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Vakra Tund Maha Kaay Surya Koti Samahprabah
Nirvighnam Kurumaydeva Sarvkarya Shu Sarvada

Vakra	Bent
Tund	Elephant’s Trunk. Vakra Tund is the name given to Ganesha as most of his portraits and pictures have his trunk in bent form.
Maha	Big. Huge. Greater. More than regular.
Kaaya	Form. Thus, Maha Kaaya means one of large or huge form. Ganesha is often shown to be heavier and pot-bellied as compared to other Devas and Gods who are shown to have excellent human form.
Surya	Sun
Koti	Many. Nowadays, it is equated to ‘million’. Often people say, ‘koti koti pranaam’ (many many salutes) to ones they respect a lot.
Samah	With
Prabah	Prabah is brilliant like sun’s shine. Sun is also called Prabhat at times.
Nir	A negation
Vighnam	Obstacle. So, Nir Vighnam is removal of obstacles.
Kuru	Do
May	My
Deva	Devta, divine being, highly revered one
Sarv	All
Karya	Actions, work, jobs
Su	-
Sarvada	Always

Sanskrit does not map into English. Nor the words or the sentence formation. It is always recommended to learn Sanskrit or at least Hindi to understand the mantras.

As is typical, the first line addresses the deity/devi/deva the mantra is addressed to. It usually takes form a praise describing some aspect of the deity that the mantra’s composition is based on. Here the focus is on Ganesha’s Maha Kaaya which denotes well-being, sufficiency, wealth, have more of and goodness in abundance.

Here is an attempt to translate it using words explained above:
Bent-trunk one, huge form one, one who shines like a million suns; remove obstacles my deva always in all tasks I do.

Om Bhurbhuvaha Swaha Tat Savitur Varayneyum
Bhargo Devasya Dhimahi Dhi Yo Naha Prachodayat

Mantra, grammatically refer to as meter. English poem readers would know of common meters like a couple or triplets. Urdu Shayari readers would also know that most of the compositions are also couplets. Similarly, Gayatri is also a meter used often in Vedas. That is what “Gayatri Mantra” means, grammatically. The actual mantra (composition) that we usually refer to when we say Gayatri Mantra is, to be more accurate, a Surya Gayatri Mantra from Rig Veda. Thus, it is a Mantra, written in Gayatri meter, dedicated to Surya Dev from the Rig Veda.

Om	Om
Bhur	Bhu is land, earth. When combined with Bhuvaha, Bhu becomes Bhur
Bhuvaha	Air, atmosphere
Swaha	Beyond the atmosphere. Antariksha, universe, cosmos
Tat	Tat is sanskrit for pronoun ‘that’. Tat is the pronoun used by Hindus to refer to what is often refered to as God.
Savitur	Sun. When Savitur is used to refer to Sun, it is not the star called Sun. In that case word Surya is used. Savitur referes to the divine or spiritual Sun that shines with knowledge. It is that divine form of Sun that is the light of wisdom.
Varayneyum	That what is worth Varan. Vanan means to mention. Talk about. Discuss. Adore. Talk with respect. Chant, Repeat. Describe
Bhargo	illumination
Devasya	Dev like. Divine.
Dhimahi	to contemplate. we contemplate
Dhiyo	derived from Dhi is intellect, knowledge, deep learning
Yo	who
Naha	ours
Prachodayat	request, urge, lead, inspire

Sanskrit does not map into English. Nor the words or the sentence formation. It is always recommended to learn Sanskrit or at least Hindi to understand the mantras. Here is an attempt to translate it using words explained above:

We meditate about Om, Bhu, Bhuvaha and Swaha
About ‘Tat’
On Savitur’s divine illumination
Who is Varayneyum
May/to Prachodayat our Dhiyo

The Rig Veda (10:16:3)

Why this essay

Simplification, unless done carefully, is same is distortion. The over-simplified, “Diwali is celebration of the victory of the Good over the Evil”, is not only a distortion, but a misleading statement. It actually is exactly what Diwali is not about. Diwali is the celebration of the victory of the right action over the wrong action.

