science based - Multidimensional Time-Lines - Worldbuilding Stack Exchange
3 The Theory of Multidimensional Reality | Chapter 3. The Theory . information, transmitted from another time-space relationship, into our space and time. Three Totally Mind-bending Implications of a Multidimensional Universe . To the 3+1 dimensions of space-time, add 5th-dimensional .. consummating that marriage at 9 is made unequivocally clear in Muslim 'holy' texts. relationships of distance and time. 2. The expansion of Space does not stop at the boundary of galaxies, but incrementally within the atom itself.
And one could imagine a theory in which all threads are followed—and the universe in effect has many histories. And to understand this, we have to do something a bit similar to what Einstein did in formulating Special Relativity: Needless to say, any realistic observer has to exist within our universe. So if the universe is a network, the observer must be just some part of that network. Now think about all those little network updatings that are happening. If you trace this all the way through —as I did in my book, A New Kind of Science —you realize that the only thing observers can ever actually observe in the history of the universe is the causal network of what event causes what other event.
3 Mindbending Implications of Our Multidimensional Universe
Causal invariance is an interesting property, with analogs in a variety of computational and mathematical systems—for example in the fact that transformations in algebra can be applied in any order and still give the same final result. Here, as I figured out in the mids, something exciting happens: In other words, even though at the lowest level space and time are completely different kinds of things, on a larger scale they get mixed together in exactly the way prescribed by Special Relativity.
But because of causal invariance, the overall behavior associated with these different detailed sequences is the same—so that the system follows the principles of Special Relativity. At the beginning it might have looked hopeless: But it works out. Here the news is very good too: The whole story is somewhat complicated. First, we have to think about how a network actually represents space. Now remember, the network is just a collection of nodes and connections. Just start from a node, then look at all nodes that are up to r connections away.
If the network behaves like flat d-dimensional space, then the number of nodes will always be close to rd. One has to look at shortest paths—or geodesics—in the network. One has to see how to do everything not just in space, but in networks evolving in time. And one has to understand how the large-scale limits of networks work.
But the good news is that an incredible range of systems, even with extremely simple rules, work a bit like the digits of piand generate what seems for all practical purposes random. I think this is pretty exciting.Spacetime Explained in Hindi - SpaceTime क्या है ?
Which means that these simple networks reproduce the features of gravity that we know in current physics. There are all sorts of technical things to say, not suitable for this general blog.
Quite a few of them I already said long ago in A New Kind of Science —and particularly the notes at the back.
A few things are perhaps worth mentioning here. All these things have to emerge. When it comes to deriving the Einstein Equations, one creates Ricci tensors by looking at geodesics in the network, and looking at the growth rates of balls that start from each point on the geodesic. The Einstein Equations one gets are the vacuum Einstein Equations. One puts remarkably little in, yet one gets out that remarkable beacon of 20th-century physics: Particles, Quantum Mechanics, Etc.
Another very important part is quantum mechanics. But then their behavior must follow the rules we know from quantum mechanics—or more particularly, quantum field theory.
A key feature of quantum mechanics is that it can be formulated in terms of multiple paths of behavior, each associated with a certain quantum amplitude. But what about in a network? Because everything is just defined by connections. And the tantalizing thing is that there are indications that exactly such threads can be generated by particle-like structures propagating in the network. How might we set about finding such a model that actually reproduces our exact universe?
The traditional instinct would be to start from existing physics, and try to reverse engineer rules that could reproduce it. But is that the only way? What about just starting to enumerate possible rules, and seeing if any of them turn out to be our universe? Before studying the computational universe of simple programs I would have assumed that this would be crazy: So what happens if one actually starts doing such a search?
They just freeze after a few steps, so time effectively stops. Or they have far too simple a structure for space. Or they effectively have an infinite number of dimensions.
Telling if they actually are our universe is a difficult matter. There are plenty of encouraging features, though. For example, these universes can start from effectively infinite numbers of dimensions, then gradually settle to a finite number of dimensions—potentially removing the need for explicit inflation in the early universe. In the end, though, one needs to reproduce not just the rule, but also the initial condition for the universe.
But once one has that, one will in principle know the exact evolution of the universe. So does that mean one would immediately be able to figure out everything about the universe?
Of course this would be an exciting day for science. But it would raise plenty of other questions. And why should our particular universe have a rule that shows up early enough in our list of all possible universes that we could actually find it just by enumeration?
Where are we at with all this right now? And though it was described in simple language rather than physics-speak, I managed to cover the highlights of it in Chapter 9 of the book—giving some of the technical details in the notes at the back. But after the book was finished inI started working on the problem of physics again.
I found it a bit amusing to say I had a computer in my basement that was searching for the fundamental theory of physics. But that really was what it was doing: I was pretty organized in what I did, getting intuition from simplified cases, then systematically going through more realistic cases.
There were lots of technical issues. Like being able to visualize large evolving sequences of graphs. I accumulated the equivalent of thousands of pages of results, and was gradually beginning to get an understanding of the basic science of what systems based on networks can do.
