Re: http://www.dd.chalmers.se/~f93jojo/sidan2.htm

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: : : A powerful new X-ray telescope has yielded evidence that virtually : : : clinches the case for the existence of a supermassive black hole at the : : : center of our galaxy, astronomers say. : : : Scientists generally hold that almost every galaxy revolves around a : : : black hole. Previous studies have estimated that the center of our : : : galaxy, the Milky Way, contains something very dense and massive, : : : which most scientists already believed was a black hole. : : : ****When speaking of black holes, and worm holes (not referring to Isaacs urethra!) refer to the treatise below: : : : Introduction : : : In many science fiction books and films one often find the story of people travelling backward : : : or forward in time. How many haven't seen the film "Back to the Future", where Michael J. : : : Fox travels back in time to where his mother and father where young and then his mother falls : : : in love with him instead of his father and therefore he ceases to exist. That is science fiction : : : but what is really allowed if one take into account the Law of Physics? Is it possible to travel : : : in time and is it possible to change the past and therefore also change the present? We should : : : here try to give a short description of what physicist know about time travels today. To be : : : able to talk about time travels we will first have to explain what a wormhole is. : : : Description of a wormhole : : : A wormhole is a geometry of four-dimensional spacetime (for an explanation of spacetime see : : : "spacetime" and "spacetime diagrams") in which two regions of the universe are connected by : : : a short narrow throat. A classical large scale wormhole is a solution of the Einstein's field : : : equations, which governs the curvature of spacetime. The most interesting thing with : : : wormholes is that they could provide relatively easy means of travelling to distant regions of : : : space or even of travelling backwards in time. : : : : : Figure 1. A wormhole with two mouths making a shortcut in spacetime. : : : The problem is that a macroscopic wormhole is not a static structure, it´s rather a shape that : : : expands from a singularity with zero throat radius to maximum radius and then shrinks back : : : to a singularity again. This expansion-reduction of the radius would be very quick. Even light : : : would not have a chance to pass through the wormhole before it shrinks back to zero radius : : : again. In fact any now known matter that would fall into the wormhole would pull it together : : : through gravity. If constructing a mathematical model of an open wormhole that allows : : : passage, the equations of general relativity says that matter with an enormous negative : : : pressure is needed to uphold the wormhole gravitationally. The magnitude of the tension of : : : the matter must be greater than the energy density of the matter itself. This would leave us : : : with a material that will have a negative energy density relative to a light beam travelling : : : through it. This kind of material is called exotic matter because there is no such matter now : : : known. There are some indications that exotic matter can exist. For example between two : : : metal plates there can be field fluctuations that has a negative energy density relative to the : : : field fluctuations in free vacuum. Evaporating black holes also implies that exotic matter can : : : exist. : : : Another problem with wormholes is that fields can destroy them. Fields are in some solutions : : : able to increase its strength for each passage through a wormhole. If the wormhole has a : : : focusing effect, the total field strength becomes infinite and will therefore destroy the : : : wormhole. If the hole is defocusing, it converges towards a finite value and the wormhole can : : : survive. The only matter that can make the wormhole defocusing is exotic matter. If exotic : : : matter exists and has the ability to uphold a wormhole without interacting with and harming : : : the traveller, then there is a physical possibility of a traversable wormhole and for it to even : : : work as a time machine. A wormhole can be turned into a time machine by keeping one : : : mouth of the wormhole fixed while moving the other. This can be made through gravitational : : : attraction or by charging it electrically while moving it with electric fields. Travelling from the : : : stationary mouth to the moving and back again could then send a traveller back in time. : : : How time travel is possible, "the Twin Paradox" : : : It is easy to see how one can make a time machine if one consider the "twin paradox" in : : : special relativity (for an explanation of this paradox see "Explanation of the twin paradox"). : : : Let an observer A be fixed in a frame and let B be another observer moving with (high) : : : velocity u relative to A. The clock moving with B is then going with a slower rate than a A's : : : clock because of the time dilation in special relativity. One can write an expression that relate : : : both time as: T=gamma*T' where gamma is the Lorentz factor: : : : : : : Since gamma is always > 1 B's clock is going slower than A's. To have a time machine A and : : : B must be able to hold on to one of the wormholes mouths each. A and B can then : : : communicate either through space or through the wormhole. A message sent through space : : : travels with the speed of light while a message sent through the wormhole takes a shortcut in : : : spacetime. A message sent through the wormhole will therefore arrive almost at once if the : : : wormhole is short. In figure 2 one can see a spacetime diagram of the situation. : : : : : Figure 2. Spacetime diagram of a possible time machine. : : : In the figure one can see how