 2018
Lib
May 28, 2019 – October 19, 2019
Oph
June 26, 2020 – December 10, 2020
Sgr
July 30, 2021 – January 22, 2022
Aqr
September 10, 2022 – March 1, 2023
Psc
October 21, 2023 – April 5, 2024
Ari
November 28, 2024 – May 5, 2025
Tau
January 1, 2026 – May 28, 2026
Gem
February 2, 2027 – June 16, 2027
Leo

The orbital periods of Saturn, Uranus, and Neptune are 29.5, 84.0, and 164.8 years, respectively, so we can see why they take a successively longer amount of time to traverse their circle of constellations.  You’ll also notice that the interval of visibility shifts later each year, but the shift is less with increasing orbital distance.  The synodic periods of Saturn, Uranus, and Neptune are 378.1, 369.7, and 367.5 days, respectively.

Saturn

Dates – At Least 10° Above the Horizon
at the End of Evening Twilight
Constellation
May 31, 2017 – October 25, 2017 Oph
June 10, 2018 – November 11, 2018 Sgr
June 20, 2019 – November 28, 2019 Sgr
June 30, 2020 – December 12, 2020 Cap – Sgr
July 12, 2021 – December 27, 2021 Cap
July 24, 2022 – January 9, 2023 Cap
August 7, 2023 – January 23, 2024 Aqr
August 21, 2024 – February 4, 2025 Aqr
September 5, 2025 – February 17, 2026 Psc
September 20, 2026 – March 2, 2027 Cet – Psc

Uranus

Dates – At Least 10° Above the Horizon
at the End of Evening Twilight
Constellation
October 2, 2017 – March 16, 2018
Psc
October 7, 2018 – March 20, 2019
Ari
October 12, 2019 – March 23, 2020
Ari
October 15, 2020 – March 27, 2021
Ari
October 20, 2021 – March 31, 2022
Ari
October 25, 2022 – April 4, 2023
Ari
October 30, 2023 – April 7, 2024
Ari
November 3, 2024 – April 12, 2025
Tau
November 8, 2025 – April 16, 2026
Tau
November 13, 2026 – April 20, 2027
Tau

Neptune

Dates – At Least 10° Above the Horizon
at the End of Evening Twilight
Constellation
August 13, 2017 – January 30, 2018
Aqr
August 16, 2018 – February 2, 2019
Aqr
August 19, 2019 – February 4, 2020
Aqr
August 21, 2020 – February 6, 2021
Aqr
August 24, 2021 – February 8, 2022
Aqr
August 27, 2022 – February 11, 2023
Aqr
August 30, 2023 – February 13, 2024
Psc
September 1, 2024 – February 15, 2025
Psc
September 4, 2025 – February 17, 2026
Psc
September 7, 2026 – February 17, 2027
Psc

Two Paths to Low Mass

A brown dwarf (also known as an infrared dwarf) is, in a way, a failed star.  Early in their lives, these ultra-low-mass stars (13+ MJ) fuse deuterium into helium-3, and in the highest mass brown dwarfs (65-80 MJ) lithium is depleted into helium-4, as shown below.

But the mass is too low for fusion to be sustained (the temperature and pressure in the core aren’t high enough), and soon the fusion reactions peter out.  Then, only the slow process of thermal contraction provides a source of heat for the wanna-be star.

There is another, very different, path to a brown dwarf star.  A cataclysmic variable usually consists of a white dwarf and a normal star in a close binary system.  As material is pulled off the “donor star” (as the normal star is called) onto the white dwarf, the donor star can eventually lose so much mass that it can no longer sustain fusion in its core, and it becomes a brown dwarf star.

When we see a white dwarf / brown dwarf binary system, how do we know that the brown dwarf wasn’t always a brown dwarf?  Strong X-ray and ultraviolet emission provides evidence of an accretion disk around the white dwarf, and astronomers can calculate the rate of mass transfer between the two stars.  Often, this is billions of tons per second!  Using other techniques to estimate the age of the binary system, we sometimes find that the donor star must have started out as a normal star with much more mass than we see today.

