If you ask someone to name a woman scientist, they will probably name Marie Curie. If you ask them to name another, most will not know what to say. And if you ask someone to name a woman mathematician, most people will not be able to name a single one. Why is that? Have there not been any woman mathematicians? Or have people not bothered to find about woman mathematicians. I think it is important for our children to know that there have been great woman mathematicians and scientists and that science, and more specifically mathematics is not just a province of men. In today’s VERITAS we will talk about a great woman mathematician who made huge contributions to physics and mathematics. Her work led to a new insight into the fundamental laws of Physics and resulted in major developments in modern physics. The name of this mathematician was Emmy Noether and this is what Einstein said of her: “Fraulein Noether was the most significant creative mathematical genius thus far produced since the higher education of women began.”

# Category Archives: Physics

# 100 years of General Relativity part 7: Gravitational Waves, a New Window to the Universe

Friends,

This is the seventh and last part of the VERITAS series on General Relativity. Just to remind our readers: We are doing this series on Einstein’s Theory of Relativity to celebrate the 100th Anniversary of General Theory of Relativity. If you have missed any of the first six parts, you can read them here:

https://unvarnishedveritas.wordpress.com/tag/100-years-of-general-relativity/

# 100 years of General Relativity part 6: Origin and Evolution of the Universe

This is the sixth part of the VERITAS series on General Relativity. Just to remind our readers: We are doing this series on Einstein’s Theory of Relativity to celebrate the 100th Anniversary of General Theory of Relativity. If you have missed any of the first five parts, you can read them here:

https://unvarnishedveritas.wordpress.com/tag/100-years-of-general-relativity/

In the previous parts we have studied the basic ideas behind special and general relativity. We have discussed how gravity bends space time and slows down time. We have also explored one of the most interesting and astonishing results of relativity: black holes. If you have not read the previous parts, I suggest you read them before reading this one.

In this article we will apply General Relativity to the biggest possible problem that can be thought of: the whole universe. We will understand the current theory of how the universe originated and how it evolved after that. We will also see how the universe will evolve into the future. We will also learn about dark energy and dark matter. But before we move further, think about the magnitude of what modern physics allows us to do: we, tiny creatures living on a small planet revolving around a small star in one corner of a medium sized galaxy( which contains over 100 billion stars) have developed the ability to ask and try to answer questions about the whole universe which contains billions of galaxies like our own!

Continue reading 100 years of General Relativity part 6: Origin and Evolution of the Universe

# 100 years of General Relativity Part 5: Black Holes

Friends,

This is the fifth part of the VERITAS series on General Relativity. Just to remind our readers: We are doing this series on Einstein’s Theory of Relativity to celebrate the 100th Anniversary of General Theory of Relativity. If you have missed any of the first four parts, you can read them here:

https://unvarnishedveritas.wordpress.com/tag/100-years-of-general-relativity/

In the previous parts we discussed the fundamental idea behind General Relativity- The Equivalence Principle and its consequences. We used the equivalence principle to show that light is bent by gravity. And then we reasoned that gravity bends space-time and that objects moving along this distorted space-time seem to be moving under the influence of a force. We also saw that gravity slows down time. If you have not read the previous parts, I suggest you read them before reading this one.

Continue reading 100 years of General Relativity Part 5: Black Holes

# 100 years of General Relativity Part 4: Gravity causes time to slow down

Friends,

This is the fourth part of the VERITAS series on General Relativity. Just to remind our readers: We are doing this series on Einstein’s Theory of Relativity to celebrate the 100th Anniversary of General Theory of Relativity. If you have missed any of the first three parts, you can read them here:

https://unvarnishedveritas.wordpress.com/tag/100-years-of-general-relativity/

In the previous part we discussed the fundamental idea behind General Relativity- The Equivalence Principle. We used the equivalence principle to show that light is bent by gravity. And then we reasoned that gravity bends space-time and that objects moving along this distorted space-time seem to be moving under the influence of a force. If you have not read that part( or the previous ones), I suggest you read them before reading this one.

