il tempo
http://www.finedeltempo.it/finedeltempo_index/il_tempo/il_tempo.html
un poco di teoria...dal concorso FQXi del 2008 sulla natura del tempo (con un’impressionante livello di partecipazione) ad un più casalingo seminario svoltosi a Bruxelles, citando qualche ricerca interessante..iWeb 3.0.4http://www.finedeltempo.it/finedeltempo_index/il_tempo/il_tempo_files/IMG_0238.jpgil tempo
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viaggi nel tempo
http://www.finedeltempo.it/finedeltempo_index/il_tempo/Voci/2012/12/6_viaggi_nel_tempo.html
7bb9936e-8f42-456c-b900-12c00c50ec93Thu, 6 Dec 2012 00:52:11 +0100<a href="http://www.finedeltempo.it/finedeltempo_index/il_tempo/Voci/2012/12/6_viaggi_nel_tempo_files/time-travel-wormhole.jpg"><img src="http://www.finedeltempo.it/finedeltempo_index/il_tempo/Media/object005_1.jpg" style="float:left; padding-right:10px; padding-bottom:10px; width:183px; height:137px;"/></a>Original by Jon J. Thaler.<br/><br/>Time Travel: Fact or Fiction?<br/>We define time travel to mean departure from a certain place and time followed (from the traveller's point of view) by arrival at the same place at an earlier (from the sedentary observer's point of view) time. Time travel paradoxes arise from the fact that departure occurs after arrival according to one observer and before arrival according to another. In the terminology of special relativity time travel implies that the timelike ordering of events is not invariant. This violates our intuitive notions of causality. However, intuition is not an infallible guide, so we must be careful. Is time travel really impossible, or is it merely another phenomenon where "impossible" means "nature is weirder than we think?" The answer is more interesting than you might think. <br/>The Science Fiction Paradigm<br/>The B-movie image of the intrepid chrononaut climbing into his time machine and watching the clock outside spin backwards while those outside the time machine watch the him revert to callow youth is, according to current theory, impossible. In current theory, the arrow of time flows in only one direction at any particular place. If this were not true, then one could not impose a 4-dimensional co-ordinate system on space-time, and many nasty consequences would result. Nevertheless, there is a scenario which is not ruled out by present knowledge. This usually requires an unusual spacetime topology (due to wormholes or strings in general relativity) which has not yet seen, but which may be possible. In this scenario the universe is well behaved in every local region; only by exploring the global properties does one discover time travel.<br/>Conservation Laws<br/>It is sometimes argued that time travel violates conservation laws. For example, sending mass back in time increases the amount of energy that exists at that time. Doesn't this violate conservation of energy? This argument uses the concept of a global conservation law, whereas relativistically invariant formulations of the equations of physics only imply local conservation. A local conservation law tells us that the amount of stuff inside a small volume changes only when stuff flows in or out through the surface. A global conservation law is derived from this by integrating over all space and assuming that there is no flow in or out at infinity. If this integral cannot be performed, then global conservation does not follow. So, sending mass back in time might be all right, but it implies that something strange is happening. (Why shouldn't we be able to do the integral?)<br/>General Relativity<br/>The possibility of time travel in GR has been known at least since 1949 (by Kurt Godel, discussed in [1], page 168). The GR spacetime found by Godel has what are now called "closed timelike curves" (CTCs). A CTC is a worldline that a particle or a person can follow which ends at the same spacetime point (the same position and time) as it started. A solution to GR which contains CTCs cannot have a spacelike embedding - space must have "holes" (as in donut holes, not holes punched in a sheet of paper). A would-be time traveller must go around or through the holes in a clever way.<br/>The Godel solution is a curiosity, not useful for constructing a time machine. Two recent proposals, one by Morris, et al. [2] and one by Gott [3], have the possibility of actually leading to practical devices (if you believe this, I have a bridge to sell you). As with Godel, in these schemes nothing is locally strange; time travel results from the unusual topology of spacetime. The first uses a wormhole (the inner part of a black hole, see figure 1 of [2]) which is held open and manipulated by electromagnetic forces. The second uses the conical geometry generated by an infinitely long string of mass. If two strings pass by each other, a clever person can go into the past by travelling a figure-eight path around the strings. In this scenario, if the string has non-zero diameter and finite mass density, there is a CTC without any unusual topology.