A new Particle System for 4D.

[Keiji]

I found something on the wiki about Coilatopes. So here is my idea.

Remember that this is a totally different particle system to what we know.

We can write an electron with n coils as E_n. E₁ is a simple ring. These coils would be based around two axes, with the rings of the coil a certain distance from each other in the third dimension.

I will say now that in this particle system, if a proton has a charge of 1, an electron has a charge of -c, where c is the number of coils it has. This axiom prevents having infinitely many coilatopes of the same atom, so that the system becomes much more stable.

Each electron surrounds the nucleus, rotating at the same time. Multiple electrons can surround the same nucleus if they are at a different position in the fourth dimension.

We can write an atom as x_y(e_n), where x is the number of protons, y is the number of neutrons, e is the number of coils around an electron and n is the number of those electrons in the atom. If we need multiple types of electrons in the same atom, we can have additional e_n parts, separated by commas like this:

3₄(1₁, 2₁) - Lithium with one E₁ and one E₂.

Now, when two atoms collide, the electrons of one may "interlock" with electrons of the other, bonding them. To break these bonds involves precisely reversing the process. If there are multiple bonded electrons this is very difficult because both electrons must align correctly at the same time.

So we can have very complex molecules. The simplest example is this:

1₁(1₁) <1-1> 1₁(1₁) - Two bonded hydrogen atoms

The numbers in the angle brackets indicate which electrons are bonded to which. Multiple bonds can be represented by e.g. <1-2, 2-1>.

Three hydrogens bonded is possible, but there is a very high chance that one will free itself due to the connections between the electrons. Here is the equivalent of H₃:

1₁(1₁) <1-1> 1₁(1₁) <1-1> 1₁(1₁)

However a much more common thing to find is the equivalent He₃:



Note its triangular form. Triangular molecules are very stable (and thus unreactive) ones in this particle system.

Of course we don't have to stick to simple molecules. Since the equivalent of CH₄ would not be stable at all in this particle system, here is the equivalent of CH₃:



And here's a possible reaction:
CH₃ + NH₄ -> CNH₅ + H₂

Note that NH₂ exists but the nitrogen atom there is a different coilatope to what is needed for making CNH₅. The nitrogen in NH₂ can be 7₇(3₁, 4₁), 7₇(2₁, 5₁) or 7₇(1₁, 6₁) as opposed to 7₇(1₁, 2₃).

Anyway, here's CNH_5:


I'll create a list of atoms and molecules in order and post it up later. For now, discuss

[Nick]

I don't understand what E_n is supposed to be. I understand the _n part, but what does the E mean? Is it the atomic number?

Also, the bonds in the angle brackets dont make sense. If the numbers represent the number of bonds, why are there two numbers? Are there two different connections, each one in a different 2d plane?

I'm no expert, though I'd like to be... if you could explain a bit more?

[Keiji]

I don't understand what E_n is supposed to be. I understand the _n part, but what does the E mean? Is it the atomic number?

E_n just means an electron with n coils. E means electron.

Also, the bonds in the angle brackets dont make sense. If the numbers represent the number of bonds, why are there two numbers? Are there two different connections, each one in a different 2d plane?

The bonds in the angle brackets show which electron is bonded to which. To show why this is important, have an example. Out of the six possible isomers, there are two very similar ones:
2₂(1₂) <1-1, 2-2> 2₂(1₂) [Reactivity: Medium]
2₂(1₂) <1-2, 2-1> 2₂(1₂) [Reactivity: Low]

Note that in the second isomer, the electrons are cross-bonded. So instead of o=o we have oxo (where o is a helium atom, and = and x show the bonds). Cross bonds are harder to form but once formed they are very stable. They are also only possible in the 4th dimension (to see why, try putting two short slinky springs on each of your arms, and then get someone else to try and link them together so that the links cross over. Unless you have very big slinky springs (or very small arms), you'll find it's impossible.

I'm no expert, though I'd like to be... if you could explain a bit more?

I don't really know how to explain it in general any more, but I can answer specific questions.

By the way, I have realized that making bonds would release energy due to friction, and this would also slow down the electron's rotation. Breaking bonds can happen in two ways. The easy way is to heat something up, such that the particles move faster and try to break apart. The other way is what I call "atom stealing" - some highly reactive molecule collides with a more stable molecule, and bonds with one or more of its atoms. This however makes the electron that was bonded with very unstable, so it will break the bond with the other atom it is bonded to.

There is one "golden rule" to do with reactivity, and it is this: The more coils an electron has, the less likely it is to make OR break bonds.

