Showing papers by "Roger Penrose published in 2006"

Before the big bang: An outrageous new perspective and its implications for particle physics

Abstract: Proposals for describing the initial state of the universe hardly ever address a certain fundamental conundrum [1] — yet this is a conundrum whose significance is, in a certain sense, obvious. The issue arises from one of the most fundamental principles of physics: the Second Law of thermodynamics. According to the Second Law, roughly speaking, the entropy of the universe increases with time, where the term “entropy” refers to an appropriate measure of disorder or lack of “specialness” of the state of the universe. Since the entropy increases in the future direction of time, it must decrease in the past time-direction. Accordingly, the initial state of the universe must be the most special of all, so any proposal for the actual nature of this initial state must account for its extreme specialness. Proposals have been put forward from time to time (such as in various forms of “inflationary cosmology” and the previously popular “chaotic cosmology”) in which it is suggested that the initial state of the universe ought to have been in some sense “random”, and various physical processes are invoked in order to provide mechanisms whereby the universe might be driven into the special state in which it appears actually to have been in, at slightly later stages. But “random” means “non-special” in the extreme; hence the conundrum just referred to. Sometimes theorists have tried to find an explanation via the fact that the early universe was very “small”, this smallness perhaps allowing only a tiny number of alternative initial states, or perhaps they try to take refuge in the anthropic principle, which would be a selection principle in favour of certain special initial states that allow the eventual evolution of intelligent life. Neither of these suggested explanations gets close to resolving the issue, however. It may be seen that, with timesymmetrical dynamical laws, the mere smallness of the early universe does not provide a restriction on its degrees of freedom. For we may contemplate a universe model in the final stages of collapse. It must do something, in accordance with its dynamical laws, and we expect it to collapse to some sort of complicated space-time singularity, a singularity encompassing as many degrees of freedom as were already present in its earlier nonsingular collapsing phase. Time-reversing this situation, we see that an initial singular state could also contain as many degrees of freedom as such a collapsing one. But in our actual universe, almost all of those degrees of freedom were somehow not activated. What about the anthropic principle? Again, this is virtually no help to us whatever in resolving our conundrum. It is normally assumed that life had to arise via complicated evolutionary processes, and these processes required particular conditions, and particular physical laws, including the Second Law. The Second Law was certainly a crucial part of evolution, in the way that our particular form of life actually came about. But the very action of this Second Law tells us that however special the universe may be now, with life existing in it now, it must have been far more special at an earlier stage in which life was not present. From the purely anthropic point of view, this earlier far more special phase was not needed; it would have been much more likely that our present “improbable” stage came about simply by chance, rather than coming about via an earlier even more improbable stage. When the Second Law is a crucial component, there is always a far more probable set of initial conditions that would lead to this same state of affairs, namely one in which the Second Law was violated prior to the situation now! As another aspect of this same issue, we may think of the vastness of our actual universe, most of which had no actual bearing on our existence. Though very special initial conditions were indeed required for our existence in our particular spatial location, we did not actually need these same special conditions at distant places in the universe. Yet as we look out at the universe, we see the same kind of conditions, acting according to the same Second Law of thermodynamics, no matter how far out we look. If we take the view that the Second Law was introduced in our vicinity merely for our own benefit, then we are left with no explanation for the extravagance of this same Second Law having to be invoked uniformly throughout the universe, as it appears to be as far as our powerful instruments are able to probe.

Before the big bang: An outrageous new perspective and its implications for particle physics

Abstract: Proposals for describing the initial state of the universe hardly ever address a certain fundamental conundrum [1] — yet this is a conundrum whose significance is, in a certain sense, obvious. The issue arises from one of the most fundamental principles of physics: the Second Law of thermodynamics. According to the Second Law, roughly speaking, the entropy of the universe increases with time, where the term “entropy” refers to an appropriate measure of disorder or lack of “specialness” of the state of the universe. Since the entropy increases in the future direction of time, it must decrease in the past time-direction. Accordingly, the initial state of the universe must be the most special of all, so any proposal for the actual nature of this initial state must account for its extreme specialness. Proposals have been put forward from time to time (such as in various forms of “inflationary cosmology” and the previously popular “chaotic cosmology”) in which it is suggested that the initial state of the universe ought to have been in some sense “random”, and various physical processes are invoked in order to provide mechanisms whereby the universe might be driven into the special state in which it appears actually to have been in, at slightly later stages. But “random” means “non-special” in the extreme; hence the conundrum just referred to. Sometimes theorists have tried to find an explanation via the fact that the early universe was very “small”, this smallness perhaps allowing only a tiny number of alternative initial states, or perhaps they try to take refuge in the anthropic principle, which would be a selection principle in favour of certain special initial states that allow the eventual evolution of intelligent life. Neither of these suggested explanations gets close to resolving the issue, however. It may be seen that, with timesymmetrical dynamical laws, the mere smallness of the early universe does not provide a restriction on its degrees of freedom. For we may contemplate a universe model in the final stages of collapse. It must do something, in accordance with its dynamical laws, and we expect it to collapse to some sort of complicated space-time singularity, a singularity encompassing as many degrees of freedom as were already present in its earlier nonsingular collapsing phase. Time-reversing this situation, we see that an initial singular state could also contain as many degrees of freedom as such a collapsing one. But in our actual universe, almost all of those degrees of freedom were somehow not activated. What about the anthropic principle? Again, this is virtually no help to us whatever in resolving our conundrum. It is normally assumed that life had to arise via complicated evolutionary processes, and these processes required particular conditions, and particular physical laws, including the Second Law. The Second Law was certainly a crucial part of evolution, in the way that our particular form of life actually came about. But the very action of this Second Law tells us that however special the universe may be now, with life existing in it now, it must have been far more special at an earlier stage in which life was not present. From the purely anthropic point of view, this earlier far more special phase was not needed; it would have been much more likely that our present “improbable” stage came about simply by chance, rather than coming about via an earlier even more improbable stage. When the Second Law is a crucial component, there is always a far more probable set of initial conditions that would lead to this same state of affairs, namely one in which the Second Law was violated prior to the situation now! As another aspect of this same issue, we may think of the vastness of our actual universe, most of which had no actual bearing on our existence. Though very special initial conditions were indeed required for our existence in our particular spatial location, we did not actually need these same special conditions at distant places in the universe. Yet as we look out at the universe, we see the same kind of conditions, acting according to the same Second Law of thermodynamics, no matter how far out we look. If we take the view that the Second Law was introduced in our vicinity merely for our own benefit, then we are left with no explanation for the extravagance of this same Second Law having to be invoked uniformly throughout the universe, as it appears to be as far as our powerful instruments are able to probe.

Some developments in twistors and space-time

Abstract: On twistors, strings, and the cosmological constant.