<br/>Grandfather Paradoxes<br/>With the demonstration that general relativity contains CTCs, people began studying the problem of self-consistency. Basically, the problem is that of the "grandfather paradox": What happens if our time traveller kills her grandmother before her mother was born? In more readily analyzable terms, one can ask what are the implications of the quantum mechanical interference of the particle with its future self. Boulware [5] shows that there is a problem - unitarity is violated. This is related to the question of when one can do the global conservation integral discussed above. It is an example of the "Cauchy problem" [1, chapter 7].<br/>Other Problems (and an escape hatch?)<br/>How does one avoid the paradox that a simple solution to GR has CTCs which QM does not like? This is not a matter of applying a theory in a domain where it is expected to fail. One relevant issue is the construction of the time machine. After all, infinite strings aren't easily obtained. In fact, it has been shown [4] that Gott's scenario implies that the total 4-momentum of spacetime must be spacelike. This seems to imply that one cannot build a time machine from any collection of non-tachyonic objects, whose 4-momentum must be timelike. There are implementation problems with the wormhole method as well.<br/>Tachyons<br/>Finally, a diversion on a possibly related topic.<br/>If tachyons exist as physical objects, causality is no longer invariant. Different observers will see different causal sequences. This effect requires only special relativity (not GR), and follows from the fact that for any spacelike trajectory, reference frames can be found in which the particle moves backward or forward in time. This is illustrated by the pair of spacetime diagrams below. One must be careful about what is actually observed; a particle moving backward in time is observed to be a forward moving anti-particle, so no observer interprets this as time<br/> t<br/>One reference | Events A and C are at the same<br/>frame: | place. C occurs first.<br/> |<br/> | Event B lies outside the causal<br/> | B domain of events A and C.<br/> -----------A----------- x (The intervals are spacelike).<br/> |<br/> C In this frame, tachyon signals<br/> | travel from A-->B and from C-->B.<br/> | That is, A and C are possible causes<br/> of event B.<br/><br/>Another t<br/>reference | Events A and C are not at the same<br/>frame: | place. C occurs first.<br/> |<br/> | Event B lies outside the causal<br/> -----------A----------- x domain of events A and C. (The<br/> | intervals are spacelike)<br/> |<br/> | C In this frame, signals travel from<br/> | B-->A and from B-->C. B is the cause<br/> | B of both of the other two events.<br/>The unusual situation here arises because conventional causality assumes no superluminal motion. This tachyon example is presented to demonstrate that our intuitive notion of causality may be flawed, so one must be careful when appealing to common sense. See the FAQ article on <a href="http://math.ucr.edu/home/baez/physics/ParticleAndNuclear/tachyons.html">tachyons</a>, for more about these weird hypothetical particles.<br/>Conclusion<br/>The possible existence of time machines remains an open question. None of the papers criticizing the two proposals are willing to categorically rule out the possibility. Nevertheless, the notion of time machines seems to carry with it a serious set of problems.<br/>References<br/> 1. Kip S. Thorne, "Black Holes and Time Warps" Norton and Co (1994)<br/> 2. S.W. Hawking, and G.F.R. Ellis, "The Large Scale Structure of Space-Time," Cambridge University Press, (1973).<br/> 3. M.S. Morris, K.S. Thorne, and U. Yurtsever, PRL, 61, 1446 (1989). How wormholes can act as time machines.<br/> 4. J.R. Gott, III, PRL, 66, 1126 (1991). How pairs of cosmic strings can act as time machines.<br/> 5. S. Deser, R. Jackiw, and G. 't Hooft, PRL, 66, 267 (1992). A critique of Gott. You can't construct his machine.<br/> 6. D.G. Boulware, University of Washington preprint UW/PT-92-04. Available on the <a href="mailto:hep-th@xxx.lanl.gov/">hep-th@xxx.lanl.gov</a> bulletin board: item number 9207054. Unitarity problems in QM with closed timelike curves. <br/> 7. "Nature", May 7, 1992. Contains a very well written review with some nice figures.<br/>_________________________________________<br/>Original by Scott I. Chase.<br/><br/>The Superluminal Scissors<br/>A Gedanken experiment<br/>Imagine a huge pair of scissors, with blades one light year long. The handle is only about two feet long, creating a huge lever arm, initially open by a few degrees. Then you suddenly close the scissors. This action takes about a tenth of a second. Doesn't the contact point where the two blades touch move toward the blades' tips much faster than the speed of light? After all, the scissors close in a tenth of a second, but the blades are a light year long. That seems to mean that the contact point has moved down the blades at the remarkable speed of 10 light years per second. This is more than 108 times the speed of light! But this seems to violate the most important rule of special relativity — that no signal can travel faster than light. What's going on here?