Tuesday, 5 April 2016

We All Actually never understood Einstein's Theory Of Relativity

According to Google, Albert Einstein, in his theory of special relativity, determined
that the laws of physics are the same for all non-accelerating observers, and he showed that the speed of light within a vacuum is the same no matter the speed at which an observer travels.

In a popular science magazine, I read about the ABC of this 'gobbledygook' an article on the Gravity Waves, explained by T R GOPALAKRISHNAN & concluded that the principles of the theory are actually quite easy to understand by learning about gravitational waves in just four simple steps.
I am sharing the superficial elements of the article as what I understood :

1) THE CONCEPT OF SPACE-TIME

-According to Newton, gravity was a force- that a body attracts another body over a distance. But Einstein said that there could be a better explanation for gravity.

-Einstein actually took the concepts of SPACE & TIME (which are related) & wove them together in a single idea, called Space-time.

-Thinking of space-time as fabric, and the universe as a trampoline, Einstein's theory says space-time can be curved, & what we feel as 'gravity' is the "effect" of that curvature.

2) SPACE-TIME & GRAVITY

-Now imagine what would happen to the trampoline, if we place a huge solid Gold ball over it?

-Yes, obviously.. the trampoline would sink & cause a curvature.

-Now, suppose if we drop another solid Silver ball, smaller in size, on the periphery of the trampoline.. what would happen?

-Undoubtedly, it'd roll down towards the huge Gold ball.

-So, the conclusion here is, the earth is the Gold ball, the moon is the silver ball & the curvature or gravity you can say, is what attracts the moon to earth.

-The bigger the mass of an object, the deeper the curvature it causes.

3) GRAVITY & GEODESICS

-In case of trampoline, the silver ball would roll down to the huge gold ball in a straight line. But it doesn't happen so in the real world.

-Throw a ball into the air, & it makes a parabola in space. Similarly, a celestial body follows a path called geodesic (the equivalent of a straight line in the four-dimensional space-time).

-The moon also orbits the earth in a geodesic.

4) GRAVITY AS WAVES

-Firstly, we need to know what are gravitational waves?

-Let's suppose two heavy iron balls circling each other in the trampoline. Their movement causes ripples in the fabric, which spread outward.
In space-time, such ripples are called gravitational waves.

- When dense bodies such as neutron stars & black holes orbit around each other, the ripples in space-time resemble that of the surface of an agitated pond.

-The denser the objects, the more powerful the waves they generate.
-The faster the objects move, the more waves they produce.
-And the waves travel at the speed of light.

-Einstein's Point Of View :

-What at LIGO (Laser Interferometer Gravitational-wave Observatory) detected was the gravitational waves produced by the circling-around & subsequent collision of two black holes, which were 29 & 36 times the mass of the sun.

-The collision resulted in a bigger black hole, which was 62 times the mass of the sun.

-But, 29+36=65. The new black hole had a solar mass of 62. So, here the question arises where did the mass equivalent of three suns go?

-I was unable to guess the answer properly, but my guess was somewhere close to the explanation.
-Wave is a form of energy, and energy is a form of matter. E= mc^2, which means the mass equivalent of three suns went as energy of the gravitational waves.

-There's you have just thought like Einstein.   :-)

-But....
-Scientists found that it does not happen so.
-Reason- An unknown energy was deforming the tunnels, changing their length ever so slightly. As a result, the distance travelled by the beams varied, and they were not reaching the beam splitter at the same time.
Bingo, said the scientists as they had finally caught a gravitational wave.

-Thanks to the wave's effect, the lasers were recombining in such a way that it produced a measurable signal at the light detector.
-What I found interesting was - When converted to an audible sound, the waves made an unmistakable 'chirp', the loudness of which helped scientists make a rough estimate of the age of the waves.
In this case, (to my amaze) 1.3 billion years!!

P.S. - Now, I can say that Albert Einstein's theory of Relativity is not completely beyond my brain. :-)

Saturday, 2 April 2016

Making judgements & Being Judgemental are two different things my dear !