Most of us know the background, the subtle assertions and philosophy. So, the over simplified statement looks like an agreeable statement. But for the aliterate and many non-Hindus, it creates a wrong impression of how things are to be understood. Hence, this essay.

About Ravana and the War

Also, called Deepawali, the festival of Diwali started off from the Ramayana.

Ravana (or Ravan) was the king of Lanka (Some scholars disagree that the Lanka in Ramayana is same as today’s Sri Lanka. But some claim it to be so. Unfortunately, there has not been any extensive study, aiming at finding any information on this subject). He propounded a life of materialism. The kingdom was prosperous, well defended and did not have many enemies.

He was also a very learned and accomplished person. He was great devotee of Lord Shiva, and had obtained many boons He was well versed in Vedas, and other scriptures. He used to worship Lord Shiva daily. His bravery, courage, administrative abilities and expertise in weaponry was admired by all. He had great skills in using Mayawi-Shakti (that let him fly in the air, become invisible, create rains of water or fire, etc).

Then what went wrong!

Driven by excess of selfishness, egoism and pride (which he promoted all over his kingdom too), he kidnaps Devi Sita, wife of Bhagwan Ram.

That brings Ram and his allies to Ravana’s kingdom. Before the war ensues, Ram offers a peaceful alternative. If Sita was returned immediately, the kingdom would not have to face a war and pay for Ravana’s mistakes.

But Ravana, having committed a mistake, opts not to rectify the situation. He refuses the offer. The war starts.

Ultimately, on the Dusshera day, Ravana dies and Devi Sita is rescued. It is on the day of Diwali, that on the end of the exile, Bhagwan Ram and Devi Sita return to their home in Ayodhya. That is why the lights, festivities and sweets.

The Lessons and the Morals

Whenever the story of Ramayana is told, the accomplishments of Ravana are stressed upon. Also, stressed upon is the fact that when he is about to die, Bhagwan Ram asks his younger brother, Laxman to learn as much as he can from Ravana. All this to emphasise the fact that Ravana was a very learned person. And to emphasise the fact, that no one is immune to making mistakes.

That is the most important lesson that is passed on every year during Dusshera and Diwali.

While Ravana implemented his knowledge of administration well, he did not implement his knowledge of right action when, driven by ego and pride, he kidnapped Devi Sita. Mere possessing knowledge does not guarantee good actions. That knowledge has to be implemented well.

There is no Good or Evil. A person is as good or as bad as that each action he or she performs. It is the action that have good or bad effects.

We are all prone to make mistakes. Even a very learned person, unless careful, can make a mistake that will lead to bad result. Once committed, by not rectifying it, commit another action that has bad effect. By kidnapping Devi Sita, Ravana brought war to the gates of his prosperous kingdom. By not taking the peaceful offer, he refused to rectify his mistake, bring war and end to his kingdom and family.

Hindus burn the effigy of Ravana on Dusshera every year. If Ram killed Ravana, then why do we have to burn the effigy every year? The answer is simple. To remind us that we can make the same mistakes and pay for them. And unless we act on not to commit them or to rectify them, we will become like Ravana and face end in hands of someone like Bhagwan Ram. That is the lesson of Ramayana that is still relevant today.

The lesson of Diwali is same as it ever was and has not changed. Those who always choose to act right and rectify their mistakes, prevail.

Diwali is the celebration of the victory of the right action over the wrong action.

Another Over-simplification

In order to explain Diwali, I have read and heard people say, “Diwali is like Christmas”, or something like that.

Unless you are specifying that the comparison is just in term of desire to celebrate and share celebratory mood, there are no apparent similarities. Actually, it is Diwali celebration that is like Christmas celebration. For Hindus, Diwali is one of the many festivals that teach a lesson and have some cultural significance gelled in.

And not all Hindus celebrate Diwali is same manner, that is if they celebrate it. The dates are definitely auspicious and festivals like Onam and Durga pooja coincide with the period.

One-liners for the Impatient

There is no Good or Evil.

A person is as good or as bad as that each action he or she performs.