In this episode of this VERITAS series we will show how gravity causes time to slow down. We will also consider a practical application of this phenomenon.

Continue reading 100 years of General Relativity Part 4: Gravity causes time to slow down

# 100 years of General Relativity Part 3: Gravity bends Space-Time

Friends,

This is the third part of the VERITAS series on General Relativity. Just to remind our readers: We are doing this series on Einstein’s Theory of Relativity to celebrate the 100th Anniversary of General Theory of Relativity. If you have missed any of the first two parts, you can read them here:

https://unvarnishedveritas.wordpress.com/tag/100-years-of-general-relativity/

In the previous part we reviewed the Special Theory of Relativity that Einstein proposed in 1905. That theory combined space and time into a single concept, space-time and showed us that time does not flow equally for every object in the universe- time is a relative concept and its flow can vary based on the observer’s frame of reference. We also learnt that if an observer finds that two observations are simultaneous, a different observer in a different reference frame may not find those events simultaneous. We also learnt about some amazing and fantastic consequences of Special Relativity- time dilation, length contraction, twin paradox etc. If you have not read the VERITAS on Special Relativity, I suggest you read it before you start reading this one.

Around 1907 Einstein started think about expanding Special Theory of Relativity to include non-inertial( accelerating) frames. As we have already discussed, Special Relativity only considered uniformly moving frames. In 1907 Einstein was still working as a clerk in the Swiss patent office. His 1905 papers had created quite a stir in the scientific community. But he was still unknown outside the scientific community.

Continue reading 100 years of General Relativity Part 3: Gravity bends Space-Time

# 100 years of General Relativity Part 2: Introduction to Special Relativity

Friends,

As you know, in this series we are celebrating 100th anniversary of General Theory of Relativity. This is the second part of this series. You can read the first part at : https://unvarnishedveritas.wordpress.com/

Before we discuss General Theory of Relativity, we need to understand the concepts of Special Theory of Relativity. In this VERITAS article, I will give you an introduction to the Special Theory of Relativity.

1905 was a very important year for Einstein and his scientific pursuits. Einstein turned 26 years old in March of that year. He was employed as a clerk in the Swiss patent office in Bern, he was already married and had two sons. His work at the Swiss patent office was neither creative nor did it involve much science. Einstein balanced his work in office, his family life and his real interest, Physics. Like today’s age, the greatest scientific breakthroughs in those days came from universities and laboratories. Einstein was far away from these institutions and was working completely alone( he did discuss his ideas with his friends but none of them were professional scientists). And he had limited access to scientific journals. But he still published 4 papers that year and each one of those papers was a breakthrough in the world of physics. The first of these papers explained the photoelectric effect and laid the foundations of quantum physics, the second paper dealt with Brownian motion, the third paper proposed the Special Theory of Relativity and in the fourth paper Einstein derived the most famous equation of Physics: E= mc^2. It is amazing that a 26 year old clerk could come up with 4 amazing ideas that would change the course of physics in a single year. This year( 1905) is often referred to as Einstein’s Annus Mirabilis ( Miracle year). If you want to read Einstein’s biography, I would recommend “Einstein: The Life and Times” by Ronald Clark and “Einstein: His life and Universe” by Walter Isaacson.

Continue reading 100 years of General Relativity Part 2: Introduction to Special Relativity

# 100 years of General Relativity Part 1 : Introduction

Friends,

Exactly a hundred years back, in November 1915, Albert Einstein published a paper that would change the way we look at the universe. He called this theory, “The General Theory of Relativity”. Ten years earlier Einstein had published the Special Theory of Relativity which for the first time combined space and time into a single inseparable “fabric” known as space-time. That was a revolution too but at a slightly smaller scale. The Special Theory applied only to objects moving at a uniform rate. The General Theory of Relativity included accelerating objects and explored the relationship between acceleration and gravity.

