Astronomy compels the soul
to look upwards and lead us
from this world to another.
~Plato

The history of astronomy
is a history of receding horizons.
~Edwin Powell Hubble

Last week, I discussed the possible shapes our universe could take. I offhandedly mentioned that not only is the universe expanding, but that that expansion is accelerating. We attribute this expansion to a mysterious phenomenon we call dark energy. This week, I want to explore the history of this idea and the beautiful experiments that tell us all is not as it seems.

The Static Universe and Einstein’s Greatest Blunder

Einstein’s theory of general relativity predicts that spacetime is warped and curved by mass and energy, and that this is what causes gravity. After Einstein published his theory, people asked the same question we did last week: So what shape does the universe take?

In 1922, Russian physicist Alexander Friedmann sought to answer exactly this question. Friedmann guessed that, if we look at the universe on a large enough scale, matter will be evenly distribruted throughout the universe. Then he simply plugged this assumption into Einstein’s equations. (Friedmann’s guess was by no means guaranteed to be correct, although most experimental observations do seem to back it up.) What Friedmann discovered was very surprising.

When Einstein made his theory public, people believed that the universe was static, neither expanding nor contracting. However, Friedmann discovered that the universe cannot be static. If you stick a reasonable amount and distribution of mass into the equations, the universe must either expand or contract—it can’t stay still.

Friedmann took his discovery to Einstein himself, who was very skeptical. Even after Friedmann was able to convince Einstein that his calculations were correct, Einstein rejected the physics. Instead, Einstein assumed there must be something wrong with his theory. He began developing a new theory of gravity with an added term in the equations, which he called the cosmological constant, in order to keep the universe it predicted static.

While Einstein was working on his static theory of gravity, Friedmann died in 1925, mostly unrecognized. In 1927, Georges Lemaitres independently rediscovered Friedmann’s dynamic universe. He, too, took his discovery to Einstein–but by this time, Einstein was quite convinced of his static theory. He told Lemaitres: “Your calculations are correct, but your physics is atrocious.”

In 1929, Edwin Hubble observed that the universe is expanding, validating Friedmann and Lemaitres. The universe they discovered is now called the Friedmann–Lemaître–Robertson–Walker metric (a mouthful, I know), and is a central part of modern cosmological theory. Einstein called the cosmological constant his “greatest blunder.”

Hubble’s Discovery

So how did Hubble observe that the universe is expanding? Hubble took advantage of relativistic redshift. The effect is quite complicated, so I won’t go into it too deeply, but I will try to describe it by analogy. Imagine that Paul Dirac and Leopold Kronecker are playing catch, as shown below. Each second, Kronecker throws a ball to Dirac, who catches it. Thus, the frequency of balls that Dirac catches is 1 Hertz (Hz)—one per second, or one inverse second.

But now imagine that Dirac starts backing away from Kronecker. Kronecker continues to throw at a rate of one ball per second. However, since Dirac is moving away from the balls, each one takes longer to get to him. Thus, he catches the balls at a rate slower than one per second…say, one every 1.5 seconds.

A similar thing happens with both light and sound. (In the case of sound, we call it the acoustic Doppler effect.) Light is a wave, and the frequency of a light wave is analogous to the frequency at which Kronecker throws balls at Dirac. A wave has peaks and troughs, so instead of counting the number of times Dirac throws the ball, we count the peaks of the wave. The frequency of a light wave also determines its color; high frequencies are blue, while low frequencies are red. Because of the Doppler effect, starlight from a receding source will appear to an observer as redder than it should, because its peaks are getting further away  from each other. This “stretching” of a light wave (and corresponding decrease in frequency) is called a redshift.

Hubble wanted to compare the redshifts of stars to their distance from Earth. Of course, to do this, he needed to know how far away the stars were in the first place. To measure distance, astronomers use standard candles. Imagine that Dirac and Kronecker are finished playing catch and now want to play with light. Dirac lights a lantern and hands it to Kronecker, who starts walking away. Dirac observes that the lantern appears dimmer as Kronecker gets more and more distant.

Astronomers use a similar idea to measure distances: They find similar celestial objects and measure their distances from Earth by observing how bright the objects are with respect to each other. The dimmer the object, the further away it is from Earth. Of course, it’s important to know a lot about the star you’re looking at. Otherwise, a distant lighthouse could be mistaken for a nearby lantern (or an even-more-distant star). When astronomers find objects that they think they understand well enough to use for measuring distance, they call them standard candles.

Hubble made his measurements using Cepheid variable stars in spiral galaxies as his standard candles. He discovered that the further away a star was, the more redshifted its light was. Moreover, he discovered that this relationship was linear–double the distance, and the redshift doubles, too. We now call this Hubble’s Law.

How do we interpret this? If we imagine that the space between us and a distant star is made up of little squares, then the total speed of the star as it moves away from us must be equal to the sum of the rates at which all the squares expand. If we assume that all the squares are expanding at a constant rate, this explains Hubble’s Law by telling us that the universe is expanding at a constant rate.