Diwali is the celebration of the victory of the right action over the wrong action.

Diwali celebration is just like Christmas celebration.

Asato Ma Satgamaya Tamaso Ma Jyotirgamaya Mrityor Ma Amritamgamaya

from untruth lead us to truth from darkness lead us to enlightenment from death lead us to immortality

Why this essay

I have been asked many times that being a Hindu, if I meditate and if I do, then how. Though not regularly, I do meditate and it seems like a good idea to share my thoughts on it with people. This article is part of my attempt to share and hence understand the meaning of being Hindu.

Introduction

We take in the physical elements of the environment into our body in two ways.

One way is in the form of food. We eat to nourish ourselves. The food we eat, the time which we eat our food at and the quantity we eat out food directly affects our body. The act of eating is a conscious effort and its effects are very much apparent. One can say that this intake belongs to the conscious realm. That this intake belongs to the physical realm. That this intake belongs to the materialistic realm.

The second way is in the form of breath. Unlike eating, breathing is not a conscious effort. We breathe even when we are sleeping or working diligently on something that has our mind and body engrossed. One can say that this intake belongs to the unconscious realm. That this intake belongs to the mental realm. That this intake belongs to the spiritual realm.

To understand breathing is the first step in understanding meditation.

Just like understanding food products and habits is a way to good eating habits so we stay physically fit, understand breathing is the way to proper meditation so we stay mentally and spiritual fit.

Places, Postures and Period

Now we realise the importance of breathing in meditation, we can move to the next set of issues. First is where to meditate, the second is, what posture to meditate in and the third is, for how long to meditate.

Broadly speaking, you can meditate anywhere. Once you have understood the philosophy and method of meditation you want to follow, the places where you won’t be able to meditate will be clear to you. It would be hard to meditate in a smoke filled room, noisy environments, etc. (Though once you have had a lot of practice, all this may not really matter.)

Broadly speaking, you can meditate any posture. Choose one that is comfortable and one that facilitates breathing with ease. A straight spine helps keep rib cage free of any undue pressure and hence facilitate breathing.

Broadly speaking, you can meditate as long as you want. You should try to meditate till you feel relaxed. After meditating a number of times, you will recognize that point in your state of mind where you would feel yourself to be in a meditative state. Try to get there often and if possible, stay there as long as possible.

Also, it is a very good idea to follow the tradition. The sages who gave us concepts of meditation also gave us suggestions on postures and places.

A well ventilated place, a religious place or an open place if good for meditation. Also, places close to nature like a park, lakeside or a forest are a good idea. Sit cross-legged, keeping your spine straight and with hands in your lap or on your knees. Palms can be facing up or down as whatever you feel comfortable then.

Or you can strictly follow some Yoga Aasan recommended for meditation.

So Hum

‘So Hum’ is a chant from the Vedas. Translating from Sanskrit, ‘That is me’, ‘So Hum’ is supposed to be the simplest chant that all living being chant. The sound of incoming breath is that of ‘So’ and the sound of outgoing breath is ‘Hum’.

Meditating

Close your eyes.

Pay attention to you breathing. Watch it and follow it. Monitor it as you breathe in and breathe out. Do not force a breathing pattern. You breathing pattern will keep changing. Throughout, keep paying attention to your breathing. The intake, the pause, the outgo and the pause. Just be a witness to this unconscious activity.

Hear and feel your breath make gentle sounds. Watch your breath with a ‘So Hum’ in your mind. ‘Soooo’ as you breath in and ‘Hummmm’ as you breathe out.

Do not force or control thoughts that come to you. If any of them grab your attention, the moment you realize this, move you attention back to breathing. Thought will keep coming to you. Don’t resist them. Just keep going back to ‘So Hum’ and pay attention to the breathing.

A Beginning

There are as many ways to meditate, as there are people willing to meditate. Once you understand the philosophy and disciple behind this concept, your own self can be your guru.

Meditation is relaxing. It is way to understand yourself, the world around you and beyond. It is a simple beginning to a long journey.