Continue reading 100 years of General Relativity Part 1 : Introduction

# Types of Black Holes

Friends,

We have all heard or read about black holes in popular science books/articles. The general idea is that a black hole is a region from which nothing, not even light can escape. And many of us know that black holes are formed when large stars reach the end of their lives.

The physics of Black Holes is very complex and vast. To understand black holes we require the knowledge of Einstein’s General Relativity. In this VERITAS I will just tell you about the various kinds of black holes and how these black holes are formed. But before I mention the kinds of black holes it is important to realize that anything can become a black hole if it is compressed to a high density. Every object in the universe has what is known as Schwarzschild radius and if you compress the mass of that object into a sphere of that radius you will get a black hole. For Earth the Schwarzschild radius is about 9mm( the size of a peanut). So if you want to make a black hole using Earth you will have to compress the whole mass of Earth into the size of a peanut! The Schwarzschild radius for the sun is about 3 Km.

There are three kinds of black holes:

- Stellar black holes: When most us talk about black holes, this is the kind we are referring to. These are formed when large stars collapse under the influence of gravity. The mass of these black holes ranges from 3 solar masses( ie 3 times the mass of our sun) to several tens of solar masses. To understand how these are formed we will have to first understand how a star is formed. A star starts its life with the gravitational collapse of a clould of interstellar gas consisting mostly of hydrogen. Compressional heating raises the core temperature to such a high level that thermonuclear reactions are ignited- hydrogen is fused to form helium and this process releases energy. Lots of it! The star reaches a steady state in which the energy lost to radiation is balanced by the energy produced by thermonuclear reactions. At this time our Sun is in a steady state. But after billions of years the star may run out of hydrogen to burn. And then gravitational collapse starts again. Smaller stars end up as white dwarfs or neutron stars. But if the original star was larger than about 3 times the mass of our sun, the gravitational collapse continues forever and what we get is a black hole. Nothing, not even light can escape its pull. How are such black holes detected? By their effect on nearby stars, gravitational lensing and Hawking radiation. These effects are very interesting but I cannot talk about them in this short article. There are many objects which scientists suspect are black holes. The nearest one to Earth is known as A0620-00 and is about 3000 light years away and has a mass of about 12 times that of our sun.

- Supermassive black holes: A supermassive black hole, as the name suggests is huge! Much bigger than stellar black holes. The mass of a supermassive black hole ranges from millions to billions of solar masses. These black holes are typically found in the centres of galaxies. Scientists believe that our own galaxy, the milky way also has a supermassive black hole in its center. These black holes are formed when the centre of a galaxy collapses under extreme gravity. However, this is not the only way: Sometimes gravitational collapse occurs when galaxies collide or merge and sometimes a galaxy forms around an preexisting supermassive black hole. The nearest supermassive blackhole to Earth is the one at the center of our galaxy. It is about 26000 light years away and has the mass of about 4 million suns!

- Primordial Black Holes: Primordial black holes are very different from stellar and supermassive black holes. Whereas stellar and supermassive black holes can form at any time due to the collapse of stars or centres of galaxies, primordial black holes could only have been formed during the early stages of the universe. Immediately after the Big Bang the universe became a place with enormous temperature and pressure. Today we know( from the study of cosmic background radiation) that the universe at that time was very smooth but had some tiny fluctuations in the density- in other words, the matter density all over the universe was the same but there were some places where the density was different. Some of these places with density fluctuations may have undergone a gravitational collapse to create small black holes. The mass of these black holes could be as small as 10^-8 kg ( The mass of a flea’s egg)! Of course, they could also be bigger. No primordial black hole has yet been detected but some scientists think that primordial black holes may be the prime candidate for dark matter in our universe.

