What Are the Unique Properties of a Universe with Four Spatial Dimensions?

[alkaline]

has anybody done any thinking on the properties of a universe with four "normal" spatial dimensions? I've done a bit and some interesting properties have surfaced. I've discovered that rivers don't need bridges, sponges and screens can pass through each other, and there are several types of wheels. I created a webpage a while back with an introduction to the fourth dimension. It discusses some properties of a world with a fourth spatial dimension:

http://tetraspace.alkaline.org

i'd be grateful if people could visit the site and give me comments on it. I have the best collection of links to other fourth dimension pages, plus a forum for discussing the fourth dimension.

 

[selfAdjoint]

I did visit your site, and it's quite an interesting resource. I'm not quite ready to comment on it's content, but I recommend it to others who visit this forum. I'm happy to see you have a posting support too. Very nice work.

 

[QuantumNet]

Originally posted by alkaline
has anybody done any thinking on the properties of a universe with four "normal" spatial dimensions? I've done a bit and some interesting properties have surfaced. I've discovered that rivers don't need bridges, sponges and screens can pass through each other, and there are several types of wheels. I created a webpage a while back with an introduction to the fourth dimension. It discusses some properties of a world with a fourth spatial dimension:

Fourth Dimension: Tetraspace

i'd be grateful if people could visit the site and give me comments on it. I have the best collection of links to other fourth dimension pages, plus a forum for discussing the fourth dimension.

Due to that energy-packages would be cubes, the atom wouldn't work at all so spunges wouldn't exist
(one of the reasons why the only universe that exist is threedimensional made of strings.)

www.quantumnet-string.tk[/URL]

 

[alkaline]

what exactly do you mean by the statement "Due to that energy-packages would be cubes, the atom wouldn't work at all"? What are energy-packages, and why do they have to be cubes? I'm interesting in calculating the particle physics of the fourth dimension, so I'm curious to know what people know already of restrictions on what's possible.

 

[alkaline]

i think i just figured out what you meant by "energy packages would be cubes". In the third dimension, wave energy drops off using an inverse square law, so a portion of the wave front is a square. In the fourth dimension, wave energy drops off using an inverse cube law, so a portion of the wave front is a cube. Someone else posted on the forum on my fourth dimension page that the inverse cube law would make atoms unstable, which agrees with what you said. However, i still don't know why this is so.

 

[selfAdjoint]

Atoms i don't know, but orbits are unstable under an inverse cube law. This used to be given, in a sort of primitive Anthropic Principle, as a reason space was three dimensional. If it were four dimensional, no stable orbits means no human beings to ask the question.

 

[alkaline]

i did some brief scanning on the internet, and apparently it has something to do with the fact that there are no solutions to the two-body problem. Orbits below a particular threshold spiral to impact, and orbits above that threshold are sent into infinity. Also, the hydrogen atom in the fourth dimension has no bound states because of the schroedinger equation.

 

[John]

Why an inverse square law instead of inverse cube?

If you have a wave source, like a rock splashing in a calm pond, the waves make about four concentric circles that travel out and dissipate. They dissipate because the waves are being stretched longer as they make bigger concentric circles. How do waves on a flat surface dissipate? It is according to the inverse square law?

Waves from a light or radio source make concentric spheres in 3D space. These waves are curved sheets that are dissipating in every flat direction as a 2D plane, whereas water waves dissipate as 1D lines that are being stretched. Question: Do water waves dissipate with an inverse 1D relationship, whereas light and similar waves that form concentric spheres dissipate with a 2D (inverse square) relationship?

My guess is that water waves dissipate with an inverse square relationship, which begs a huge question. But first, if you take two points on a water wave and map them as they travel out, they form a triangle in a plane. They cover a 2D space as they dissipate. What about light waves? They cover a 3D space as they dissipate. How can they have an inverse 2D rate of dissipation? (By the way, water waves that are parallel straight lines don't dissipate.)