Introduction

Dharma broadly refers to a universal value system. The word ‘dharma’ is derived from ‘dhr’, which means support or to sustain. Thus the meaning of the word is – that which supports. However, with time and after much evolution of this system, it now conveys a sense of duty and responsibility, which is based on virtues.

The concept of dharma comes to us from various Dharamasastras that were written by many sages at different times. Hindus do not consider these Sastras as the final and binding word on ones dharma. In fact, as these Sastras were written over a long period, each one builds on the previous ones or elaborates on one aspect of dharma or the other. These sages have always held that the society is always free to accept, modify or reject their views, which the Hindus have!

Dharma has three broad aspects:

• Aacara
• Vyavahara
• Prayaschitta

Aacara

Aacara talks about the cleanliness and purity of both body and mind in physical manner and in ceremonial manner. Without abiding by this dharma, one cannot attain abhyudaya (worldly progress) or nissreyasa (spiritual wellbeing).

Thus, there are two kinds of aacaras: sad-acara (good conduct) and dur-acara (bad conduct).

The sad-acara includes the sat-karmas (six daily rituals). These are:

• Snana & Sandhya (bath and Morning Rituals)
• Japa (chanting or repetition of Mantras or name of God)
• Homa (making offering to sacred fire)
• Devapuja (worshiping gods)
• Aatithya (taking care of the guests)
• Vaisvadeva (offering food cooked to gods)

The sad-acara also includes sodasa-samskaras (sixteen sacraments during ones life). The important ones are:

• Upanayana (the sacred thread ceremony or the yajnopavita during with the gayatri Mantra is imparted)
• Vivaha (marriage)
• Antyeshti (cremation and other rituals)

The sad-acara also includes living ones life in accordance to the varna-ashrama-dharma. The four ashrams are:

• Brahmacharya (studentship, spiritual disciplines maintaining chastity with all focus on gathering knowledge)
• Grihastha (married state of a householder)
• Vanaprastha (retirement and living with detachment as an anchorite with or without the spouse in a secluded place or ‘forest’)
• Sannyasa (renunciate living alone as a monk or nun)

The varna aspects differs as per our position, place and use in the society. Each person who belongs to one varna or the other has to abide by the duties. As a computer programmer, it is my dharma to deliver my output in accordance to expectations in terms of time, efficiency and quality!

Another Sad-acara is Tarpana. The symbolic or ceremonial offering of water with appropriate mantra to devas (gods), rishis (sages) and pitrs (souls of the ones who have died).

Vyavahara

Vyavahara refers to ones conduct. In some Dharamasastras, there is more of legal discussion on this, laying out civil and criminal laws to define ones vyavahara. There are around eighteen aspects:

• Rinadana (debts)
• Sambhuya-samutthana (partnership)
• Samvid-vyatikarma (breach of promise or contract)
• Kraya-vikraya (purchase and sale)
• Svami-pala-vivada (dispute between employer and employee)
• Simavivada (boundary disputes)
• Dandaparusya (assault)
• Vakarusya (libel)
• Steya (theft)
• Strisangrahana (abduction of women)
• Stripumdharma (relation between husband and wife)
• Vibhaga (partition)

Prayaschitta

Humans will always make mistakes. Nevertheless, one has to remedy and reform. This means one has to repent, resolve not to repeat the mistake and under go penance to get over the guilt and guilty feeling.

Thus, if one commits a paapa (sin) one has to commit prayaschitta (expiation or penance to get over the guilt and guilty feeling).

The prayaschitta depends on the paapa. The paapas are categorized into two:

• Mahapatakas
• Upapatakas

Mahapatakas include brahmahatya (killing a person of knowledge – bhramana), surapana (drinking wine and other intoxicating liquids – and given the advent modern times and a hindus right to modify specifics for oneself, I add smoking and taking intoxicating and mind/mood altering drugs to this) and incest.

Upapatakas include forsaking sacred fire, offending ones Guru (Vedic teacher, mentor), thefts, nonpayment of debts, selling prohibited articles, cutting down trees or killing harmless animals.

Prayaschitta include tapas (austerities) like fasting, japa) chanting or repetition of Mantras or name of God), daana (giving away gifts, charity or donations), pilgrimage, etc.

