Squeezed Space and Stretched Time

A better version of this article is — THEORY OF RELATIVITY IN BRIEF which is also a featured article on our blog. So, we recommend you to read that article instead of this, and, also that article describes RELATIVITY completely.

Click HERE to read THEORY OF RELATIVITY IN BRIEF →

INTRODUCTION

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. 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.

2. LENGTH CONTRACTION – SQUEEZED 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.

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.

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 20 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.

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