Degrees of Freedom

Autor ....... Davide Castelvecchi | November 6, 2011 |


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Objects may be closer than they appear; in the distant universe, objects are, in a sense, even farther than they appear

The observable universe is one big, giant magnifying lens.

At large distances, objects appear to be larger than their true size, and the farther they are, the bigger they look. The most distant observable objects are so magnified that their images in the sky—if we could see them—would be blown up by a factor of 1,000 or more.

If there were a road leading from here to the edge of the universe, you wouldn’t see it getting smaller and smaller and finally converge to a point, the way you see straight roads on earth vanish to a point on the horizon, as in the picture above. Instead, you’d see the two shoulders get closer for a while, reach a minimum width, and then start moving apart again.

To get some visual intuition about what happens then, it is helpful to look at the technique that artists have codified as reverse perspective, also known as Byzantine perspective. While in ordinary perspective lines converge to a point “at infinity,” in reverse perspective, sometimes seen in Byzantine icons, they converge to a point in front of the scene depicted. Here is an animation of a city in reverse perspective, made by London-based video artist Jeremy Mooney-Somers.

And here’s another mind-bending example:

And another one:

But the comparison between the distant universe and reverse perspective is only partially correct. In our universe, lines do not converge to a point nearby either. Instead, lines follow ordinary perspective nearby (and by “nearby” I mean within several billion light-years) and reverse perspective farther away.

This cosmic magnifying lens is, to me, one of the most mind-blowing features of our universe. And although chances are you have never heard of it, it is among the most basic predictions of the big bang theory: “It is this that was believed to be the most direct geometrical test for the reality of expanding space,” wrote the great astronomer Allan Sandage in 1988 (italics in the original).

In fact the test was proposed in the late 1950s by Fred Hoyle​ in the hope of disproving the big bang theory, which he opposed: he had famously coined the term “big bang” disparagingly, and had concocted a rival theory called the steady-state universe. In a steady-state universe, no such magnification would happen, Hoyle observed. If our universe failed the test–in other words, if astronomers could demonstrate that there is no magnification, no reverse perspective–the big bang theory would be disproved. This is called the angular size test, or angular diameter test, because it requires measuring the angle that an object subtends in the sky.

(Hoyle however was not the first cosmologist to become aware of the magnification effect, points out Roger Blandford, director of the Kavli Institute for Particle Astrophysics and Cosmology at Stanford. “Robertson and Walker, Tolman et al. understood all of this,” he says. Howard Robertson and Arthur Walker are among the guys who in the 1920s realized that general relativity, Albert Einstein​’s theory of gravitation, predicted the expansion of the universe. Soon after, Richard Tolman​ studied the connection between magnification and apparent brightness of an object.)

Ironically, while many other exhibits of evidence for the big bang’s case have accumulated since then—so that virtually no cosmologist nowadays doubts that the big bang happened—it appears that Hoyle’s original challenge is still standing: no one has demonstrated the magnification effect directly. Cosmologists have tried to crack the problem before, and they seem to have given up. “No one is in that business,” was a comment I heard from an expert.

(The fact that angular diameter tests have fallen into near-oblivion may be the reason that you don’t read about them too often. After all, science magazines such as Scientific American are news-driven—they tend to cover current research. But what I find profoundly puzzling that it isn’t mentioned more often in popular cosmology books.)

You see, to estimate how the magnification of an object varies with its distance you have know three things: 1) how far the object is; 2) how large it appears in the sky; and 3) how large it actually is. To be precise, cosmologists would like to know how the magnification varies as a function of redshift, the stretching of light waves that we observe in the light from distant galaxies. Redshift is a proxy for distance because the farther galaxies are, the more stretched their light gets, as a result of the expansion of the universe.

But the transition from ordinary perspective to reverse perspective takes place for galaxies that are so far away that their light has traveled for nearly 10 billion years (with a redshift of 1.65, Blandford told me, meaning that the light’s wavelength has stretched by 165 percent) before reaching us. As you can imagine, that light looks exceedingly faint by now.