The philosophy in brief

The Dharamasastras recognize the importance of physical wellbeing. Our health, strength and energy are important for any achievement in life. Thus, they advise us to stay in best of health.

Equal importance is given to cultivations of values. These values include samanya-dharma (universal principles), self-control, decent and dignified behaviour to men and women, honesty, earn livelihood in right way, performing ones duty at work, to the family and the society, not harm others, keep environment clean and not abuse nature, study and listen to works of sages, austerity and work towards self-realization.

List of Dharamasastras

Some of these texts are believed to be as old as 450-300 BCE and as latest as 1600 AD. Here is a list of some:

Dharmasutras

• Apastamba
• Ausanasa
• Baudhayana
• Gautama
• Harita
• Hiranyakesi
• Vaikhanasa
• Vasistha
• Vishnu

Smritis

• Angirasa
• Atri
• Brahaspati
• Brhat-Parasara
• Daksha
• Devala
• Gobhila
• Katyayana
• Manu
• Narada
• Parasara
• Samvarta
• Vyasa
• Yajnavalkya
• Yama

Nibandhas

• Caturvargacintamani
• Kalpataru
• Nirnayasindhu
• Smrticandrika
• Smrtikaustubha
• Smrtiratnakara
• Smrtitattva
• Viramitrodaya

We perceive world in 4 dimensions. Three dimensions in space and one in time. So, do more dimensions exist in space?

Flatland

There is an amazing book by this name. Here are some thoughts from it.

Suppose you and I live on a flat table. We are flat organisms that can only perceive 2-D. Front, back, left and right were the only directions we knew. Now, if I am in front of you I will just see a line. If I have to get past you, I will slip and slide past you. Imagine if some one said we had a third dimension of height, how blind would be to that concept! Say someone picked me up and placed on you other side, it would be nothing less than a miracle for you. I disappeared in front of your eyes and appeared at another place out of no where as I can see you leave the surface of our flat table and move above me and land on the other side. Well, in mythology we hear about people having such powers. In real science?

Cubeland

Suppose we extended the flatland to one more dimension. Now imagine we were 3-D organisms. We would be pinned to a 3-D membrane. And someone picked me and moved me through the 4th dimension and place on you other side? A miracle!?

Dijets and Monojets

In a dijet event two quarks scattering off each other inside detector of an accelerator. Now if we are able to detect just one of them, it is refereed to as a monojet. If detected in a detector of any accelerator, a monojet would seem to violate the conservation of momentum. But, a dijet could look like a monojet if one of the pair escapes detection. A very simple reason.

But there are doubts it could be this reason.

To Extra-Dimension and Back

Here’s a case in point: the monojet – a single quark or gluon spotted in a particle detector, appearing to recoil against nothing. Could it be recoiling against another quark, which is in another dimension?

Proof by Elimination

At an experiment in Fermilab called DZero, a recent result from detector tells us we haven’t yet reached that last place to look- but we have trimmed the list. Although experiments have not seen extra dimensions, they were able to set rather strict limits on their size.

They are also looking for the effects of extra dimensions in collisions that produce different types of particles, such as quarks. They are also looking for events where gravitons are produced in the collisions and then leave our three-dimensional world, traveling off into one of the other dimensions. This would cause an apparent non-conservation of energy from the point of view of our three dimensional world.

Stuff We are Made Of

We are made of stars. Stars and we are made of same basic matter. But stars and we are all only ~20% of matter that is in universe. What about the rest 80%?

The rest 80% is what we refer to as the dark matter (Note: Dark matter has _nothing_ to do with black holes).

If we could see dark matter, it should seems to us that universe is made of huge skein/mess of dark matter with stars shining brightly at various spots where the mesh strands cross each other.

Believing Your Eyes Only

Now if you can’t see the dark matter, how do we know that it exists? Simple, by the phenomenon of gravitations lens. I have mentioned gravitational lens before. But I will re-visit.

