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Einstein's Big Mistake?

Another big problem goes right back to the way Einstein guessed his equations in 1917. Physics is a mathematical subject, and often the mathematics we use gives a choice of answers. For example, if x² = 1, x can be +1 or -1. Einstein had the choice of including a constant in his equations, called the cosmological constant, or Lambda. At first he decided to include it, for an interesting reason.

Negative Pull

Newton, who invented the first theory of gravity in the 17th century, knew there was a problem with a Universe governed by gravity. The reason is that a collection of masses in space is unstable; they will all pull on each other, and collapse together. The only obvious way around this is to give them some energy so that they fly away from each other instead. Sound familiar? 

In 1917, though, Einstein (and everyone else) thought that the Universe was a static place, neither expanding nor collapsing. Without Lambda, the cosmological constant, Einstein's equations obstinately would not allow a static universe. With it, however, a static universe was a valid solution. So far so good, but when the expansion of the Universe was discovered in 1923, Einstein junked the cosmological constant and described its introduction as the biggest mistake of his life.

The cosmological constant made a stable Universe possible because it represents an anti-gravitating "something" spread uniformly in space, repelling instead of attracting. You can see how this would balance out the attractive, collapsing tendency of the "real" masses. The trouble was that there was no other evidence whatsoever for this anti-gravitating stuff, and Einstein probably found it embarrassing that it had been put into the theory just to make it agree with the then-current observations. However the cosmological constant had a right to be there, from a mathematical point of view, and it turns out that the math knew something that no one else did.

The Cosmological Constant Becomes Respectable

Within a decade, there were signs in another branch of physics that there might indeed be something repulsive about empty space.  Quantum theory is the name of the branch of physics that you can think of as Newton's Laws of Motion for things the size of atoms. Quantum theory is even stranger than relativity. In addition to providing next-to-perfect explanations of the workings of all sorts of familiar things, from fluorescent lights to body scanners, quantum theory has some very odd things to say about empty space.

By "empty space" physicists mean what you'd hope they would mean, empty space with nothing in it. Alas for common sense, quantum theory tells us that empty space has a mass. This is part of what the cosmological constant is also telling us. So far, perhaps this isn't too bad. There is no good reason to expect empty space to be weightless. After all, if you tried to weigh some, there would be just as much empty space on the other side of the scales! But for the Universe as a whole, the mass of empty space might matter.

The bit I can't explain to you is that this empty-space mass has a repulsive gravitational effect. It actually speeds up the expansion of the Universe, rather than slowing it down (as you'd expect from our homely example of the flung stone). This is one of those things that is hard to explain without math. It came straight out of Einstein's theory of relativity, and also, by a totally different route, out of quantum theory. In both cases, the nature of empty space is really inherent in the way the theories are set up. The strange idea that empty space exerts a repulsive force can't be explained by itself.

But it's possible to measure some of the effects of empty space in the lab, and the answers come out right. Unfortunately we can't measure the mass in lab-sized experiments and quantum theory (while it can get some predictions right) makes a complete mess of predicting the total effects. In fact the prediction is in error by at least a factor of 10¹⁴⁰. That's ten followed by 140 zeroes - a largish mistake. This prediction is tied up with unfinished business deep in the foundations of quantum theory. But these predictions and experiments gave some reason to believe in the cosmological constant, quite independently of Einstein's equations and the problems of expanding universes.

A Useful Size of Lab Is the Universe Itself! 

If empty space has a mass, it will do two things. Its mass will affect Omega, and so play a part in whether the Universe is infinite or not. The second thing is more complicated. Empty space has "push" in it as well as "pull". Although we can take account of its mass with Omega like ordinary matter, the "push" has an extra effect. It accelerates the expansion of the Universe. As the Universe expands, space gets bigger, and so more and more empty space, with more and more "push" in it, appears. So if the cosmological constant is there, it's likely that it is making the Universe expand faster and faster.

Incidentally, this ability of empty space to make more of itself, which makes more of itself, and so on, may actually be what started the Big Bang off in the first place! I'll leave you to follow this one in the related links. It's connected with an Omega of 1.0 being our best (theoretical) bet.