The answer to why water waves that dissipate over a plane surface and light waves that dissipate in 3D space are the same is that space is not really 3D, but is made of 2D planes. Not stacks of planes, one on top of the other, but stacks of planes stacked that are also angled in seven different directions. When a snowflake forms, it forms on one of those planes of space. It is perfectly flat and made only of 60 degree and a few 30-degree angles, indicating a plane that has only three or occasionally six directions.

The reason all waves dissipate with an inverse square relationship is they are all only traveling on 2D planes, like water waves.

 

[selfAdjoint]

John, you are incorrect. Light in 3D space spreads out in a sphere. The formula for the surface area of a sphere is 4 \pi r^2. So as the light spreads farther, the area it has to cover increases as the square of the distance. And thus the intensity at anyone point decreases as the square of the distance. The interior of the sphere doesn't enter into it. And in your water wave example the intensity of the wave varies inversely as the first power of the radius of the circle.

 

[John]

I didn't know what rate water waves dissipated, so I came up with the idea about everything traveling in planes. When talking about how most things work, you are talking at a level above the six extra dimensions of string space.

But the idea of spherical waves being "branes" obeying the laws of 2D surfaces is normal classical physics. I had figured the same thing.

Then I thought if flat water waves dissipated at the same rate as spherical waves, we had something basic that was evidence of string space. I know how much of physics only describes what happens and does not describe why it happens. So if water waves and spherical waves dissipated at the same rate, it's possible no one would wonder why.

 

[selfAdjoint]

Those surface water waves are linear (decrease as the radius), but of course underwater sound waves like those of sonar, are spherical and go as the inverse square of distance. It's generally true of anything that spreads out in 3D space, including (approximately) gravity.

 

[alkaline]

what do you mean by your statement that gravity "approximately" follows the inverse square law?

 

[selfAdjoint]

In the Newtonian approximation it does, but in the better General Relativity there is a smally difference due to curved spacetime.

 

[alkaline]

is there any way to construct a fundamentally different physics system for the fourth dimension where gravity diminishes with an inverse square law instead of inverse cube law?

 

[selfAdjoint]

It's really an interesting question what radiation would be like in four spatial dimensions. The boundary of a ball in four-space would be a three-sphere - which is like all of our three dimensional space plus a "point at infinity". On a simple minded analogy, there would be one of these three-spheres at each distance and their volumes would inclrease as the cube of the radius. Radiation would fill the volume of the succesively large three-sp-heres and its intensity would then decrease as the cube of the distance.

 

[alkaline]

i understand the radiation/energy wave diminishing principle, where in 3-space it diminishes with the square of the distance, but in 4-space it diminishes with the cube of the distance. I was just wondering if it was possible to have a force that didn't diminish like radiation, but diminished with the square of distance in 4-space. It would require fundamentally different physics.

 

[Jeebus]

Originally posted by alkaline
i understand the radiation/energy wave diminishing principle, where in 3-space it diminishes with the square of the distance, but in 4-space it diminishes with the cube of the distance. I was just wondering if it was possible to have a force that didn't diminish like radiation, but diminished with the square of distance in 4-space. It would require fundamentally different physics.

I'm not as advanced as you guys but I was just curious doesn't this principle conclude and go with the Huyghens principle of rays of light passing along by a heavenly body which suffers a deflexion to the side of the diminishing gravitational potential, that is, on the side directed toward the heavenly body, of the magnitude?

 

[alkaline]

maybe you're more advanced than me, i don't know what the Huyghen's principle is.

Back to my original question of how to create a force in the fourth dimension that diminishes with the square of distance. What if all particles had a 3-plane of gravity extending from them, and this 3-plane of gravity would have orientation. Thus, only particles that are within this 3-plane would be attracted to the particle emitting the gravity. Particles that didn't lie on this 3-plane extending from the particle wouldn't be attracted to its gravity. I personally don't know how to mathematically sum the gravities of a large body of particles possessing this property. Anyone have any ideas?