Revelations.

For these past few months, I've pondered about the dimensionality of the Universe and the reason (if any) of our existence. Life is fleeting, life is impermanent (as my father quoted succinctly) and life is a mystery in itself. What is life?

The issue of life and its unplumbed mysteries aside, I came across a book that outlined the concept of space and time, and how they represent, hypothetically, the 4 dimensions we live in. Imagine a Cartesian plane of 4 dimensions, x, y and z, followed by a fourth dimension, time, t.

Who is to say there isn't a fifth dimension? Geometry is an interesting subject. That much is true, yet I find myself inexorably drawn into Physics, rather than the purely mathematical side of it. Still, I'll reserve my standing for later, can't afford to antagonize any aspect of a subject I'm going to study for the next 3 years! (Maybe more.)

Just to liven things up a bit, here's a little topographically intriguing shape called a Mobius strip. It only has one side, and one edge. Rather peculiar if you ask me!



Anyways, what really got me into Physics is the General Theory of Relativity by Einstein. Here's the gist of it. Well, maybe not. I'll just dump everything I find relevant.

Imagine two observers. One standing on a platform which moves a relative velocity to the other. A (on the platform) then shines a beam of light towards a mirror located on top of him. Assuming that we are able to examine time frame by frame (so to speak), the beam would first travel vertically upwards towards the mirror before propagating downwards back towards its source.

For observer A, he finds that the beam traveled a total distance of 2d (d: distance between source and mirror) in time, t1 with a speed of c (c being the speed of light, 3.0x10^8ms-1).

Now Einstein's conjecture is that light always travels with speed c no matter how you look at it, from A or from B. From a moving frame of reference, or from a stationary one. It is irrelevant since there is no definite frame of reference, at least that's what I understand so far.)

Now when it comes to B, the onlooker from a stationary standpoint relative to the moving platform, the light appears not to travel in a straight line, rather it propagates at an angle towards the mirror before getting reflected downwards, albeit at the exact same angle. It forms an imaginary triangle. The best way to illustrate this would be to show it on a diagram.



(Taken shamelessly from another website as I'm too lazy to draw it out by hand. Yay.)

In other words, the distance traveled by the light as observed by B would be startlingly different than the first, A.

Using Pythagoras's theorem, the equation derived from B would surmise the total distance as (2d)^2 + [v(t1)]^2 = D^2 ; D being the total distance observed by B.

Alas, I'm stumped as to what happens next as my maths is beginning to fail me, utterly. How do I simplify the above equation? >.< Gah. I'll update this post when I know how. For now, au revoir!