Receding Horizons: Dark Energy and the Expanding Universe

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

Einstein and Hubble
A meeting of minds: Albert Einstein (left), Edwin Hubble (middle), and Walter Adams (right) looking through the one hundred-inch telescope at the Mount Wilson Observatory. It was here that Edwin Hubble discovered that the universe is expanding. (Image source.)

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.

Kronecker and Dirac Playing Catch While not Moving
Leopold Kronecker (left) and Paul Dirac (right) playing catch. Every second, Kronecker throws a ball to Dirac, who catches it. Thus, the frequency of balls caught is 1 Hz. (Source for Kronecker can be found here. Source for Dirac can be found here.)

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.

Dirac moves away from Kronecker.
Dirac starts moving away from Kronecker. Because it takes the balls longer to reach Dirac, he only catches one every 1.5 seconds, even though Kronecker still throws the balls at a rate of one per second. (Source for Kronecker can be found here. Source for Dirac can be found here.)

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.

Wave with labels
A light wave has peaks and troughs. The number of peaks that pass by Dirac in a given second is analogous to the frequency of the wave.

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.

Expanding universe in the discrete lattice model
A constant expansion rate leads to a linear redshift. If we break space up into little squares, each expanding at a constant rate, then the total speed of a star moving away from us is the sum of all the squares’ expansion rates. (Source for Earth image here. Source for star image here.)

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.)

Redshift from spacetime growth.
If a wave of light spans the distance between a distant star and Earth, the expanding universe will stretch the wave out, increasing its wavelength and making its light appear redder. (Source for Earth image here. Source for star image here.)

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 10^{120} 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

Questions? Comments? Hatemail?

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

About jonah

Jonah is the author of The Physics Mill.
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14 Responses to Receding Horizons: Dark Energy and the Expanding Universe

  1. There’s a pretty good book on the story of the discovery of cosmic acceleration:
    “The Extravagant Universe: exploding stars, dark energy, and the accelerating universe.”
    Of course, I am biassed a bit, because I wrote it, but has a view from inside the High-Z Team that you might find interesting. It is still in print and available from Princeton University Press or from Amazon.

    • jonah says:

      Thanks very much for the recomendation, Professor Kirshner! I’ll check it out, and suggest my readers do too. I hope you enjoyed my description of your experiment.

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  4. Isaac Domagalski says:

    Minor correction: The 2011 Nobel Prize went to Perlmutter, Schidt and Riess.

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  6. Pseudonymous says:

    Hello!

    Well, i tried to imagine why the universe is expanding.Here it is:(It might sound absurd, but considering that I am still a school student, i think this is the best i can come up with!)

    If we take an empty bottle(with nothing but air in it), and try to suck out the air in it with our mouth, we feel our lips/tongue being pulled into it with a kind of suction force.

    This shows that in vacuum things get sucked in to fill the empty space(vacuum.)

    Similarly, beyond the universe there must be vacuum in all the sides(the universe includes everything so beyond it there must be nothing.)Now, as we have seen, vacuum tends to suck things into it to fill the empty space.So if the vacuum beyond the universe tries to suck matter in, our universe will obviously expand from all the sides!It will continue to do so because there will always be vacuum(nothing at all beyond the universe.)

    What do you think about it?

    • jonah says:

      This is a nice idea, Pseudonynmous. What you’ve just described is something we call “pressure.” We can’t test your hypothesis, of course, because we can’t see outside the universe, but it’s possible.

      Usually scientists don’t think of the universe existing inside anything at all. It’s counterintuitive, but the mathematics allows it. Instead, we imagine that distance itself is increasing. It’s not just that things are moving further away from each other, more empty space is being generated between them! Imagine two boats in a canal. They sit peacefully, not moving much. Now imagine that another river feeds into the canal, right between the two boats. The two boats will be pushed apart by the influx of water. But it’s not that the boats are moving on their own… there’s simply more water between them.

      The reason we think this way is that general relativity models spacetime itself… it’s not obvious what, if anything, could be outside of that.

  7. Pseudonymous says:

    If there’s an influx of ‘space’ in the universe, i seriously need to know what EXACTLY space is!Where is this coming from anyway?

