Wednesday, April 7, 2010

On dimensions…

                     As promised in the overview of what my blog was all about, about everything in life being mystery etc, really try to look at things differently around you & you will discover wonderful aspects & gain amazing understanding about the unexplored nature of normal mundane things which we are unaware of almost all the times
       We are living in 3 dimensions of space & one dimension of time. The 3 dimensions are length, breadth & height. The time has forward & backward direction. The forward is marked by the increase in entropy, yes this is the important criteria which distinguishes forward passage of time. Whatever you do, contributes to increase in entropy, the rate of incease ion entropy may vary but entroy or disorder in universe increases always. Or more generally in this direction of time, the causes precede the effects in any event. Coming to spatial dimension, starting with a point, has no dimensions at all, no length breadth etc. A string has one dimension. It has length only, an ant can move forward backward, of course ant is 3 dimensional organisms, but just ignoring this fact for simplicity in understanding. What do we mean by one dimension is we need one parameter to locate a point i.e the length parameter, considering some point as fixed or popularly called origin. A 2 dimensional space is popularly called in Flatland. You can be a line square or rectangle or any favorite geometrical 2 dimensional shape you may like. Why organisms really cannot exist in flatland is described by Stephen hawking in his book Brief history of time as the food canal & the excretory system which should be essentially present in a living organism will divide the body into two. Hence the existence of two dimensional organisms is ruled out. We need two parameters length & breadth to specify a point’s location in such a space. The Cartesian coordinate system or polar coordinate systems are just different ways to identify the location of point.  
               Coming to the most familiar one, the 3 dimensional space which we live our lives & see the universe is most essential one for sustaining life as organisms cant obviously exist in one dimension or flatland. Now, the easiest way to imagine 4th dimension of space is imagine I lock you in a room & come outside. & you happen to find way to come outside & surprise me outside the room. Assuming the exaggeration that there may be many ways you can come out, one possibility is through 4th dimension. The room is a cube taking 3 parameters length, breadth & height essentially to define the position of a point. A 4 dimensional cube is called a tesseract or hypercube. It becomes more & more difficult for human mind to comprehend dimensions with the increase in dimensions as we have not seen or experienced them. This would essentially have a extra direction perpendicular to all three axis length, breadth & height axis. As a 3D object like cube casts a 2d shadow on a plane, we can expect the hypercube to cast a 3D shadow, with its 3 D structure visible in 3D completely, but one part extending out in 4th dimension which we cannot see or touch or feel but easily mathematically comprehensible.
         The most popular theory Big Bang theory states that our universe sub-plank length smaller than about 10 to the power (-35) m. So, Can I say that universe started as zero dimension, an infinitesimally small point. The space itself came into existence after big bang. So universe evolved into 3 dimensional spaces as we see it today & perhaps more dimensions which we don’t see.  Scientists explain this observation in a weirs way. If you see a water pipe from a distance it appears as a line segment, but actually if you go near & observe it’s a 3 dimensional object with water flowing inside it. So here in this example the 3rd dimension is curved & on itself & cannot be inferred when seen form a distance. Similarly 4th & higher dimensions may exhibit similar characteristics. Imagine the universe existed as a flatland & it’s curved say in form a sphere etc, then a flatland creature would travel from a point & reach same point if he kept traveling. So space is finite & unbounded. Similarly extending this same idea to 3 dimensional space, it can be curved in on itself i.e if you stary traveling in space marking the initial point & travel faster as we know the universe is quite big, after infinite time you may reach the same point where you just started the quest. Then the universe is finite & bounded. Now, the interesting part is what makes universe bend onto itself, matter as we know is ion large quantities to bend space time continuum onto itself. If quantity of matter is not more than some threshold value, then space is open & non bounded & infinite.        
Various paradoxes emerge when we are conceptualizing such things. In fact there was an interesting article in ‘New Scientist’ which said that instead of sphere, universe could be shape of funnel. If you are at the extreme tip of the funnel you could see back of your own head. If you throw a catapult fast enough, assuming universe is finite & bounded then instead of returning to you it may come & hit you at back of your head. 

     This wrapped onto itself universe actually coincides with the observable universe. All galaxies are moving from each other, the farther they are apart they seem to be moving at faster rate from each other. Just like dots when you are blowing up a balloon. 

to be continued...

Sometimes i wonder there just aren't enough stars. . . 

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