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If modern physics has taught us anything, it is that our normal intuition of how the universe works cannot be trusted. A perfect example is Einstein’s Special Theory of Relativity, which states that the speed of light is the only constant, length and time can vary, and our notion of the simultaneity of two events is incorrect. Another example is quantum mechanics, which says that properties of an object such as momentum and position cannot be determined precisely, only probabilistically. A concept regarding the structure of the universe that again opposes our instincts is that of extra dimensions.


What is a dimension?
To be precise, "the dimension of an object is a topological measure of the size of its covering properties." (Weisstein) Fortunately, this can be explained in simpler terms that correspond with our everyday experience. Imagine a line, which we will call one-dimensional. We can identify each point on the line with exactly one number or coordinate. For a plane, which is two-dimensional, each point needs two coordinates for identification. For the three-dimensional space that we are most familiar with, each point has 3 coordinates. The dimension of a space can thus be thought of as the number of coordinates needed to specify the location of a point in that space.


What about four dimensions? ...or five?
Einstein's General Theory of Relativity confronts our notions of dimension by describing the universe in four dimensions: three familiar spatial dimensions, plus the dimension time. This makes sense if one thinks of an event happening at not only a certain location in the universe, but also at a specific time in history. This concept led to the term spacetime to describe the universe.

As elegant as Einstein's theory was in explaining the gravitational force and the large-scale geometric structure of the universe, it could not fully explain any forces, gravitational or otherwise, at very small scales. Indeed, as quantum mechanics was developed throughout the middle part of the 20th century, it became increasingly clear that general relativity and quantum mechanics were incompatible.

One attempt at unifying general relativity with a force, electromagnetism, at small scales was made by mathematician Theodor Kaluza in 1919. He found that by adding an extra, "curled up" dimension to the framework of general relativity, the resulting equations corresponded with those given by Maxwell years earlier for electromagnetism. This remarkable insight garnered even Einstein's approval, but led to theoretical results that conflicted with experimental evidence. The focus of most research at the time was on developing the groundwork for quantum mechanics, so Kaluza's ideas went largely ignored while quantum mechanics was being explored.



What are extra dimensions?
What did Kaluza mean when he suggested that the universe might contain an extra, curled up spatial dimension? Although it is difficult, if not impossible, to clearly visualize anything more than three spatial dimensions, we can make analogies to help us understand such a seemingly bizarre concept.

One simple example is to think of a thread composed of several, much smaller threads that are braided together. When viewed from a distance, one sees the larger thread, and one can describe it with two coordinates: length and a radius. Upon closer inspection, one would notice the other, smaller threads, and see that more information is required to describe them. (Pandian)

Brian Greene gives a similar analogy in The Elegant Universe. Imagine a hose of several hundred feet stretched out over a canyon, and imagine an ant crawling on the hose. From very far away, one sees the hose as a one-dimensional object: a line with no thickness. If viewing with binoculars, one may then notice that the ant, instead of being limited to travel in one dimension, has the ability to travel around the surface of the hose. Thus, magnifying the hose reveals another dimension. This previously unnoticed dimension is analogous to how a tiny, curled up dimension might exist in reality. It would be very small, much smaller than our current technology would enable us to measure, smaller than a billionth of a billionth of a meter, and its influence would obviously not be felt on any larger scales. The ideas of Kaluza, later refined by another mathematician named Oskar Klein, hypothesized the existence of such curled-up dimensions at all points in space, just at this very small scale. Thus, we have a distinction between dimensions that are very large and expansive, such as those we experience in everyday life, and those that are very small and curled up. (Greene.)


Why are extra dimensions important?
The whole point in hypothesizing the existence of extra dimensions is to unify the fundamental physical forces -gravity, electromagnetism, and the strong and weak nuclear forces- under one single theory. The two pillars of modern physics, general relativity and quantum mechanics, are the most well-tested and experimentally verified theories in existence. Each have been rigorously examined for the better part of the last century, and have stood up amazingly well under all scrutiny. A problem arises, however, when one attempts to probe the depths of ultramicroscopic scales that quantum mechanics describes so well. General relativity gives us a picture of smooth spacetime, but according to quantum mechanics, this is not the case at very small levels. The main thrust of quantum mechanics, the uncertainty principle, says that on such small scales, properties of objects that we take for granted, such as velocity, position, momentum, etc, are all uncertain and probabilistic. "Particles and fields undulate and jump between all possible values consistent with the quantum uncertainty. This implies that the microscopic realm is a roiling frenzy, awash in a violent sea of quantum fluctuations." (Greene) General relativity is thus unable to make sense of the tumultuous "quantum foam" found at small scales.

