C H A P T E R 6
THE MEASURE OF ALL THINGS
I believe with Schopenhauer that one of the strongest motives that leads men to art and science is escape from everyday life with its painful crudity and hopeless dreariness from the fetters of one’s own everyday desires. . . . A finely tempered nature longs to escape from personal life into the world of objective perception and thought.
—Albert Einstein
Iam not sure that I completely agree with Einstein’s romantic view of the scientific (or artistic) enterprise, having always felt that these activities, as human endeavors, are intimately connected with the rest of our existence, dreary or otherwise. But perhaps that is one of the many reasons why Einstein was Einstein, and I am me. In any case, for over twenty years I have devoted most of my scientific effort to questions about the origin, nature, and future of our expanding universe that are about as far removed from the world of my everyday experience as can be. While I like to think that my contributions have helped us move forward in our knowledge, nothing truly prepared me for the revolutionary developments of the past decade, which is why I want to make a brief digression from the historical presentation thus far, and jump to a present-day result that has finally addressed the question first asked by Einstein almost a hundred years ago. I remember, from the time I taught at Yale, a conversation with a senior member of its astronomy department, Gus Oemler. I used to visit him regularly with crazy ideas about how one might measure such fundamental quantities as the expansion rate and the geometry of the universe. With his wealth of experience, he brought valuable skepticism to any discussions we had. On this particular day we were discussing how to measure what has become known as the Hubble constant, a quantity that describes the expansion rate of our universe and which, in a manner characteristic of much of astronomical nomenclature, is actually not in general a constant quantity at all, but varies over cosmological time. In any case, in the course of our talk Gus revealed to me a theorem he had about the universe: “I believe that the universe will always conspire to make any fundamental and precise measurement of cosmological quantities such as the Hubble constant impossible.” As outrageous as this claim might seem, it was based on decades of experience in astronomy. On many occasions over the past thirty to forty years, astronomers had claimed to make definitive measurements about such quantities as the curvature of the universe or its expansion rate, and each time it turned out that subtle uncertainties that had not been anticipated by the observers clouded their results, ultimately invalidating many of them.
Thus it was that in 1999 I was unprepared for a totally clean and unambiguous observation, using a method that I had in fact written about in a slightly different context almost a decade earlier: a profound and direct measurement of the geometry of the universe in which we live. Equally remarkable is the fact that the method used is almost identical, at least in principle, to that used by Lobachevsky over 150 years earlier to first explore for a possible curvature of space. The only difference is that the triangles we now use “as reference points” span not the distances to the nearest stars, but rather the distance across the entire visible universe. This observation became possible because of the accidental discovery, forty years ago, of a then-mysterious thermal bath of radiation bombarding us from all directions, with a temperature of about three degrees above absolute zero (on the Kelvin temperature scale, in which absolute zero, the coldest temperature possible, is labeled zero, unlike the Fahrenheit scale, where absolute zero is minus 459.67 degrees). It didn’t remain mysterious for long, however. When the perplexed scientists at Bell Laboratories who had found this excess “noise” in their antennas went down the road with their findings to Princeton University, the scientists there informed them that they had discovered the afterglow of the big bang. Shortly after Edwin Hubble’s discovery in 1929 that the universe is expanding, it was realized that by following this expansion backward in time one might hope to trace out the thermal history of the universe. By going back over ten billion years, the universe one would encounter would have consisted of a hot, dense gas of particles and radiation in thermal equilibrium. Such an extrapolation was, of course, bold, but it did make many theoretical predictions possible, all of which could be tested against observations. The most robust of them, perhaps, involved the prediction of a background of radiation left over from the big bang that would have permeated the universe, and would have been cooling as the universe expanded over the billions of years between the big bang and now.
We can understand why this microwave radiation bath exists and what its origin is by remembering one of the fundamental facts of electromagnetism: Light travels at a finite velocity through space, so that the farther out we look in the universe, the further back in time we are looking. Every time we peer through a telescope, we are doing cosmic archaeology. Pushing this idea to its logical limit means that in principle, if the universe had a beginning a finite time ago in the past, if we look out far enough with sufficiently powerful telescopes, we should be able to witness the big bang itself! Unfortunately, however, there is a fundamental roadblock to actually achieving this goal. Between the big bang and now, the universe went through an opaque period when it was so hot and dense that light could not travel unimpeded throughout space, unlike the present time, when it can traverse the vast distances between stars and galaxies.
