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.

The hallmark of Einstein’s work is that he starts with the simplest of ideas or axioms and builds a complex, beautiful theory using those ideas. The special theory of relativity is based on only two assumptions/axioms:

The laws of Physics are the same in all inertial frames of reference. An inertial frame of reference is one that is not accelerating. For example a car moving at a constant speed, or a rocket moving in space at a constant speed are examples of inertial frames of reference. So Einstein basically says that any person in any inertial reference frame will see the same results of any experiment performed in it. There is no inertial reference frame better than any other.
The speed of light in free space has the same value ( scientists write it as c) in all inertial reference frames. So a person moving in a rocket or moving in a bus or stationary on a chair will all get the same value if they measure the speed of light.

So just these two assumptions are needed to derive the entire theory of Special Relativity. These assumptions come from experimental results( like Michelson-Morley experiment). When Einstein explored the consequences of these two assumptions, he found some surprizing results. The first casualty was simultaneity. The concept that two events may occur at the same time is an essential part of how we perceive this world. Indeed, even our concept of time is based on the assumption that all clocks reach a particular time all at once( or simultaneously). But Einstein showed that events that are simultaneous in one reference frame may not be simultaneous in another reference frame.

relativity1train_small

See the figure above. We see a moving train and two observers. One observer is inside the train and the other is standing outside on the platform( but can see the events inside the train). At a certain time t there is a flash of light at the center of the train. For the observer inside the train the light from the flash reaches the front of the train and the back of the train at the same time. But the observer on the platform sees a different sequence of events: according to him the back of the train is moving towards the flash of the light and so light has to travel less distance to meet it. The front of the train is moving away from the flash of the light and light has to travel more distance to meet it. So he sees that the two events: light meeting the two sides of the train are not simultaneous . So we have shown that simultaneity is a relative concept: it depends on the frame of reference.

Now lets look at another situation illustrated in the following diagrams:

dialation1

 

dia2
In the first diagram we see a moving train in which there are two mirrors: one on the floor and other on the ceiling. There is a person on the train who is trying to measure time by reflecting light from the mirrors. He sees a beam of light coming from the bottom mirror, strikes the top and returns to a detector on the bottom mirror. So he says that the time needed for light to come back to the original position is : 2d/c where d is the distance between the mirrors and c is the speed of light. Now, lets consider how a person standing on the platform will see the experiment. See the second diagram. This person sees that the light from the mirror at the bottom has to travel at an angle to meet the mirror on the top. This is because by the time the light travels from the bottom mirror to the top, the top mirror has already moved ahead because the train is in motion. Similarly when the light reflects from the top mirror it has to travel at an angle to meet the bottom mirror. The time spent in this round trip is not 2d/c. it is more because light has to travel a larger distance. So if the two observers are using this mirror-light mechanism to measure time then we have to say that the time recorded by the two observers is different! If you do the calculations carefully using basic trigonometry you will be able to derive Einstein’s formula for time dilation: Moving clocks run slower than stationary clocks. For the first observer the clock( light mirror mechanism ) is stationary, for the 2nd observer the clock is moving and we have seen that the time intervals in the moving clock( for observer 2) are slower than time intervals recorded for the stationary clock( observer 1). So time slows down when a body is in motion! You may say: wait a minute! You have done this experiment with light and mirrors but I don’t use that to measure time: I use a quartz watch. I will say this: This is only an illustration. You can use any mechanism to measure time and you will see that time observed for a moving clock will be slower than time observed for a stationary clock!

From these thought experiments( experiments imagined by a scientist), it became clear to Einstein that we cannot think of a universal time that flows equally for all observers. The duration of time elapsed and the events which occur at the same time are dependent on the frame of reference of the observer. So time is not an absolute quantity- Time is relative. This idea is of fundamental importance and created an enormous change in the course of physics. Before special relativity, scientists would be content with marking the coordinates of any object by three variables: x, y and z. Einstein told us that the three coordinates of space( x, y and z) are not enough to describe the physics of any situation: we need time too. This is how pure space and pure time died and a new concept was born: space-time. So modern physicists rely on 4 coordinates: x, y , z and t to describe any event or location of any object. Space-time diagrams help us understand how objects move through 4 dimensional space-time and how they interact with each other. For more information refer to space-time diagrams on the internet.

