Special Theory of relativity

 

Special Theory of Relativity

            There are many theories that exist in the world but the theory that is more famous in the world of physics is the Theory of relativity. The theory of relativity consists of 2 theories, one is special theory another is general theory. In this article, I will discuss Special theory. The special theory of relativity was proposed by famous physicist Albert Einstein in 1905. This theory revolutionized our understanding of space, time, and motion. Now let’s discuss in details.

What is Theory?:

            Let’s first discuss what theory is? In a simple way, a theory is an explanation or a set of ideas that helps us understand how something works or why something happens. It's like a framework or a model that helps us make sense of the world around us. They are based on observations, experiments, and evidence gathered by researchers. Theories can be tested and refined over time as new evidences are discovered. This means predictions made in theory are tested over time. If the technology is available then we test the postulates of theory if the postulate proves right then theory becomes strong and strong. Like Einstein in his theory mentioned about black holes, time dilation etc. But at that time there wasn’t an advance technology to test these. Now we have tested and these predictions of Einstein’s proved right so his theory becomes stronger and stronger. Theories can also be used to guide further research and exploration in a particular field.

Background:

            Let’s discuss the history of what people thought before Einstein’s theory. During the late 19th and early 20th centuries, the scientific landscape was primarily dominated by classical physics, with Newtonian mechanics being the prevailing theory. Newtonian mechanics, developed by Sir Isaac Newton in the 17th century, provided a framework for understanding the motion of objects based on the concepts of force, mass, and acceleration. One key concept prevalent during that time was the belief in absolute space and time. It was believed at that time that space and time are absolute. Let me explain what it means. Absolute time means that time is the same everywhere in the universe suppose it’s 10:00 pm on Earth then there will be the same time on the planet of another solar system 10:00 pm means there is a single universal time that is the same for everyone. Absolute Space means that imagine there are 2 points in a sheet and the distance between these 2 points will remain the same and will never be changed. Another concept prominent during that period was the concept of ether. Ether was believed to be a hypothetical substance or medium that filled the empty space and served as a medium for the propagation of light waves. The ether was thought to be responsible for carrying light waves through space, like how air carries sound waves. Like other waves, it was believed that light waves required a medium through which they could travel. The Michelson-Morley experiment, conducted in 1887 by Albert A. Michelson and Edward W. Morley, played a crucial role in inspiring Albert Einstein to develop the special theory of relativity. The experiment aimed to detect the existence of the ether, a hypothetical medium believed to be responsible for the propagation of light waves through space. It was thought that as the Earth moved through the ether, the speed of light would vary depending on the direction of motion. However, the Michelson-Morley experiment yielded a surprising result: it failed to detect any significant variations in the speed of light, regardless of the direction in which the Earth was moving. This experimental outcome challenged the prevailing understanding of the nature of light and motion, which relied heavily on the existence of ether. This experimental result left scientists puzzled and searching for an explanation. One individual who was deeply influenced by this experiment was Albert Einstein. The null result of the Michelson-Morley experiment, along with his deep understanding of the principles of electromagnetism, sparked Einstein's curiosity and led him to question the existing notions of space, time, and motion.

Special theory of relativity’s postulates:

            Now let’s start discussing the Special Theory of Relativity. The 2 main postulates of the theory are:

1)     All laws of nature are the same in all inertial frames of reference.

2)     Speed of light is constant in all frames of reference.

I will explain first what’s the frame of reference. Imagine you are sitting inside a moving train and looking out of the window. As the train moves, you see objects passing by outside, such as trees, buildings, and other trains. These objects appear to be moving relative to you. Now, let's consider two scenarios:

Inside the train: From your perspective inside the train, you are at rest, and the objects outside are moving past you.

Outside the train: If someone is standing outside the train and watching it pass by, they would see you and everything inside the train moving at the same speed as the train itself.

In both scenarios, we have a different point of view or "frame" to describe the motion of objects. This is what we call a "frame of reference”. A frame of reference is a coordinate system that helps us describe the motion and positions of objects relative to something else.