If we imagine that the very fabric of space is expanding, we can also explain redshift in a very simple, effective way. Imagine that a light wave is travelling from a distant star to us. Because it’s a wave, it spans the entire distance. However, because the universe is expanding, the wavelength of the wave expands with it, causing the light to appear redder. (This is still an analogy, but I think it’s a good one.)

Hubble’s discovery made waves in the scientific community—nearly everyone was as surprised by the expanding universe as Einstein was. The implications are fantastic. As Stephen Hawking said:

We observe that distant galaxies are moving away from us. They must have been closer together in the past.

If we extrapolate, all matter must have been infinitely close together at some point in the distant past. Indeed, Friedmann’s solution to Einstein’s equations predicts that the universe itself was infinitely compact, such that distance meant nothing. And thus the Big Bang theory was born.

Dark Energy

Although Hubble gave us the birth of the universe, we didn’t yet know how—or if—it will ever die. Would the universe continue to expand forever? Or would the combined gravity of all the mass in the universe overcome the expansion and pull everything back together into a “Big Crunch?” This was precisely the question that the High-Z Supernova Search Team sought to answer from 1994 through 1998. Led by Brian Schmidt and Nicholas Suntzeff, the team sought to improve upon Hubble’s redshift measurements by using better standard candles to observe very distant objects.

Because light travels at a finite speed, it can take a long time for light from distant galaxies to reach us. For this reason, the further we look out into space, the further we look back into time. The High-Z Supernova Search Team wanted to look back to a time just after the Big Bang in order to see if the expansion of the universe was greater in the past than it is now. If the team observed more redshift in the distant past than we observe today, that would mean that the ancient universe was expanding more quickly than the current universe. In turn, this would imply that the expansion of the universe is slowing—and that it would eventually stop, reverse, and end in a Big Crunch.

So what standard candles did the team use? As their team name would imply, they used supernovae! Specifically, the team scanned the sky looking for the telltale signs of type 1a supernovae, which have a very consistent peak brightness. After finding one, the team would quickly measure the redshift before the explosion finished, then wait for another one. (Incidentally, if you ever need to hook a ten-year-old boy on astronomy, you should tell him that astronomers measure distance by looking at exploding stars. That’d get me hooked.)

No one could ever have predicted what the team discovered. The team observed that the redshift of distant galaxies was slightly less than the redshift predicted by Hubble. This means that galaxies were moving away from us less quickly in the distant past than they are now. Not only is the universe not going to collapse, the expansion of the universe is actually speeding up!

For the expansion of the universe to accelerate, we’d need vastly more energy in the universe than typical matter. No one knows what this stuff could possibly be, so we call it “dark energy” as a placeholder name. We can also stick dark energy into Einstein’s equations by restoring Einstein’s cosmological constant. Although Einstein used it to ensure a static universe, we can give it more power to describe the accelerating expansion of the universe. So there you have it: Einstein’s greatest blunder still contributes significantly to science. I wish my blunders were that good.

Dark Energy and Quantum Mechanics

Quantum field theory predicts that each point in space has a vacuum energy, or a small amount of energy intrinsic to empty space, associated with it. We sometimes think of this as energy allowed by the Heisenberg uncertainty principle—if we know a point’s position in time well enough, we can’t know its energy. Originally, scientists hoped that the vacuum energy could explain the cosmological constant.

The vacuum energy of quantum field theory does indeed predict a “dark energy.” Unfortunately, it’s times more energy than we actually observe. Some people have called this “the worst theoretical prediction in the history of physics.” The current hope is that a fully developed theory of quantum gravity will resolve this discrepancy. The dark-energy problem is currently one of the biggest problems facing theoretical physics. If you can explain it, you’ll win a Nobel Prize.

Further Reading

• Saul Perlmutter  heads the Supernova Cosmology Project, a competitor to the High-Z Supernova Search Team. He shared the 2011 Nobel Prize with Brian Schmidt and Adam Riess. You can find an interview with him here.
• Robert Kirshner, who was a member of theHigh-Z Supernova Search Team wrote a book for the public on the experiment. You can find it here on Amazon and here on Princeton University Press. This is an inside look on the experiment by a very respected scientist, so I definitely recommend it.
• NASA has a terse page on dark matter and dark energy.
• NASA’s Hubblesite has some fancy videos and animations for dark energy and dark matter. It’s pretty cool.
• There’s an experiment going on right now to improve on the High-Z Supernova Search Team’s results. It’s called the Dark Energy Survey, and the website has some cool stuff on it.
• The Smithsonian has a great article on dark energy.
• The website for a planned telescope, the Large Synoptic Survey Telescope, has an article on dark energy.
• Michio Kaku has a video on dark energy.
• This is a bit technical, but it’s too good to pass up. Here’s a book chapter that catalogues the efforts of Einstein and his competitor, David Hilbert, as they struggled towards a theory of general relativity.

Questions? Comments? Hatemail?

As always, if you have any questions, comments, corrections, or insults, please let me know in the comments!