    • jonah says:

      I don’t know what space is, exactly. The simplest questions are the hardest to answer, and I don’t think science has an answer to that one yet. Much smarter people than I have been struggling with this question for a long time. Both Sir Isaac Newton (of Newton’s laws) and Gottfried Liebnitz (co-inventor of calculus, a powerful mathematical toolbox. Newton was the other inventor) argued about this. Check it out: http://plato.stanford.edu/entries/spacetime-theories/

      What I can tell you is this. We use the equations of general relativity to study gravity and the shape of the universe, of space and time. They’ve been very successful. They predict the wobbling of Mercury’s orbit, the bending of light around massive objects (like in this image: http://www.roe.ac.uk/~heymans/website_images/abell2218.jpg), and the fact that time moves more slowly high in Earth’s orbit, where the GPS satellites are. And we’ve observed all of these effects.

      In these equations, space is more than something we live inside or inhabit. It’s a dynamical, living, breathing thing that can grow, shrink, and change. I don’t have a good intuitive explanation for this… at least not a short one. All I can do is point you to some of my articles which try to tackle this idea. The first time I tried to talk about space and time was in a three part series I wrote about why it is impossible to travel faster than the speed of light and how we might theoretically get around this restriction.
      Part 1, why the speed of light is constant: http://www.thephysicsmill.com/2012/11/19/the-speed-of-light-is-constan/
      Part 2, why this means we can’t go faster than light: http://www.thephysicsmill.com/2012/11/25/the-universal-speed-limit/
      Part 3, how we can warp space and time to get around this: http://www.thephysicsmill.com/2012/12/02/ftl-part-3-general-relativity-shortcuts/
      Later I wrote about “Minkowski space,” which unifies space and time to make special relativity easier to understand:
      http://www.thephysicsmill.com/2013/02/10/a-space-time-cocktail-minkowski-space-and-special-relativity/
      The most useful articles would probably be the ones where I try to describe what it means for spacetime to be curved. That’s these two:
      http://www.thephysicsmill.com/2013/03/17/for-there-we-are-captured-the-geometry-of-spacetime/
      http://www.thephysicsmill.com/2013/04/08/rock-me-einstein-some-questions-on-special-and-general-relativity/

      Sorry that I can’t say more… and that I can’t say anything succinct about this topic. It’s a tricky one.

      • Pseudonymous says:

        No problem :) It answers a few of my other questions, so thanks!

        By the way, i have read a book on science FAQs by Biman Basu.It states that, if we leave the earth in a spacecraft traveling at nearly the speed of light, and if we return to the earth after-say 2yrs, for the earth might have been 200 yrs or so.

        This is because, when we travel at almost the speed of light, the speed of the earth is definitely slower.Then, the earth would move faster in time than the spacecraft, because ‘more the speed of an object, lesser would it move in time.’

        Example:

        If a ball is rolling down a distance of 10m, with a speed of 2m/s;
        then:

        speed=distance/time;
        2m/s=10m/(time);
        =time=10/2;
        =time=5s.

        but if we increase the speed to 5m/s;

        =time=10/5
        =
        time=2s.

        This shows that greater is the speed, lesser is the time.

        In this way, sitting in a spacecraft traveling at the speed almost equal to light, we could age just a bit and come back to see the earth, having aged multiple times more due to its lesser speed.In this way, we could go the earth’s future!

        What do you think about that?!Any more info on time travel is always welcomed.

        • jonah says:

          Yes, if we travel close to the speed of light, time slows for us compared to those who don’t speed up. But this isn’t suggested by the equations you wrote down. Those equations just say that the faster you go, the less time it will take to get to your destination. This is different from time slowing down, it’s just the intuitive idea that going fast gets you places faster.

          Instead, the reason that time slows down for the space traveler has to do with the fact that speed of light is constant. Check out the three part series I mentioned. It should explain it:
          http://www.thephysicsmill.com/2012/11/19/the-speed-of-light-is-constan/
          http://www.thephysicsmill.com/2012/11/25/the-universal-speed-limit/
          http://www.thephysicsmill.com/2012/12/02/ftl-part-3-general-relativity-shortcuts/

          As you said, this let’s us travel to the future fairly easily! All we need to do is travel extremely fast! And as a matter of fact, some subatomic particles do travel to the future this way. Muons (https://en.wikipedia.org/wiki/Muon) have a lifetime of about two MILLIONTHS of a second. However, we see them for much longer than a millionth of a second. Indeed, we often see them for minutes! How do they accomplish this? Because the muons travel at almost the speed of light, time is slowed down for them and sped up for us. A millionth of a second for a muon is a minute for us!

          Traveling back in time is much harder. There are a couple of ways that it is theoretically possible that come from general relativity. One way is to travel through the singularity of a charged spinning black hole. But I don’t recomend it. Other methods tend to require either infinite mass or negative mass, both of which are generally considered impossible. Perhaps I’ll write an article about this at some point.

          Actually, there’s an excellent youtube video about time travel. Check it out:

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