There are 2 types of frame of reference one is an inertial frame of reference and another is a non-inertial frame of reference. An inertial frame of reference is a special type of frame where Newton's first law of motion holds true. This law states that an object at rest will remain at rest, and an object in motion will continue moving at a constant velocity in a straight line unless acted upon by an external force. In an inertial frame, these principles are valid without the need to account for any additional forces or accelerations. In simple words, if you are in a frame of reference that is not accelerating or experiencing any forces, you are in an inertial frame of reference. A non-inertial frame of reference is a frame that is accelerating or experiencing forces. In such a frame, objects do not obey Newton's first law. In simple terms, if you are in a frame of reference that is accelerating or experiencing forces (for example, a car turning around a sharp bend or an elevator moving up or down with varying speeds), you are in a non-inertial frame of reference. By acceleration, it means either changing velocity or changing direction or both. So, most people ask the question is The earth an inertial frame of reference? So, the answer is no because Earth is not in state of constant velocity and changes it direction as well.

            Let’s discuss the postulates. The first postulate of the special theory of relativity states that all the fundamental laws of physics, the laws that govern how the universe works, are the same in all inertial frames of reference.  

Let's consider a scenario involving two observers, Alice and Bob, who are in separate inertial frames of reference. Imagine that Alice is inside a moving spaceship, and Bob is standing still on a planet. From Alice's perspective inside the spaceship, she conducts various physics experiments. For example, she measures the speed of light, observes how objects move, and measures the behavior of particles. She writes down all her experimental results and discovers certain laws of physics based on her observations. Now, from Bob's perspective on the planet, he also conducts the same physics experiments as Alice did inside the spaceship. He, too, measures the speed of light, observes the motion of objects, and studies particle behavior. Like Alice, Bob writes down his experimental results and formulates laws of physics based on his observations. According to the first postulate, the laws of physics that Alice discovered inside the moving spaceship and the laws of physics that Bob formulated while standing on the planet are exactly the same. Their observations and experimental results will lead them to the same fundamental principles, regardless of their relative motion. This is what the first postulate ensures - the laws of physics are universal and consistent for all inertial observers, no matter how they are moving relative to each other.  The second postulate of the special theory of relativity states that the speed of light in a vacuum is the same for all observers, regardless of their relative motion. No matter how fast an observer is moving, the speed of light remains constant and is always measured to be approximately 299,792 kilometers per second (or about 186,282 miles per second).

This idea is quite different from our everyday experiences with other objects. For example, if you are on a moving train and you throw a ball forward, the speed of the ball relative to the ground will be the sum of the ball's speed with respect to the train and the train's speed with respect to the ground. However, this is not the case with light. The speed of light is always the same, whether you measure it while moving toward the light source or away from it. The constancy of the speed of light is a fundamental principle of the special theory of relativity and has profound consequences for our understanding of space, time, and motion. Try to understand consider a bus that is moving at 200000 km/s and same in parallel the light is moving at a speed of 300000 km/s so the normal person in the bus will say that the speed of light will be 100000 km/s but this is not true the speed of light will appear to be 300000 km/s.

 

Consequences:

            We explored the foundational postulates of the Special Theory of relativity, which revolutionized our understanding of the universe. Now, let’s dive deeper into the consequences that arise from these postulates.

Let’s first discuss the length contraction:

Length contraction is a consequence of the special theory of relativity. It states that the length of an object moving at a high speed appears to be shorter than its actual length when measured by an observer who is not moving with the object. This is because the speed of light is the same for all observers, regardless of their motion. So, if an object is moving at a high speed, the light that reflects off of it will be compressed in the direction of motion. This will make the object appear shorter to the observer who is not moving with the object. Let’s try to understand simply why this contraction happens. 

Consider the train is moving towards an observer at a high speed so the light from the front of the train has to travel a short distance to reach to observer’s eyes and light from the back of the train has to travel more to reach to observer’s eyes so the difference of distance the front light and back light travelled to reach observer’s eyes would be the length of train that will appear to the observer if the distance is long then length will appear long and if difference of  distance that light from front of train and light from back of train covers to reach the observer eyes is shorter then the length of train will appear more shorter to an observer. So, in short the length of train that will appear to observer depends on the difference of distance that light from front and light from back of train covers to reach the observer’s eyes. Example if train is moving with 0.2c speed then the difference of distance discussed earlier will be longer and length of train will be appeared long and if train moves with 0.8c then the difference of distance discussed earlier will be shorter and length will be appeared contracted.