<br/>Explanation<br/>We have mistakenly assumed that the scissors do, in fact, close when you close the handle. But in fact, according to special relativity, this is not at all what happens. What does happen is that the blades of the scissors flex. No matter what material you use for the scissors, SR sets a theoretical upper limit to the rigidity of the material. In short, when you close the scissors, they bend.<br/>The point at which the blades bend propagates down the blade at some speed less than the speed of light. On the near side of this point, the scissors are closed. On the far side of this point, the scissors remain open. You have, in fact, sent a wave down the scissors, carrying the information that the scissors have been closed. But this wave does not travel faster than light. It will take at least one year for the tips of the blades, at the far end of the scissors, to feel any force whatsoever, and, ultimately, to come together to completely close the scissors.<br/>As a practical matter, this theoretical upper limit to the rigidity of the metal in the scissors is far higher than the rigidity of any real material, so it would, in practice, take much much longer to close a real pair of metal scissors with blades as long as these.<br/>One can analyze this problem microscopically as well. The electromagnetic force binding the atoms of the scissors together propagates at the speed of light. So if you displace some set of atoms in the scissor (such as the entire handles), the force will not propagate down the scissor instantaneously. This means that a scissor this big must cease to act as a rigid body. You can move parts of it without other parts moving at the same time. It takes some finite time for the changing forces on the scissor handles to propagate from atom to atom, letting the far tips of the blades "know" that the scissors have been closed.<br/>Caveat<br/>The contact point where the two blades meet is not a physical object. So there is no fundamental reason why it could not move faster than the speed of light, provided that you arrange the experiment correctly. In fact, it can be done with scissors provided that your scissors are short enough and wide open to start, very different conditions than those spelled out in the gedanken experiment above. In this case it will take you quite a while to bring the blades together — more than enough time for light to travel to the tips of the scissors. When the blades finally come together, if they have the right shape, the contact point can indeed move faster than light.<br/>Think about the simpler case of two rulers pinned together at an edge point at the ends. Slam the two rulers together and the contact point will move infinitely fast to the far end of the rulers at the instant they touch. So long as the rulers are short enough that contact does not happen until the signal propagates to the far ends of the rulers, the rulers will indeed be straight when they meet. Only if the rulers are too long will they be bent like our very long scissors, above, when they touch. The contact point can move faster than the speed of light, but the energy (or signal) of the closing force cannot.<br/>An analogy, equivalent in terms of information content, is, say, a line of strobe lights. You want to light them up one at a time, so that the `bright' spot travels faster than light. To do so, you can send a luminal signal down the line, telling each strobe light to wait a little while before flashing. If you decrease the waiting time with each successive strobe light, the apparent bright spot will travel faster than light, since the strobes on the end didn't wait as long after getting the go-ahead, as did the ones at the beginning. But the bright spot can't pass the original signal, because then the strobe lights wouldn't know to flash. time, a workshop
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d758c07e-c1fc-496b-a1a8-b6a46a8e9f7aMon, 5 Nov 2012 23:14:19 +0100<a href="http://www.finedeltempo.it/finedeltempo_index/il_tempo/Voci/2012/11/5_tempo,_elementi_di_un_seminario_files/image_6.png"><img src="http://www.finedeltempo.it/finedeltempo_index/il_tempo/Media/object038_1.jpg" style="float:left; padding-right:10px; padding-bottom:10px; width:183px; height:137px;"/></a>Killing Time<br/>quest’Essere a corsa lanciato nel gorgo di Cause e d’Effetti<br/>tutte le cose già furon compiute senza di lui<br/>gli viene gettato dinanzi l’Oggi, pretesto lucente<br/>ed il Domani sarà quel che già pronto era Ieri<br/>This Beeing running into the maelstrom of Causes and Effects<br/>every thing without him already was done<br/>before him Today is thrown, glowing pretext<br/>and Tomorrow will be what for Yesterday already was prepared<br/> Omar Khayyåm<br/><br/><br/><br/><br/><br/><br/><br/>A- Why time is a problem? some hard facts<br/>1: t,-t : symmetrical -> <br/>no change in the laws, both in classical and quantum Physics <br/>(two problems: at the macroscopic scale entropy, which gives an arrow, and at the particle scale kaon decay, which violates CPT and gives matter prevalence over antimatter) -> theoretical possibility of time machines; <br/>(where is the contraddiction ?) <br/><br/>2- existence of solutions of General Relativity with Closed Timelike