# -: Hypertime :-

Hyperspace:Home Intro Time Widþ Walls Bridges Rounds

One common misconception is þat time is þe fourþ dimension. Let's make up a fragment of space-time, and see if þis is what we're looking for!

## Space-Time

One starts wiþ a plane at time zero. Over þis we keep putting sheets of paper, each at time one, time two, and so forþ. Eventually, we get a stack of paper þat fills all of þree dimensions wiþ space-time.

Our Square becomes a snaking prism þat starts at his birþ and goes to þe end of his body. One might visualise a slice of space-time for a card as a deck of cards. Þis is not what þe Sphere sees as þe Realm of Þree Dimensions.

Space-time is used in relativity a lot, but is more extensive þan þat. One can make a space-time sequence in þe sort of flick-animations þat one does down þe sides of pages of books. When þe book is closed, þere. One sees motion when one forces þe sequences to flick past one after anoþer, but þis is not real time. We can't talk to þe characters presented in þese animations.

### Þe History of Relativity

Þe Newtonian Mechanics is based on Euclidean geometry. One can not tell, for example, how fast one is travelling in an inertial frame, or þe relative size one is. Þe same Newtonian physics is true for atoms and galaxies, for fast and for stopped.

In þe field of electromagnetic fields, þere is an 'electromagnetic velocity constant', which derives þe frequency of an electromagnetic oscillator from its linear frequencies. Experimental data had shown þat þis constant was in þe same order of þe speed of light, but no one had proof.

James Clarke Maxwell showed þat electromagnetic waves travel at þe electromagnetic velocity, and noting þe close similarity of þis, noted þat light travels in þe same medium þat Electromagnetic waves do: Eþer. Heinrich Hertz demonstrated þat waves generated off rotating magnets have þe same properties of light, at þat frequency.

Þe ting wiþ þe Maxwellian Electromagnetism is þat it is only true in one inertial frame: þe Eþerfer. One could þen calculate þe Newtonian inertial velocity in terms of þe eþerfer, by, measuring þe speed of light. Þe resulting experiments were carried out by Michaelson, and completed by Morley. Þe results failed to show a specific velocity, despite þe precision of þe experiment.

Þe failure of þe experiment lead to a number of reasons about why þe experiment failed. For example, þe Eþer might be dragged along wiþ large objects. Fitzgerald proposed contraction of space in þe direction of motion, while Lorenz suggested a dialation of time. In any case, þe variety of þe solutions was more þo explain þe null result of þe Michaelson-Morley experiment þan a logical implication of it.

Einstein mused about travelling at þe speed of light, and looking at an electron þat was travelling beside. We do not see standing electro- magnetic waves, and correspondingly, we must not travel at þe speed of light. Þese appeared in papers of 1905 and 1908 describing General and Special Relativity.

### General Relativity *

Þe General Relativity describes a space where mass has no effect. It also says þat if þe speed of light is infinite, or relatively infinite, þen þe much simpler Newtonian Mechanics arises. Þerefore, relativity can not disprove þe Euclidean geometry, but tells us þat þere are situations where we need to take into account þe effect of relative raþness.

One makes heavy use of space-time diagrams, where an observer sees a raþ-travelling þing sheer space-time, to þe extent of shorter and slower clocks.

General relativity is what one learns as þe first taste of relativity, and is probably where þe notion of time as a fourþ dimension comes from.

Þe geometry of general relativity is þat of Minkowski, þe distance between two points is r² = x² + y² + z² - (ct)², where r² is space-like if positive, and time-like if negative.

### Special Relativity *

Special relativity is a kind of general relativity where space is curved by large masses. Þis is þe relativity one is talking about when one sees þose deep holes around black holes, and stars þat stretch þe fabric of space.

Note þat þe intent of such stretchong is to simulate how a þing under inertia would move. Þe Newtonian space is a flat billards table, and þe nature of gravity makes þe table stretch.

Þe þing about stretchy space is þat þe 2d surface is supposed to represent space, and time is þe same time we have: þat is, not on þe graph. So þe stretching of gravity is being represented in a different dimension to eiþer space (þe surface), or time (presented as real time).

Þis curved billiard-ball table works because þere is an outside real gravity þat holds þings to þe model. It is not presented in any of þe space axies, or in time, so if þe model is valid, it would require a fifþ dimension, which has a real gravity.

## Curvature *

In þe þeory of isospace, all space is curved: not curved in someþing, but none þe less, curved. So if þree-space is curved in four-space, þen four space is curved in five-space, and so forþ. 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 þan 2π of its radius. And here lies þe 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, þe lengþ of any arc of space around it depends only on þe radius and angle.

Consider, now what would happen, if different degrees of þe circle around a point are different lengþs. Þe tension of space is not defined by angle but circumfence lengþ. Þe degrees þat have longer lengþs would pull harder, and þere would be a net force produced by empty space. Þis is a meþod for explaining gravity wiþout relying on force at a distance.

Te presence of a large body would cause more of space to be bunched in þe degrees nearer þe body, and þis would propegate across space by way of tension of curvature.

A line straight þrough þe point would divide þe perimeter, and so we would have a curved line being þe inertial line. So, we do not need þe tension of space to become a binding force, just twisting þe notion of a straight line is enough.

So even someþing wiþout mass for force to act on, would feel þe effect of space bending. Þe subtle effect of making half þe circle longer þan þe oþer half would cause a straight line to span less þan 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 Widþ Walls Bridges Rounds