Posted by P on September 06, 2001 at 17:35:20:
In Reply to: link? posted by Primer Gray on September 06, 2001 at 16:05:36:
: : 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, itīs 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.