Curves, that is, time travel<br/>(first by Godel, with a rotating universe, then by others)<br/><br/>3- virtual particles in Quantum Mechanics, which come in and out of the vacuum going forwards and backwards in time (see also antipartcles which go backward in time in Feynman diagrams)<br/><br/>4- in GR there no global time, but only local times, different for each observer (twin paradox)<br/><br/><br/><br/>different observers (O1 and O2) see the same two events in inverted sequence: causality has a problem<br/><br/>5- causality has also problems with QM, because of the uncertainty principle and the superposition (see Schrodinger’s cat)<br/><br/>6- there has been a lot of debate among the best theoretical phisicists about the very nature of time, its topological nature, and also time travel (some of them-Thorne, Novikov,..) have also been part of an informal group (the Consortium) to investigate the practical possibility ot time machines (and some have been devised).<br/><br/>7- in GR time can be seen as displayed all at once: all the story already written; as Einstein put it: “Time is an illusion”; morover, in the Wheeler-deWitt equation which is the master equation of canonical quantum gravity ( ) there’s no evolution, no dynamics: no time.<br/>_<br/><br/><br/><br/><br/><br/>_________________________________________________________ <br/><br/>So, from many good reasons, it seems that time travel is possible.(But, if time doesn’t exist?)<br/>Of course there are problems: entropy is one of them, with it disturbing arrow:<br/><br/><br/><br/><br/>And our consciousness usually tells us that we can go only forward. <br/>But what exactly is time, is still unclear, so before speaking of arrows we need to speak of time: remembering the famous lament of Augustine: “What is time? if nobody asks me, I know, but if I want to explain it to someone, then I do not know”’<br/><br/><br/>_____________________<br/>B)-Setting the stage: subject and actors<br/>Since the subject is too vaste, I’ll concentrate on one specific point of view: <br/>that is, the new sinthesis between GR and QM: quantum gravity, <br/>and the way it deals with time. <br/>There’s a caveat about all this stuff: as once Feynman pointed out, “one had to loose one’s common sense in order to perceive what was happening at the atomic level”; I’ll try to start from common sense whilst dealing with concepts that are out of it, and in the meanwhile realizing what’s wrong with our common sense-be it physiological or cultural. The real problem is that often we are left in a noman’s land, and don’t know what to trust.<br/>It’s quite easy to present GR and QM...<br/>but the sinthesis is difficult: that’s because a)GR (very large scale) and b)QM (very small scale) are not compatible, and it’s mainly because of a philosophical reason, which for the moment beeing we trace back to Newton: <br/>in his sinthesis of the gravitational force (which set the standard for all succesful physical theories because of its simplicity and power) he had bodies movies against a fixed background, space: that is, a fixed frame and objects changing position along a regular timeline. It is as if these walls (even if not visible) where given once and forever, and things were flowing against this background and along an invisible but also fixed and given time axis. (isn’t it what most of us think when we speak of movement?)<br/>While in b)QM, this kind of conception still holds: all particles and their wavefunctions (however strange they may look) evolve against this kind of background (assumed as external), <br/>in a)GR there’s a unique spacetime, without any external structure: its metric is the main element for describing and explaining movement and forces (more later on the meaning of Minkowsky’s geometry) .<br/>That’s why philosophy is so important in solving the problem of the Grand Unified Theory: it can’t be just a sum of the two, but it has to be something different, which has as limits GR (in the large scale) and QM (In the small scale). And this GUT needs a deep reflection on the base concepts, space and time.<br/><br/><br/>so we present the actors:<br/>1- time itself (?) /clocks/<br/>a) pendulum<br/>b) light and mirrors:<br/><br/>this is the simplest clock: a particle (photon) bouncing between two mirrors<br/><br/>this is the same clock, but in a moving object ; the path is longer, and since the photon speed is costant=c, then time (v/s) must be longer! <br/><br/>s<br/><br/><br/><br/> s=1/2vt<br/><br/><br/><br/> s=1/2vt <br/><br/><br/> O inside s=ct<br/> O’ outside<br/><br/> s=÷c2t2-v2t2<br/> ct=÷c2t2-v2t2 ct=t÷c2-v2 ct=ct÷1-v2 /c2 <br/> t=t÷1-v2 /c2 t=t/÷1-v2 /c2 >t : slower <br/><br/><br/><br/> Mirror<br/><br/><br/><br/><br/> MirrorA simple clock: a photon bouncing between two mirrors<br/><br/><br/><br/><br/> Mirror<br/> this is the core of Special Relativity.