Would having a fourth spatial dimension preclude life?

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Postby Plat » Tue Nov 08, 2005 10:26 pm

I know this is a silly question but could a 4D universe be so different that, it has properties that we is beyond our imagination?, why do people assume that a 4D universe will just be our universe but with an extra spatial dimension, might there be different laws of physics in a 4D universe?
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Postby wendy » Wed Nov 09, 2005 6:49 am

It is best to assume life exists in four and higher dimensions, because this happens to be true.

From this, instead of denying that life can exist, we probe to find out what sort of conditions are needed to make this happen.

One notes that stable circular orbits exist in all dimensions, but stable elliptical orbits exist only in three dimensions. In four and higher dimensions, one has things not reckoned with in three dimensions: fibulation.

I am not exatly sure as what effect, if any, fibulation might have on four dimensions, but it is quite possible for a system of charges to accumulate on a single circle or torus around the globe, and that the effect of this globe makes for the stability of orbits. It could be that the size of the slant coupled with the size of the fields from the sun, makes for a stable condition in a finite range around the sun, rather like an acreation-disk.

Atoms are indeed stable in four dimensions, because the electrons do not orbit the nucleus, the orbitals are solutions to standing waves in the vacinity of the nucleus. Electrons and protons are hardly kith and kin to planets and suns.

For the most part, one gets a pretty stable physics by setting G to be 1e-9 in the fps units, such that Gc = 1. This pretty much works in all dimensions, for recollection.

Atoms &c are decided by the quantisation granulation: i can hardly see any real reason to go past the linear granulation that we see in our world: that is, atoms of roughly 1e-9 ft, and 273.16E24 protons to the pound.

The laws of physics is borne on the laws of geometry &c, and there are indeed a good deal of differences. But these differences mean for example, that vortices happen in some different way, and that there is possible for different kinds of fibulation-vortices (which swirl around a point), which we do not have in 3d.

If one follows the night sky in four dimensions, to watch the stars rise and set, one gets away from the notion that there is an equator and poles, but that there is a different kind of heaven. Yes, there are indeed seasons. One has season-zones like we have time-zones.

Having in one hands on three-dimensional paper is like trying to solve the problems of three-dimensional geometry by using Euclid's 2d stuff. It looses its way rather than you be supprised!

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Postby Batman3 » Wed Nov 09, 2005 7:24 pm

In 3d you can work out the periodic table by the sequence of orbitals:1s(2)2s(2)2p(6)3s(2)3p(6)4s(2)3d(10)4p(6)5s(2)4d(10)5p(6)6s(2)4f(14)5d(10)... etc.
This formula gives the 3d periodic table. I understand how(that) the s2 and p6 orbitals can be united into sp(8 orbitals but I don't understand the thinking about the 4d(10) orbitals.

In 4d It is the same but instead of the numbers in parenthesis going up by 4 (2..6..10..14..), they go up by 6 (2..8..14..20..). Thus 4d s(2) is still s(2) but p( 6) becomes p(8 and p(10) becomes p(14) and d(10) becomes d(14) and f(14) becomes f(20). NOTE don't let the 14 in both cases confuse you it is coincidence.

The s and p orbitals combine simply into sp(10) orbitals agreeing nicely a 4 3d 120-degree orbitals (5 4d (?)-degree orbitals). I don't understand how 14 electrons of 4d(14) could fit themselves into the 4d space around the nucleus any more than how 10 electrons can in 3d. In both the rare-earth elements are a mystery.
Since there are 5 sp orbitals, fitting nicely into 4d space it is a pretty safe bet that the first 3 rows of the per. table are ok. The difference from 3d is that in 4d, there are 3 types of Carbon and similarly 3 types of Silicon. Between them is an entirely symmetrical type with 5 half-filled obitals. On either side are types which link up with 4 other atoms(greater or lessly electronegative). Perhaps we need new names for Carbon and Silicon. The rest of the elements can keep their names but they behave differently than in 3d.
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Postby Batman3 » Wed Nov 09, 2005 7:29 pm

Wendy, could you describe fibulation vortices and different vortices?
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Postby PWrong » Thu Nov 10, 2005 11:24 am

It is best to assume life exists in four and higher dimensions, because this happens to be true.

Really? How did you find that out? Can they talk?

One notes that stable circular orbits exist in all dimensions, but stable elliptical orbits exist only in three dimensions. In four and higher dimensions, one has things not reckoned with in three dimensions: fibulation.

According to Google, fibulation is spelt "fibrillation", and it's a medical term. Usually, when an object is almost in orbit, it will spiral in and out again. Sometimes when it comes out it never comes back, sometimes it keeps oscillating, tracing out a flowery pattern.

Atoms are indeed stable in four dimensions, because the electrons do not orbit the nucleus, the orbitals are solutions to standing waves in the vacinity of the nucleus. Electrons and protons are hardly kith and kin to planets and suns.


That doesn't mean the inverse square law doesn't pose a problem. In the Schrodinger's equation thread, I've mentioned that energy isn't quantised in 4D hydrogen. The reason is that the potential energy is k/x^2 instead of k/x.