Kaluza's and Klein's 5-dimensional version general relativity that contains both electromagnetism and 4-dimensional general relativity, although flawed, is an example of such an attempt to unite the forces of nature under one theory. It led to glaring contradictions with experimental data, but some physicists felt that it was on the right track, that it in fact didn't incorporate enough extra dimensions. This led to modified versions of Kaluza-Klein theories incorporating numerous, extremely small extra dimensions.

One potentially successful theory to bridge the gap between quantum mechanics and general relativity is superstring theory. The basics of string theory assert that the fundamental components of all matter are not particles, but tiny, one-dimensional loops of vibrating string. These loops are as small as the Plank length, 10-35 m, and as they vibrate, their resonant frequencies determine the properties, such as mass or charge, of the particles they constitute. The key behind replacing point particles by strings with some dimension is that this can remove the mathematical absurdities arising in the equations of general relativity are applied to such small scales. "String theory softens the violent quantum undulations by 'smearing' out the short-distance properties of space." (Greene) What results is a theory that incorporates all aspects of quantum mechanics and general relativity without any incompatibilities.

What does string theory have to do with extra dimensions? It turns out that string theory requires the existence of these tiny, curled up extra dimensions. In fact, it says that there are at least 6 smaller dimensions, and possibly more. This seems incredibly bizarre indeed. To help visualize, we can return to the analogy of the ant on the hose, and how the hose has an extra dimension when we view it with magnification. Now, instead of a one-dimensional line, imagine a plane in two dimensions. Just as the hose has an extra dimension at each point, we can see an extra dimension in the form of a loop or a circle at each point on the plane. If we use spheres, we now have two curled up dimensions at each point on the plane. Remember that even though the image shows spheres only at intersections of grid lines, there would be spheres at every point on the plane. As you wave your hand through the air, it would pass through the normal three large dimensions, as well as these unimaginably tiny dimensions at each point along its path of motion.




Two normal dimensions, with 2 extra, "curled-up" dimensions, represented by spheres.


What might a higher-dimensional form look like? The Calabi-Yau space is a six-dimensional form that string theory incorporates as the extra, curled up dimensions. We can also replace the sphere on our plane with the Calabi-Yau space to visualize what these curled up dimensions may look like. In reality, the universe would consist of one temporal dimension, three normal spatial dimensions, and six (or more) extra dimensions in the form of Calabi-Yau spaces, at each point in the normal three spatial dimensions.





An extra-dimensional form: the Calabi-Yau space.





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--Last edited by saucer on 2007-01-14 17:31:20 --

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version space in a 3D parameter space


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Hi Saucer.
I have just read your post which was very informative.I must admit that string theory has not taken much of my time . Mainly because it still requires something to be in.If anything is "in" something, then the something they are in needs to be made of things smaller than they are.Even if that is nothing.
  And because There are more than one and a variety of behaviours, they are still open to a "pre-string" interpretation.That doesn't mean string theory is wrong.Quite the opposite actually.
  The theory you quoted of probabilities is relavant to this. I need to change it to possibilities for an overall view , but probabilities works within a measurable state.

  To clarify:-

If I say "possibilities" , then I allow that there can under "universally apparent conditions", that something can happen.

If I say "probabilities" then I reduce the likelihood to only certain universally present conditions.

They may be size,speed,local conditions and time.(possibly others)

So, can a man fly on his own wings?...Yes, It is possible.Is it likely that within the parameters man will evolve wings?..In our lifetime , this is not probable.

Can we travel through time?....yes, it is possible. can we in our current state do this. No, this is not probable.

could a stage of the universal development include string theory and could string theory explain more than we know down to a greater degree" yes, this is probable.
But can string theory stand alone as a causality? no, this is not possible.

what I am working on makes everything possible and basically says that every concievable thing can happen. The parameters that rule what we can percieve as reality , are made up on where on the speed/time line that we inhabit. it says that parallel universes exsits alongside us but that we can only percieve those that fall within our own particular make-up.

