The universe as a line

[MirceaKitsune]

I was thinking of Einstein's spacetime concept. Particularily the part where, if an object travels near the speed of light, its velocity through space slows down its passage through time. I always understood this as particles having a limited potential, which they cannot gain or lose (without the particle changing its structure) but rather "buy or sell" between dimensions. However, one interesting problem arises: We see space as being three dimensional, and tend to envision it in three axes; Up - down, left - right, back - forth. So how is it that space doesn't show this behavior across fixed axes? A particle going at the speed of light should only be able to travel in 6 exact directions. For example, if it's using its entire potential upward, it could not spare any to move left or right and back or forth. Yet light can shine in any direction.

 

This got me pondering a new possible design for the fabric of space. I wondered if maybe, the location of a three dimensional point could be represented in only one dimension, contrary to the classic concept that you define said point using X Y Z coordinates. I noticed something I haven't considered before: You can. The geometrical concept is certainly one others have thought of, and there might even be a term that I'm not aware of... but thinking of it from a physics perspective is new at least to me.

 

This is the idea: If you have an extremely long line, which you are free to bend in a given number of directions, you can create loopable patterns which can be compressed or continued to infinity, and which would eventually take up every single fraction of space in those directions (given there was a size limit). The best description that comes to mind is "fractals made out of one line". A point can then be represented as a single value; Its location on that line. If the twisted line covers every spot of space, this one value can be used to represent the point's position in any number of dimensions.

 

A practical example: Imagine that you have a circle. In this circle, you can place a point anywhere, by defining its X and Y position. But what if you wanted to place the point using only one value? One way is filling the circle with a virtual spiral, which starts at its center and ends once it touches the edge of the circle. The spiral has enough repeats so that it covers the smallest unit to which you could possibly position your point, and has reached the state where it cannot get more dense without crashing into itself. You then specify the point's location between 0 and 1... where 0 is the center of the circle where the spiral starts, and 1 is where the spiral touches the edge of the circle and ends. You can place any number of points on this pattern, in all possible locations you could with individual X and Y coordinates.

 

Some might argue that no matter how dense you make the spiral, there's always space left in between, so it could never cover every fraction of space. But think about this: No matter how many decimals you'd add to the X and Y coordinates, you could always go even lower. Consider that you're initially able to define a point's position using numbers with one decimal... for example 0.3. Then you want to go lower and allow two decimals, so you change a coordinate to 0.61. Then you want even lower, and do 0.078... and so on to infinity. Same with a pattern like our spiral: If you want it to cover more space, you give it even more loops and make it more dense. Both of the two approaches can theoretically go on forever, unless space itself has an unit which is the smallest anything can get.

 

If space does have such a size limit, something remarkable can be considered; When the line becomes so dense that there's no space left inside, there's a point where it will merge with itself. This creates a location where a represented point has two or more values at once. If the point continues to manifest its velocity / inertia past this moment, it can end up taking one path out of many.

 

Imagine the shape of the number eight, or the symbol of infinity... which has two circles and one junction point between them. Consider that our "8" is a line twisted in a pattern. It starts in the center, so that is position 0. The highest part (top most location) is 0.25. Then we begin to descend back toward the middle, which is 0.5. We next start moving toward the bottom, where the lowest part (bottom most location) is 0.75. Then we climb to the center once more and that's 1. Now 0.25 and 0.75 are unique locations, so a point can only be at one or the other. But 0 and 0.5 and 1 are the same place! When a point is at one, it's at all of them... so where will it go next? In the case of the 8, at least 3 individual loops can be created between the two oo's if not more.

 

How does this relate to physics? No precise idea on that. But it could mean that all of spacetime might be one enormous line... twisted in an huge number of fractal patterns. This line is the fabric of space, and each quark is a signal that travels through it. However, particles couldn't probably travel so fast through space and time from one end of the universe to the other. Which is where the junction points come in: They would allow quarks to take paths and move through complex loops in the line, making it possible to have three dimensional objects in various universes throughout the multiverse. And what about black holes? They could be attributed to mass forcing the line to intersect itself, creating a new loop that sends timespace flying all over itself. Then there's quantum entanglement... and maybe time lines?

