Theory of Relativity in Brief

INTRODUCTION

In this article, Einstein’s Theory of Relativity will be discussed in brief.

Relativity was developed by a famous German physicist, Albert Einstein. Some contributions of Hermann Minkowski, Hendrik Lorentz and Max Planck is also there.



Theory of Relativity comes in two different ‘versions’ – ‘Special Theory of Relativity’ and ‘General Theory of Relativity’ or simply special relativity or general relativity. By name, special relativity seems to be more complex than general relativity, but actually, special relativity is much simpler than general relativity.

Special relativity is called ‘special’ because it is applicable only on objects moving with a constant speed. This is a very rare or ‘special’ case because in our universe hardly anything moves with a constant speed, almost everything accelerates in our universe.

General relativity is applicable on objects moving with a constant speed as well as accelerating objects. Acceleration is a common or ‘general’ case in our universe. 

So, we should first discuss the MEANING OF RELATIVITY.

Relativity means ‘to be relative’. It can be understood by an example. Suppose there is a very hot cup of tea. It is very hot, but, hotter from what? Now, suppose another cup of tea which is further hotter than the first one.

So, which cup should be referred as hot?

The right answer to the question is that the first cup is colder than second one or second is hotter than first one. This is what we call relativity.

There isn’t anything fixed. No quantity (except speed of light) is fixed.

So, more technically, relativity can be explained as any quantity measured by one observer may be different from that measured by another observer. Let’s understand it with an example.

Suppose you are in a train and let the train is moving with 40 mph (miles per hour) of speed. When you will see a person sitting in the train in front of you, the speed of the person will seem to be zero for you but an observer outside the train, the person will be moving with a speed of 40 mph.

So, this can be elaborated as, with respect to you, the person is in rest, but, with respect to an observer outside the train, the person is in motion. This is the basic principle on which the theory of relativity is based on. So, we can observe that the basic principle of relativity is –

Nothing is absolute in this universe, but everything is relative to each other. Only the speed of light is absolute, it doesn’t depend on velocity of observer.

So, RELATIVITY tells us that every motion should be considered relative.

Source: GOOGLE IMAGES

1. SPECIAL THEORY OF RELATIVITY

As described above special relativity is called ‘special’ because it is applicable only on objects moving with a constant speed. This is a very rare or ‘special’ case because in our universe hardly anything moves with a constant speed, almost everything accelerates in our universe.

It is actually the special theory of relativity which tells us that the size of a moving object contracts and that the time for a moving object slows down, and, also a moving object has its mass increased.

The most FAMOUS conclusion of special relativity is that energy and mass are inter-convertible, and they are the same thing.

As described above special relativity is based on the principle that everything is relative.

The whole Special Relativity is based on two postulates:

  1. 1. The laws of physics remain same for every object moving at a constant speed (or, is at rest).
  2. 2. The velocity of light remains constant for all the observers no      matter what their velocity.

1.1 THE IDEA OF FOUR DIMENSIONAL SPACE-TIME

According to the second postulate of special relativity, velocity of light is independent of velocity of observers, this means velocity of light is absolute.

We know that space is not absolute.

It should be noted that space and distance are not dissimilar things because they are measured in a same FUNDAMENTAL unit, that is, METER. (There are also other units like CENTIMETER, KILOMETER, MILES etc. but the standard unit is METER)

For example, when you look at the night sky filled with stars, the distance between them seems to be very small, but they are actually many light years away from each other! (One Light Year is the distance travelled by light in an year. One light year is equal to 9,461,000,000,000 kilometers.) So, this proves that distance (or space) is not absolute.

And we also know that,

velocity of light = distance travelled by light ÷ time taken

so, time taken = distance travelled by light ÷ velocity of light 

⇒ time = non-absolute quantity ÷ absolute quantity

⇒ time = non – absolute quantity

So, special relativity concludes that TIME isn’t absolute and is dependent upon distance (or space) and space is also dependent upon time.

