| © Features the other press ¢ Barbara. Adamski e¢ opfeatures@telus.net Can You Disappear? Wojceich Langer OP Contributor Can you disappear while reading this ? Chances are that you can. Your newspaper, the earth, the planets, and the universe you are familiar with can disappear as well. We all can disappear in a flash of light, without warning. To understand how this can hap- pen, let’s take a look at matter’s state of meta-stability, its phase transition by tunneling; and properties of the void or vacuum. Meta-stability, chaotic behavior, and symmetry Water can cool to below its freez- ing point, but will suddenly freeze when a speck of dust is put into it. In 1942, hundreds of horses were killed when they became trapped in the frozen waters of Ladoga Lake. The horses were escaping a forest fire caused by bombardment, and jumped into the lake, which was not frozen despite a prolonged period of extremely cold weather. When the horses had reached the opposite shore and were about to leave the lake, a loud sonic “boom” was heard. The lake froze suddenly, crushing and immobilizing the poor animals in solid ice. Water can be maintained a liquid state at temperatures more of than 150° C. In such a meta-stable state, well above the boiling point, any liq- uid is under tension. But one quick injection of energy is enough to start violent vaporizing. At this moment the energy barrier of the liquid is lowered and a transition takes place. One can produce such an effect by heating a cup of water in a microwave oven for too long. Manufacturers of these appliances often warn to take care and to guard against being splashed by a sudden “explosion” of total rapid evapora- tion. Chaotic systems should also be mentioned. The defining character- istic of chaotic systems is their extreme sensitivity to any, even tiny, changes of a given condition, which results in their behaving unpre- dictably. Edward Lorenz first discov- ered this effect in 1960, calling it the “butterfly metaphor.” He suggested that the flap of a butterfly’s wings might affect the weather not only far away but also a week or so in the future. Since then, the theory of chaotic behaviour (very common in com- plex systems) has provided impor- tant new insights into the nature of classical physical systems, including many that surround us in everyday life. Examples of complexity are: * turbulence of liquid flow, * unpredictability of weather * the way living things grow * earth’s ecological system. It is impossible to apply linear extrapolation or any equations in order to predict exactly how com- plex events occur. For example, honey has a habit of sometimes twisting its flow and running down the outside of the jar and onto the table. Typically, the stability or insta- bility of any particular state depends on one or more parameters charac- terizing various aspects of the sys- tem. Systems can remain for some time in a quasi-stable state, but a small perturbation or gradual varia- tion of a parametre can drive a sys- tem to a completely different, more stable state. Quite often such change will be of catastrophic proportion. A good example is Euler's 1744 study (Fig.1). What we see is buck- ling of a thin semi-elastic rod under a compressive force. For a sufficient- ly small but growing force, the rod remains vertically straight. When the force exceeds some critical value, the straight form becomes unstable, and the rod suddenly takes up the buckled position. FF (6) So a @ ©) ©) Figure 1. Figure 1. Euler's Experiment For force FE, the rod remains almost straight despite inevitable small dis- turbances. When F exceeds critical value F(c), the rod becomes unstable and takes up one of the two buckled positions. Generally speaking, a more stable complex state is achieved by the spontaneous breaking of its physical symmetry. The following examples explain the appearance of symmetry: * A snowflake is more complex (less symmetric) and more stable than the original sphere of water vapor. * The ferromagnet has less symme- try but more order than the original iron bar having rotational symme- try, but no magnetic field at higher temperatures. ¢ Force interactions between Standard Model particles can also be described in terms of symmetry. * Space-time is approximately the same in all directions; therefore, it has rotational symmetry. However, imbalance exists because stars, plan- ets, asteroids—everything—is made of matter. But where is antimatter? How do meta-stability, complexi- ty, chaotic behavior, and symmetry relate to the disappearance of the universe? The universe is a complex system and has been in a relatively stable state for a long time. The question is whether this state is meta-stable or not. Has our universe reached the lowest energy density yet? Tunneling through the energy bar- rier Kinetic energy depends on momentum, while potential energy depends on position. In quantum mechanics, the Heinsenberg uncer- tainty principle forbids any simulta- neous, definite values of momentum and position; therefore, the kinetic and potential energy cannot both be exactly zero. Energy of a system can never be exactly zero but the system has a ground state in which the ener- gy is as low as it can be. All physical systems (nucleus, atoms, pounds, and space configuration of the universe itself) tend to find their lowest “ground” energy state. The uncertainty rule also leads to the phenomenon of tunneling. In classical mechanics, a ball at rest in a com- bow! will never be able to get out. In quantum mechanics, position is not sharply defined but is spread over a (typically infinite) range. Asa result, there is a definite probability that the ball will be found on the other side of the barrier (bowl). This means the ball tunneled through the wall (barrier). A physical system must have more than one energy state with an energy barrier between them so that transi- tion