I'm writing this blog post based on a technical point of view, rather than abstract thinking (as unlike most of my previous ones.)
But also, I've not gone for a literature review kind of thing. It's still a piece of my thought process just including a bit of technicalities.
Okay.. Now if you pay attention it's actually a loaded question :
What is the difference between making judgements & being a judgmental person?
Everyone make judgements all the time so
why are only certain people accused of being judgmental?
Well.. answer to this question can be easily obtained from a dictionary. Yeah!
If we look up the word judgmental in the dictionary there are generally two meanings :
1)One has to do with making judgments; so, yes, at a basic level, making judgments is being judgmental :-)
2) The other meaning of judgmental has to do with being 'overly critical' in an unhelpful way :-(
It is when we make judgments in ways that have harmful or negative consequences that we are being judgmental in ways that are best to avoid.

Okay.. Now moving forward.. I'll try to elucidate the process & associated things behind this, adopting a statistical approach. (My newfound attitude! ;-))

•In any kind of scientific investigation or survey sort of things, a small portion (sample) of the entire targeted population is used for study. And on the basis of the information contained in the sample, we draw out conclusions about the population & that's how generalisations originate.
Best example of its kind: Conducting exit polls to predict the election results.
This procedure can also be used to predict about the events, which are yet to occur, on the basis of past events. This is very much the concept of Inferential Statistics; closely tied to the logic of hypothesis testing.

•In hypothesis testing, we have a particular value in mind.
(Now it seems that the post is going abstruse, let's take an example to understand this concept.)
- Particular value, here, can be understood as our preconceived notions about a person (He always does so, he's this way only) ,
thing (Glasses <3 are meant to be broken) ,
situation (First job interview: Fear or not to Fear? etc.)
We 'Homo sapiens' tend to hypothesize that this value "characterise" the population of observations.

Actually, what we are supposed to do :

•In estimation, no particular population value need to be stated.
-(We actually don't require to view everybody with the same frame of mind. We need to understand that everyone is different & unique in their own ways & so needed our perspective to be: WIDE)

Rather, we need to question is, what is the population value? (What all there is in this being, that makes me consider him twice? What are his strengths, his potential, his source of energy, his VALUE?)

•Hypothesis testing is one of the important areas of our analyses, decision -making process that we come across in our day-to-day situations. (Most often in judging our surroundings) & then taking decisions or resolutions to change ourselves either by adopting or withdrawing from the situation. (Ah! we the complex beings!!)

How This Is Done?

• Firstly, we define our hypothesis as a statement, which may or may not be true about our target (whosoever going to be judged by us).
Here, it could be a possibility that the probability distribution of our assumption that we wish to validate, is not in a convincing ratio. ( For e.g., Not all men are impassive. Mind it! )
Most of the times, our experiences are gained from 2-3 persons (random samples, you can say), instead of entire population. And we draw our conclusions regarding this world, (a giant word in itself, indeed!). That's the very thing which should not be done. AT ALL!!
•Before drawing inferences about the entire population (here, world) it should always be kept in mind that the observed results might have come due to chance factor .(Let's suppose your boss is the typical stricter among the lot, but this can merely be a chance factor that you're the only one chosen to survive him! bad luck though ;-))  
So, One of the very precautionary thing here, is that the Chance Factor needs to be ruled out in order to have a balanced perspective towards this world.

•Now for avoiding these chance factors,  probability of chance occurrence of the observed results need to be examined.

This can be done by examining :
1) Null Hypothesis
2) Alternative Hypothesis

Null hypothesis is that we assume that the two samples (with or without having chance factor) came from the same population.

While, Alternative hypothesis is counter proposition to Null hypothesis; which assumes that the two samples belong to two different populations.

•Now, in these..the alternative hypothesis is not directly tested, rather its acceptance or rejection is determined by the rejection or retention of the other one. (The Null Hypothesis)
And all this acceptance & Rejection game is mostly played in the dimensions of probability.
-If the probability value of our assumption being correct is quite high, & observed results are not significant. NULL HYPOTHESIS IS ACCEPTED. Or otherwise REJECTED.

P.S.- I've taken my best efforts to blend  layman understanding with statistical approach. Even then, if it fails to strike  the chords of your brain wires, I'd suggest you to reread later.
May the incubation effect work!