In fact we can see everything that occurs.but locality and speed gives us an unrealistic view of the events that occur.Zoom in and we see  chaos until we got close enough to create order. zoom out and we lose even the simple perceptions we have now.

If we zoomed in to the limit.(to a singular particle), time does not exist and there are no objects to percieve, because we could not see where weve been.

if we zoomed out we see exactly the same thing. because the greatest masses would be too small to individualise. we would see nothing.also time does the same thing as in the smaller state. nothing moves.

We inhabit a state that is equal between the two. if it were not equal. constants could not exist , even for a short while. We would see the chaos of atomic and the uncertainty principle would invade this reality to a much greater degree.

Cheers
Iseason  

--Last edited by Iseason on 2007-04-06 03:54:52 --

Hi Saucer.

Actually , I have seen something within the different posts we and Ferme and Zee are talking in that helped solve motion.First I need to lay out the problems.

1. If the particle can 'give' energy away' then it is not the first causality.
2. If it can move in random fashion in order to keep reality , then it is not the only particle. (since it cannot inhabit the whole universe.)
3. If it can alter states. in other words , if the particle changes in any way , then it is not singular.
4. If it can be positive and negative as suggested . this equals a change of states and is not allowed.

So In another post , to answer my problem of motion , Zee suggested Diagonal. I had asked him to expand the thought , but am happy to expound in the meantime . feel free to join us Zee.

If time and space is in fact curved as Einstien predicted, there is another possibility that we can explore.

That time is not moving in a straight line. The next "occurance" of the particle can be in front and to the left or right. So when we see events unroll, we see in front of our eyes events that have already occurred .(looking into the distance)

Nothing need actually exist at the same time, and the particle need not change in order for time to behave in this fashion.Motion is essential (as an illusion) , to cause us to see this happening.

Time is actually not a "thing". It is an invention of man in order to measure the occurances we percieve.The fact that there is an order to this which allows us to percieve the universe does not mean that it does. (all at the same time)

What we are using is the particle itself. So how can it be us and keep the universe whole>it's goes back to things already having happenned. We are using the viewpoint of the particle to see reality. In other words , we are privy to , and part of the particles memory.

If time were a straight line we would be looking through a spyhole the particles own width. essentially we would only see the particle , since no variation were possible.But with the particle varying the order of it's memory to suit the reality it creates. we share a unique "position".

Cheers
Iseason

I've come back to the same post to stop going all over the place with this.

In considering the thought process allowing for perspective of the universe to be variable upon position, the rainbow came to mind, and refraction in general. Perhaps the rainbow simply shows that light travels via a differing pathway to what we "observe".
Ok . Let's say the wave function of light equals the curvature of the travel path. It will arrive at a point in space on a regular wave cycle. The distance across the "bow" is important and will vary depending upon the medium it is travelling through.

Cheers
Iseason  

--Last edited by Iseason on 2007-04-09 01:06:42 --

Hi Iseas.
Yes, I think your Number 1 premise, is good, for a lot. Definately.


Maybe premise 4s' "ground-state" where viz: hypothetise, quote " ..a change of states" unquote, MAY REALLY NOT BE ALLOWED!

and so

(: fits as "the correct" hypothenuse!)     zee  

--Last edited by zee on 2007-04-09 05:14:16 --

Very good Zee.

I am starting to think that one is really one.As I say though , it poses unusual problems.

It cannot give away energy to create motion, and cannot be within anything it did not create itself.a working "memory" within the 'one' indicates a smaller causality.

here's a thought.one can cancel itself out from one position using the -1+1 sum.Only we are using the one as "being the whole universe" in this instant.(it's particle/anti-particle theory)

If I am one and create myself one degree turned on my axis, I have moved nowhere , but have created the first change in the universe which does not require me to go anywhere. there are infinate orientations i can make of myself.

Since in this "altered state" I cannot continue to occupy the first position, since there is no space for me to move to , I must occupy another version of the universe, but still in the same position. The plus position "creates a negative position" of the original particle.