In 1908, Hermann Minkowski (one of the former mathematics professors of Albert Einstein), using the above principle of non-absolute time, presented the idea of four-dimensional structure called space-time or Minkowski space.

He suggested that the three dimensions of space and single dimension of time are fused in a single four-dimensional structure called space-time or Minkowski space.

1.2 THE RELATIVISTIC EFFECTS

Using some Mathematics, which will not discussed here due to technicality, many equations which describe some ‘Relativistic Effects’ can be derived.

RELATIVISTIC EFFECTS are the effects which are relative. These tell us, mathematically, that nothing is absolute except the speed of light.

These are —

  1. TIME DILATION  — This effect tells us that for a moving object, time slows down.
  2. LENGTH CONTRACTION — This effect tells us that the size of a moving object decreases.
  3. RELATIVISTIC MASS — This tells us that the mass of a moving object increases.
  4. MASS-ENERGY EQUIVALENCE — This is a quite different effect from the above three. It tells us that mass and energy are same thing, and, are inter-convertible. The nuclear (atom bomb) and thermonuclear (hydrogen bomb) bombs are based on this principle of the special theory of relativity.

It should be noted that the ‘movement’ of ‘MOVING OBJECT’ listed above is relative to another object/observer.

There are other relativistic effects, which are quite more complex. They will not be discussed here because they are actually the derivatives of the above four effects and are more technical.

1.2.1 TIME DILATION — STRETCHED TIME

Special relativity puts an end to absolute time. The time  runs slow (or dilates) for a moving observer (or object) as compared to an observer (or object) at rest.

The relation between these two times is given by the equation below —

Time Dilation Equation
( ‘Δ’ is ‘delta’, a Greek Letter, used to represent amount of change in a quantity) Δt is time for rest observer (or object), Δt’ is the dilated (or slowed) time for moving observer (or object), v is the velocity (or speed) of moving observer (or object) and c is the velocity of light whose value is 300,000 km/s.


1.2.2 LENGTH CONTRACTION — CONTRACTED SPACE

An object’s size will be contracted if it moves with some speed (or velocity)

The relation between these contracted and original sizes or lengths is given by the equation:

L0 is the proper length or size, L is the contracted length or size, v is velocity of observer or object and c is velocity of light.

1.2.3 THE FAMOUS EQUATION

According to special relativity, the mass of a moving object increases. But according to the law of conservation of mass, mass remains conserved (that is, it doesn’t changes).

According to Einstein’s Energy-Mass Equivalence, mass can be converted into energy and energy can be converted into mass.

When a body is in motion, it possesses some energy called ‘Kinetic Energy’. This is the energy which is converted into mass when a body is in motion.

This increased mass can’t be observed in our daily life (because, in our daily life, the speeds of objects are very slower than that of light), it can be observed when objects travel near to the speed of light because when velocities are near the speed of light, there is a huge amount of Kinetic Energy, leading to large amount of increase in mass.

The relation between increased mass and original mass is given by the equation:

m0 is original mass when the object is at rest, m is the increased mass, v is velocity of the object and c is speed of light.

Einstein’s Energy-Mass Equivalence tells us that mass can be converted into energy and energy can be converted into mass and the amount of energy or mass gained when one of them is converted into other is given by the equation:

E is energy, m is mass and c is the speed of light

When an object has very high velocity, it will have very high  kinetic energy, so, most of the energy will add up to its mass and it will be difficult to increase the velocity, so anything can’t travel at a speed greater than light.

We know that:

m0 is original mass when the object is at rest, m is the increased mass, v is velocity of the object and c is speed of light.

and when an object will travel equal to the speed of light, its velocity,

v = c

when we will put c at the place of v in the above formula, after doing some mathematics, we will get

⇒ m = m0 / 0 

⇒ m = infinity (when any non-zero number is divided by 0, the result is infinity)

So, now if we put this value of in the relation of mass and energy, we found that the value of energy, becomes infinite.