Gravitational Lens

Huge massed body’s gravity bend light. That is the basis of the gravitational lens we observe in space. A picture from Hubble was a good example. In the picture observers saw small-lighted spots along the edges of a cluster of galaxies. Soon they realized that these spots were galaxies behind the cluster of galaxies. The cluster of galaxies was acting like a gravitational lens and squashing the light from behind into a smaller area.

So Where is the Dark Matter?

They tried to calculate the mass of matter needed to make such a powerful gravitational lens and then calculated the mass of the galaxies in that cluster and there was a HUGE difference. When they accounted to the dark matter ratio, the scores settled perfectly.

Is There Dark Matter in Earth’s Vicinity?

No and a yes. Depending on what we refer to as vicinity. Close to our solar system we do not have any. But given the huge size of universe, there is dark matter all around us and close to us in that proportion.

Red-Shift

We know due to Doppler’s effect we see a red-shift in color of a star moving away from us.

To Catch a Wobbling Star

Now consider a star that has only one planet revolving around it. As the planet revolves, it also moves the sun under influence of it gravity. Though very small effect, it does cause the star to wobble a bit in its position.

Modern day astronomy has become so accurate, that we can measure the minute difference in red-shift that can be caused by this wobbling. To the extent that we can measure the red-shift effect even in a walking star (walking speed is 4-5 km/hr).

And this is what astronomers are using to find stars that have planets.

Binary Stars

Binary stars are a pair of stars revolving around each other. Now, a star that has a binary star will also wobble.

Twinkling Stars

So, how do we know that a wobble is due to a plant and not a star? Simple, use method called trans. Watch the light carefully. If a binary star is so aligned that when revolving, it will pass between the star and us, the intensity of light of the star increases. But if a planet passes in front of it, the intensity drops. However small the drop is, the accurate observation detects that drop and identifies that as a planet.

Flaring Sun

We know that sun has solar flares. So might an others star? So, how do we know that the drop in intensity is not due to a flare at lower temperature (and hence less bright than the star surface). Simple, solar flares will not be as periodic as the planet’s revolution. Also, the “exact” intensity shift due to a flare is known.

Testing the Theory

In few years, Venus will pass between earth and sun and observational astronomers will use the observed drop in intensity to confirm the value the use in these experiments.

Search for Earth-like planets

With this great tool in hand, they are now searching for earth like planet having a sun like stars. Once the find interesting planets, they will request time on Hubble to observe these planets.

Also check http://www.exoplanets.org/

The Color of Black Holes

Wait. I just mentioned previously that black holes have so much of gravity that light can not escape it. How come then a black hole have color? A hint. Event horizon. Black holes have no hair nor color. But event-horizon, the only observable part of black hole is a very colorful and alive.

Step in theories of Stephen Hawkins of evaporating black holes.

Evaporating Black-Holes

The black holes can evaporate. A black hole emits particles at the event horizon. This is based on the uncertainty principle which says that at any given point, we can never be sure of both energy or location of an atomic/sub-atomic particle. This defines there is always a “zone” where the probability of find that particle. Thus, a space is never stark empty. Any given piece of space is part of this “zone” for a close by particle.

The vacuum in quantum field theory is not really empty; it’s filled with virtual pairs of particles and antiparticles that pop in and out of existence, with lifetimes determined by the Heisenberg uncertainty principle. (less than h/E, where h is Planck’s constant and E the energy).

Sometimes one member of a pair crosses the horizon, and can no longer recombine with its partner. The partner can then escape to infinity, and since it carries off positive energy. The negative energy falls into black hole and the energy (and thus the mass) of the black hole decrease. To an observer the decrease will be exactly same as the the particle that got freed and will deduce that the particle was emitted by the black hole and it lost the equivalent mass/energy.

In quantum field theory, modes with positive frequencies correspond to particles, and those with negative frequencies correspond to antiparticles.

Note that this doesn’t work in the other direction – you can’t have the positive-energy particle cross the horizon and leaves the negative-energy particle stranded outside, since a negative-energy particle can’t continue to exist outside the horizon for a time longer than h/E. So what ever falls into black hole will only be negative energy part of the pair. So an observer will only see a steady stream of particles only.

