The younger Twin

Thanks to Amrita for asking this question about Twin Paradox. It was a thoughtful question, and the right questions at right time can lead to Big progress and good understanding. I have quoted below this dialog as it is. It reminds me of one story from Puranas, which indicates that the superfast(close to c) time travel could have been possible earlier.

The story goes like this:-

There was a King and he had a pretty daughter. He couldn't find a suitable groom for his pretty daughter, and so he set himself and her on a travel to Brahmaloka. When he reached Brahmaloka, Brahma gave him blessing and asked him to marry her to the King of a certain country on Earth. Happy, the King traveled back to the Earth with his daughter. Coming to the earth, he was so surprised that his city, his buildings and people were not there at all. In his City, he himself and all the human beings were as tall as a coconut tree. And he was shocked to see the human beings in the size of 5-6 feet, so small compared to him and her daughter. Upon inquiry, the King got to know that their civilization used to exist several thousand centuries ago! Though the King and his daughter had only aged by an year or so, the time had elapsed much faster on the earth. The King got his daughter married to a noble Prince and they lived happily ever after.

Conclusion:- the King and his daughter had traveled very fast, and Brahma loka could have been a really far away place!

Thanks

Amrita said...

Hi,I was reading theory of relativity and found that "Time Dilation is a reciprocal effect",if it is so then why in case of twin paradox,one of the twins who goes to the space and come back, remains younger than the other who stays back on the earth!

November 23, 2009 10:41 PM

Abhay Karnataki said...

good question.
now here we have to understand that though there is no single absolute inertial frame for all observers, you can definitely make out if your frame is inertial or not.
if you are in a car and close your eyes, then even when the car turns, your body bends to one side or other, showing the acceleration, and hence non-inertial nature of the frame attached to the car.
Similarly, in the twin brothers travel, one brother is definitely getting accelerated at the end of the journey, and he is the one who comes out to be younger. the brother in his rest frame doesn't experience any acceleration at any time.
if the other brother would not have returned any time, then the time dilation is exactly reciprocal.

November 23, 2009 10:47 PM

Newton's laws of motion

The Newton's first law of motion states ''A body continues to be in the state of rest or constant motion unless it is acted upon by an external agency.''

The Newton's second law states "The acceleration of a particle is directly proportional to the external force applied on it and inversely proportional to the mass of the particle."

The Question that should naturally arise in a student's mind is, if F=0, what is the need to state the first law separately, because it can be deduced from second law that a=0 and hence velocity is constant. So is the first law necessary!?

Ans:-

The measurement of distances and time are done in a reference frame. The first law of motion defines a reference frame where the motion doesn't change unless and otherwise acted upon by an external agency. e.g. you could be in a car that's going along a hillside region of ups and downs and turns. In a reference frame attached to the car, a particle within the car will not remain stationary or in constant motion. So in such a reference frame, the first law is not applicable, and such frame is ruled out in the Newton's scheme of study of dynamics directly. But you could choose a frame fixed to earth say, in which the first law will hold, even if Car moves around. Such a frame where first law holds, is called inertial frame of reference- inertia of a body is maintained. Now again, a frame attached to earth is not infinitely inertial frame of reference, as the earth itself rotates and revolves. for a trajectory of a plane e.g., Earth's frame becomes non-inertial. So you can use a bigger frame at rest w.r.t Sun. But then even it is non-inertial, when you discuss motion of comets, as the Sun moves in the galaxy... So use even bigger frame at the center of galaxy... and finally even bigger in the outer space in between galaxies and galaxy clusters, so that first law is valid in that reference frame.

Either you can keep changing a reference standard for inertial frame, or you can say that so and so part of the space is a good ''local'' inertial reference frame, observed for a so and so interval of time, over which the first law is valid.

In such an inertial frame, second law can be used to calculate the acceleration 'a'.

Mysteries in Sound Phenomena

One friend asked, why in the place that is an empty square covered at a sixth floor ceiling and surrounded by classrooms in a college, echos a lot? 

After some discussions, we came to a simple conclusion: they had used that place after college hours, when there is absolutely no-one in the college. During the day-time, when it is flooded with students, it doesn't echo at all! The absence of students here, is giving rise to a lack of any absorbing medium for the sound energy, and it finds it easy to bounce back and forth. This effect can be seen in any empty place, flat, hall, most famous being the hilltops, as the sound seems to come back from distant hills.

Our staircase has hollow pipes as hand railings. I was having fun striking the metal with my metal keys, and it would create quite a sound! I checked striking on different sized pipes, and the sound is so very different! When the metals being stroked the same, why did the sound differ?