Oh, and here's every possible coilatope of the first 8 elements (I am using the most common isotope from 3D chemistry to represent them):

Hydrogen: 1₁ (1 coilatope)
- (1₁)
Helium: 2₂ (2 coilatopes)
- (1₂)
- (2₁)
Lithium: 3₄ (3 coilatopes)
- (1₃)
- (1₁, 2₁)
- (3₁)
Beryllium: 4₅ (5 coilatopes)
- (1₄)
- (1₂, 2₁)
- (1₁, 3₁)
- (2₂)
- (4₁)
Boron: 5₆ (7 coilatopes)
- (1₅)
- (1₃, 2₁)
- (1₂, 3₁)
- (1₁, 2₂)
- (1₁, 4₁)
- (2₁, 3₁)
- (5₁)
Carbon: 6₆ (11 coilatopes)
- (1₆)
- (1₄, 2₁)
- (1₃, 3₁)
- (1₂, 2₂)
- (1₂, 4₁)
- (1₁, 2₁, 3₁)
- (1₁, 5₁)
- (2₃)
- (2₁, 4₁)
- (3₂)
- (6₁)
Nitrogen: 7₇ (15 coilatopes)
- (1₇)
- (1₅, 2₁)
- (1₄, 3₁)
- (1₃, 2₂)
- (1₃, 4₁)
- (1₂, 2₁, 3₁)
- (1₂, 5₁)
- (1₁, 2₃)
- (1₁, 2₁, 4₁)
- (1₁, 3₂)
- (1₁, 6₁)
- (2₂, 3₁)
- (2₁, 5₁)
- (3₁, 4₁)
- (7₁)
Oxygen: 8₈ (22 coilatopes)
- (1₈)
- (1₆, 2₁)
- (1₅, 3₁)
- (1₄, 2₂)
- (1₄, 4₁)
- (1₃, 2₁, 3₁)
- (1₃, 5₁)
- (1₂, 2₃)
- (1₂, 2₁, 4₁)
- (1₂, 3₂)
- (1₂, 6₁)
- (1₁, 2₂, 3₁)
- (1₁, 2₁, 5₁)
- (1₁, 3₁, 4₁)
- (1₁, 7₁)
- (2₄)
- (2₂, 4₁)
- (2₁, 3₂)
- (2₁, 6₁)
- (3₁, 5₁)
- (4₂)
- (8₁)

One thing I would like to know is if that sequence of numbers (1,2,3,5,7,11,15,22) is actually mathematical in some way... I should continue with finding these coilatopes

[Nick]

So the "E" (which means electron) is replaced with the atomic number of the atom? Ok, that makes sense.

Here's one final question: how do you know that certain bonds between certain electrons are more or less stable?

[Keiji]

So the "E" (which means electron) is replaced with the atomic number of the atom? Ok, that makes sense.

No it isn't... E₁ means an electron with 1 coil. E₂ means an electron with 2 coils. Etc. You don't replace the E with anything... :?

Here's one final question: how do you know that certain bonds between certain electrons are more or less stable?

By thinking about it.

e.g. A double bond (<1-1, 2-2>) is stronger than a single bond (<1-1>) because there is more than one bond. A crossover bond (<1-2, 2-1>) is stronger than a double bond because they overlap.

[Nick]

By thinking about it. Razz

e.g. A double bond (<1-1, 2-2>) is stronger than a single bond (<1-1>) because there is more than one bond. A crossover bond (<1-2, 2-1>) is stronger than a double bond because they overlap.

That makes sense.

No it isn't... E1 means an electron with 1 coil. E2 means an electron with 2 coils. Etc. You don't replace the E with anything... :?

If E isn't replaced with anything, then why does it say under hydrogen -(1₁)? Where did the 1 (that isn't in subscript) come from?

[Keiji]

p_n(e_c) means that the atom has p protons, n neutrons, and c E_es.

So:
1₁(1₁) means it has one E₁.
2₂(2₁) means it has one E₂.
2₂(1₂) means it has two E₁s.

Get it now?

[Nick]

Ohh! I get it now. This particle system seems legit to me... anyone else?

[Keiji]

Well, I wrote a computer program to find all possible coilatopes for each element. And here are the numbers of coilatopes for each element, up to number 22:

1, 2, 3, 5, 7, 11, 15, 22, 30, 42, 56, 77, 101, 135, 176, 231, 297, 385, 490, 627, 792, 1002

I ended up with this triangle of differences:



Now what I would like to know is if there is any mathematical formula for this sequence.