<br/><br/><br/>2- General Relativity /tensors/<br/><br/>:Einstein’s equation<br/><br/>it’s written in tensorial form<br/>(a tensor is a mathematical object whose components are vectors)<br/>and it simply states that the metric tensor is proportional to the energy tensor<br/><br/><br/><br/>we have to remember that we deal with a four-dimensional space: <br/>3 spatial coordinates and one time coordinate : <br/>when a part is bended (by the action of some matter/energy field) space and time vary with relation to the other parts; <br/>the bodies on it follow geodetics (that are the shortest lines lying on a surface and passing along two given points)<br/><br/><br/><br/><br/><br/><br/><br/><br/>3- Quantum Mechanics /wave packets/<br/>: Schroedinger’s equation<br/>it relates the Hamiltonian (energy) operator to the wave function of a particle<br/><br/><br/>interference of a single particle<br/><br/>tunnell effect<br/><br/><br/><br/><br/>4- Consciousness /selfsustained excitations/<br/>There’s a lot of debate about consciousness, but the important thing is that, while until recently it was mainly an object/subject of speculation, in these last years it has also been the object of experiments: a lot of physiological and neurophysiological findings have given a new basis for its understanding .<br/>Apart from a primary objection of philosophers about the very possibility of defining it, there are some tentative but strong hypothesis about it (Damasio, Edelman, Tononi).<br/>And we know a lot about circadian clocks, neural rythms, cohordinate/chaotic firing of groups of interconnected neurons, about memory and perception...<br/>So it’s possible to have a better basis to confront us with the problem: How is time related to our consciousness? Or even more, is it a product of consciousness?<br/><br/>“When voluntary saccadic eye movements are made to a silently ticking clock, observers sometimes think that the second hand takes longer than normal to move to its next position1. For a short period, the clock appears to have stopped (chronostasis). Here we show that the illusion occurs because the brain extends the percept of the saccadic target backwards in time to just before the onset of the saccade. This occurs every time we move the eyes but it is only perceived when an external time reference alerts us to the phenomenon”<br/><br/>the brain in the act of processing signals<br/><br/><br/><br/>b) the chorus:<br/>1- Old and new philosophers<br/>Zeno, Parmenides,Heraclitus, Aristoteles,Plato<br/>Z:“Contatti sono le totalità e le non totalità, il convergente e il divergente, il consonante e il dissonante: e fuori da tutte le cose ne sorge una sola, e fuori da una cosa sola sorgono tutte”:<br/>a world of relations: “Contacts (relations) are totalities and non-totalities, convergent and divergent, consonant and dissonant: and out of all things comes one, and out of one all things come”<br/><br/><br/><br/>Achylles and the tortue<br/>P: “motion is an illusion, there is no time”<br/>H: “panta rei-everything’s changing” <br/>“Negli stessi fiumi tanto entriamo quanto non entriamo, tanto siamo quanto non siamo”, “a coloro che entrano negli stessi fiumi continuano ad affluire acque sempre differenti” , “il mondo di fronte a noi-il medesimo per tutti i mondi-non lo fece nessuno degli dei né degli uomini, ma fu sempre, ed è, e sarà, fuoco sempre vivente, che divampa secondo misure e si spenge secondo misure” <br/>“In the same rivers we enter and we do not enter, we are and we are not” “ to those who enter the same rivers always different waters come” “the world in front of us-the same for all worlds- was not made by any man or god, but always has been and is and will be, always living fire, which according to measures burns and according to measures dies out”<br/><br/><br/>and let’s quote a comment on presocratic philosophy :<br/>-...l’attimo come intuizione precede la scossa; nel fluire del tempo si erge improvvisamente un istante, che “non è in nessun tempo”, dice impropriamente Platone, ma che a rigore dà inizio al tempo, è già nel tempo, però allude a qualcosa che non è nel tempo, lo ripercuote, lo esprime.... “ogni cosa governa la folgore”. La dottrina dell’istantaneità è perciò un’indicazione ottimistica: l’attimo appartiene al tessuto della rappresentazione, allude al punto in cui questo viene lacerato...<br/>E dietro Dioniso “il dio primordiale da cui tutti gli altri prendono inizio -secondo la teogonia rapsodica, il Tempo...Mnemosine ci insegna che l’origine di tutti i ricordi - là dove il tempo non è ancora cominciato- è quello appunto che si deve recuperare. Tale è l’insegnamento misterico, tutto il tempo che bisogna attraversare all’indietro per raggiungere il senza tempo, tutte le generazioni di dèi e di uomini, tutti i miti narrati da Orfeo, non sono altro se non giuochi di apparenze.” E nei primi principi di un’altra teogonia orfica leggiamo: “ si chiamava Tempo senza vecchiaia...e a lui era congiunta Ananke ( Necessità)...Tempo e necessità: una coppia decisiva di categorie: il nesso delle rappresentazioni sensibili - cioè il loro principio- può davvero pretendere di chiamarsi tempo, come il nesso delle rappresentazioni astratte può pretendere di chiamarsi necessità”. (Colli)<br/>“..the istant as an intuition comes before the shock; in the flow of time an instant towers abruptly which “is in no time” as Plato unapproprietely says, but actually is the beginning of time, is already in time but hints to something which is not in time, expresses it and and echoes it.. “everything is ruled by the lightning”. The instantaneity doctrine is thereafter optimistic: the instant is a part of the tissue of representation, it hints to the point where that is torn...