 

Thanks to everyone who had the time and energy to read this long post. Please let me know what you think, and what other knowledge there is as to how this concept could apply to physics. I wasn't sure if to put this in the Speculations thread... but since it's not something I claim to be an actual discovery nor certain fact, I thought here would be best.

[`hýsøŕ]

sorry if this sounds offensive but the first few paragraphs simply do not make sense at all (at least to me)

 

as for the spiral idea, sure the spiral can cover all the area in a circle but then the length along the spiral tends towards infinity (you're coiling it around more and more times to make it cover more and more area, so it gets longer and longer)

[MirceaKitsune]

Don't think I can word anything better than that, although I hoped I expressed what I think understandably at least.

 

And I don't think that would be the case with the spiral. Since when I said "if space has a minimum size limit" I didn't mean one that scales down with the spiral. It means the line does have a width in all possible dimensions, which is always this minimum limit. I don't know if in reality quarks have a radius of some sort as well, but I personally believe even the fundamental building blocks of matter stop somewhere.

[Mordred]

there is one fundamental problem in the first paragraph, an observer who watches the particle near the speed of c will see the time delay, however the particle itself would experience time as normal. This has no effect on the particles energy, as such there is no need or risk of the particle changing its potential. A particles direction also does not affect the particles energy, unless it is traveling into or out of a gravity well. Due to those misunderstandings the rest of your post also makes no sense as your understanding is incorrect.

 

Another problem you don't understand is space is not I repeat not a fabric, it is simply geometric volume, filled with the energy-density contents of the universe. When cosmologists refer to space curvature etc, what they really mean is the curvature of the gravitational energy-density distribution. or the shape of the area of influences due to gravity. It does not mean space is a curved fabric. Same with overall space geometry. Space geometry is the energy-density relations between gravity and the cosmological constant. Flat space means its actual density is close to its critical density. The energy-density relations has a corresponding pressure relation shown by the equations of state.

 

http://en.wikipedia.org/wiki/Equation_of_state_%28cosmology%29

 

Universe geometry is explained here

 

http://cosmology101.wikidot.com/universe-geometry

page 2 is here (FLRW metric and distance measures)

http://cosmology101.wikidot.com/geometry-flrw-metric/

 

the rest of your write up is also incorrect there is no minimal volume change, space is volume only and as such a change of volume can be any quantity.

Edited June 3, 2014 by Mordred

[MirceaKitsune]

Ok. I wasn't sure if it's known whether space itself (the area in which matter can manifest) has a form or not. Since for example, black holes act as if they break that space.

 

Otherwise, I'm uncertain if the rest of my idea could still make sense. I imagine quarks are still multi-dimensional, and the behavior we see in matter could be the result of simple movement but in a complex pattern / direction. Like I said however, this was just a thought that went through my mind... although the concept sounds interesting and between the lines, this feels like it makes some sense.

 

Another relevant idea might be concept that the universe is actually the projection of a 2D hologram... which was said by several scientists. Although I understand that even less, so there's little I can say on it.

Edited June 3, 2014 by MirceaKitsune

[MigL]

Aside from the physical misconceptions, how would you define a specific point on the spiral ?

[MirceaKitsune]

Aside from the physical misconceptions, how would you define a specific point on the spiral ?

 

I mostly wanted to discuss it from a geometrical point of view, then relate that to how the concept could be used in physics if there is a way. Especially since many users said they wish to see more mathematics behind such ideas, so I felt this could be theoretically possible enough to do so. I admit there might be a lot of things wrong here, since I'm very far from a mathematician and more of a thinker if anything.

 

Like I said, a point in this system would be defined as its location on the bent line. Easiest way would be to consider the starting point 0 and the ending point 1, and anything in between 0.x.

 

An even simpler version of my concept would be: If you have a theoretical space, in any number of dimensions (2D, 3D, etc), in which there is a "lowest size limit" which can be expressed as a fixed value, and that size limit applies as both the radius of a point and the radius / thickness of a line in which you can position that point, there should theoretically be patterns in which you can curl up that line to take every bit of space possible. Which in turn, would allow any number of points to be positioned inside that line, as a value between its start and its end point, letting it be placed anywhere in the X dimensions that line is twisted around.

[MigL]

My point was, that unless you have other parameters to define the curvature of the spiral, you cannot locate a position on a curved line.

You still need more than one dimension, if the spiral is in a plane you need two, if in a volume you still need three.