Hyperspace:Home Intro Time Width Walls Bridges Rounds
One common misconception is that time is the fourth dimension. Let's make up a fragment of space-time, and see if this is what we're looking for!
One starts with a plane at time zero. Over this we keep putting sheets of paper, each at time one, time two, and so forth. Eventually, we get a stack of paper that fills all of three dimensions with space-time.
Our Square becomes a snaking prism that starts at his birth and goes to the end of his body. One might visualise a slice of space-time for a card as a deck of cards. This is not what the Sphere sees as the Realm of Three Dimensions.
Space-time is used in relativity a lot, but is more extensive than that. One can make a space-time sequence in the sort of flick-animations that one does down the sides of pages of books. When the book is closed, there. One sees motion when one forces the sequences to flick past one after another, but this is not real time. We can't talk to the characters presented in these animations.
The Newtonian Mechanics is based on Euclidean geometry. One can not tell, for example, how fast one is travelling in an inertial frame, or the relative size one is. The same Newtonian physics is true for atoms and galaxies, for fast and for stopped.
In the field of electromagnetic fields, there is an 'electromagnetic velocity constant', which derives the frequency of an electromagnetic oscillator from its linear frequencies. Experimental data had shown that this constant was in the same order of the speed of light, but no one had proof.
James Clarke Maxwell showed that electromagnetic waves travel at the electromagnetic velocity, and noting the close similarity of this, noted that light travels in the same medium that Electromagnetic waves do: Ether. Heinrich Hertz demonstrated that waves generated off rotating magnets have the same properties of light, at that frequency.
The ting with the Maxwellian Electromagnetism is that it is only true in one inertial frame: the Etherfer. One could then calculate the Newtonian inertial velocity in terms of the etherfer, by, measuring the speed of light. The resulting experiments were carried out by Michaelson, and completed by Morley. The results failed to show a specific velocity, despite the precision of the experiment.
The failure of the experiment lead to a number of reasons about why the experiment failed. For example, the Ether might be dragged along with large objects. Fitzgerald proposed contraction of space in the direction of motion, while Lorenz suggested a dialation of time. In any case, the variety of the solutions was more tho explain the null result of the Michaelson-Morley experiment than a logical implication of it.
Einstein mused about travelling at the speed of light, and looking at an electron that was travelling beside. We do not see standing electro- magnetic waves, and correspondingly, we must not travel at the speed of light. These appeared in papers of 1905 and 1908 describing General and Special Relativity.
The General Relativity describes a space where mass has no effect. It also says that if the speed of light is infinite, or relatively infinite, then the much simpler Newtonian Mechanics arises. Therefore, relativity can not disprove the Euclidean geometry, but tells us that there are situations where we need to take into account the effect of relative rathness.
One makes heavy use of space-time diagrams, where an observer sees a rath-travelling thing sheer space-time, to the extent of shorter and slower clocks.
General relativity is what one learns as the first taste of relativity, and is probably where the notion of time as a fourth dimension comes from.
The geometry of general relativity is that of Minkowski, the distance
between two points is
Special relativity is a kind of general relativity where space is curved by large masses. This is the relativity one is talking about when one sees those deep holes around black holes, and stars that stretch the fabric of space.
Note that the intent of such stretchong is to simulate how a thing under inertia would move. The Newtonian space is a flat billards table, and the nature of gravity makes the table stretch.
The thing about stretchy space is that the 2d surface is supposed to represent space, and time is the same time we have: that is, not on the graph. So the stretching of gravity is being represented in a different dimension to either space (the surface), or time (presented as real time).
This curved billiard-ball table works because there is an outside real gravity that holds things to the model. It is not presented in any of the space axies, or in time, so if the model is valid, it would require a fifth dimension, which has a real gravity.
In the theory of isospace, all space is curved: not curved in something, but none the less, curved. So if three-space is curved in four-space, then four space is curved in five-space, and so forth. Any practical model of curvature not involving being bent in space must also equate to being bent in space, if room exists.
A model of curvature would be to add or subtract circumference to a circle. A circle drawn on a sphere has a smaller circumference than 2π of its radius. And here lies the secret of curvature.
So instead of having curvature at points, we make point and direction a feature of curvature. In an isospace, at any point, the length of any arc of space around it depends only on the radius and angle.
Consider, now what would happen, if different degrees of the circle around a point are different lengths. The tension of space is not defined by angle but circumfence length. The degrees that have longer lengths would pull harder, and there would be a net force produced by empty space. This is a method for explaining gravity without relying on force at a distance.
Te presence of a large body would cause more of space to be bunched in the degrees nearer the body, and this would propegate across space by way of tension of curvature.
A line straight through the point would divide the perimeter, and so we would have a curved line being the inertial line. So, we do not need the tension of space to become a binding force, just twisting the notion of a straight line is enough.
So even something without mass for force to act on, would feel the effect of space bending. The subtle effect of making half the circle longer than the other half would cause a straight line to span less than 180 degrees, and light (which moves in a straight line), to 'bend'.
Such is observed in gravitational lensing, where a distant quasar appears above and below a galaxy.
Hyperspace:Home Intro Time Width Walls Bridges Rounds