Now lets compare these three kind of black holes using the Hawking radiation coming out from them. In 1974 Stephen Hawking applied quantum mechanics to the study of black holes and found that they must radiate and the radiation is inversely proportional to their mass. Hawking also showed that black holes decrease in mass due to this radiation. For stellar and supermassive black holes the radiation is very small and does not cause much mass loss. In fact, for stellar and supermassive black holes the mass gain due to absorption of nearby matter completely overwhelms any mass loss to Hawking radiation. But even if the black hole did not absorb anything the rate of mass loss due to Hawking radiation for a stellar or supermassive black hole is very small over the age of the universe. But for a primordial black hole this is very different. Since the mass is very small the Hawking radiation is much more.

As a primordial black hole radiates, it decreases in mass and therefore radiates more. This results in runaway evaporation resulting in a massive explosion just before the black hole completely vanishes. Many small primordial black holes would have already exploded because of Hawking radiation. Scientists have calculated that primordial black holes of the mass of about 10^11 Kg( the mass of a mountain on earth) would be exploding now. So to detect primordial black holes, scientists are looking for explosions which are caused by Hawking radiation. These explosions would be coming from a very small area- the Schwarzschild radius for a black hole of this mass is less than a nanometer! If a primordial black hole is detected we will have very strong evidence of Big Bang, Einstein’s general relativity, the theory of how the universe evolved after Big Bang and also Hawking radiation.

The physics of black holes is very interesting. Einstein’s General theory of Relativity can tell us how black holes are formed and some of their properties but there is a lot of stuff that we still do not know. And the biggest mystery is at the centre of a black hole- a place known as the singularity. At this place the known laws of physics completely break down. This is the place of infinite gravity and curvature. This is the place where both quantum mechanics and general relativity completely fail! But we absolutely do want to understand singularities! This is because the universe at the time of the Big Bang was a singularity. So to understand the beginning of our universe we must understand singularities.

But the most interesting thing( and also the most frustrating thing!) about a singularity is that it may never ever be observed. And this is because of something known as the Cosmic Censorship Hypothesis. Basically what it says is this: all singularities are covered by black holes. So there is no “naked” singularity. In other words: An observer can NEVER observe a singularity. What happens inside a black hole stays within the black hole!

So black holes and their singularities are the ultimate mysteries of Physics. Nothing else even comes close.

Regards

Kanwar

============= ============ =================== ============== ========= =====

Go wondrous creature, mount where science guides

go measure earth, weigh air, state the tides,

instruct the planets in what orbs to run

correct old time, regulate the sun

====== ======= =========== ============================== =============

# Modern Version of Galileo’s Leaning Tower of Pisa Experiment

Friends,

Galileo’s leaning tower of Pisa experiment is one of the most famous and important experiments in the history of science. In today’s VERITAS article we will examine the status of that experiment today.

The question that you may ask is: that experiment was done. Why do we need to examine its modern status? The answer is that in scientific method there is no final answer to anything. So experiments need to be repeated again and again. And new experiments should be an improvement over previous ones. For a history of the scientific method read my book: Pilgrims of Episteme: Story of the Scientific Method.

Before we start, lets recall Galileo’s experiment and understand its significance. Aristotle believed that if two objects, one heavier and the other lighter were dropped together, the heavier one will fall faster and therefore reach the ground first. The problem with Aristotle was that he was a great philosopher but he did not like to experiment. So he just imagined that the heavier object would fall faster and formulated his “theory” of gravity. The problem with the world was that they just followed what Aristotle said- and they believed that he had to be right- for nearly 2000 years! But Galileo was different. He wanted to test this and so in 1589 he went up to the top of leaning tower of Pisa and dropped a wooden and a lead ball. The balls landed at the same time much to the astonishment of Aristotelian teachers. This experiment is extremely important because it formed the basis of Newton’s theory of gravity and also the equivalence principle which formed the basis of Einstein’s general relativity.