Einstein’s Special Relativity has some amazing and mindboggling consequences. Here are some of them:

Einstein was able to show that for moving objects the length shortens along the direction of motion. This is known as length contraction.
We have seen that moving clocks run slower. This leads us to a very interesting situation known as the twin paradox. Imagine two twins: one stays on earth and the other sits in a space ship and travels into space at a speed very close to the speed of light. After about 2 years she come back and finds that her sister on earth has aged 50 years. So the sister that travelled in the rocket grew only 2 years older but the one that stayed on earth was 50 years older. Sure, one can say that moving clocks run slower so the time elapsed on the spaceship would be less. But the situation is more complicated. The sister in spaceship could say: according to my point of view, I was stationary but my sister on Earth moved away from me at a speed close to light, so she should be younger. So we have a “paradox” because looking at the same situation from two different angles give us two different results. But there is really no paradox. We can solve this problem using space-time diagrams and that will tell us that the sister in the spacecraft would be younger. Essentially this is because the situation is asymmetrical. In order to meet, one of them has to turn around and it is that person who would appear younger. If the sister who goes into space turns around and comes back to earth to meet her twin, she would be the one who is younger. It is the turning around that causes the asymmetry. Note: this is just a brief explanation. You can read up on twin paradox on the internet for more details. A similar paradox for length contraction is known as the ladder paradox and is also very interesting.
Time dilation and length contraction depend on the speed of the moving body. At the speed of light, time completely stops and length becomes equal to 0.
Einstein was able to show that momentum and energy are related at a deeper level ( just as space and time are related). This resulted in the famous equation E= mc^2
Einstein was also able to show that Electricity and Momentum are just two views of the same phenomenon- so relativity can help explain how magnetism “arises” from electricity.

Now, let me discuss a common question that gets asked when someone learns that time slows down for an object in motion. This makes people think that this is an illusion and not a real phenomenon. People also argue that the twin paradox is not possible because people cannot age faster or slower. These questions are based on an incorrect premise: that biology and physics are different. The distinction between biology, physics and chemistry is artificial and was created to make the lives of school and university teachers more convenient. All chemistry and biology is ultimately based on atoms and molecules and therefore all theories of matter, energy, space and time must apply to biology also. So if Relativity says that time slows down in a moving rocket, it slows down no matter how you measure it- using a swiss watch, or a cellphone, or a clock based on atomic phenomenon, or a biological clock or any other type of clock that you can imagine. But note: if you move at close to the speed of light with respect to say an object A, you will not notice the slowdown in your clock- this is because every possible measure of time has also slowed down. Also, for you, the clock is stationary and you are stationary. Only another person who is stationary with respect to A can compare his clock with yours and will be able to see the slowdown in your time. And this is important: different people will measure time differently. Time is relative. There is no absolute time.

Special Relativity is a very successful theory and its predictions have been tested through thousands of experiments to a very high level of accuracy. Even its strangest consequence- time dilation has been measured in the decay of elementary particles. There are too many experiments and I cannot into the details of these in this short article. But I will mention that in 2010 an experiment showed that time dilation occurs exactly as predicted by Einstein’s equations in a body that was moving at just 10 m/sec which is the speed of a car on the crowded streets of Delhi( 36 km/hour).

If you want to study Special Relativity in detail, I would recommend the book “Introduction to Special relativity” by Robert Resnick. Note: this does not cover General relativity. I will tell you about a few good books for General Relativity when we discuss that theory.

Friends, in today’s short article we have discussed the basic ideas that Einstein proposed in 1905. These ideas form the basis of a even greater theory that was proposed by Einstein in 1915- The General Theory of Relativity. And that would be the topic of discussion in the subsequent articles in this series.

And before we end this article here is a quote by Einstein:

Imagination is more important than knowledge. For knowledge is limited, whereas imagination embraces the entire world, stimulating progress, giving birth to evolution. It is, strictly speaking, a real factor in scientific research.
Regards,
Kanwar

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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

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