For many years I had been interested in the problem of computational knowledge, and in building an engine that could comprehensively embody it. And as a result of my work on A New Kind of Science, I became convinced that this might be actually be possible—and that this might be the right decade to do it.
By it was clear that it was indeed possible, and so I decided to devote myself to actually doing it. The result was Wolfram Alpha. And once Wolfram Alpha was launched it became clear that even more could be done—and I have spent what I think has probably been my most productive decade ever building a huge tower of ideas and technology, which has now made possible the Wolfram Language and much more.
And when I now look at my filesystem, I see a large number of notebooks about physics, all nicely laid out with the things I figured out—and all left abandoned and untouched since the beginning of Should I get back to the physics project? I definitely want to. Though there are also other things I want to do.
The two lines of longitude, meet the equator at a right angle, 90 degrees. The two lines of longitude also meet each other at the north pole, at a right angle, or 90 degrees.
Thus one has a triangle with three right angles. The angles of this triangle add up to two hundred and seventy degrees. This is greater than the hundred and eighty degrees, for a triangle on a flat surface. If one drew a triangle on a saddle shaped surface, one would find that the angles added up to less than a hundred and eighty degrees. The surface of the Earth, is what is called a two dimensional space.
That is, you can move on the surface of the Earth, in two directions at right angles to each other: But of course, there is a third direction at right angles to these two, and that is up or down. That is to say, the surface of the Earth exists in three-dimensional space. The three dimensional space is flat. That is to say, it obeys Euclidean geometry. The angles of a triangle, add up to a hundred and eighty degrees. However, one could imagine a race of two dimensional creatures, who could move about on the surface of the Earth, but who couldn't experience the third direction, of up or down.
They wouldn't know about the flat three-dimensional space, in which the surface of the Earth lives. For them, space would be curved, and geometry would be non-Euclidean.
It would be very difficult to design a living being that could exist in only two dimensions. Food that the creature couldn't digest would have to be spat out the same way it came in. If there were a passage right the way through, like we have, the poor animal would fall apart. So three dimensions, seems to be the minimum for life.
But just as one can think of two dimensional beings living on the surface of the Earth, so one could imagine that the three dimensional space in which we live, was the surface of a sphere, in another dimension that we don't see.
If the sphere were very large, space would be nearly flat, and Euclidean geometry would be a very good approximation over small distances. But we would notice that Euclidean geometry broke down, over large distances. As an illustration of this, imagine a team of painters, adding paint to the surface of a large ball.
As the thickness of the paint layer increased, the surface area would go up. If the ball were in a flat three-dimensional space, one could go on adding paint indefinitely, and the ball would get bigger and bigger.
However, if the three-dimensional space, were really the surface of a sphere in another dimension, its volume would be large but finite.
As one added more layers of paint, the ball would eventually fill half the space. After that, the painters would find that they were trapped in a region of ever decreasing size, and almost the whole of space, was occupied by the ball, and its layers of paint.
So they would know that they were living in a curved space, and not a flat one. This example shows that one can not deduce the geometry of the world from first principles, as the ancient Greeks thought. Instead, one has to measure the space we live in, and find out its geometry by experiment. However, although a way to describe curved spaces, was developed by the German, George Friedrich Riemann, init remained just a piece of mathematics for sixty years.
It could describe curved spaces that existed in the abstract, but there seemed no reason why the physical space we lived in, should be curved.
This came only inwhen Einstein put forward the General Theory of Relativity. General Relativity was a major intellectual revolution that has transformed the way we think about the universe. It is a theory not only of curved space, but of curved or warped time as well.
Einstein had realized inthat space and time, are intimately connected with each other. One can describe the location of an event by four numbers. Three numbers describe the position of the event.
They could be miles north and east of Oxford circus, and height above sea level. On a larger scale, they could be galactic latitude and longitude, and distance from the center of the galaxy. The fourth number, is the time of the event. Thus one can think of space and time together, as a four-dimensional entity, called space-time.
Each point of space-time is labeled by four numbers, that specify its position in space, and in time. Combining space and time into space-time in this way would be rather trivial, if one could disentangle them in a unique way.
- Multiple time dimensions
That is to say, if there was a unique way of defining the time and position of each event. However, in a remarkable paper written inwhen he was a clerk in the Swiss patent office, Einstein showed that the time and position at which one thought an event occurred, depended on how one was moving.
This meant that time and space, were inextricably bound up with each other. The times that different observers would assign to events would agree if the observers were not moving relative to each other. But they would disagree more, the faster their relative speed.
So one can ask, how fast does one need to go, in order that the time for one observer, should go backwards relative to the time of another observer.
The answer is given in the following Limerick. There was a young lady of Wight, Who traveled much faster than light, She departed one day, In a relative way, And arrived on the previous night. So all we need for time travel, is a space ship that will go faster than light. Unfortunately, in the same paper, Einstein showed that the rocket power needed to accelerate a space ship, got greater and greater, the nearer it got to the speed of light.