Now some historians doubt whether this experiment actually took place. But Galileo had done several other experiments and shown that gravity causes the same acceleration in all falling bodies. Galileo had also created a thought experiment to show that a heavier body and a lighter body will fall at the same rate. Here is how it goes: if we say that a heavier body falls faster than a lighter one then what would happen if the heavier and the lighter body are tied together using a string? Would the light body not slow down the fall of the heavier body? But this cannot be right because the combined weight of the two bodies is a sum of their individual weights. So it should fall at a speed greater than either of them. So this is a paradox because we get different answers depending on how we approach the problem and we have logical inconsistency. The only way to solve the paradox is to reject the assumption that the heavier body would fall at a faster rate. Therefore all bodies fall at the same rate irrespective of their weights.

This is a nice thought experiment but the ultimate test of all science is experiment. In this VERITAS I want to tell you the status of this experiment today. When we say that all bodies fall at the same rate, this is a scientific theory. An experiment can NEVER say something like that. An experiment can only state the limits or accuracy to which this theory( or any other theory) has been verified. So the aim of experimental scientists is to keep creating better experiments to test a theory to a greater limit or accuracy than previous experiments.

The modern version of Galileo’s experiment does not measure the rate of fall of two balls. It measures the rate of fall of Earth and Moon towards the sun! So the experiment is done on a massive scale. And this experiment has been going on for over three decades and will continue to give us new data for many years to come. The name of the experiment is Lunar Ranging Experiment. And this is how it was done: Apollo 11, 14 and 15 missions to the moon from 1969 to 1971 left hundreds of corner-cube retroreflectors on the surface of the moon. A corner cube retroreflector is a device that has the property that it reflects any incident light back in the direction from where it came, no matter what its incident angle was.

For more than 30 years laser pulses have been sent from earth to the moon. Each pulse lasts 200 pico seconds and such laser pulses are sent 10 times each second. These laser pulses strike the retroreflectors and return back to earth where they are detected. From this we can calculate the distance between Earth and Moon to the precision of a few mm!

By observing the return times of the pulses, scientists have confirmed that the moon and Earth fall or accelerate towards the sun at the same rate – to the precision of 1.5 X 10 ^ -13. If the rate of fall of the earth and moon was different, it would have shown in the results of this experiment as deviations in trajectory and therefore distance between Earth and the moon.

So we know that the theory that all masses accelerate equally under the influence of a gravitational field is true to the accuracy of the 13^{th} place of decimal. This is one of the most accurate experiments done in the history of science. But we still keep doing more experiments and keep improving the accuracy of the Lunar Ranging experiment because even if we find that this principle is not valid to a place of decimal after the 13^{th}, we will reject the theory, and consequently reject Einstein’s general relativity and look for a better theory of gravity.

In this article I had made reference to the equivalence principle which forms the basis of Einstein’s general relativity which is the currently accepted theory of gravity. Let me briefly describe this very interesting principle. Einstein noted that if a person falls in a gravitational field and only observes objects around him, he would think that he is weightless ie does not experience any gravitational field. To illustrate the principle, lets take a person and a few objects( say a cup, a ball and paper) and put them in a closed box. Now lets drop this box from a great height on Earth( or any planet). While the box is falling, the man, the objects inside the box and the box itself are all falling at the same rate( as shown by Galileo’s experiment and its modern version- the Lunar Ranging experiment). Since the man, the box, the ball, the paper and the cup are falling at the same rate, the man would not think that he or any other object is moving at all- the relative velocity of these objects with respect to each other is 0. Now lets place the same box( with the same objects) in outer space, far away from any gravitational field. Since there is no gravitational field, the man, the box and the other objects are at rest with respect to each other. So the man feels weightless. Einstein said that no experiment can distinguish between these two scenarios- the box freely falling on Earth and the box floating about in outer space are equivalent to each other for all objects inside the box. This principle is one of the central assumptions of Einstein’s general relativity- and we have see that this too is based on Galileo’s experiment and its modern version – the Lunar Ranging experiment.

Kanwar

============= ============ =================== ============== ========= =====

Go wondrous creature, mount where science guides

go measure earth, weigh air, state the tides,

instruct the planets in what orbs to run

correct old time, regulate the sun

====== ======= =========== ============================== =============