So, we can conclude that to accelerate anything to the speed of light, one would require an INFINITE amount of energy which actually can’t happen.

1.3 LIGHT CONES

Now, we should come on a quite interesting topic of LIGHT CONES. To understand this, we should find out what PHYSICS tells us about EVENTS and time.

An event is a point in space-time whose position can be defined using 4 numbers (3 numbers of three space dimensions and one of time dimension).

So, an event is a point in space-time whose position can be described with maximum of 4 numbers. When an event occurs it emits LIGHT and light is a WAVE. A wave is a disturbance in a medium or field. For example, when you drop a stone in water, water ripples are created like this:

wave

In the above image, the source of the wave is the point where stone is dropped, that is, point A. But when this image is represented with time, it will look something like this:

In the above image, time is represented on the vertical axis (Y – Axis) and space is represented on the horizontal axes (X and Z Axes) and a cone is formed. The source of wave is represented by P. Similarily, when light is emitted from an event, we can construct two ‘light cones’ like this:

The Future Light Cone is in the future of Event P (i.e. all the events in future light cone occur after the event P) and The Past Light Cone is in the Past of Event P (i.e. all the events in the past light cone had already occurred before event P).

The Event P is affected by the events in its Past light cone (i.e. Present is affected by Past) and the Event P affects all the events in its Future Light cone (i.e. Future is affected by Present).

For example, all the events occurring in the universe lie in the light cone of the Big bang Singularity (Big Bang Singularity is the point from which the whole universe emerged). Take a look at the light cone of Big Bang:

Source: WIKIPEDIA

In the above light cone of Big Bang, time is represented on X – axis (Horizontal Axis), instead of Y – Axis (Vertical Axis) So, all the events which are occurring today are directly (or indirectly) affected by The Big Bang.





2. GENERAL THEORY OF RELATIVITY

Before discussing the GENERAL THEORY OF RELATIVITY, we should first discuss what is gravity in NEWTONIAN THEORY.

Sir Isaac Newton was best known for his work on GRAVITY.

According to Newton’s theory of gravity, every object in the universe attracts every other object in the universe.

The strength of gravity according to Newton’s theory is given by:

F  is force of gravitation, G is universal gravitational constant whose value is about 0.00000000006, M and m are gravitational masses of the two bodies and R is the distance between them.

This equation is so accurate, that we still use it for practical purposes like flying a rocket from Earth and landing it on moon or any other planet.

But, there are two problems with Newton’s theory –

  1. It fails for strong gravitational fields like a neutron star.
  2. The way Newton described gravity was not correct.

The orbits of all planets (except Mercury), predicted by general relativity (the currently accepted model of gravity) are same as those predicted by Newton’s theory of gravity because sun’s gravitational field beyond planet MERCURY is weak (Actually, strength of gravitational field decreases with increase in distance).

2.1 THE PRINCIPLE OF EQUIVALENCE

So, if Newton’s description of gravity is WRONG, so what is its correct description?

Today, the currently accepted model of gravity is Einstein’s general theory of relativity, which is based on the PRINCIPLE OF EQUIVALENCE.

The equivalence principle states:

The effects in a gravitational field are same as the effects in accelerated bodies or objects

or in other words you can’t be 100% sure that if you are at rest in a gravitational field or you are accelerating uniformly.

We can understand it by the given two cases:

  1. A man is in a rocket at rest on Earth, he drops a ball in the rocket.
  2. The man, now, is in the same rocket without any contact with a gravitational field and the rocket is accelerating in ‘empty space’ at acceleration of 9.8 m/s2 (m/s2 is unit in which acceleration is measured.) (9.8 m/s2 is the acceleration due to gravity on Earth.) Now, again he drops a ball.