By the way, just for fun, one of the 147,273 coilatopes of Cadmium (48 protons - that's as much as I let my computer process, hehe) is:
48₆₄(1₁, 2₁, 3₁, 4₁, 5₁, 6₁, 7₁, 8₁, 12₁).

[houserichichi]

Your sequence of numbers has an order. See it here.

[Nick]

house, did u make this up, or did you already find this?

[Keiji]

Well what does all this mean then?

G.f.: Product_{k>0} 1/(1-x^k) = Sum_{k>= 0} x^k Product_{i = 1..k} 1/(1-x^i) = 1+Sum_{k>0} x^(k^2)/(Product_{i = 1..k} (1-x^i))^2.

a(n) - a(n-1) - a(n-2) + a(n-5) + a(n-7) - a(n-12) - a(n-15) + ... = 0, where the sum is over n-k and k is a generalized pentagonal number (A001318) <= n and the sign of the k-th term is (-1)^([(k+1)/2]). See A001318 for a good way to remember this!

a(n) = (1/n) * Sum_{k=0, 1, ..., n-1} sigma(n-k)*a(k), where sigma(k) is the sum of divisors of k (A000203).

a(n) ~ 1/(4*n*sqrt(3)) * e^(Pi * sqrt(2n/3)) as n -> infinity (Hardy and Ramanujan).

a(n) < exp( (2/3)^(1/2) pi sqrt(n) ) (Ayoub, p. 197).

G.f.: Product (1+x^m)^A001511(m); m=1..inf. - Vladeta Jovovic (vladeta(AT)Eunet.yu), Mar 26 2004

a(n)=sum(i=0, n-1, P(i, n-i)), where P(x, y) is the number of partitions of x into at most y parts, and P(0, y)=1. - Jon Perry (perry(AT)globalnet.co.uk), Jun 16 2003

G.f. : product(i=1, oo, product(j=0, oo, (1+x^((2i-1)*2^j))^(j+1))) - Jon Perry (perry(AT)globalnet.co.uk), Jun 06 2004

G.f. e^{Sum_{k>0} (x^k/(1-x^k)/k)}. - Frank Adams-Watters (FrankTAW(AT)Netscape.net), Feb 08 2006

Euler transform of all 1's sequence (A000012). Weighout transform of A001511. - Frank Adams-Watters (FrankTAW(AT)Netscape.net), Mar 15 2006

a(n) = A027187(n)+A027193(n) = A000701(n)+A046682(n). - Reinhard Zumkeller (reinhard.zumkeller(AT)lhsystems.com), Apr 22 2006

:?

Anyway, I also came up with this: how quarks might work in 4D.

+Quark - charge +0.2, mass 0.2
-Quark - charge -0.3, mass 0.2
xQuark - charge -0.16r7, mass 0.0001

Proton - charge 1, mass 1, made of 5 +quarks.
Neutron - charge 0, mass 1, made of 3 +quarks and 2 -quarks.
Electron - charge -c, mass 0.0006c, made of 6c xquarks where c = number of coils.
Catron - charge -3, mass 2, made of 10 -quarks.

What's a catron, you ask. Well, since electrons are "stuck" to the atoms, it's impossible to have metallic bonding or electricity. So catrons answer that. But before I explain that, here's something on radioactivity. Obvious fact: the bigger a group of neutrons is, the more protons surround them. So that makes more positive charge. This charge will cause the quarks in neutrons to rearrange themselves. However, this will only happen in a group of five neutrons, and they will become three protons and a catron. If you want to artificially create catrons, just fire neutrons at the nucleus of a large atom - chances are, this will make a group of five.

Now, how catrons are useful. Like electrons, catrons don't stay in the nucleus, because they have twice the mass they don't fit correctly. However, they will still be attracted to the protons in the nuclei. This means that they can hold together "multimolecular solids" - solids which aren't giant lattices. These multimolecular solids act just like metals in 3D chemistry: they are malleable, easy to cut, etc. Catrons can also function in the same way as electrons when electricity is concerned.

[/post]

[Nick]

+Quark - charge +0.2, mass 0.2
-Quark - charge -0.3, mass 0.2
xQuark - charge -0.16r7, mass 0.0001

Proton - charge 1, mass 1, made of 5 +quarks.
Neutron - charge 0, mass 1, made of 3 +quarks and 2 -quarks.
Electron - charge -c, mass 0.0006c, made of 6c xquarks where c = number of coils.
Catron - charge -3, mass 2, made of 10 -quarks.