Using well-known laws of physics, we can actually calculate the precise time before which the universe was opaque. At a temperature of greater than about three thousand degrees Kelvin above absolute zero the ambient radiation present is sufficiently energetic to break apart the bonds that hold atoms such as hydrogen together. Hydrogen is the simplest atom, made up of a single proton, surrounded by an electron. At extremely high temperatures, absorption of energy from a radiation bath is sufficiently great to allow the electron to be knocked free of its electronic bond to its host proton. While it could be captured again by another bare proton, the radiation would once again knock it free. At the high temperatures of the early universe, therefore, hydrogen was ionized, meaning that its charged particles (protons and electrons) were separated and not bound together into neutral atoms. Now, ionized matter, being charged, interacts very strongly with electromagnetic radiation. Thus, a light ray cannot permeate a configuration of ionized atoms, which we call a plasma, without being constantly absorbed and reemitted. This means that as we attempt to look back farther and farther we eventually hit a metaphorical wall. If we try to look back to earlier times, we simply cannot do so using electromagnetic radiation, just as we cannot look behind the walls in the room that surround us, because the radiation cannot penetrate their surface. Indeed, when we look at a wall, we are seeing radiation that has been absorbed at the surface, and later reemitted into the room, making its way through the transparent air to our eyes.
Similarly, as the universe cooled below three thousand degrees, and neutral atoms could finally form, space became transparent to radiation. Thus, we should expect to be able to see a “surface” located billions of light years away from us that represents the time when the universe first became neutral, when it was about three hundred thousands years old. From this surface we should expect to receive a bath of radiation coming at us from all directions. Since the universe has been expanding and cooling since the time that that surface originally emitted the radiation, by the time it gets to our sensors the radiation should have cooled considerably. The first people to propose that such a radiation background should exist were a research group associated with the scientist and writer George Gamow, whose many popular books inspired generations of young people (including me) to think about science. At the time that Gamow’s colleagues Robert Alpher and Robert Hermann made their proposal, no one really took the big bang picture seriously. However, as I mentioned previously, twenty years after his prediction two young wouldbe radio astronomers at Bell Laboratories in New Jersey discovered an unusual source of noise in a sensitive radio receiver they planned to use to scan the he
avens. The noise was characteristic of a background of radiation at a temperature of about three degrees above absolute zero. While they had no idea of it at the time, this was more or less precisely the temperature such a radiation bath remnant of the big bang was predicted to now possess.
Because this radiation emanates from within the first three hundred thousand years after the big bang, it has become one of the most important probes of cosmology. By carefully measuring its properties, one can hope to glean a wealth of information about the early universe. In 1999 an experiment was launched near the South Pole to measure this background radiation with unprecedented accuracy. A microwave radiation detector was set aloft on a huge balloon that would rise to a hundred thousand feet above the earth, well above most of the atmosphere that would otherwise absorb some of the radiation before it could reach the earth. The balloon with its important payload took almost two weeks to circle Antarctica, returning close to the spot from where it had been launched (which is why it was called the boomerang experiment), and during this time the microwave radiometer focused on a small patch of the sky, measuring the temperature of the background radiation across the patch to an accuracy of better than one part in one hundred thousand.
What the experimenters who built and operated the device were looking for was a very particular distribution of hot and cold spots about one degree across in the microwave sky. This angular size has a special significance, for it represents the distance light could have traveled across points on the “surface” from which the microwave background emanates, about three hundred thousand years following the big bang. Since no signal can be transmitted faster than light, this distance, about three hundred thousand light years, thus represents the largest distance over which the effects of any physical disturbance located at one place could propagate.
Put another way, this scale is the largest scale over which local physical processes could respond to macroscopic conditions. For example, a bit of excess mass in some region might, by its gravitational selfattraction, begin to collapse. The increased density in this region would then cause a corresponding increase in pressure. Such effects of pressure responding to gravity could only occur across regions smaller than or equal to three hundred thousand light years across, however, because on larger scales lumps of excess mass do not even know they are lumps—light cannot have traveled across them. This is why the angular scale associated with this distance is special—it is associated with the largest size regions within which there is causal contact. For this reason, one would expect to see a residual imprint on the microwave background on such scales.