So the black hole can lose energy to vacuum fluctuations, but it can’t gain energy. That means, there is continuous drain in black holes energy. This is the gradual erosion of a black hole. And one day, when it’s gravity is so low that it can not hold itself, it will explode in form of a burst of gamma ray showers.

The average life expectancy of a black hole is 10 billion years.

To understand the colors, let us plunge into the black hole.

Falling into Black Hole

Say there is a scout mission to go inside a black hole and report back as much as possible before crushing under it’s gravity.

The Mothership’s view: They will see the scout ship plunge into the black hole and it would seem to them to take forever.

As the ships reaches the event horizon, the reflected light (which helps us see) finds it harder and harder to get out. So objects that fall into a black hole appear from the outside to freeze in time at the moment they cross the event horizon.

As the light struggles to get out we will observe a red-shift. The scout will not vanish. But will fade from white to red till invisible light only makes it out and soon, when no light is able to come out as he falls at huge speed which is approaching c. If we could see a clock in the scout probe, the clock would appear to us to slow to a halt.

As the probe and other bodies are absorbed into black hole and they go red-shifting, we can see a the whole range of colors just above the even horizon. Black hole, will appear to very colorful indeed.

The Scout’s view: Remember, Einstein said, all laws of physics are same when the speed of light is approached. For the scout, every thing will appear normal. The light is crossing the event horizon so he will be able to see the mother ship till the gravity stretches it and flattens on the black hole.

General Relativity

Before we understand the Theory of General Relativity, let us understand some underlying concepts.

e=mc²

We all know this equation for energy mass conversion. That energy can be converted to mass and vice versa. But there is another great concept in this. The one that fascinated me the most. We always just notice the e and m. Let us look closely at c.

The equation said that the term c (speed of light) was a constant. In spite of all experimental data, Einstein was the first physicists to boldly state so. Let us understand the implications of this.

Say I am running at you with some speed. Now the ground I am running at you also starts moving towards you at some speed. So, my net speed has increased. Right? Right.

But if I were light, I would still be approaching you at same constant speed.

The idea that anything can have constant speed is contrary to our common-sense. We know speed and motion are relative.

But, even if the source of light was a star moving at amazing speed away from us, and another at amazing speed moving towards us or just another candle in the wind, the speed of light would always remain the same.

Another aspect. Say I am throw a stone at you faster than speed of light (well, can it travel so fast is another interesting topic), the speed of light remaining same, we will see the stone arrive after the stone actually has.

Analogous like we see the thunder first and hear it later. Only in this case, when the stone hits you, it would literally hit you before you ever saw it coming.

Establishing Relation Between Gravity and Acceleration

Let us consider two elevators: one at rest on the ground on the Earth and another, far out in space away from any gravitational pull accelerating upward with an acceleration equal to that of one Earth gravity (9.8 meters/second2).

If a ball is dropped in the elevator at rest on the Earth, it will accelerate toward the floor with an acceleration of 9.8 meters/second2. A ball released in the upward accelerating elevator far out in space will also accelerate toward the floor at 9.8 meters/second2.

Einstein used this to formulate the equivalence principle. “There is no experiment a person could conduct in a small volume of space that would distinguish between a gravitational field and an equivalent uniform acceleration.”

Hence, you can not distinguish between being weightless far out in space and being in free-fall in a gravitational field.

The Elevator Experiment

Suppose I am going up in an elevator somewhere in space in a space-ship at little less than speed of light. There is a hole on right side of the elevator from which a ray of light enters. As it crosses the elevator and falls on the other side, the elevator had moved up. So, I will see the ray of light bend downwards and hit the spot little lower on the other side. It may seem to be that the light is bending.

If it is going up at constant velocity, the ray of light will fall at an angle in straight line to a point lower than where it fell when the elevator was at rest.

If it is accelerating upwards, the light will appear to bend down in a curve.

Applying Equivalence Principle to the Elevator Experiment

Applying  Equivalence Principle we had deduced that what seems to be effect of gravity can be seen as effect of acceleration too.

