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| Author | Topic: Time Hypotheses |
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Real Time (Moderator) |
posted 10/11/03 10:06 AM
Real time New Scientist vol 180 issue 2415 - 04 October 2003, page 36 Are past, present and future just a figment of the human imagination? Not according to physicist Fay Dowker, who reckons we can go beyond relativity to restore the flow of time to its rightful place NOTHING is more fundamental to human experience than the impression of time passing. We can hardly make sense of our lives other than in the context of a fixed past of events that can never be changed and a future of unrealised potentialities. Between them sits the mysterious and elusive moment of "now". This basic human perception of the flow of time is, however, at odds with accepted scientific theory. In Einstein's general relativity, space and time are combined into the indivisible block known as space-time, in which past, present and future all exist together. Space-time is a frozen fabric that does not evolve. Our own existence, from birth to death, is set out in space-time in a timeless way. There is no flow, and no place for now. At least that is the generally accepted way of looking at it. But there is another way of thinking about space-time that I and others believe may reclaim time and allow it to flow. It arises from our attempts to tackle the problem of quantum gravity: the problem of how to unify general relativity with our other most successful theory, quantum mechanics. Our approach is called "causal set theory", and it was proposed in 1987 by Rafael Sorkin of Syracuse University in New York state and colleagues. In recent years, we have discovered how, in causal set theory, space-time can "grow" in such a way that time appears to flow rather than being a static dimension. The most popular conception of general relativity considers space-time as a smooth four-dimensional fabric, with gravity being a result of its geometry or curved shape. There is a famous analogy for representing how planets are attracted to the sun, by thinking of them as marbles rolling on a rubber sheet that is weighed down at the centre. But space-time has a very special property that the rubber sheet analogy does not begin to capture. This property arises from the fact that there is a maximum speed at which anything can travel: the speed of light. This speed limit means we can think of space-time not in terms of shape, but as an order in which things can happen. The impossibility of exceeding the speed of light provides an order to space-time because it prevents some points from being causally influenced by what happens at other points. For example, nothing that happens on Earth now can be affected by events happening right now in some distant galaxy because it takes many millions of years for light from those events to reach us. The aggregated information about which space-time points can influence which other space-time points is called the causal order of space-time. It turns out that if we started off not knowing the geometry of space-time, but instead knew this causal order of all the points within it, we could reconstruct almost everything about space-time. This result, due to David Malament of the University of California at Irvine, is almost spectacularly neat. Almost, because the causal order defines everything about space-time apart from its "bulk" or "physical size": the physical "scale" is not given by the causal order. Causal set theory fills this gap. Most physicists believe that in any final theory of quantum gravity, space-time itself will be quantised and grainy in nature. Quantum mechanics implies that there is a tiniest measurable scale, called the Planck length, which is 10-33 centimetres. Likewise, the Planck time is 10-43 seconds. So the smallest possible volume in four-dimensional space-time, the Planck volume, is 10-142 cubic centimetre seconds. If we assume that each of these volumes counts a single space-time quantum, this provides a direct quantification of bulk: a space-time volume of one cubic centimetre that lasts for one second is composed of 10142 space-time elements. This number is large enough to make space-time appear smooth at all scales that we can currently probe experimentally. The set of these space-time elements is called the causal set, because the elements are ordered by causality. One way to get a grip on this idea is to think in terms of the terminology of ancestry and descent. Thus we think of the elements of the causal set as members of a family in which a member can have any number of "parents" or direct ancestors. We say element X is an ancestor of element Y if X is at a position that can causally influence Y. The causal set we have made is a branching set of elements related by causation. The major challenge for people working on this approach is how to make sure that the causal set behaves like a continuous structure that obeys Einstein's equations of general relativity at large scales. To do this, we need to define a "law of motion", a set of quantum-mechanical equations that govern the behaviour of the causal set and give rise to the equations of general relativity at large scales. In 2000 David Rideout, now at Hamilton College in New York, and Sorkin took an important step towards this goal. Their space-time grows, element by element, starting with a single one. At each stage one new element is born, its existence caused by a