B's clock goes slower than A's. If A sends a message to B at t = : : : 0 through space and B replies through the wormhole the message will return to A at a time t : : : larger than zero. But because time dilation add up while B is moving relative to A there will : : : after a while be a time when the A observer receives the message at the same time he sends it. : : : This is the so called "time travel boundary". After that time closed time-like curves are formed : : : and A receives his message before he sends it. This implies that time travel is possible, but of : : : course you have to find a macroscopic, stable wormhole to be able to travel through it and : : : you must also be able to control its mouth. One sees in the spacetime diagram that it isn't : : : possible to go back to times before the time travel boundary was formed. This is a severe : : : limitation of such time travels. : : : The Principle of Self-Consistent Solutions, "the Grandparent : : : Paradox". : : : One of the problem with time travel is the so called "grandparent" paradox. Suppose you are : : : moving backwards in time and kill your grandparent before he or she has any children. Could : : : you do this and not, in doing so, eliminating your own existence? And even if you do that, : : : then no one killed your grandparent in the first place and your birth is possible again! You : : : could form a postulate that states that these events are forbidden, but that would in a sense : : : mean that you have no free will since you are not "allowed" to kill your grandparent then. The : : : essence of this problem is pinpointed in the billiard ball analogy. Suppose you have a billiard : : : table with two holes. These holes are connected by a wormhole. : : : : : Figure 3. Self-consistent and not self-consistent solutions to the billiard ball problem : : : If you shoot a billiard ball towards and into a wormhole and it is shot out of the other mouth, : : : but at an earlier time (due to hole's time travel effect) and then collides with the billiard ball : : : before it reaches the first hole, it would change its direction so much that it doesn't reach the : : : hole in the first place. Is such a solution allowed? If it is we have a real paradox. This is : : : illustrated in figure 3A. If you change the initial conditions slightly you often receive an infinite : : : number of solutions but not all of them are self-consistent. Self-consistency means that an : : : event is not allowed to change the past and that the future already has affected the past! This : : : means that we are able to neglect all the solutions when the first ball misses the hole due to : : : the collision with the second. The solutions listed below and in figure 3A-F above and they all : : : use Newtonian mechanics everywhere except in the wormhole that is linking the two mouths. : : : I will from now on call the ball that we have in our hand before we begins as the "first" ball : : : and call the time-travelled version for the "second". If the second ball hits the first ball at just : : : a slightly different angle and only giving it a glancing blow so that the first still will fall into the : : : hole, but at a different angle than it had "before", then the solution will be self-consistent : : : (figure 3 B). In the figure there are demonstrated a number of different solution classes. The : : : figure D is one of the most interesting. There the first's vector is missing the hole altogether, : : : but the second ball appears from one of the holes and collides with the first, and by doing so : : : forces the first into the hole and thereby enables it to collide with "itself". This is quite similar : : : to the fluctuations of quantum mechanics and the probability for such an event has a certain : : : value, and are therefore not necessarily forbidden. The most common solutions are the ones : : : in figure 3 E and F. : : : All these different solutions are just different approaches to the "true" grandparent paradox. : : : But this is not really a paradox, as it first seems. It seems that the past is already set, but so is : : : the future! But this limits the free will of a person, since he is not allowed to kill his : : : grandparent due to the laws of causality (for an explanation of causality see "causality"). But : : : these restrictions of free will are a common part of our daily life. Even if you want to walk on : : : the wall, gravity prevents the efforts to do so. So it is no paradox and the rules of physics are : : : preserved. This gives us reason to believe that time travel may be physically more possible : : : than we perhaps may think, although there are a lot more to learn in the subject. : : : Conclusions : : : We have seen that time travels, in the way that is given above, doesn't violate the law of : : : physics, although it seems that we cannot realise it in the nearby future. We are in fact not : : : even sure that exotic matter exists and if it exists it isn't very probable that we can collect : : : enough of it to feed a wormhole. We also have to find a macroscopic wormhole to feed with : : : this exotic matter. The problems are many and if it really is possible it will take many years : : : before we overcome them. Physicists don't agree if time travel is possible. Stephen Hawking : : : wrote in 1993: "... the best evidence we have that time travel is not possible, and will never : : : be, is that we have not been invaded by hordes of tourists from the future". Time travels : : : might be allowed theoretically but real ones are still science fiction. : : I want to see the graphs to which the article refers. Could you post a link? This is fascinating, thank you for posting. : : PS, Betty Blowtorch sounds like one hell of a live show. I wish they were coming through Dallas. My kinda band.

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