Table of Contents

# Relativity and Maxwell’s Equations

In this article I have discussed about the Relativity and Maxwell’s Equations. Sometimes you may wonder how electromagnetics varies when relativity is considered. Or you can question about “how Maxwell’s equations are modified to conform to Einstein’s relativity”.

It is well known that Newton’s basic tenets of physics and the concept of space and time developed mainly by Galileo and Newton had to to be radically changed to accommodate relativity.

You may be surprised to know that there were **NO CHANGES** made to the Maxwell’s equations. In fact special relativity follows directly from the Maxwell’s equations.

Maxwell’s equations predict that electromagnetic waves exist and their speed is 3×10^{8} m/sec, which is the speed of light. However these equations do not state what this speed is relative to. For example, when a car driving down the highway turns ON its lights, the light travels away at the speed of light, relative to the car.

The same is true for the radio waves sent out by a cellphone in the car. Assume that the car is travelling at 60 miles per hour. Ordinary experience tells us that if you are standing still on the side of highway, you would measure the speed of both the light waves from the headlights and the radio waves from the cell phone to be the speed of light plus 60 miles per hour.

Maxwell’s equations however state that the speed of radio waves and light wave is always the same under any measurement.

Einstein was an imaginative thinker. He said that Maxwell’s equations are correct as they were first written, and it was newton’s laws of physics and Newton-Galileo laws of space and time that needs to be modified. It was obviously a bold statement made by Einstein. He used physics as back up for supporting his statement. It took decades, but Einstein’s theory of relativity gradually gained full acceptance of scientific community after countless experiments proved him to be correct.

At this point in 21st century, I think it is safe to say that Einstein was correct and perhaps his theory should now be called the law of relativity. Close to 100 years of scrutiny and experimentation have passed without a single failure.

Of course general relativity is not the end of the physics. Most notably, relativity and quantum physics have yet to be merged. There has been hope in recent years that string theory will provide the unified theory of physics, commonly called the theory of everything.

The basic premise behind Einstein’s work is that we should be able to write the laws of physics such that any event or phenomenon can be described by the same laws, regardless of who does the measurement.

In other words, there should be a universal set of laws to describe observations, regardless of whether the observer is stationary, moving at a constant speed or accelerating. Moreover, there must be a set of equations to translate measurements from one reference frame to another.

## What is the special relativity?

When Einstein first introduced his theory in 1905, he covered the topics of stationary and constant speed observers. This subset of relativity is called the special relativity. Later in 1916, Einstein introduced his theory of general relativity, which not only provided the framework for any type of motion, including acceleration, but also provided the new theory of gravity.

Gravity is not like other forces. Gravity manifests itself as curvature of space time. Mass causes space-time to curve, and the curvature of space-time determines how other masses move.

For the understanding of electromagnetics, special relativity is all that is really needed. The entirety of special relativity can be summarized in two simple statements.

- Light travels at the same speed when measured by any observer.
- The laws of physics are the same in any inertial (gravitational and acceleration free_ reference frame.

From these two simple statements, all of special relativity can be derived. The first statement is the consequence of the Maxwell’s equations, so in some sense it is really only the second equation that defines special relativity.

A reference frame is the coordinate system of the observer who is performing the measurement. The term inertial basically means that the observer is not being accelerated. Accelerated motion is very different from the uniform motion.

## Newton’s Laws

Newton’s first law states that the body in motion will continue in uniform motion unless a force acts upon it.

Newton’s second law states that the mass of an object times the acceleration of the object is equal to the net force acting upon it. Newton’s second law can be expressed as:

**F=ma **

The force provides the energy to change the object’s velocity.

### Example

The magnitude of the gravitational force is F=40×10^{21} N. This force points from the earth to the sun. The force of the earth on the sun has the same magnitude but points from the sun to the earth as shown in the following figure.

Newton’s third las states that action are reaction are always equal but in opposite direction.

Electromagnetic radiation can be produced only if there is a force acting on a charge. This force provides the energy of radiation. If I were to hold a charged ball in my hand and I wave it. I provide energy that is radiated away. In other words, I must burn calories to move my arm, some more calories to move the ball, and even more to move the ball’s electric field. Hence the electric field itself has inertia or mass, just as the ball has the mass.

There are further differences between the uniform straight line motion (inertial motion) and accelerated motion (noninertial motion). If you are sealed inside a windowless compartment and are travelling in uniform motion, there is no way for you to determine how fast you are going or whether you are moving or not. Uniform straight-line motion is completely relative. For instance, if you are travelling in uniform motion in a car or plane, the laws of physics are not different.

You do not feel any different when you are in a plane travelling seven hundred miles an hour. If you drop a ball, it falls straight down in your frame of reference. On the other hand, if the plane is accelerating, you can feel it. The movement of liquid in your inner ear is the main source of determining acceleration.

Furthermore, if you drop a ball in an accelerating plane or a car, it does not travel straight down. It curves towards the back of vehicle as it falls because once it leaves your hand it is no longer accelerating, whereas you and the vehicle still are accelerating.

## Relativity and Maxwell’s Equations in modern era

**Relativity: Unveiling the Fabric of Spacetime**

**Special Relativity:**This theory, developed by Einstein, revolutionized our understanding of space and time. It established the constant speed of light and introduced concepts like time dilation and length contraction. These concepts are crucial in fields like**high-energy particle physics**where particles reach speeds close to the speed of light.**General Relativity:**Einstein’s theory of gravity, general relativity, builds upon special relativity and describes gravity as a curvature of spacetime caused by mass and energy. This theory is essential for understanding phenomena like**black holes**and the large-scale structure of the universe.

**The Intertwined Dance:**

**Maxwell’s Equations and Special Relativity:**Interestingly, Maxwell’s equations themselves hint at the need for special relativity. The constant speed of light, a prediction of the equations, clashed with the prevailing understanding of velocity addition in classical mechanics. This inconsistency became a driving force behind Einstein’s development of special relativity.

**Modern Interpretations:**

**Quantum Electrodynamics (QED):**While Maxwell’s equations are incredibly successful, they are a classical description. In the quantum realm, a more sophisticated theory, QED, takes over. However, QED can be viewed as a**quantum version of Maxwell’s theory**, highlighting the enduring importance of the original framework.

**Future Directions:**

**Unification:**A grand unified theory that combines all the fundamental forces, including electromagnetism described by Maxwell’s equations and gravity described by general relativity, remains a holy grail of physics. Understanding how these forces interact at high energies likely necessitates further exploration of both relativity and electromagnetism.

In conclusion, Maxwell’s Equations and relativity continue to be immensely relevant in the modern era. From forming the foundation of numerous technologies to shaping our understanding of the universe’s grand structure, these theories remain at the forefront of scientific exploration.

### Assignment 2 Electromagnetic Field Theory

Also read here:

## The Electric Field of Direct Current (DC) and Alternating Current (AC)

## Discuss the Electric Field of a Static and a Moving Charge