The energy of the stroke gives rise to an impulse of vibration in the solid of the pipe. This impulse is a superposition of a huge number of frequencies. These all frequencies get transmitted to the air within the pipe. Due to the size of the pipe, the back and forth oscillations are sustained only at the natural frequencies of that length and radius of the pipe. So the standing waves are dependent on the radius of the pipe, thus giving different sound in different sized pipes.

Friction - Evil or God !

Everywhere you see, one is attempting to reduce Friction. E.g. the lubricating oils in ball bearings, door hinges. However, have you thought about what would happen if there was no Friction!
Without Friction, you can't even walk on the floor! That's what happens, in rain, if the floor is slippery, you tend to fall down. Why, because the Friction has got reduced. Its a strange thing that the force of Friction, which opposes every motion, is actually supporting the entire mechanism of motion!
Let's say you want to walk. Now suppose you were in Space, then unless someone gave you a push, you wouldn't move from where you are! So when you walk, what you do is you push back on the ground. The only way you can push something is when you have some grip over it. That's Friction. Without Friction, when you attempt to walk, you will actually roll over and fall!
When a wheel moves on the floor, three things can happen: It can slide like a sledge- this happens when your wheels are break locked and there is no rotation of wheel, or It can rotate without any translation, as it happens when a wheel is stuck in a ditch of mud, and any amount of acceleration only gives it rotation, no translation. Third thing which is expected, normal behaviour, is rotation and translation. This can happen only when there is adequate Friction.
What is Friction. On a microscopic level, the smooth looking surface is not a regular plane. There are hills and valleys at atomic level. Whenever two surfaces meet, they form temporary contacts, and molecules of one surface invade in hills and valleys of other surface. They interlock and push each other. So if a top surface is moving forward on a bottom surface, the bottom surface pushes the top one back, and the top surface pulls the bottom one forward.
This is easily seen in case of liquids. The analog of Friction is Viscocity. An Oil is more viscous than water and Honey is more viscous than Oil. In a mixer, when the blade rotates, it carries along with it the layer of liquid next to it, and that layer drags the next layer with it and so on, the subsequent liquids are set in motion. Had there been no Viscocity, you wouldn't be able to stir your coffee!

Stability of Vehicles

You think you do a big job when you are balancing a 2 wheeler while driving it? You hardly do anything! A major role is played by rotating wheel. To see why, just imagine yourself balancing the 2 wheeler that is stationary, for as long as you generally drive! Balancing a stationary 2 wheeler is tough. Do it with cycle, you will have to do some good amount of acrobatics!

Why would a rotating wheel be more stable? What is fall of a bike? Its essentially tilt that doesn't reverse, and continues till it touches the ground. A rotating wheel, when tilted, actually turns - that's how you take turns - rather than falling by side.

A complex mechanics equation and formulae and vectors show why this is necessary. To get a simple idea, think of it this way:- a sledge moving on ice has a tendency to move in the same direction. If you apply sideways force, the direction of motion will be very slightly changed to that side, while it continues to move in more or less same direction.

In case of rotating wheel, it has a tendency to continue to rotate around the same axis - say the axle of wheeel - unless you tilt it. When it is falling, it just shifts the direction of axle - like the small direction change in sledge motion - and continues to rotate around this new axis.

When a wheel tends to fall, instead of falling sideways and continuing to move in the same direction, it will change the direction of travel, and spiral towards fall. This is easily seen by anyone playing with a cycle wheel and pushing it by hitting at back. The wheel will roll on, and depending on which side it bends, it will spiral in that side and fall. What it doesn't do, is to go in straight direction and fall sideways!

Spinning top also shows the similar stability. It can balance itself on a needle end. It will keep balancing and rotating and once friction eats up the energy, it falls down spiralling.
It also shows another behaviour, when, after throwing it may not have landed vertically, and slight tilt causes its rotation axis to go in circle around the vertical axis. Notice that even though its tilted, because its rotating, it goes in circles, rather than falling down. A stationary top will simply fall down. This is called as Precession.

The larger the speed, more the stability. Of course, more speed invites other dangers.Also, this means that falling sideways is much easier on smaller speeds and sharper curves. So be careful!

One hour day and Half hour night

I always feel grateful for being in a Research Institute. Its this sheer opportunity to meet some of the most brilliant people on the planet. Today we had a talk by the Astronaut Claude Nicollier, "My experience in Space".He showed some amazing pictures of the earth from space, it was simply fantastic to see the entire Himalayas in one picture. Also, the distribution of river Ganga where it meets the ocean.
It was also an absolutely stunning picture to see that on top of one of the desserts, the cloud coverage is exactly on top of the sea, and it ends on the coastline.