If an electron has 0 charge, how come it has more +quarks than -quarks? Wouldn't that give it a positive charge?

What are xQuarks supposed to be; in other words, what problem in your theory are xQuarks supposed to fix?

[houserichichi]

Well what does all this mean then?

...

It's just ugly ASCII math. You can find it written properly (in the language of mathematica, anyway) here.

[Keiji]

Never used Mathematica... too expensive -_-

[PWrong]

One thing I would like to know is if that sequence of numbers (1,2,3,5,7,11,15,22) is actually mathematical in some way... I should continue with finding these coilatopes

It's a very important sequence. It's the number of rotatopes in n dimensions .

I like your idea, even though it seems a bit arbitrary. Of course, it would be better to use quantum mechanics, but that hasn't worked so far.

I don't know about your attempt at 4D particle physics. Is every particle a coil, or just electrons? And how do you make a coil out of six quarks?

+Quark - charge +0.2, mass 0.2
-Quark - charge -0.3, mass 0.2
xQuark - charge -0.16r7, mass 0.0001

Where did these numbers come from? In 3D we have 6 flavours of quark, in three different colours, plus their antiquarks (that's 36 different quarks). Why are there only three in 4D? Also, you've left out the muon, tau, and three kinds of neutrino.

[Keiji]

One thing I would like to know is if that sequence of numbers (1,2,3,5,7,11,15,22) is actually mathematical in some way... I should continue with finding these coilatopes

It's a very important sequence. It's the number of rotatopes in n dimensions .

Dude, I didn't know that O.o

I like your idea, even though it seems a bit arbitrary.
Of course, it would be better to use quantum mechanics, but that hasn't worked so far.

Quantum mechanics makes no sense to me... it's just completely illogical :?

I don't know about your attempt at 4D particle physics. Is every particle a coil, or just electrons? And how do you make a coil out of six quarks?

+Quark - charge +0.2, mass 0.2
-Quark - charge -0.3, mass 0.2
xQuark - charge -0.16r7, mass 0.0001

Where did these numbers come from? In 3D we have 6 flavours of quark, in three different colours, plus their antiquarks (that's 36 different quarks). Why are there only three in 4D? Also, you've left out the muon, tau, and three kinds of neutrino.

So I tried simplifying things a bit, so sue me. It's only a hypothetical model, if it doesn't work it can be fixed

[PWrong]

Quantum mechanics makes no sense to me... it's just completely illogical

Well, you could reject quantum mechanics altogether by setting planck's constant = 0, just like you can reject relativity by making a universe where c is infinite. Alternatively, the coil shape could really be the shape of the electron's wavefunction. For instance, an electron with one coil would be spread over a kind of toroidal shape (which often happens in 3D).

So I tried simplifying things a bit, so sue me. It's only a hypothetical model, if it doesn't work it can be fixed

Ok, fair enough. But if you want to make things simpler, then I don't see the point of introducing quarks at all. If you want them, you might as well make them the same as in 3D.

What's a catron, you ask. Well, since electrons are "stuck" to the atoms, it's impossible to have metallic bonding or electricity. So catrons answer that.

So is a catron a coil or a point particle?

[Keiji]

Now that I have more time to write...

Ok, fair enough. But if you want to make things simpler, then I don't see the point of introducing quarks at all. If you want them, you might as well make them the same as in 3D.

If I didn't have quarks I wouldn't be able to explain the catron.

Although, I admit that the electron quark configuration is farfetched. Maybe I should just have an E-quark and the electrons E_n made from n connected E-quarks?

So is a catron a coil or a point particle?

Electrons are the only coil particles. Protons, neutrons and catrons are glome (not point) particles because they are made of + and - quarks.

Where did these numbers come from? In 3D we have 6 flavours of quark, in three different colours, plus their antiquarks (that's 36 different quarks). Why are there only three in 4D? Also, you've left out the muon, tau, and three kinds of neutrino.

5 quarks in a group is the most stable configuration in 4D. So that's why there's 5 quarks in a proton and neutron. A catron has 10 quarks because 10 in a group is also stable. No, not all multiples of 5 are stable - I have yet to work out the sequence, but only needed the first two terms which were easy to find by logic alone.

[PWrong]

If I didn't have quarks I wouldn't be able to explain the catron.

Although, I admit that the electron quark configuration is farfetched. Maybe I should just have an E-quark and the electrons En made from n connected E-quarks?

Well, in our universe, electrons aren't made of quarks at all. They're fundamental particles.

5 quarks in a group is the most stable configuration in 4D.

