What is Special Relativity?

The theory of special relativity discusses how space and time are related to objects traveling along a straight line at a constant speed. Simply stated, as an object reaches the speed of light, its mass becomes infinite and it is unable to move faster than light. This interstellar speed limit has been the topic of much debate in astronomy, and also in science fiction when people consider how to fly over large distances. 

It is one of the most renowned works by one of the greatest physicists of all time, Albert Einstein, and was published in 1905. This is the theory that tells about the relationship between space and time. This theory is also known as the special theory of relativity. The theory was developed on these two postulates i.e., 

• The first is based on the fact that the laws of physics are identical in nature which means they are fixed, and they cannot be changed, for all the inertial frame of reference. This inertial frame of reference is known as the reference frame which is having zero or no acceleration. 
• The second one says that the speed of light remains the same when it travels in a vacuum and the motion of any light source or the observer does not have any effect on it. 

Special relativity helps in handling the situations of mechanics where the motion takes place with the speed which is nearly or equal to the speed of light when the gravitational as well the quantum effects are considered as zero. For low velocities, Newton’s model is still enough accurate and valid. These postulates combine with the other laws and talk about the equivalence of energy as well as mass, which is mathematically expressed as; 

E=mc²

where m is the mass and c is the speed of light in a vacuum medium. This equation further demonstrates that mass increases with time, essentially limiting how quickly objects will travel through the universe. Simply stated, the speed of light (c) is the fastest distance at which an object in a vacuum will travel. The mass of an object changes as it passes. At the speed of light, the mass approaches zero and will take unlimited energy to travel, limiting how far an object can move. The only reason light travels at such a fast rate is that the photons, the quantum particles that makeup light, have no mass. This theory also helps in explaining the electricity as well as the magnetism phenomenon. 

Conclusion of Einstein’s observations

 One of these will be an unusual situation in the small universe known as "quantum entanglement". It is perplexing because it seems to entail quantum particles interacting with one another at speeds greater than the speed of light. Measuring the property of one particle, for example, will automatically tell you the property of another particle, no matter how far apart they are. Much is being written about this phenomenon, which is still not completely clarified in terms of Einstein's assumptions. 

Another unusual result of Einstein's experiments is the understanding that time shifts relative to the observer. Time dilation occurs while an object is in motion, which means that time travels more slowly when it is moving than when one is stationary. Therefore, the person in a reference frame which is moving ages more slowly than a person at rest. This attribute is contributed to space travel by the astronauts and gravitation plays a significant role in it. The gravitation theory of being a linear field theory as well changed in the course of study and Einstein objected to the theory for the weak field. 

In special relativity, the mass of an inertial body is dependent on the speed of the body, that is the higher will be the speed of the body, the more will be the mass of the body. For example, this was observed during the high-energy particle accelerator experiment, in which elementary particles were accelerated to speeds approaching the speed of the light. Inside the accelerator, electrons are made to move at a speed almost equivalent to 99.99% of the speed of light. However, there was an increase in mass, which made it almost impossible to reach the speed of light and the faster object gets the more difficult it becomes to reach a speed of light. 

The theory has also replaced the Galilean Transformations with the Lorentz transformations which tells that time and space are not separate features but are combined in a single continuum, which is known as spacetime. This also arises the fact that the event occurring at one time for an observer can also occur for another observer at different times. 

The specialty of the theory is that it is applied to the flat spacetime, which means that the spacetime curvature and gravity considered negligible. 

Two postulates related to special relativity 

1. The principle of relativity- It tells that, all the equations which are being described with laws of Physics remains the same for all the frame of references. 
2. Principle of invariant light speed- Light travels with a certain speed in the empty space which is independent of the motion of the body from which it is emitted. 

Principle of Relativity 

Reference frames and relative motion- This plays a major role in the special theory. It is an observational frame which is considered in space which I not in any kind of motion and it has the ability to measure the events timings. It is used to measure any point in space along any of the axes. 

An event is considered as something that has occurred at some point or at some location in the space with respect to the frame of reference which is called the point in spacetime. A common example of an event is the explosion of the bomb. The event can be easily specified with various coordinates, i.e. the event occurring time and the reference point defined with the three-dimensional location. The coordinates of any event can also be calculated with the help of various reference frames. And the equations which relate to the measurements in various frames are termed transformation equations. 

This figure is showing two different reference frames.

Configuration of Reference Frame

The setup of the frames is done in a standard configuration to get to understand how the coordinates are measured by an observer. This standardized form helps in further calculations and the conclusions are also found the same as required. In the figure above, two Galilean reference frames are shown in relative motion. The first frame belongs to the observer O while the other one is observed by the observer O’. It has been observed that- 

• All the axes i.e. x,y,z of the first frame are oriented parallel with respect to frame two.  
• The second frame moves in only one direction i.e., the X-direction of the first frame with a certain constant velocity, and is measured in the first frame.  
• The origins of both the frames will be coincident when t=t’=0, for both the frames. 

Lack of Reference Frame 

According to the relativity principle, laws of physics are supposed to be constant for all the frames of reference this was provided in Newtonian physics. Physicists started claiming that the universe is filled with a substance called ‘ether’, which is responsible for the movement of electromagnetic waves. It was supposed as the only reference frame which exists and based on that frame all the speeds can be measured. It was supposed to be enough elastic for the movement of electromagnetic waves. These waves can interact with the matter but were not supposed to provide resistance to the bodies through which they are passing. Various results led to the fact that there is no such substance as ‘ether”. Einstein helped in getting to the conclusion that there is no such thing as ether. The relativity principle tells that the reference frame will show the laws of Physics in any reference frame which is moving at a uniform velocity. 

Relativity in the Absence of a Second Postulate 

The transformation of spacetime between the inertial frames can be defined as Euclidean, Lorentzian or the Galilean, this is obtained from the relativity principle without assuming the speed of light as constant. 

Lorentz Transformation 

This was given by the Dutch physicist, named, Hendrik Lorentz. This is the transformation which shows the relationship between the two different coordinate frames of references and which are moving with a constant velocity and are related to each other. Frames can be of inertial type i.e., motion with velocity constant, and non-inertial i.e. they have rotational motion and move with constant angular velocity and is accelerating in the curved path. This is generally related to the inertial frame of references. 

Context and Applications    

This topic is significant in the professional exams for both undergraduate and graduate courses, especially for  

• Bachelors in Science (Physics ) 
• Masters in Science ( Physics) 
• Bachelors in Technology  (Mechanical)