<br/>And after Dyonisus “ the primeval god who gives origin to all the other ones”-according to rapsodic theogony- Time...Mnemosine teaches us that is the origin of all memories-there where time didn’t yet begin-that’s exactly what we have to recall. This is the mysteric teaching; all the time we have to cross backwards to reach the timeless, all the generations of of gods and men, all the myths that Orpheus narrates, they are nothing more than a play of appearance” And in the first principles of another orphic theogony we find: “it was called Time without aging..and Ananke (Necessity) was his kin...Time and Necessity: a fundamental pair of categories: the nexus of sensory symbolizations-indeed their beginning- may well be called time. as the nexus of abstract symbolizations may well be called Necessity”<br/><br/>Kant, ...later on,<br/><br/><br/>Newton: absolute space and time (a fixed frame)<br/> “I do not define time, space, place, and motion, as being well known to all. Only I must observe, that the common people conceive those quantities under no other notions but from the relation they bear to sensible objects. And thence arise certain prejudices, for the removing of which it will be convenient to distinguish them into absolute and relative, true and apparent, mathematical and common. <br/><br/>I. Absolute, true, and mathematical time, of itself, and from its own nature, flows equably without relation to anything external, and by another name is called duration: relative, apparent, and common time, is some sensible and external (whether accurate or unequable) measure of duration by the means of motion, which is commonly used instead of true time; such as an hour, a day, a month, a year. <br/><br/>II. Absolute space, in its own nature, without relation to anything external, remains always similar and immovable. Relative space is some movable dimension or measure of the absolute spaces; which our senses determine by its position to bodies; and which is commonly taken for immovable space; such is the dimension of a subterraneous, an aerial, or celestial space, determined by its position in respect of the earth. Absolute and relative space are the same in figure and magnitude; but they do not remain always numerically the same. For if the earth, for instance, moves, a space of our air, which relatively and in respect of the earth remains always the same, will at one time be one part of the absolute space into which the air passes; at another time it will be another part of the same, and so, absolutely understood, it will be continually changed.”<br/><br/>Bergson, Heidegger: later on<br/><br/>2- Literature<br/>3- Phisicists old and new<br/>4- sparse Mathematicians<br/>the stage: <br/>should be nature, reality, space, spacetime...but is there a stage?<br/><br/>_________________________________________________<br/>3- At first we’ll deal with the topology of time, that is, we want to throw some blows at the common ideas about the structure of time: linearity, uniformity, continuity (all referred to the concept and assumptions of the real line)<br/><br/>this is regular time<br/><br/>this is different for the two<br/><br/>this is not regular for one<br/><br/>now it is bended (say, by a gravitational wave, but why not everyday?)<br/><br/>this is a worse situation (maybe a black hole passing nearby, but again still: why not everyday?)<br/><br/>this is quite weird: look how the system tunnels into another part<br/><br/>now let’s look into the evolution of a system: it’s a sequence of states: does it have a time, or is it just that, a sequence?<br/><br/><br/><br/><br/><br/><br/>Literature, History will help us in this task:<br/><br/><br/><br/>New Zealand<br/><br/>Braudel on India:<br/><br/><br/><br/><br/><br/><br/>or Bloch:<br/>“un intersecarsi di diversi piani del tempo, un contrappunto di squilibri temporali fra diversi popoli, classi, individui, tra diverse sfere culturali e sociali, e non la fila indiana del prima e del dopo”<br/>A crossing of different time planes, a contrapunctus of time disequilibria among different populations, classes, individuals, among different culstural and social spheres, not the indian queue of before and after”<br/><br/>So we need to escape from the simplistic concept of progress and its underlying implied linearity.<br/>“Berkeley negò che vi fosse un oggetto dietro le impressioni dei sensi; Hume, che vi fosse un soggetto dietro la percezione dei mutamenti. Il primo aveva negato la materia. Il secondo negò lo spirito...Negati materia e spirito, che sono continuità, non so con che diritto terremo per noi quell’altra continuità che è il tempo...Non basta un solo termine ripetuto per disordinare e confondere la storia del mondo, per affermare che questa storia non esiste? Negare il tempo è due negazioni: negare la successione dei termini di una serie, negare il sincronismo dei termini di due serie...and yet...negare la successione temporale, negare l’io, sono disperazioni apparenti e consolazioni segrete. Il nostro destino non è spaventoso perché irreale; è spaventoso perché è irreversibile. Il tempo è la sostanza di cui son fatto. Il tempo è un fiume che mi trascina, ma io sono il fiume...”