is possible. The interesting case arises when a physical system is trapped in a state of higher energy and can, in princi- ple, make the transition at some time in the future. When, for exam- ple, an electron makes the transition from one energy state (higher valley) to another (lower valley), it effec- tively passes through an energy bar- rier that it did not have enough energy to go over. In this sense, the electron tunnels through the barrier. The Stages Modern cosmologists are quite con- fident about stages that our universe went through in the past. There were two of them, possibly three (Fig.2), affecting the current shape of space. acceleration expansion inflation Figure 2. Figure 2. Cosmic time line seen as a cut from the universe bubble sphere Inflation started not necessarily from the “particle” point and lasted only about 10 to the power of (-30) seconds. Shortly after, the universe, as we observe it, expanded classical- ly in real, physical time of about 15 billion years. When exactly accelera- tion started is not precisely indicated. The initial early period is called inflation, which is a very rapid, exponential inflation. This inflation- ary stage enlarged the tiny space bubble. The speed involved was faster than light and lasted just a very small fraction of time, called the Planck Epoch. The next stage is called the Big Bang. What astronomers and_astrophysicists observe now is a direct result of the Big Bang. What they see today is fast, but not explosive, cosmic expansion that has led to our present habitat. In 1998, we learned that visible space expansion accelerates. This acceleration implies an extra repul- sive cosmic force that could indicate small but steady changes of cosmic parameters (look again at the description of Euler’s strut experi- ment). Current knowledge tells us that we live in a universe with a crit- ical value of mass representing galax- ies. This visible mass is unable to stop expansion, but a dark (or vacu- um) energy appears to be causing the expansion to accelerate. Inflation before the Big Bang pro- vided us with an elegant, big, and old universe, a universe with lots of entropy and relatively little matter. By past inflation of space-time by the magical factor of ten trillion quadrillion, the universe as we per- ceive now seems destined to live for a long time. But is this a certainty? Void and rolling fields In the hot, extremely high-energy initial universe model, the matter content of the universe was perhaps uniformly distributed plasma, dust, or scalar fields representing particles. Modern physics concludes that this simple, symmetric void almost empty of matter transformed in the past into the complex, asymmetric universe filled with visible and invis- ible “dark” matter, because that uni- verse is more stable than the void itself. Very early, the energy density of the universe was dominated by vac- uum and its mysterious dark energy that exhibits the curious property of negative pressure. Einstein's cosmo- logical equations allow for this ubiq- uitous outward-pulling force in the universe. This force behaves like a rubber ball. The more you try to squeeze it, the more it tries to expand. Vacuum energy can be found as a component of Friedmann’s Equation that connects cosmologi- cal parameters: Hubble constant, mass density, and curvature of space. A vacuum corresponds to the energy states of empty space. And again, because of the uncertainty principle, the vacuum can never be truly empty: Associated with a given value of the vacuum field is potential energy. As the universe expanded and cooled, it passed through several temperatures at which the breaking http://www-.otherpress.ca = eee of symmetry occurred in a landscape of potential energy. we are here possible tunneling residual stress time Figure 3. Figure 3. Breaking of the potential energy symmetry We may not yet have reached the bottom. We may exist in a metastable “false”? minimum. The height of the minimum above the zero line determines the residual value of the dark energy stress in the universe. Tunneling out of false val- ley is possible, causing total phase transition of the universe. Fig. 3 shows the universe energy field rolling toward the bottom of its potential. But the expansion of the universe introduces cosmological friction, impeding the descent. The level of the current energy value could have been placed at any level above the zero line. Our knowledge of physics does not tell us where it should be. However, if this level is above the “ground” zero line, then it will leave energy that behaves exact- ly like the mentioned negative pres- sure in the universe. The effect of negative pressure grows steadily with respect to the Newton force of gravity, as the uni- verse gets bigger. Now, as we observe, it is becoming the domi- nant force after billions of years of expansion of the universe. Therefore, we can consider the pos- sibility that the universe, much like electron sitting in the bowl, is cur- rently in a “false” meta-stable vacu- um state. In other words, the uni- verse is now trapped in a configura- tion with “large” vacuum energy, but a lower energy vacuum state exists. This period of entrapment has been 15 billions years long, but one day, things may change. Dimensions Our matter- and radiation-filled universe seems to have four dimen- sions: we are three-dimensional beings, and we live in a curved three-dimensional space-time (solu- tion to the Einstein field equation describes not only curvature of space, but also a warpage of time due to strong gravity near the terres- trial objects). The dimension of time extends back at least 15 billion years into the past. Mathematicians and physicists have long analyzed the properties of theoretical spaces that have any number of dimensions. The idea of extra dimensions, in effect, contin- ues the Copernican tradition in Page 19