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Of Jumping Frogs and Supercooling

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  • Of Jumping Frogs and Supercooling

    THE FABRIC of the COSMOS, Brian Greene, 2004
    ```(annotated and with added bold highlights by Epsilon=One)
    Chapter 10 - Deconstructing the Bang
    Of Jumping Frogs and Supercooling
    If you caught sight of a baseball flying upward, you could use Newton's law of gravity (or Einstein's more refined equations) to figure out its subsequent trajectory. And if you carried out the required calculations, you'd have a solid understanding of the ball's motion. But there would still be an unanswered question: Who or what threw the ball upward in the first place? How did the ball acquire the initial upward motion whose subsequent unfolding you've evaluated mathematically? In this example, a little further investigation is all it generally takes to find the answer (unless, of course, the aspiring big-leaguers realize that the ball just hit is on a collision course with the windshield of a parked Mercedes). But a more difficult version of a similar question dogs general relativity's explanation of the expansion of the universe.

    The equations of general relativity, as originally shown by Einstein, the Dutch physicist Willem de Sitter, and, subsequently, Friedmann and Lemaitre, allow for an expanding universe. But, just as Newton's equations tell us nothing about how a ball's upward journey got started, Einstein's equations tell us nothing about how the expansion of the universe got started. For many years, cosmologists took the initial outward expansion of space as an unexplained given, and simply worked the equations forward from there. This is what I meant earlier when, I said that the big bang is silent on the bang.

    Such was the case until one fateful night in December 1979, when Alan Guth, a physics postdoctoral fellow working at the Stanford Linear Accelerator Center (he is now a professor at MIT), showed that we can do better. Much better. Although there are details that today, more than two decades later, have yet to be resolved fully, Guth made a discovery that finally filled the cosmological silence by providing the big bang with a bang, and one that was bigger than anyone expected.

    Guth was not trained as a cosmologist. His specialty was particle physics, and in the late 1970s, together with Henry Tye from Cornell University, he was studying various aspects of Higgs fields in grand unified theories. Remember from the last chapter's discussion of spontaneous symmetry breaking that a Higgs field contributes the least possible energy it can to a region of space when its value settles down to a particular nonzero number (a number that depends on the detailed shape of its potential energy bowl). In the early universe, when the temperature was extraordinarily high, we discussed how the value of a Higgs field would wildly fluctuate from one number to another, like the frog in the hot metal bowl whose legs were being singed, but as the universe cooled, the Higgs would roll down the bowl to a value that would minimize its energy.

    Guth and Tye studied reasons why the Higgs field might be delayed in reaching the least energetic configuration (the bowl's valley in Figure 9.1c). If we apply the frog analogy to the question Guth and Tye asked, it was this: what if the frog, in one of its earlier jumps when the bowl was starting to cool, just happened to land on the central plateau? And what if, as the bowl continued to cool, the frog hung out on the central plateau (leisurely eating worms), rather than sliding down to the bowl's valley? Or, in physics terms, what if a fluctuating Higgs field's value should land on the energy bowl's central plateau and remain there as the universe continues to cool? If this happens, physicists say that the Higgs field has supercooled, indicating that even though the temperature of the universe has dropped to the point where you'd expect the Higgs value to approach the low-energy valley, it remains trapped in a higher-energy configuration. (This is analogous to highly purified water, which can be supercooled below 0 degrees Celsius, the temperature at which you'd expect it to turn into ice, and yet remain liquid because the formation of ice requires small impurities around which the crystals can grow.)

    Guth and Tye were interested in this possibility because their calculations suggested it might be relevant to a problem (the magnetic monopole problem 8) researchers had encountered with various attempts at grand unification. But Guth and Tye realized that there might be another implication and, in retrospect, that's why their work proved pivotal. They suspected that the energy associated with a supercooled Higgs field — remember, the height of the field represents its energy, so the field has zero energy only if its value lies in the bowl's valley — might have an effect on the expansion of the universe. In early December 1979, Guth followed up on this hunch, and here's what he found.

    A Higgs field that has gotten caught on a plateau not only suffuses space with energy, but, of crucial importance, Guth realized that it also contributes a uniform negative pressure. In fact, he found that as far as energy and pressure are concerned, a Higgs field that's caught on a plateau has the same properties as a cosmological constant: it suffuses space with energy and negative pressure, and in exactly the same proportions as a cosmological constant. So Guth discovered that a supercooled Higgs field does have an important effect on the expansion of space: like a cosmological constant, it exerts a repulsive gravitational force that drives space to expand. 9

    At this point, since you are already familiar with negative pressure and repulsive gravity, you may be thinking, All right, it's nice that Guth found a specific physical mechanism for realizing Einstein's idea of a cosmological constant, but so what? What's the big deal? The concept of a cosmological constant had long been abandoned. Its introduction into physics was nothing but an embarrassment for Einstein. Why get excited over rediscovering something that had been discredited more than six decades earlier?
    Last edited by Reviewer; 10-13-2012, 07:01 AM.