So it would take an infinite amount of power, to accelerate past the speed of light. Einstein's paper of seemed to rule out time travel into the past. It also indicated that space travel to other stars, was going to be a very slow and tedious business. If one couldn't go faster than light, the round trip to the nearest star, would take at least eight years, and to the center of the galaxy, at least eighty thousand years. If the space ship went very near the speed of light, it might seem to the people on board, that the trip to the galactic center had taken only a few years.
But that wouldn't be much consolation, if everyone you had known was dead and forgotten thousands of years ago, when you got back. That wouldn't be much good for space Westerns. So writers of science fiction, had to look for ways to get round this difficulty. In his paper, Einstein showed that the effects of gravity could be described, by supposing that space-time was warped or distorted, by the matter and energy in it.
We can actually observe this warping of space-time, produced by the mass of the Sun, in the slight bending of light or radio waves, passing close to the Sun. This causes the apparent position of the star or radio source, to shift slightly, when the Sun is between the Earth and the source. The shift is very small, about a thousandth of a degree, equivalent to a movement of an inch, at a distance of a mile.
Nevertheless, it can be measured with great accuracy, and it agrees with the predictions of General Relativity. We have experimental evidence, that space and time are warped. The amount of warping in our neighbourhood, is very small, because all the gravitational fields in the solar system, are weak.
However, we know that very strong fields can occur, for example in the Big Bang, or in black holes. So, can space and time be warped enough, to meet the demands from science fiction, for things like hyper space drives, wormholes, or time travel. At first sight, all these seem possible. For example, inKurt Goedel found a solution of the field equations of General Relativity, which represents a universe in which all the matter was rotating.
In this universe, it would be possible to go off in a space ship, and come back before you set out. Goedel was at the Institute of Advanced Study, in Princeton, where Einstein also spent his last years. He was more famous for proving you couldn't prove everything that is true, even in such an apparently simple subject as arithmetic. But what he proved about General Relativity allowing time travel really upset Einstein, who had thought it wouldn't be possible.
We now know that Goedel's solution couldn't represent the universe in which we live, because it was not expanding. It also had a fairly large value for a quantity called the cosmological constant, which is generally believed to be zero. However, other apparently more reasonable solutions that allow time travel, have since been found. A particularly interesting one contains two cosmic strings, moving past each other at a speed very near to, but slightly less than, the speed of light.
Cosmic strings are a remarkable idea of theoretical physics, which science fiction writers don't really seem to have caught on to. As their name suggests, they are like string, in that they have length, but a tiny cross section.
Space and Time Warps - Stephen Hawking
Actually, they are more like rubber bands, because they are under enormous tension, something like a hundred billion billion billion tons. A cosmic string attached to the Sun would accelerate it naught to sixty, in a thirtieth of a second. Cosmic strings may sound far-fetched, and pure science fiction, but there are good scientific reasons to believed they could have formed in the very early universe, shortly after the Big Bang.
Because they are under such great tension, one might have expected them to accelerate to almost the speed of light.
What Is Spacetime, Really?
What both the Goedel universe, and the fast moving cosmic string space-time have in common, is that they start out so distorted and curved, that travel into the past, was always possible.
God might have created such a warped universe, but we have no reason to think that He did. All the evidence is, that the universe started out in the Big Bang, without the kind of warping needed, to allow travel into the past.
Since we can't change the way the universe began, the question of whether time travel is possible, is one of whether we can subsequently make space-time so warped, that one can go back to the past. I think this is an important subject for research, but one has to be careful not to be labeled a crank.
If one made a research grant application to work on time travel, it would be dismissed immediately. No government agency could afford to be seen to be spending public money, on anything as way out as time travel. Instead, one has to use technical terms, like closed time like curves, which are code for time travel. Although this lecture is partly about time travel, I felt I had to give it the scientifically more respectable title, Space and Time warps.
Yet, it is a very serious question. Since General Relativity can permit time travel, does it allow it in our universe? And if not, why not. Closely related to time travel, is the ability to travel rapidly from one position in space, to another. As I said earlier, Einstein showed that it would take an infinite amount of rocket power, to accelerate a space ship to beyond the speed of light. So the only way to get from one side of the galaxy to the other, in a reasonable time, would seem to be if we could warp space-time so much, that we created a little tube or wormhole.
This could connect the two sides of the galaxy, and act as a short cut, to get from one to the other and back while your friends were still alive. Such wormholes have been seriously suggested, as being within the capabilities of a future civilization.
But if you can travel from one side of the galaxy, to the other, in a week or two, you could go back through another wormhole, and arrive back before you set out.
You could even manage to travel back in time with a single wormhole, if its two ends were moving relative to each other. One can show that to create a wormhole, one needs to warp space-time in the opposite way, to that in which normal matter warps it. Ordinary matter curves space-time back on itself, like the surface of the Earth.