Homogeneity and Isotropy

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

4.2.2 Indirect determination: justifying a Friedmann-Lemaître geometry
Considered on a large enough angular scale, astronomical observations are very nearly isotropic about us, both as regards source observations and background radiation; indeed the latter is spectacularly isotropic, better than one part in 104 after a dipole anisotropy, understood as resulting from our motion relative to the rest frame of the universe, has been removed.

No matter what direction we look, the universe looks statistically the same at a scale of hundreds of millions of light years.  We call this property isotropy.  Case in point: when compared one to the other, the Hubble Deep Fields look remarkably similar, even though they are about 135° apart in the sky.

Hubble eXtreme Deep Field in the constellation Fornax
Hubble Deep Field in the constellation Ursa Major

Taken individually, both of these deep fields also exhibit homogeneity, that is, they generally show a fairly uniform distribution of galaxies across the field.

Does the dipole anisotropy in the cosmic background radiation (CBR), due to our motion with respect the rest frame of the universe, indicate an absolute frame of reference?  Not at all.  Though the rest frame of the universe is the preferred frame for cosmology, it is not a particularly good frame of reference to use, for example, in describing the motion of the planets in our solar system.  The laws of physics are the same in all inertial (unaccelerated) reference frames, so none of them can be “special”—or absolute.  An absolute frame of reference would be one in which the laws of physics would be different—indeed simpler—but no such reference frame exists.  And any non-inertial (accelerated) reference frame indicates there is an external force outside the system acting on the system, so it can never be used as an absolute frame of reference.

We’re moving toward Leo and away from Aquarius, relative to the cosmic background radiation
Top: CBR with nothing subtracted; Middle: CBR with dipole anisotropy subtracted; Bottom: CBR with both dipole anisotropy and galactic emission subtracted
Cosmic Background Radiation from the Planck spacecraft with anisotropies removed

If all observers see an isotropic universe, then spatial homogeneity follows; indeed homogeneity follows if only three spatially separated observers see isotropy.  Now we cannot observe the universe from any other point, so we cannot observationally establish that far distant observers see an isotropic universe.  Hence the standard argument is to assume a Copernican Principle: that we are not privileged observers.  This is plausible in that all observable regions of the universe look alike: we see no major changes in conditions anywhere we look.  Combined with the isotropy we see about ourselves, this implies that all observers see an isotropic universe.

The Copernican principle states that we are not privileged observers of the universe.  Any observer elsewhere in the universe will see the same universe that we do.  The laws of physics, chemistry, and biology are truly universal.  The Copernican principle is a good example of the application of Occam’s razor: unless there is evidence to the contrary, the simplest explanation that fits all the known facts is probably the correct one.

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]

Designated Night Sky Viewing Areas

Governor Dodge State Park was established in 1955 and is the fourth largest state park in Wisconsin.  It offers several excellent locations for astronomical observation, most notably the large open grassy area just east of the Twin Valley Lake picnic area, and the paved parking lot for the backpack campsites.  The latter location is the furthest away from the urban skyglow of Dodgeville that offers a good view of nearly the entire night sky.

State park regulations require everyone to leave the park by 11:00 p.m., with some exceptions made for overnight campers, fishing, and public programs in progress (such as public star parties).  Since most stargazing can only be done after 11:00 p.m. (especially during the warm months of the year), this rule greatly diminishes access to our state parks for astronomical activities.  I would like to see one designated area of Governor Dodge State Park—the Twin Valley Lake picnic area site—open all night long for astronomical activities.  So, we would add an additional exception to the 11:00 p.m. curfew:

7. Registered stargazers may at the designated observing site during closed hours.

A “registered” stargazer would be anyone who has a current annual state park pass and has registered with the park as an amateur astronomer / stargazer.  Whenever possible, those planning to visit the designated observing site after hours should notify park staff that day before the park office closes, but this should not be required as sometimes the sky unexpectedly clears or a northern lights display commences after hours that cannot be anticipated beforehand.

Here’s another idea.  The Wisconsin DNR could issue an extra-fee annual astronomy sticker which would allow registrants 24-7 access to designated astronomy areas in participating state parks.  This is an attractive idea because it would be another revenue source for our cash-strapped state park system.  Administration and site maintenance costs would be minimal.

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.

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]

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.

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]