Such a situation in principle provides us with all the ingredients we need to be able to directly probe the geometry of the universe, by giving us a large triangle, as shown below. Two of the sides of the triangle represent the distance from Earth out to the surface from which the microwave background emanates. The third side is this special distance across the surface, representing the maximum distance a physical signal could have propagated at that time, about three hundred thousand lightyears. General relativity implies that light rays travel in space in straight lines, but if the underlying space is curved, the trajectories of the light rays themselves will be curved. Thus, the light rays emanating from the edges of a region spanning a distance of three hundred thousand light-years across would follow one of three different kinds of trajectories on their way to the earth. If the universe is positively curved, then the light rays would bend inward on their travels. If it were negatively curved, the light rays would bend outward. And if the universe is flat, the light rays would follow straight lines.
From the point of view of an observer on Earth, then, the angular size of these regions will depend upon what the geometry of the universe is. If space is negatively curved across the universe, the apparent angular size of these hot spots and cold spots will be reduced. If it is positively curved, the hot and cold spots will appear enlarged. If it is flat, the size will be somewhere in between. In 1999 the boomerang experiment released its results, with complex charts demonstrating the quantitative features of the temperature variations across the region of the microwave sky that it observed. However, in the spirit of the statement that a picture is worth a thousand words, the experimental team also produced a graphical representation of their findings. Here is an actual false color image (rendered here in shades of gray) of the data, with hot spots one shade and cold spots another, compared to three computer-generated versions of what you might expect for a positively curved, flat, and negatively curved space.
Here, for the first time in human history, was an empirical observation capable of disentangling the geometry of the entire visible universe. And
you don’t have to be a rocket scientist to discern the answer. As in the Goldilocks story, the lumps predicted in the positively curved universe were too large compared to the observations, while the lumps in a negatively curved universe were too small. A precisely flat universe, however, would produce more or less precisely what was observed. Just as Lobachevsky had inferred 150 years earlier, on a scale that we now recognize would have been far too small to detect the minute curvature of space that might have existed on these scales, observations of the cosmic microwave background have now convincingly suggested that we live in a flat universe.
One’s first response might be “How boring.” Of all the interesting possible universes to live in that are allowed by general relativity, why should we live in one that is precisely flat on large scales?
Before I attempt to answer that, let me attempt to clear up a possible misconception that you may have arrived at from what you have just read. Remember that I described earlier how Einstein’s theory of general relativity was first experimentally confirmed in 1919 by witnessing the fact that light rays bent around the sun. Yet I have now just argued that light rays that traverse the universe travel in straight lines. These two facts are not inconsistent. Matter can locally curve space in its vicinity, as the sun, the earth, and even you do. However, the fundamental question that has puzzled physicists since Einstein first proposed his theory was whether the sum total of all the matter and energy in the universe produces a net curvature of space on the largest scales. If it did, one could imagine, for example, as Einstein first did, that space could ultimately curve back upon itself so that one could live in a finite universe, but one without end. Namely, if you looked far enough in any direction, you would see the back of your head! It is like a three-dimensional version of living on the surface of an expanding balloon.
A finite but endless universe is fascinating, but it does have one drawback. If matter and radiation are all that make up such a universe, general relativity implies that it must ultimately recollapse back into a hot, dense reverse of the big bang. This provides a rather unpleasant end, and so it is fortunate that other possible geometries for the universe exist that may imply less violent finales. A negatively curved universe, like a three-dimensional version of a horse’s saddle, can be infinite in spatial extent, and such a universe containing matter and radiation will expand indefinitely. With time the universe would cool down, its stars would ultimately burn out, and it would become cold and dark. This, too, is not a particularly pleasant future, but the timeframe over which the darkness would fall is so gradual—trillions of years—that such a universe, which ends with a whimper rather than a bang, seems more hospitable, at least from a human perspective. Falling right between these two extremes is a flat universe. In such a universe containing matter and radiation, our expansion will continue to slow with time, but it will never quite stop. Like a negatively curved universe, it, too, can be infinite in spatial extent. However, because the expansion rate slows more quickly in this universe than in a negatively curved space, the time it takes before such a universe becomes cold and empty is far longer.
Longevity is not the reason that theorists preferred a flat universe long before observations confirmed this to be the case, however. The reason for their preference is partly aesthetic an
d partly practical. Einstein’s equations from general relativity establish a relationship between the curvature of the universe, the rate of its expansion, and the total density of matter and energy within it. Observations of the expansion of the universe and measurements of the total matter density had long established that these quantities were within an order of magnitude or so of what was required to produce a flat universe.
Hiding in the Mirror: The Quest for Alternate Realities, From Plato to String Theory (By Way of Alicein Wonderland, Einstein, and the Twilight Zone) Page 7
