calculating the fourth dimension

[alkaline]

I have a plan to calculate the properties on the world of the fourth dimension. It will go in steps:

1. Calculate 4d quantum physics
2. using 4d quantum physics, generate the 4d table of elements
3. using the 4d table of elements, generate 4d chemistry
4. calculate 4d newtonian physics
5. using 4d chemistry and physics, create 4d biology
6. using 4d biology, figure out the possible wildlife of the fourth dimension

then, you would have most of the properties of the fourth dimension. in working through these sciences, you would know how possible it was to live in the fourth dimension.

[Polyhedron Dude]

3. using the 4d table of elements, generate 4d chemistry

It's been calculated that 4-D atoms would be unstable due to an inverse cube law instead of a stable inverse square law - but there is a neat way to fix that. Suppose the electrons were not point-like, but were ring-like - this should make the atoms stable again - but there is an interesting side effect - each electron could have it's own phase - and different phases could give different chemistries. Consider 4-D hydrogen, the electron could be a simple ring, or a 5-coiled spring shape, or a 7/3 coiled spring (7 coils, with three orbits). So imagine 50 or so stable "hydrogens" instead of just one. We could call them names like 5-coiled hydrogen, or 23/5-coiled hydrogen - one of these may be a gas, another may be a light weight metal - 4-D chemistry could be a pandoras box well worth investigating. An element collector, like myself, would have a horrendous time collecting the elements - especially if there are thousands of different "coilatopes" of each one. So far all of the above is just speculation - but could give us a clue on 4-D chemistry.

Polyhedron Dude

[alkaline]

that's really fascinating. do you know where this is described - a book, or maybe a website?

So, as i understand it, the inverse square law refers to the rate of reduction of energy in a wave as it spreads out from its source in the third dimension. Thus, the inverse cube law would be the equivalent in the fourth dimension. Why does this make electrons unstable? And why would making electrons into rings make them stable?

according to string theory, isn't the shape of certain particles that of a ring? in string theory, is an electron a ring also?

i think that it's possible we could come up with several possible theories of 4d quantum mechanics and particles. We could give them names and build up whole universes out of each theory. Even if one of them turns out to be less likely, the results of it would still be fascinating. I'm willing to start developing a universe out of the theory you have described.

[Polyhedron Dude]

String theory does consider an electron as a ring, but this ring is way too small - the kind of ring I'm refering too is one big enough to ring the nucleus (like Saturn's rings does Saturn) - this would multiply a factor of d (distance) - turning the inverse cube back to inverse square. The problem with inverse cube is that it creates a field that gets stronger a lot faster as the objects get nearer - I've done a model on a computer to see how an inverse cube orbit would go - the orbit kept spiralling inwards faster and faster until it crashed into the core object. It could also spiral outwards, but the spiraling would slow down.

Polyhedron Dude

[alkaline]

It sounds like you were calculating classical orbits, like that of planets or something. I don't think electrons orbit nuclei classicly - i think they actually form a standing wave around the nucleus. We only picture them as point-orbiting because it's easier to think of them that way. So what exactly does your solution of using a ring for an electron mean? would it be a ring that encircled the entire nucleus? if so, it wouldn't have an easy time swapping back and forth to other nuclei, and it wouldn't give the properties of electricity that 3d electrons do.

In any case, it sounds like it would be harder to form a solar system in the fourth dimension because of the inverse cube law - gravity would drop off a lot faster and planets couldn't form stable orbits as easily.

[Keiji]

1. Calculate 4d quantum physics

And how do you plan on doing that?

[Polyhedron Dude]

It sounds like you were calculating classical orbits, like that of planets or something. I don't think electrons orbit nuclei classicly - i think they actually form a standing wave around the nucleus. We only picture them as point-orbiting because it's easier to think of them that way. So what exactly does your solution of using a ring for an electron mean? would it be a ring that encircled the entire nucleus? if so, it wouldn't have an easy time swapping back and forth to other nuclei, and it wouldn't give the properties of electricity that 3d electrons do.

They would be circle (or springy circle) shaped rings that go around the nucleus, they would also form a standing wave around the nucleus due to quantum effects - the ring would be the particle form of the electron, the standing wave would be the wave form - how this ring version would effect electricity - I have no idea - haven't really dug into quantum mechanics that much.

Polyhedron Dude

[alkaline]

1. Calculate 4d quantum physics

And how do you plan on doing that?

Well they have lots of complicated wave equataions for 3d quantum physics, so i would take those and generalize them to the fourth dimension. First, i have to learn how the 3d equations work, though...

EDIT by Irockyou: It was iNVERTED that said that, not bobxp... how come no one noticed before now?