From here i'd be guessing.(not at all like me.

Night
Iseason

Keeping with the nature of a straight line being an impossibility within this "space", The fact is that it is a mathematical probability. "the maintainance of a straight line is another thing entirely".

  So we go to both ends of possibility and see that at both ends , a straight line is possible. but within the "guts" of reality, it breaks down.'Largest ' size + straight line. (with no other reference point) . 'Smallest size', Straight line = ok. (with no other particle to cause a deviation.

So , The two "dimensions" are in cahoots. If we could "see" in a straight timeline, we could make out that our point of view is moving across a holographic universe. (I first heard this said by US2U).

For every pixel space we cross , we go through all the possible angles. Only one of those is a straight line. But all of them are a straight line depending on your direction of travel.

So in fact we only ever see the larger universe in smaller snatches, depending on the angle that we are looking , we can gauge the depth of the universe to that level.

So one is still correct, Because one exists as smallest and largest object. Perspective is the only variation , and that is not a thing. It is an action which doesn't change what the two "things" were Doing. Which was nothing.

In that case , What is the reality that we inhabit? It is a reflection which is necessary to give the both ends , Large and small, Thier reality.

Cheers
Iseason

Quote :

Iseason wrote : Hi Saucer. Actually , I have seen something within the different posts we and Ferme and Zee are talking in that helped solve motion.First I need to lay out the problems. 1. If the particle can 'give' energy away' then it is not the first causality. 2. If it can move in random fashion in order to keep reality , then it is not the only particle. (since it cannot inhabit the whole universe.) 3. If it can alter states. in other words , if the particle changes in any way , then it is not singular. 4. If it can be positive and negative as suggested . this equals a change of states and is not allowed. So In another post , to answer my problem of motion , Zee suggested Diagonal. I had asked him to expand the thought , but am happy to expound in the meantime . feel free to join us Zee. If time and space is in fact curved as Einstien predicted, there is another possibility that we can explore. That time is not moving in a straight line. The next "occurance" of the particle can be in front and to the left or right. So when we see events unroll, we see in front of our eyes events that have already occurred .(looking into the distance) Nothing need actually exist at the same time, and the particle need not change in order for time to behave in this fashion.Motion is essential (as an illusion) , to cause us to see this happening. Time is actually not a "thing". It is an invention of man in order to measure the occurances we percieve.The fact that there is an order to this which allows us to percieve the universe does not mean that it does. (all at the same time) What we are using is the particle itself. So how can it be us and keep the universe whole>it's goes back to things already having happenned. We are using the viewpoint of the particle to see reality. In other words , we are privy to , and part of the particles memory. If time were a straight line we would be looking through a spyhole the particles own width. essentially we would only see the particle , since no variation were possible.But with the particle varying the order of it's memory to suit the reality it creates. we share a unique "position". Cheers Iseason I've come back to the same post to stop going all over the place with this. In considering the thought process allowing for perspective of the universe to be variable upon position, the rainbow came to mind, and refraction in general. Perhaps the rainbow simply shows that light travels via a differing pathway to what we "observe". Ok . Let's say the wave function of light equals the curvature of the travel path. It will arrive at a point in space on a regular wave cycle. The distance across the "bow" is important and will vary depending upon the medium it is travelling through. Cheers Iseason

THOUGH when I say: "good for a lot.." ( Re your premise 1..) I, think your premise needs qualifying, "a little further ..."


namely; What EXACTLY do you mean by: quote; ' give energy away?' unquote ......

...IT DOES SEEM ~ b has occured!

Could you qualify this point a little further Iseason ...

I am not referring to the physical-event of ' giving energy away..'







though..,

..I see other "latidudes" (in your reference of: "giving energy away."!)

ie:

If 'a' is not 'giving energy away,' or a "null state" (..a "neutral-positive.") Then, 'b' may be: a reference-point (..as it were) acknowledging (selectively) 'a' exists / existed ..~ zee  

--Last edited by zee on 2007-04-17 11:35:21 --

Hi Zee
  I couldn't read any answer in your last post. Perhaps the colour got lost.

I was wondering about your thoughts about light and it's variations BEING the eather. If this were true . you could not affect any speed as such. Only intensity of wavelenght.

Cheers
Iseason