(Borges)<br/>“Berkeley denied there was any object undelying the impressions of senses; Hume that there was a subject behind perception of changes. The first had negated matter. The latter negated spirit...Once we negate matter and spirit, which are continuities, what gives us the right to keep for us that subsequent continuiy that’s time?..Doesn’t it suffice a single repeated term to shuffle and obscurate all of world’s history, to deny the very existence of this history? To negate time is a double negation: negate the sequence of the terms in a series, to negate the synchronism of the terms of two series...”<br/><br/>But again, what’s time?<br/><br/><br/>“The hardest thing of all is to find a black cat in a dark room, especially if there is no cat” Confucius<br/><br/>floppy economic theory<br/>Fermat’s last theorem<br/>Riemann’s conjecture<br/><br/>4- first definitions of time<br/><br/>a) operational definition: time is what is beeing measured by a clock (a circular definition, since any interval needs a reference)<br/> clocks<br/><br/>We usually assume as clock a whole class of regular/cyclical events (the pendulum is the prototype), or simply regular ones (as the radioactive decay of an atom); on top of this there’s a class of parameters of a system that’s usually taken as indices of its evolution, such as entropy (or physiological ones such as cellular replication and death).<br/>We can also make a distinction between internal clocks (like the ones which give way to circadian rythms) and external ones, as long as we remember that they have a strict albeit illdefined relationship; <br/>we can make the following nonsimmetric statements: no internal clock is indipendent from its environment (weak), no external clock is independent from the observer (strong, and it deserves further investigation). Given this assumptions, a well defined clock is related to the observer’s perceptions, and it can be seen as the relation between two sequences, one internal (mediated by an integration of memory and consciousness) and one external.<br/>In order for an event/sequence to be a real clock it has to satisfy three conditions:<br/>a) that this relationships creates a complete ordering of events (before and after)<br/>b) that it be dense everywhere (between any two points there’s another one)<br/>c) that we may define on it a measure satisfying the 3 conditions :d(AB)=d(BA); d(AA)=0;d(AC)<d(AB)+d(BC).<br/>But these conditions are not automatically satisfied by clocks: they depend on the set to be measured, so we are back to circularity.<br/><br/>b) other definitions are equally circular: time is that interval (of time...) in which things/movements happen - or tautological: time is the reference of movement<br/><br/>c) so we may begin to think that time is something we superpose to events; even if it looks hard to give a definition of movement without any reference to time (our idea of velocity has time at its very base: v=Ds/Dt ). [see the significance of Zeno’s paradoxes]. But we may speak of displacement, of a system that changes its state (changing one or more parameters), even of evolution (change as a function of these parameters)<br/><br/>d) the next step we usually make is to substitute to one of these internal parameters an external entity, typical of the observer (Augustine: extensio animae) or taken from external regular (cyclical) phenomena (like the sun changing its position) [but along this way you don’t escape circular tautologies]. The other way is a kind of mystical breath by which one inhales the temporal fluid of which everything is permeated. <br/><br/>e) for the physicist, in order to take a measure, he must assume an infinite coherence and repetibility of the event he takes as a measure of time. That’s an assumption based on the proper character of the event: for the pendulum there is no reason to suspect it could not be regular, and from this on, all events with a well known law and a fixed frequency will do. But this is no escape from the problem of what are we measuring. And, because of the problems that the lack of a proper notion of time gives, there have been attempts to formulate the physical laws without any reference to it (one of the first was Lorentz, and then we arrive to quantum gravity...)<br/><br/>f) let’s tackle a typical philosophical problem: what is now?(the moment you think of it it’s already gone): it goes back to the definition of a point on the real axis, but unfortunately we don’t give a definition of point, it’s assumed to be a ‘primitive concept’: but by and large the debates are quite similar. And we have no clear solution.And it’s connected to another famous problem that arises from the greek paradoxes: movement and changing:if I’m here I can’t be there, and when I’m there I’m no more here; and if I’ve changed it’s not the same person who’s in another place/time.......(so I don’t really move or change)<br/><br/>g) as we pointed before, one thing everybody knows is that he cannot change his past; so time at least has an arrow, but if there is a direction there must also be something going along that direction. So goes the common sense. But again this is the realm of conscious experience, and we have two possible ways: or to trust it to the limit of making it the basis of physical laws, or to try the other way round: to understand from the laws of nature why our consciousness gives us that kind of perception. (Penrose believes that in the forthcoming theory of quantum gravity we’ll find also the basis for consciousness)<br/><br/>So, let’s move on to quantum gravity and some more philosophy<br/><br/><br/> tempo, teoria: concorso