EDIT by moonlord: bobxp, iNVERTED and now Rob are different names for the same user. He changed it a few times. For the sake of the "vintage" feeling, kep it like it was at the time :p

[alkaline]

They would be circle (or springy circle) shaped rings that go around the nucleus, they would also form a standing wave around the nucleus due to quantum effects - the ring would be the particle form of the electron, the standing wave would be the wave form - how this ring version would effect electricity - I have no idea - haven't really dug into quantum mechanics that much.

so by "go around the nucleus", do you mean encircle the nucleus like a ring of saturn? Would the size of this ring be bigger than the nucleus itself? that would mean it would have a big hollow area in the middle of it, and it seems like it would have a lot more mass that way than our 3d electrons do.

[Aale de Winkel]

The reader might be aware that these stuff I studied some 20 years back, so take some concideration with the validity of these notes.

I don't see whether tetraspace concideration has any impact on Newtonian machanics, won't an object not acted upon still move in a straight tetra-line. though some interesting questions emerges, can "tetronians" (like Emily) feel 3 dimensional forces? Is perhaps "gravity" some "monadian" pulling my leg?

(in an episode of star-trek the enterprise got caught in the plane of some
flatline entities heading (if I remember correctly) onto a gravitational string, counsalor Troy lost her psychic abilities and the ship could not move up nor down)

Heading toward tetra-space special relativity perhaps the following:
with

x[sub]μ[/sub] = [ict,x[sub]k[/sub] k = 1..4]

the equation

x[sub]μ[/sub] x[sup]μ[/sup] = 0

describes the expansion over time of the light Euclidian tetra-sphere. In Riemanian tetraspace this might change into

x[sub]μ[/sub] R[sup]μ[/sup][sub]ν[/sub] x[sup]ν[/sup] = 0

where the tensor R describes the tetra-space curvature, due to the presence of tetra-masses.

Since light also moves on straight (tetra)-lines things like time dilatation
and length contraction probably also won't depend on the amount of spatial dimensions.

Calculation of particle masses etc. goes far beyond this text, and my rememberence of this kind of computation. Are there still 6 quark-families in tetraspace? Are gravitons, gluons, photons (or any other force-intermediaries) mass-less(?). (tetra-space High Energy Physics).

How does one describe our tri-forces in tetra-space, I gather that tri-gravitons only move in tri-space. In contrast to tetra-gravitons which move in all tetra-directions. Probably a tri-graviton impact is describable by something like:

[sup]3[/sup]F: x[sub]l[/sub](t=0) [ict,x[sub]k[/sub] k = 1..4; x[sub]4[/sub] == 0]

When Emily is caught up in this she would probably find herself with dx[sub]4[/sub] == 0 just like the enterprise was stuck in dx[sub]3[/sub] == 0 for a while. (x[sub]l[/sub](t=0) is the tetra-position of the forces origin, pe the position of the star excerting tri-gravity upon its environment)

Note that this notation is preliminairy some [sup]3[/sup]F's might be oriented differently in tetra-space and thus having combined impact upon some intersection (quite interesting to investigate, though I doubt I will be able to in the near future)

[alkaline]

well, by newtonian physics i meant all physics that wasn't the "incredibly small" or the "incredibly fast/large", like quantum mechanics or relativity. So, all newtonian equations that are dimension-dependent would change in the fourth dimension. Examples are gravity and weight, sound & light equations, etc. I'm sure "tetronians" would feel, otherwise they wouldn't have information about their environment and they wouldn't be able to survive.

I'm not familiar with the equations of relativity so i can't comment on them. i'm pretty sure time dilation and length contraction are dimension independent.

As far as our current knowledge of physics goes, these quark-family particles are the "axioms" of matter - but we know it's possible that they could be compositional also. If we were to create a fourth dimension, we could just assert the existence of these same particles as axiomatic and work our way up from there. We would assume they had the same properties as they do in the third dimension.

i'm also unfamiliar with graviton equations so i can't comment on those either.

[Aale de Winkel]

Of course tetronians can feel, but other then when they share the same x[sub]4[/sub] with some tri-force, they would feel the effect of that tri-force

It is just when I view some paper sheet, I might feel some puny 3d gravity from it, but only when I stick my finger through some whole in the paper I experience the 2d forces which holds the paper sheet together.

[alkaline]

ahh, you're asking about gravity interaction between dimensions. I'm not sure if it's possible to use any existing physics to figure out exactly how two complete "dimensional universes" would interact.

[Polyhedron Dude]

so by "go around the nucleus", do you mean encircle the nucleus like a ring of saturn? Would the size of this ring be bigger than the nucleus itself? that would mean it would have a big hollow area in the middle of it, and it seems like it would have a lot more mass that way than our 3d electrons do.

yes - it would be a saturn like ring - but it's thickness would be small

[alkaline]

Does the inverse square law affect the standing waves of electrons in realmspace? if not, then point electrons in tetraspace would be stable because they would also be in standing waves, unaffected by the unstable inverse cube law. Another thing to think about is that if the inverse cube law does affect the standing waves of electrons in tetraspace, electrons operate in quantum levels, so they wouldn't have small deviations in their orbit to send them spiralling off into oblivion or the opposite direction (into the nucleus).