In 3D, an electron is distributed by a Legendre function. This only converges if the energy is a multiple of 1/n^2, where n is an integer.
But in 4D, the distribution is a Bessel function, which always converges.
This means that you don't get separated orbitals. The more energy an electron has, the further out it will (probably) be.

The good news is that angular momentum is still quantised. We have 3 angular quantum numbers. I've yet to work out what conditions they have yet.

In 3d you can work out the periodic table by the sequence of orbitals:1s(2)2s(2)2p(6)3s(2)3p(6)4s(2)3d(10)4p(6)5s(2)4d(10)5p(6)6s(2)4f(14)5d(10)... etc.


This is spectroscopic notation. It was developed before the Schrodinger equation was solved, so I don't know why they still use it. I still don't understand it, even though it's in my exam next week. :oops:

In 3D, you have 3 quantum numbers: n, l, m<sub>l</sub>.
Each of these has to be an integer. Also, we have the conditions 0<= l <n, and -l <= m<sub>l</sub> <= l. There's actually a 4th, m<sub>s</sub>, that can have two values, -1/2 and 1/2, so you get twice as many possible states. Spectroscopic notation derives from these four numbers. The "s,p,d,f" relates to the l number. s=1, p=2, d=3, f=4. The number outside the brackets is n, and the number in the brackets is the number of electrons with this particular state. You never know what the m<sub>l</sub> value is, but there are only 2l+1 possible values, so once they get filled up, you go to another value of l, or a higher orbital.
So 2p(3) means n=2, l=2, and 3 of the 6 possible states are filled up.

Anyway, in 4D, there's no n, but we do have l, p and m. Instead of orbitals, there are "hyperspherical harmonics", the 4D analog of spherical harmonics. Mathworld has pictures of the spherical harmonics for different values of l and m.
http://mathworld.wolfram.com/SphericalHarmonic.html

The laws of physics is borne on the laws of geometry &c, and there are indeed a good deal of differences. But these differences mean for example, that vortices happen in some different way, and that there is possible for different kinds of fibulation-vortices (which swirl around a point), which we do not have in 3d.

I don't know what you mean, or how you could know this, but it might be interesting to look at some simple vector fields in 4D. That could give us some guidelines for developing 4D magnetism.
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Postby thigle » Thu Nov 10, 2005 9:22 pm

pw: yes, they can talk. :wink: you haven't found yet but you're more than 4d, at least that aspect of you that you now just conceive of as 'life'. but that's just a name, or concept for you. you judge truth parameter of being according to models derived from what you physically see. but you don't seem to realize that the outer light of nature is balanced by inner light of your own nature (which you meet nightly in dreams - as the inner glow of your mind). but then, i assume that you assume that consciousness arises from matter. :roll: :?:
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Postby wendy » Fri Nov 11, 2005 7:39 am

in three dimensions, a vortex, or eddy, is formed when the current goes in a small circle. One could imagine that this small circle is like a ball, and there is a N and S pole. When, for example, you see the water down the drain, it swirls as it goes down the hole.

in three dimensions, it is not possible to give every point on the surface a motion, like a wind-speed, whithout having no calm spots. This is the hairy ball issue. Even the poles do not have a rotation.

In three-dimensional vortices, one can have a swirling around the equator driving a motion from pole through the centre to a pole. This is the curl function. This existance is very important in eddy currents, and also magnetic histeriosous.

in four dimensions, one can have a continious rotation of the whole surface around the centre: specifically every point follows a circular orbit in the 2d hedrix that passes through the centre. The traces of these rotations is hopf fibulation.

one interesting effect of hopf fubulation is that it behaves as a transform of points into 3d into circles in 4d. It's such a thing that one can use it to project 3d points onto 4d. Jonathan Bower's swirl-prisms are examples of the regular polytopes so treated.

Of course, in 4d water, one could have a continious swirl of water around something like a particle, which is a different kind of vortex to what we see in 3d.

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Postby thigle » Fri Nov 11, 2005 3:37 pm

what is the hairy ball issue ? toroidal surface revolving around its hole has no calm spots, but prolly i miss something ?

it's funny (or intentional) how many versions of f...ation is used in this thread: fibration, fibulation, fubulation(prolly a typo), and even fibrillation. i always thought it comes from "fibre". so fibration for me. also, <google hopf fibration> gives far more geometry.math.physics related results than any other. whatever it's proper name, it's meaning is globally relevant, and thanx to wendy now clearer. the circular orbits in the 2d hedrix passing through the centre are the 2 of 5 circles on torus that cannot be continually transformed between them, specifically the skew circles, not 2 geodesics, nor the general circle.

in 3d, a vortex-flow for particular points gets faster as it approaches closer to the centre axis, through the circle's centre, orthogonal to it's plane. so the peripheric currents are slower. is there any similarity in 4d dynamics ? how/when does acceleration/slowing happen ?
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Postby wendy » Sat Nov 12, 2005 6:34 am

a torus is hardly a sphere (ball). in practice, you are more likely to have planets congeal as a sphere than as a torus.

of fibration, it's something i don't spell well. i derived it from watching the sky rotate in four dimensions, and understood the methord before i learnt the name. ok. i even mapped out the phase space for it...

of four dimensions, i have not done any dynamic calculations, only follow the streamlines. more i can not do.
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