http://www.finedeltempo.it/finedeltempo_index/il_tempo/Voci/2012/11/5_tempo,_teoria__concorso.html
91d688e8-61a5-4c7c-a4a0-693b17f22cfdMon, 5 Nov 2012 23:13:33 +0100<a href="http://www.finedeltempo.it/finedeltempo_index/il_tempo/Voci/2012/11/5_tempo,_teoria__concorso_files/file.jpg"><img src="http://www.finedeltempo.it/finedeltempo_index/il_tempo/Media/object041_1.jpg" style="float:left; padding-right:10px; padding-bottom:10px; width:182px; height:222px;"/></a>dove si leggono le cose pazze che i fisici pensano del tempo..e sembrano anche crederci!ricerche sul tempo
http://www.finedeltempo.it/finedeltempo_index/il_tempo/Voci/2012/10/1_ricerche_suk_tempo.html
774f9a94-4f0c-4803-bad0-6168b6064381Mon, 1 Oct 2012 14:32:22 +0200Time's arrow in B mesons<br/>Nature 491, 640 (29 November 2012) <br/>A cornerstone of theoretical particle physics — the idea that not all processes run in the same way forwards in time as they do backwards — has been observed directly for the first time.<br/>Members of the BaBar Collaboration trawled data from their experiment (pictured), which ran at the SLAC National Accelerator Laboratory…<br/>____________________________________________________________________<br/>Leonard Susskind<br/>Stanford Institute for Theoretical Physics and Department of Physics, Stanford<br/>University<br/>Stanford, CA 94305-4060, USA<br/>Abstract<br/>This is the written version of a lecture at the KITP workshop on Bits, Branes and Black Holes. In it I describe work with D. Harlow, S. Shenker, D. Stanford which explains how the tree-like structure of eternal ination, together with the existence of terminal vacua, leads to an arrow-of-time. Conformal symmetry of the dS/CFT type is inconsistent with an arrow-of-time and must be broken. The presence in the landscape of terminal vacua leads to a new kind of attractor called a fractal - which both breaks conformal symmetry, and creates a directional time-asymmetry.<br/>This can be seen from both the local or causal-patch viewpoint, and also from the global or multiversal viewpoint. The resulting picture is consistent with the view recently expressed by Bousso.<br/>In the last part of the lecture I illustrate how the tree-model can be useful in explaining the value of the cosmological constant, and the cosmic coincidence problem.<br/>The mechanisms are not new but the description is.<br/>Figure 5: On the right side of the figure a red bubble is shown nucleating in de Sitter space.<br/>Ignoring later nucleations, the bubble expands to fill the causal future of the nucleation point. The tree-analog of the same process is shown in the left side of the figure.<br/><br/><br/><br/><br/><br/><br/><br/><br/><br/><br/><br/>____________________________________________________________________________________<br/>Time’s Arrow for Shockwaves ; Bit-Reversible Lyapunov and “Covariant” Vectors ; Symmetry Breaking<br/>Wm. G. Hoover and Carol G. Hoover<br/>Ruby Valley Research Institute<br/>Highway Contract 60, Box 601<br/>Ruby Valley, Nevada 89833<br/>(Dated: November 13, 2012)<br/>Abstract<br/>Strong shockwaves generate entropy quickly and locally. The Newton-Hamilton equations of motion, which underly the dynamics, are perfectly time-reversible. How do they generate the irreversible shock entropy? What are the symptoms of this irreversibility? We investigate these questions using Levesque and Verlet’s bit-reversible algorithm. In this way we can generate an entirely imaginary past consistent with the irreversibility observed in the present. We use Runge-Kutta integration to analyze the local Lyapunov instability of nearby “satellite” trajectories. From the forward and backward processes we identify those particles most intimately connected with the irreversibility described by the Second Law of Thermodynamics. Despite the perfect time symmetry of the particle trajectories, the fully-converged vectors associated with the largest Lyapunov exponents, forward and backward in time, are qualitatively different. The vectors display a time-symmetry breaking equivalent to Time’s Arrow. That is, in autonomous Hamiltonian shockwaves the largest local Lyapunov exponents, forward and backward in time, are quite different.<br/>__________________________________________________________________<br/><br/><br/><br/><br/><br/><br/><br/><br/><br/><br/><br/><br/><br/><br/><br/><br/><br/><br/><br/><br/><br/><br/><br/><br/>