Einstein thought similarly like the above cases to develop the principle of equivalence as a FOUNDATION of his 1915 general relativity.

He will see the ball fall in the same way in both cases. So, we can conclude that the effects in the accelerated rocket are same as the effects in a gravitational field.

Source: WIKIPEDIA

2.2 CURVED SPACE-TIME AND GEODESICS

So, now, we know that equivalence principle is the foundation of general relativity. But, how general relativity describes gravity?

Let us take an example to find out the answer to the above question.

Consider a rocket (that isn’t have any contact with a gravitational field) which is 300,000 kilometers long, that means, light takes one second to reach from top to bottom (and vice versa) of the rocket and according to special relativity, light’s speed will remain constant no matter what the speed of rocket. Consider, currently it is at rest or moving with a constant (or uniform) speed.

Now consider two people are standing at the top and bottom of the rocket. The man at top sends two pulses or waves (or rays) of light to the person standing at bottom of the rocket at a time gap of one minute, that is, he sends the second pulse of light after 1 minute of sending the first pulse of light.

The person, at bottom, with no doubt, receive these two pulses at a time gap of 1 minute.

Now, the rocket starts to accelerate uniformly.

Now, if the person at top sends two pulses of light at a time gap of 1 minute, the person standing at bottom will receive the second pulse in less than 1 minute.

Why does it happen?

The answer is because light has to travel less distance in this case as the person standing at bottom is moving towards the light rays. This can be understood by given image:

Image © MADHUR SOROUT and MADDYZ PHYSICS.
In the above image, blue colored arrow represents the light ray (or pulse), the green arrow represents the direction in which the rocket is accelerating.
The two circles (orange colored) represent the persons standing at top and bottom in the rocket.

The person at bottom is moving towards light ray and light ray is moving towards person and because speed of light is absolute, the distance (or space), light has to travel is decreased (or contracted). So, the person at bottom will receive the two pulses in a time interval, less than one minute.

This means that space has contracted (or shortened) for the person at bottom and time has dilated (or lengthened) for him.

What can we conclude from this?

According to equivalence principle, the effects in accelerating bodies are same as the effects in a gravitational fields.

Now, we can conclude that in a gravitational field space contracts and time dilates.

In other words, near an object having mass (or energy), space contracts and time dilates.

Now consider a simple example of an apple falling on Earth, WHY IT FALLS?

It falls because Earth has contracted the space around it and when the space contracts, it pushes everything in its path, it means that space is pushing the apple to the ground.

This ‘gravitational’ Contraction of Space and Dilation of Time is called ‘Curving of Space-time’.

There is also something special about this contraction of space — space pushes the objects in some definite paths, the straight path between any two points in 4-dimensional space-time.

This straight path between two points is called ‘geodesics’.

All the objects in four-dimensional space-time follow straight lines in 4-dimensional space-time. Because these paths are straight, so these are the shortest paths. These shortest or straight paths are called ‘GEODESICS’.

This concept seems somewhat difficult to grasp. Let us understand this concept with a simple example.

The surface of Earth is two-dimensional and curved because it is a sphere.

Now, on a globe of Earth, mark two points far enough and join them, do you get a straight line after joining them? The answer is no.

The straight line or shortest path between these two points is curved.

Now, if a rocket flies over Earth in a straight path, its shadow on Earth, that is, its path on two-dimensional surface will be curved.

This means that the rocket is moving straight in three-dimensional space but its path seems to be curved on two-dimensional surface of Earth. This can be understood by given image:

Source: A BRIEFER HISTORY OF TIME by STEPHEN HAWKING

This effect is same in 4-dimensional space-time and 3-dimensional space.

For example, space is pushing Earth and other planets to follow the geodesics, that is, the straight paths in 4-dimensional space-time but they seem to move in curved paths in 3-dimensional space.

But when an apple falls, it moves in straight path in 3-dimensional space also, that is, the apple is not moving in curved paths in 3-dimensional space when it falls.