Why? In 3D you only find quarks in groups of 2 and 3. And that's purely because of conservation laws, not geometry.

[Keiji]

If I didn't have quarks I wouldn't be able to explain the catron.

Although, I admit that the electron quark configuration is farfetched. Maybe I should just have an E-quark and the electrons En made from n connected E-quarks?

Well, in our universe, electrons aren't made of quarks at all. They're fundamental particles.

Odd, I thought they were. Oh well.

5 quarks in a group is the most stable configuration in 4D.

Why? In 3D you only find quarks in groups of 2 and 3. And that's purely because of conservation laws, not geometry.

maybe I should scrap the whole quarks thing then.

[Nick]

+Quark - charge +0.2, mass 0.2
-Quark - charge -0.3, mass 0.2
xQuark - charge -0.16r7, mass 0.0001

Proton - charge 1, mass 1, made of 5 +quarks.
Neutron - charge 0, mass 1, made of 3 +quarks and 2 -quarks.
Electron - charge -c, mass 0.0006c, made of 6c xquarks where c = number of coils.
Catron - charge -3, mass 2, made of 10 -quarks.

If an electron has 0 charge, how come it has more +quarks than -quarks? Wouldn't that give it a positive charge?

What are xQuarks supposed to be; in other words, what problem in your theory are xQuarks supposed to fix?

I don't mean to sound rude, but could someone please answer my questions?

[Keiji]

A neutron has 3 +quarks, with charge +0.2, totalling a charge of +0.6, and 2 -quarks, with charge -0.3, totalling a charge of -0.6. +0.6-0.6 = 0. so total overall charge is zero.

xQuarks - I should scrap this idea, see the discussion with me and PWrong...

[papernuke]

i dont get why its E1 and E2 tho and the diagrams are confusing

[moonlord]

The thread is kinda dead and, besides, it seems Rob's system did not actually work well...

[Keiji]

Okay, I had another think about this.

I'm now thinking that protons and neutrons may be arranged along the surface of a 3D torus, around which the coil electrons are attached in 4D.

The structure can be determined with 3 variables:
p - number of protons
n - number of neutrons
c - number of protons or neutrons around the minor radius of the torus.

The definition can be written p,n,c.

The exception is 4D hydrogen, which is 1,0,1. This is obviously just a glome, the one proton. For other atoms, they would likely have a high number of neutrons to make the structure work.

One thing to note is that p+n must be a multiple of c, otherwise the particles will not fit correctly onto the torus, and that p must be less than or equal to n, otherwise the structure will just explode from too much positive charge.

Obviously, since we now have yet another variable - c - we end up with yet another set of slightly different atoms. I will call these "raditopes". Here are what I think should be the most stable raditopes.

1,0,1
2,2,1

3,5,2
4,6,2
5,5,2
6,6,2
7,7,2

8,10,3
9,9,3
10,11,3
11,13,3
12,12,3

13,15,4
14,14,4
15,17,4
16,16,4
17,19,4
18,18,4
19,21,4
20,20,4
21,23,4
22,22,4
23,25,4
24,24,4

25,25,5
26,29,5
27,28,5
28,32,5
29,31,5
30,30,5
31,34,5
32,33,5
33,37,5
34,36,5
35,35,5
36,39,5

37,41,6
38,40,6
39,39,6
40,44,6
41,43,6
42,42,6

I'll stop there.

Anyway, with this structure, electrons do not go very far out at all from the protons and neutrons. Because of this, bonded atoms are much closer together. This means that while gases and liquids remain as light as we'd expect them to, solids are extremely heavy - a unit cube with one atom of flunar thickness would be maybe 100,000 times heavier than a unit cube of equivalent material in 3D. However, since this is all theoretical, we can compensate by simply saying that neutrons and protons have a mass 100,000 times lower than they do in 3D.

[moonlord]

But then gases and liquids would be 100 000 times lighter than in 3D.

[Keiji]

And we don't care about that

So long as our hypothetical 4D planet doesn't have so much gravity that anything built on it would collapse, it's fine.

[PWrong]

I'm a bit concerned about the way you call these things "electrons" and "protons", when I can't find any similarity between these and the real thing. They have extra dimensions (curves instead of points e.t.c.), no quantum properties, and they behave in a totally different way to 3D particles at every scale. I suppose you could say they are still "fundamental particles", but real protons aren't even fundamental, they're made of quarks. So why not call them something else?

[Keiji]

Why call them something else? They may be entirely different, but they do the same job as their equivalents in 3D. I can call them whatever I like so long as people can understand me.