The Twisted Space-Part 1

Almost everyone has come across the  terms like space time curvature,gravitational lensing,black holes, singularities, etc etc. But what do they really mean? Are they just some sophisticated gibberish?

( ha see what I did there.....sophisticated gibberish... Oxymoron( if you didn't get it)) Or do they have some deep meaning that may even alter our perspective about reality. Let's explore !

Let's start with a classical analogy( it's good to have classical analogies as we can easily conceive it, human mind finds it easy to to recreate something that it might have experienced). Have you ever observed the longitudes of earth intersecting with the equator. You might have not observed it but they intersect the equator at right angles and still manage to intersect at the poles. This clearly means that the triangle formed by two  longitudes with the equator have a sum of angles greater than 180 degrees! And in fact if you measure the angle between two longitudes that intersect at right angles at the poles also, you will find that the sum of angles formed by these 2 longitudes and the equator is 270 degrees. Astonishing, isn't it?

But you might say, the lines are not even straight lines, rather they are curves, how can we even expect them to follow Euclidean geometry? Well that's because you are seeing it from a 3 dimensional perspective I.e we know that the surface is spherical (not straight), but what if we put some very intelligent bugs(who know Euclidean geometry) on such a spherical surface who can only perceive in 2 dimensions. When these bugs start drawing straight lines, in the way illustrated above they find that although their triangle looks like any other 2- dimensional figure( in our sense) still it doesn't follow some of the basic rules of geometry( the angle sum property) given by the Euclid of bugs ( of course there might have been a Euclid bug who introduced this geometry in their world......after all the bugs are super intelligent). Similarly the area of a circle won't be pi*r^2 where r is the measured radius of the circle. In fact it will be greater than pi*r^2.

Well that description was for geometries on a sphere, what about something with the opposite curvature like the surface of a saddle? Obviously the effects will be opposite. The angle sum of the triangle will be less than 180 degrees and similarly the area of circle will also be less than pi*r^2.

So far so good. We proved most of euclid's work (which he assumed was always true) wrong...in a few minutes....so yeah we are doing pretty good I guess.

Time to up the ante. What if our own 3-d space is distorted? What if we are the bugs in this experiment now? How are we supposed to measure the curvature of 3-d space, it was pretty easy in 2-d right? 

.....to be continued.

I will give you the opportunity to entertain yourself with these questions, till my next post.

Stay Tuned for part 2.