Absolutely passionate about his work, he mentioned how he had undergone rigorous training in water chambers. Their first mission was repair of the Hubble Space Telescope. Imagine changing parts of a huge (2 meter diameter) telescope in space! In those water chambers, they make exact replica, with high fidelity modelling, of the space telescope. In space you need to stabilize your body, and move very slowly. They practised it for months before the mission, in the water chambers. Exact and detailed planning, even practise of handling unexpected failures and problems.

When you are in space, you are in a very low air pressure surrounding. Say 1/3rd of that on earth. So the nitrogen tends to get into the blood. There are Air Chambers, where you increase the air pressure to normal ones on the earth, and rejuvenate yourself. Claustrophobia is the fear of enclosed spaces. If you have it, then these small Air chambers are not meant for you! Also the Astronaut's suit can be very cumbersome to get into and carry along.

You can see here a photo of a pair of astronauts repairing the Hubble Space Telescope. Notice that one astronaut has firmly grounded his feet on the robot arm of the space ship,(you don't see the spaceship, the arm is the white rod like thing in the photo), and other Astronaut is freely floating. Whenever the Astronauts are doing such work, doing space walk, they are attached to the space-craft by a thread: they are tethered. This is to ensure that they don't just get lost in space by mistake! As he jokingly said, if an astronaut or a repair tool is lost, it becomes a useless satellite to Earth! So all the repair tools and parts are also tethered to the spaceship.

As you are orbiting, you have sunrise and sunset more often! You get 1 hour of a day and 1/2 hour of a night! Of course, you don't go to sleep in that night when you are in shadow of the earth. So you need to get used to this kind of bright and dark timings. Before the Earth becomes totally dark, and Sun goes behind it, you can see a beautiful cresent of the Earth! The moon also rises and sets quite fast. The sky is absolutely dark, and you can see Sun also as just another, closer, brighter and bigger star.

On Earth, our body has mechanisms to push lot of blood supply to the head. So much supply is not needed when you are in space. Lot of body fluid imbalance and loss of orientation can happen when you just reach the space. So if you are planning to visit and go for a space ride, be prepared for some phisiological unpleasantness! He said its like sea-sickness.

To become an astronaut, he said, you need good physical fitness, sound mental balance, and a sound educational background. After that, its a luck to be selected, as there is lot of competition and few jobs available!

A Physics Graduate, who did research in Astronomy, and took over Air Pilot job, and then worked as an Astronaut, Claude Nicollier is now full time professor in Lausanne, inspiring young students to the thrill of Space research.

Diwali crackers

I saw this cracker rocket in Diwali, I don't know how it could go zigzag, like a snake in the middle of the air. Can you figure that out.It also whistles.

Properties of light - 2

I almost can't show to you how my fan is rotating. Here is a photo of a rotating fan:
It looks stationary!
So I changed the setting on my camera from auto to night mode:
Night mode has lot of light gathering due to large aperture and longer exposure. So you see the blurred image, and because of flash reflection, you see the 3 pans too. Two bright lights are tubelights.
And when I put it on fireworks mode:
Its a very long exposure mode. Its more or less what my eye also sees. So what our eyes see and what a camera sees are different worlds! Here is a video of the same fan. Which way is it rotating?

In the video, it apears to rotate in the opposite way than in reality! This can be seen by switching off the fan:

!!! ??? So how come this illusion!!! ???
You may have taken photos like this one:
Now as a traveller, your eyes won't see such an image, wherever you look, you would see things pretty much clear only( Unless you are travelling in some super fast train!).

Whether eye or camera, each observing instrument has a characteristic exposure time, the time for which the instrument gathers light information, stores it, and then takes next information to process.
This also shows how versatile our eyes are! They are very powerful cameras!
The opposite motion of fan is due to the frequecy of camera capturing the frames of video. If it was a single pan rotating, the video would be different. It would maintain the same sense of rotation. Here, three pans replace each others' positions during the frame re-capture time, and it is done with a lag, so gives a sense of opposite motion than real.

The time taken by eye to take next frame is called Persistance of Vision. Long exposure photos often show nice slow motion, as people observe in motion of stars:

Of course, the stars appear to rotate because we are rotating!

Anytime the exposure is longer enough than the motion, we get a streak photo, as seen in the fireworks here:

Levitron

Here is a fantastic experiment demonstrating magnetism and angular momentum.