set of ancestors chosen for it from amongst the already existing elements. The choice is made at random. Once the new element has had its ancestors assigned, it has become a part of the existing causal set and another element is ready to be born, and the process repeats. The growth appears as a real, inevitable, physical process, and within it is the deep-held picture of common human experience of a fixed past and a future that is open, with the ever-changing present as the boundary. It is important to note that this model is by no means a final quantum theory of gravity. But we can use it to investigate the kinds of questions that will inevitably arise in formulating that theory. One challenge for all attempts to quantise general relativity is how to deal with the principle of "general covariance". This principle says that any predictions about the world made using general relativity should not involve any coordinates or map references, because coordinates in space-time are not meaningful in general relativity. This is like requiring that we should describe the physical features of a town without mentioning any map references or street names, because these are just arbitrary labels: so that the statement, "there is a red postbox on the corner of Walford Road and Nevill Road" is not allowed, but the statement "there is a red postbox on the corner of the two roads by the nursery and the synagogue and the converted pub" is - except, of course, that the words "postbox", "nursery" and so on are themselves arbitrary labels that need to be described in terms of their physical properties alone. And that's hard - try it! It is because the principle of general covariance tells us that labels for particular times or places are not meaningful that many physicists have concluded that space-time must be a frozen fabric. But in Rideout and Sorkin's causal set model, the problem of general covariance is solved in a way that retains an idea of time passing. In the set, each space-time element receives a label corresponding to the step of the process it is born at. General covariance says that nothing real can depend on these labels. Last year, Graham Brightwell of the London School of Economics, Raquel Garcia of Imperial College London, Joe Henson of Queen Mary, University of London, Sorkin and I found a way to describe the growing causal set independently of these labels, in a way that will never miss any important information about it (Physical Review D, vol 67, p 084031). This makes it possible to keep the idea of a growing time-like process while still making sure general covariance applies. We can have our cake and eat it too. But is there evidence that this theory is right? When, in 1998, the news was announced that astronomers had the first direct evidence that the universe is undergoing an accelerated expansion, it was greeted by causal set theorists with particular excitement. This accelerating expansion had, in fact, been predicted by Sorkin, based on the notion of the evolution of the universe as "growth". The acceleration is thought to be the result of the presence in Einstein's equations of a term known as the "cosmological constant", also called dark energy or lambda. Most theorists had assumed that lambda must be zero, but in 1990 Sorkin argued that the quantum nature of the process that gives birth to causal sets means that the value of lambda fluctuates around zero. His argument goes as follows. In causal set theory, the volume of space-time is a measure of the number of elements the set contains, and this is analogous to the time in the growth process. Because of the quantum nature of the causal set, it obeys a Heisenberg uncertainty relation. This states that the greater the uncertainty in the time of the universe's growth process, the less the uncertainty in the value of its dark energy, and vice versa. So one can estimate the size of fluctuations in the dark energy, or lambda, from the size of the fluctuations in the volume of the causal set. In causal set theory, the volume fluctuates by an amount that is roughly the square root of the current space-time volume, and this happens to give the order of magnitude for lambda that we apparently see. Causal set theory also addresses other important questions. For example, it has been applied to the problem of black hole entropy. Entropy is a quantity associated with missing or inaccessible information about a system, so it is clear why a black hole has an entropy associated with it: someone outside the black hole can have no information about what is inside. Ever since the development of black hole thermodynamics by Jacob Bekenstein of the Hebrew University of Jerusalem, Stephen Hawking of the University of Cambridge and others, theorists have been mystified by the fact that, when they calculate the entropy of a black hole, they end up with a number proportional to the area of the event horizon, measured in Planck units of 10-66 square centimetres. However, Djamel Dou of the University Centre of Eloued in Algeria and Sorkin described a black hole and its horizon in terms of a causal set. A crude calculation gives the entropy of a box of gas as roughly the number of molecules in the box. But in the case of a black hole, the event horizon prevents anything inside the black hole from getting out or affecting anything outside the black hole. So Dou and Sorkin suggested that, in the case of a black hole, entropy measures only the number of causal links that cross the black hole's