Applying it here, what seems to be effect of acceleration can be seen as effect of gravity too.

Gravity And Space-Time

Suppose I am going up in an elevator somewhere in space in a space-ship at little less than speed of light. There is a hole on right side of the elevator from which a ray of light enters. As it crosses the elevator and falls on the other side, the elevator had moved up. So, I will see the ray of light bend downwards and hit the spot little lower on the other side. It may seem to be that the light is bending.

Now we know that earth’s gravity is acceleration. By same analogy, when I am going up on elevator, the acceleration is analogous to the gravity. So the gravity of elevator’s base is bending the light.

So by same reasoning Einstein said, a beam of light moving close to a large object like planet, will be bent by it’s gravity.

With this he changed the way we define and understand gravity. And he went ahead than that. He explained why we felt the “force” of gravity.

Imagine a large trampoline. Stretch it properly at a height. Put in a large ball in it and it will bend in the middle. This is how Einstein explained large bodies curve space and time. So they bend the space around them altering the geometry of the space around them. This curved space-time is what he referred to as a space-time continuum.

Now if we put a small ball on the trampoline. It will roll towards the bigger ball. That is how Einstein said, large bodies exert the “force” of gravity. Expanding on this line of thought, if you roll the small ball at an angle, it will spiral down towards the big ball. That is why bodies have orbits.

Understanding Time Dilation

Time dilates when a body approaches the speed of light.

Say I am traveling in car that can travel nearly as the speed of light. And I have an atomic clock that is as accurate as they can be. You are standing outside the car with a clock which is in sync with my clock.

Now I travel at near speed of light for one sec by my watch. You will see me travel for more than one sec by your watch. And when we compared the clock, mine will be behind your.

It is not just time that slows down. All physical phenomenon do. Supposed we both light a cigar them burn 1 mm per second just as I start. When I stop after one second, it would have burned 1 mm. But when I stop, and we compare our cigars, yours’ would have burnt more than 1 mm.

So how much does time slow down? This is governed by the equation

T = T’ x Sqrt( 1 – (v/c)^2 )

i.e.: My time will be Time observed by you times square root of my velocity squared by speed of light squared.

Suppose, v = 0 (i.e.: my velocity is 0; I am at rest)
v/c = 0/c = 0
0^2 = 0
sqrt(0) = 0
T = T’

So as seconds are counted by our clock, they will remain in sync.

Suppose, now I travel at 1/3th the speed of light; i.e.: v = c/3;
v/c = 1/3
(1/3)^2 = 1/9
1 – 1/9 = 8/9
sqrt(8/9) = 0.942809041582063365867792482806465
Say you measured that I traveled for 1 sec (T’);
T = .9428

Thus, my atomic clock will tell me I have spent only .9428 seconds while you thought I had traveled 1 sec. The tile has slowed down for me, it has dilated!

Suppose, now I travel at the speed of light; i.e.: v = c;

v/c = 1
(1)^2 = 1
1 – 1 = 0
sqrt(0) = 0

Say you measured that I traveled for 1 sec (T’);

T = 0!!!!

Testing Time Dilation

Space shuttles and atomic clock have been used to test this theory and with a given range of error, the theory stands the experimental test.

Understanding Length Contraction

Similarly, the length of a body at rest (rest length) is always more than it’s length when in motion. It is governed by equation

L = L’ x sqrt( 1 – (v/c)^2 )

Where, L’ is the rest length

What Happens To Mass?

M = M’ / sqrt ( 1 – (v/c)^2 )

Hence, with increase in v, the mass of a body increases. A 100 kg body will have mass of 115.47 when traveling at half the speed of light.

Who is Lorentz?

Hendrik Antoon Lorentz was born at Arnhem, The Netherlands, on July 18, 1853. In 1878, he published an essay on the relation between the velocity of light in a medium and the density and composition thereof. The resulting formula, proposed almost simultaneously by the Danish physicist Lorenz, has become known as the Lorenz-Lorentz formula. These are the formulas I have used above to explain length contraction. His work was extended by Einstein with his paper on Theory of General and Special relativity.