Big bangs and the Big Bang 

It turns out that astronomers can make a good shot at measuring just this effect. They've been at it for decades, but it now looks as if it might have been done.

It is rather easy (amazingly) to measure how old the Universe was when the light we see now was emitted from a particular distant galaxy. The light gets redder because the galaxy is rushing away from us in the cosmic expansion. It's a straightforward measurement to determine this reddening, or redshift, although it may take a long time to collect the necessary data for faint objects. The redshift fixes the cosmic time at which the light was emitted. The other thing we may be able to measure about our distant galaxy is how far away it is, perhaps by using how faint it seems compared to a similar one nearby. These two measurements - distance and redshift - are enough to unravel the mystery of the expansion of the Universe. If the expansion is accelerating, distances to objects that emitted their light early in the life of the Universe will be bigger. Bigger, that is, than if the Universe was decelerating or steady. It's the relative shape of the distance-redshift curve that is the clue.

This diagram, is based on one that appeared in an article by S. Perlmutter and his colleagues*. It graphs the distance to supernovae against their brightness; their brightness depends directly on their distance. The two lines plot two kinds of Universe, with differing amounts of matter and cosmological constant. The red line is a universe almost empty of real matter, but with a big enough cosmological constant to (just) make a finite universe. The green line is the other way round, no cosmological constant but enough real matter to close the Universe. * Perlmutter et al., 1999, Omega and Lambda from 42 High-Redshift Supernovae, Astrophysical Journal, V 517, p 565.

The really hard part about this project has been finding some object - say, a galaxy - which is

• bright enough to be seen at a huge distance
• of known brightness and
• guaranteed not to be changing its properties with cosmic time.

Galaxies, for example, were brighter in the distant past (when they were making stars) and are disqualified.

One type of object that does seem to pass these tests is the particular sort of exploding star called a supernova. Some stars end their lives with a colossal explosion, a giant thermonuclear bomb. Literally decades of painstaking work has established that a certain, recognizable variety of supernova is just the thing for measuring cosmic distances. Since then, groups of astronomers have been laboriously searching the skies with giant telescopes, using computers to search through millions of images to find the handful that might show distant supernova. So far, they have found three dozen in six years.

When they plotted up the distance-redshift diagram for their supernovae, these astronomers found one of the most remarkable results of twentieth-century physics: not only is there a cosmological constant, but it has a bigger effect on the expansion of the Universe than all the ordinary matter in it. We're accustomed to the idea that space has a lot of nothing in it, but it was a big surprise to find out that nothing was so much more important than anything else! The most basic features of the Universe - its size, rate of expansion, and fate - are fixed by the nature of the vacuum. The best bet at the moment is that Omega due to empty space is about 0.7. Together with the Omega of matter of about 0.3, we have an overall Omega of 1 - just the magic number needed to balance the Universe between eternal expansion and eternal contraction, and moreover the only value for Omega for which we have any decent theoretical reason.

In this diagram the actual data observed by Perlmutter is superimposed on the lines representing two different versions of the Universe You can see the clear tendency of the data to prefer the red line to the green one. The important things to note is the small separation between the lines, which represent very different Universes, and how the high-redshift supernovae occupy the high end of the theoretical possibilities that are shown. This is the evidence for the cosmological constant. * Perlmutter et al., 1999, Omega and Lambda from 42 High-Redshift Supernovae, Astrophysical Journal, V 517, p 565.

Is That It?

No again!

First, for the same reason as before: three dozen fantastically faint supernovae is a relatively tiny sample set and will not wrap up such a difficult branch of science. Plenty of worries remain about the data. This is black-belt stuff.

Second, there is the exciting fact that quantum theory can make a prediction for the size of the cosmological constant, and hence the Omega associated with it. The quantum theory prediction is grotesquely - ludicrously - wrong. But at least it can make a prediction. Resolving the discrepancy is now of Universal importance. Quantum theory, the physics of the very small, of atoms and electrons, has been handed the job of explaining the Universe. Will it make it? Watch this space!