As the physicist Steven Weinberg​ explains in his intimidating textbook Cosmology, galaxies tend to have blurry edges. Consequently, when a galaxy is very distant, more of it will fall into obscurity than if the same galaxy were closer by. The distant galaxy’s angular diameter will appear smaller than it would if we could clearly see all of it. And if the galaxy happens to be made of unusually faint stars, it will appear smaller yet–only its core, with its dense aggregation of stars, will show up, if anything will.

These and other issues, Weinberg writes, make the angular diameter test “much less useful” than other ways of measuring the geometry of the universe, such as the type Ia superovae that earned three astronomers this year’s Nobel Prize in Physics.

Nevertheless, at least one notable attempt at performing the angular diameter test was made in the early 1990s, by Ken Kellermann of the National Radio Astronomy Observatory in Charlottesville, Va., by looking at the highly energetic jets of matter that supermassive black holes shoot out as they devour matter from their surroundings.

Some of these jets appeared to be 10 times larger than you would expect from their distance, if ordinary perspective were to hold. “This is perhaps the best direct observational support for the predictions” of the big bang cosmology, Kellermann wrote, “and is also direct evidence that the redshift of galaxies and quasars is really due to the expansion of the universe.” Below is a diagram from Kellermann’s paper.



This diagram showed the angular size, or the angle subtended in the sky, by compact radio sources of different redshifts. (Redshift is a proxy for distance, as farther objects are more redshifted.) The data suggested that the angular size bottomed out at a redshift of between 1 and 2, instead of decreasing forever as one would expect from the ordinary laws of perspective. A milliarcsecond is one-thousandth of an arcsecond, which is itself one-3,600th of a degree: for comparison, the sun and the moon each subtend about half a degree in the sky, or 1,800 arcseconds. These estimates of angular sizes were later considered unreliable. Nature Vol. 361, pages 134 – 136; January 14, 1993.

Unfortunately, Kellermann’s methodology was later put into question and the radio sources he used are nowadays generally considered unreliable. That is, astronomers are not sure they can accurately estimate the sources’ true size.

But why should such a counter-intuitive effect be true at all? It has to do with non-Euclidean geometry–with the non-flatness of the universe.

“Hold on a second,” you say, “Didn’t NASA’s WMAP show that our universe is flat? I read countless articles saying that.” Sure, but it depends what you mean by “universe.” The term is often used sloppily without regard for the fact that it can mean different things. If by universe you mean space now–call it the nowverse–then it definitely looks uncannily close to being flat. If by universe you mean spacetime, then it certainly isn’t flat, if Albert Einstein’s general relativity is true: mass and energy produce curvature, so the only way that spacetime could be flat is if it were completely empty.

But what I mean here by universe is neither the nowverse nor spacetime, but yet another thing. What I am talking about is the observed universe–the stuff we actually see in the sky. In the next post, I will explain why the observed universe is curved–as well as why it’s supposed to act as a magnifying lens.

References and further readings:

The Relation of Radio Astronomy to Cosmology, by Fred Hoyle. Radio Astronomy, IAU Symposium No. 9, p. 529; 1959.
Observational Tests of World Models, by Allan Sandage​. Annual Reviews of Astronomy and Astrophysics 1988. 26: 561-630.
The Cosmological Deceleration Parameter Estimated from the Angular-Size/Redshift Relation for Compact Radio Sources, by K. I. Kellermann. Nature 361, 134 – 136; January 14, 1993.
Testing the Angular-Size Versus Redshift Relation with Compact Radio Sources, by Youri Dabrowski, Anthony Lasenby and Richard Saunders. Monthly Notices of the Royal Astronomical Society, Volume 277, Issue 3, pages 753-757.
Poetry of the Universe, by Robert Osserman. Anchor Books, 1995.
An Introduction to the Science of Cosmology, by D. J. Raine and E. G. Thomas. Institute of Physics, 2001.
Cosmology, by Steven Weinberg. Oxford University Press, 2008.
What Do You Mean, The Universe Is Flat?, Part 1. Degrees of Freedom, July 25, 2011.
Another cool reverse perspective animation.


About the Author: Davide Castelvecchi is a freelance science writer based in Rome and a contributing editor for Scientific American magazine. Follow on Twitter @dcastelvecchi.


The views expressed are those of the author and are not necessarily those of Scientific American.