Great Discovery Great Question
How Can an object we see today be 27 billion light years away if the universe is only 14 billion years old?

by Judy Jackson

On April 13, 2000, collaborators of the Sloan Digital Sky Survey, of which Fermilab is a member, announced that the Survey had identified the farthest known object in the universe, as measured by spectroscopic redshift. Sky Survey commissioning data from March 2000 yielded an unassuming red speck of light, tagged by SDSS astronomers as a high-redshift quasar candidate. Follow-up spectroscopy from the Keck Telescope in Hawaii confirmed that the object was in fact a quasar, and established its record-breaking redshift of 5.8.

In the six days following the press release, there were 957,000 hits (requests for web pages or graphics) on the Sky Survey web site, at www.sdss.org. The normal average is three to four thousand per day. Over those six days, the SDSS Web site served up 15.4 gigabytes, an average of 31 KB every second. The one-day average peak rate was more than double that. Among the people who visited the SDSS web site to learn about the quasar were several dozen curious readers who wrote to Sky Survey webmaster Craig Wiegert with a variation of the following question:

"How can the recently SDSS-discovered quasar with a redshift of 5.8 be separated from the earth by 27 billion light-years in a universe that's only 14 (+6/- 2) billion years old?"

So many people, in fact, e-mailed in with that excellent question that Wiegert and University of Chicago/Fermilab astrophysicist Michael Turner posted a response on the Web, and we reprint it, with their kind permission, in FermiNews.

by Michael S. Turner and Craig Wiegert

Because the universe is expanding, light from distant galaxies is shifted to the red (longer wavelengths). The factor by which the wavelengths of spectral features are increased is denoted as one plus the redshift, z:

(received wavelength of light) =

(emitted wavelength) x (1 + z).

The phenomenon of redshift can be thought of as the stretching of the wavelength of light by the expansion of the universe. This is not the same thing as the Doppler shift caused by a moving object, although cosmological redshift is often inaccurately described in this way. (The Doppler shift formula z = v/c, or its relativistic counterpart, still applies in astrophysical situations where the expansion of the universe is not important.)

The redshift of a distant object tells us directly the size of the universe when the light was emitted, relative to the size of the universe today. So when the light was emitted from our redshift 5.82 quasar, the universe was a factor of 6.82 (remember, 1+z) smaller in linear size. Quasar redshifts are very easy to determine. You can check our calculations yourself! All quasars have a very prominent feature in their spectrum, the famous Lyman alpha line of hydrogen; the wavelength of Lyman alpha is 1216 Angstroms, in the ultraviolet. For our redshift 5.82 quasar this feature has been redshifted to around 8300 A, in the near infrared!

Computing the age of the universe when the light was emitted from our redshift 5.82 quasar is more challenging. It requires knowledge of the expansion rate of the universe (Hubble constant) and composition of the universe (which determines the slowing or speeding up of the expansion). Further, since the universe is expanding, the quasar is farther away now than when it emitted the light we see today, and so we must be careful to qualify statements made about its distance.

Using our best values for the cosmological parameters (for the experts H₀ = 65 ± 6 km/s/Mpc, Omega_matter = 0.35 ± 0.07 and Omega_total = 1.00 ± 0.05), we can infer that the light we see today was emitted when the universe was about 0.95 billion years old; for these parameters the universe is about 13.9 billion years old today. (The error margin on this is -1.4 to +1.7 billion years.) We are thus seeing the galaxy that hosts this quasar as it was almost 13 billion years ago.

Estimating the distance to the quasar requires a little more work yet. According to Einstein's general theory of relativity, the expansion of the universe is actually an expansion of space itself, and galaxies are moving away from each other because they are "being carried along by space." The theory does NOT limit the speed at which space expands, only the motion through space. Thus, the distance to this quasar can be greater than 13 billion light years. In fact, if we ask the question, "How fast is the distance between us and this quasar increasing?" we get the seemingly amazing answer of 540,000 km/sec or about 1.8 times the velocity of light. This number is ultimately not very interesting, both because this is not the best way to think about distant objects, and because there are objects farther away whose distance is growing even faster. To quote Fermilab's Judy Jackson, "There is no speed limit on the universe."

When we run the numbers, we find that this quasar is about 27 billion light years away today. This is the value we would obtain if we could magically freeze the universe in time and then measure the distance with a meterstick. From the redshift, we can then compute the distance to this quasar when the light we see today was emitted: it is 27 billion light years divided by 6.82, or about 4.0 billion light years. These numbers may seem paradoxical (and to be sure they depend somewhat upon our knowledge of the cosmological parameters; the uncertainties are -2.8 to +3.6 billion light years), but they do make perfectly good sense within Einstein's theory. The theory is well tested and its predictions make sense when carefully examined.

For example, although light from this distant quasar has only been traveling for 13 billion years, the distance measured today between where it began its journey to us and the position of the Milky Way is (and must be) greater than 13 billion light years because of the general expansion of the universe. In effect, the light has to fight its way "upstream" against expanding space.

In the end, the key to understanding all of this is to view the expansion of the universe as Einstein's amazing theory tells us to, as an expansion of space that scales up all distances in the universe. One way to visualize this is to imagine a universe with just two space dimensions, inhabited by two-dimensional creatures. Their expanding universe can be described as a rubber sheet that is being stretched uniformly in both directions, thus increasing the amount of space. Galaxies in this universe can be represented by dots painted on the rubber sheet. The dots move away from one another not because they are moving on the rubber sheet, but because of the expansion of the sheet. (In fact, it is simple to show that the change in separation of any two dots with time is proportional to their separation; this is known as Hubble's law.) Beyond the motion due to the expansion of the sheet, galaxies and photons can move along the sheet. The speed limit for this motion is the speed of light. However, there is no speed limit for recessional motions associated with the stretching of the sheet.

Finally, we should clarify that an expanding universe does not mean that everything in the universe is growing in size. Objects held together by forces strong enough to resist this expansion won't expand. For example, atoms are held together by the electric force, neutrons and protons are bound by the strong force, and astronomical objects like the Earth, our solar system, and our galaxy are held together by the force of gravity associated with these high concentrations of matter.