Why? Let us take an example again and find out.

When you will mark two very nearby points on a very large globe of Earth, and join them, you will find that this line or shortest path is STRAIGHT.

This means that the distance between the the two points in space (which the apple covers) is too short that its path in 3-dimensional space is also straight.

Now, what we can conclude from above discussion? What is actually GRAVITY?

The conclusion is —

Gravity is not a force like other, but, it is a consequence of curvature of space-time.

The presence of mass and energy curves space-time that means near a mass, space contracts and time dilates and away from the mass, space is less contracted and time is less dilated.

All the objects follow the shortest path, that is a straight path in 4-dimensional space-time. These paths are known as geodesics and space is pushing the objects to follow these geodesics (straight paths), but, the objects seem to move in curved paths in 3-dimensional space.

2.3 GRAVITATIONAL WAVES

A wave can be defined as a disturbance in a medium, field or any other structure.

Water waves disturbs water medium.

Sound waves can disturb any medium (solid, liquid or gas).

Light waves disturb electromagnetic field

And, Gravitational Waves disturb the space-time.

These waves can be represented as:

gravitational-wave-cover-800x433
Source: GOOGLE IMAGES

You can see how ‘ripples’ are created in this ‘FABRIC’ of space-time as are created in water when you throw a pebble in it.

Newton’s gravity predicts that gravity is an instantaneous force which means that it travels faster than light.

But this violates Einstein’s special theory of relativity, which predicts that anything can’t travel faster than light.

The speed of light is a kind of ‘cosmic speed limit’.

If sun disappears suddenly, Newton’s gravity predicts that all the planets, comets, asteroids will instantly, leave their orbit.

But general relativity predicts that when sun will disappear, waves will be created in space-time and will take some time to reach the planets and after then they will leave the orbit, for example, it will take 8 minutes for these waves to reach the Earth, and, gravitational waves travel exactly at the cosmic speed limit, the speed of light.

This catastrophe, of Sun’s disappearance is illustrated below:

Source: GOOGLE IMAGES


Thanks for Reading and Hope you Liked It!


REFERENCES

  1. Einstein, Albert, & Renn, Jurgen (2015). Relativity – The Special and General Theory. Princeton: Princeton University Press.
  2. Hawking, Stephen (2000). A Brief History of Time. New York: Bantam Books.
  3. Hawking, Stephen (2005). A Briefer History of Time. London: Bantam Press.
  4. Theory of Relativity. (n.d.). Retrieved from Wikipedia: https://en.wikipedia.org/wiki/Theory_of_relativity
  5. Chen, Susan (2017, January 1). The Basics of Special Relativity. Retrieved from Passion for STEM: https://passionforstem.wordpress.com/2017/01/02/the-basics-of-special-relativity/


About the Author – Madhur Sorout

madhur sorout profile

Sorout is currently a last third year high school student, living in India. His main fascination lies in Physics mainly in the field of general theory of relativity and topics related to it like Big Bang, Black Holes and Evolution of Universe. He likes to make out the meaning of what he see in this universe. He loves to read books by Stephen Hawking, Neil deGrasse Tyson and other authors (and Physicists).  He is an atheist and believes that Physics completely rejects the idea of a god. He likes to play cricket also and he wants to continue down the route of research in Theoretical Astrophysics.


About Madhur Sorout 17 Articles
I am a 14 years old aspiring Physicist and currently a high school student living in India. I am Founder of the blog – Maddyz Physics My main fascination lies in Physics mainly in the field of general theory of relativity and topics related to it like Big Bang, Black Holes and Evolution of Universe. I like to make out the meaning of what I see in this universe. I also love to play cricket and I like computer science and web development also. I want to continue down the route of research in Theoretical Astrophysics.

4 Comments

  1. Brother Madhur Sorout you describe the topic relativity in such a way that an average student understand the topic very well it is really good

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