event horizon, and does not include those causal set relationships that are inside it. They showed that in two very different cases - a two-dimensional model of an eternal black hole, and a black hole that is in the process of being formed - the entropy is proportional to the area of the event horizon. This is a very promising beginning. Causal set theory is not yet a full quantum gravity theory. We have not yet worked out how to incorporate the effects of quantum interference into causal set growth. But reclaiming the flow of time is an important aesthetic and conceptual advance. It releases quantum gravity theorists from a frozen space-time and holds out hope that science can be reconciled with our deep sense of the reality of the passage of time. Fay Dowker Fay Dowker is a senior lecturer at Imperial College, London, and is currently at the Perimeter Institute in Waterloo, Ontario, Canada http://archive.newscientist.com/secure/article/article.jsp?id=mg18024155.000 free login |
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| Peter T |
posted 1/14/04 6:51 PM
If Space and Time themselves are grainy, as quantum theorists suggest, within what are they grainy? If not part of a continuum, how or by what or within what is one grain or quantum of space to be separated or be distinct from another quantum of space? Superspace? More dimensions? The same would apply, I think, to quanta of time. Am I committing the error here of trying to apply macroscopic ways of thinking to the quantum world, or is it really a case of "turtles all the way down?" |
| Chris W |
posted 1/20/04 7:43 AM
Peter, An analogous question I saw answered the other day is this: What lies between water molecules? Must not there be water between them? The answer of course is that the question presupposes that water is a truly continuous substance, when in fact a given volume of water contains a finite number of molecules. The quantity of water can be specified a number of molecules, rather than the volume of space or a mass. Of course one will point out that space lies between the molecules, but this leads one eventually to think more carefully about the nature of space, and by extension, of space and time. It seems continuous, but is there another way of interpreting the evidence for this? The recurring problem in discussing these ideas is that one is easily confused by the mode of representation, eg, dots marked on a sheet of paper, and one's everyday intuitions, molded by interacting with a world in which continuity is a very good approximation. Mathematical formulation can help to see the assumptions hidden in those intuitions, which or may not be correct. Your question is also a bit like asking what lies between the prime numbers, taken as an example of a "countable" set. One can answer this question if places them within a larger set -- the positive integers, rational numbers, or real numbers, but one can also regard these other sets as constructions derived from the primes. |
| xiaozhong zhai |
posted 3/18/04 10:49 AM
A new time-space theory: Time is a expression of change in motion distance and curvature. Time-space is moving. Time-space active and passive motion form a whole world of physics. Please read the chapter 2 ( timedistance and timecurvature......time-space active and passive motion) and chapter 5 (natural force.....the durality of time-space and energy) of a new book,THING AND ITS LAW ISBN 1-58939-525-5 |
| xiaozhong zhai |
posted 8/18/04 4:38 PM
Sir: May I recommend a new book, THING AND ITS LAW (in amazon.com orvirtualbookworm.com), to you? This book dedicates to you: A new time-space concept, a new inertia view, a new energy idea, a new world outlook, a new economic thought, a new grand unified theory. A new idea of time-space is follows: 1, Time is space distance or curvature. Change in times-pace is that in distance or curvature. There are two kinds time-space. One is plan or linear time-space. Another is spherical time-space. 2, There are three kinds of clock: Current Clock: It works based on the principle of the earth rotating once 24 hours around the sun. Its second unit is 0.004167 degrees. It describing the change in the position of thing on the earth referring to the sun Thing Clock: Every thing has its own thing clock with different second-distance. This Clock tells thing self what is happening for it. Doppler Clock: Every observer has one’s own Doppler clock with different second-distance or second-curvature. Observer tells self how the space state of thing is changing. 3, Doppler phenomenon: It is a result of compress or prolongation of time-space relative to observer. According to the principle of the relative motion of time-space curvature, red-shifted does not really mean that the universe is expanding. 4, Four-dimensional Coordinates: It consists of three dimension and sphere time-space. In this coordinates, there is not real straight line or circle. 5, The motion of linear time-space is passive, but the motion of sphere time-space is active. 6, A duality of curved time-space and its two focuses: contraction energy or centripetal force on concave (converging on its centre, real focus) and expansion energy or centrifugal force on convexity (dispersing from its centre, virtual focus). Your sincerely Xiaozhong zhai |
| r. ayana |
posted 4/22/07 3:24 AM
As Peter says, Chris - it's really turtles all the way down. http://www.blogcharm.com/newilluminati be enlightened |
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