 

           

 

L' = L * √(1 - v^2/c^2)

In this equation:

L' is the observed length of the object when it is moving at high speed.

L is the rest length of the object when it is at rest (measured by an observer in its rest frame).

v is the velocity of the object relative to the observer (the speed at which the object is moving).

c is the speed of light in a vacuum, which is approximately 299,792 kilometers per second (or about 186,282 miles per second).

When the velocity of the object (v) is much smaller than the speed of light (c), the term v^2/c^2 becomes negligible, close to zero. As a result, the Lorentz contraction formula simplifies to L' ≈ L, meaning that at low speeds, the observed length (L') is almost the same as the object's rest length (L). When the velocity of the object (v) approaches a significant fraction of the speed of light (c), the term v^2/c^2 becomes significant, close to one. As a result, the square root (√) term in the equation reduces the observed length (L') significantly compared to the rest length (L).

Now let’s discuss time dilation:

Time dilation is a concept that tells us time can pass at different rates for different observers depending on their relative motion. In other words, time can appear to "stretch" or "shrink" depending on how fast someone is moving compared to another observer.

Imagine you and your friend have two identical super-accurate clocks. You stay on Earth, and your friend travels to a distant star at an incredibly high speed using a super-fast spaceship.

When your friend returns from the journey and compares their clock with yours, something mind-boggling happens: Their clock shows less time has passed for them compared to yours! In other words, your friend's clock "ticks" slower than yours.

The reason for this strange phenomenon is that the speed of light is always constant for everyone, regardless of their motion. As your friend's spaceship moves faster and faster, time slows down for them from your perspective on Earth.

This effect is not noticeable in everyday life because we typically travel at much lower speeds compared to the speed of light. But when you get close to the speed of light, even tiny differences in speed can cause significant time dilation.

t' = t * √(1 - v^2/c^2)

t' is the time experienced by the moving observer (your friend on the spaceship).

t is the time experienced by the stationary observer (you on Earth).

v is the velocity of the moving observer (your friend's speed).

c is the speed of light in a vacuum.

As your friend's velocity (v) approaches the speed of light (c), the term v^2/c^2 becomes significant, and the square root (√) in the equation reduces the experienced time (t') significantly compared to the stationary observer's time (t). This is why time dilation becomes more pronounced at higher speeds.

From the perspective of the person on Earth (the stationary observer), they will see the clock on the spaceship ticking slower than their own clock. In other words, they observe time dilation for the person in the spaceship. From the perspective of the person inside the spaceship (the moving observer), they will see their own clock ticking normally. They will not perceive any time dilation for themselves. However, when they look at the clock on Earth, they will observe that it is ticking faster than their own clock. From the perspective of the person inside the faster spaceship (the moving observer), they will perceive time as passing normally for themselves. This means that, according to the person in the spaceship, their own clock will tick at its usual rate, and they will not experience any time dilation. Time appears to flow as it always does for them.

If you still facing difficulty let’s discuss the famous Twin paradox. Imagine we have two identical twins, Alice and Bob. Alice remains on Earth, while Bob boards a spacecraft and travels at an incredibly high speed, close to the speed of light, to a distant star and then returns to Earth. According to the Special Theory of Relativity, due to time dilation, the traveling twin (Bob) will experience time passing more slowly than the stationary twin (Alice) during his journey. This means that while Bob is traveling, he will age more slowly compared to Alice on Earth. Upon Bob's return to Earth, something paradoxical happens. Both twins will be able to notice a significant difference in their ages. Bob, the traveling twin, will be much younger than Alice, the stationary twin.

Now let’s discuss the mass variation:

In classical Newtonian physics, mass is considered an intrinsic property of an object, and it remains constant regardless of its motion. However, the Special Theory of Relativity introduced by Albert Einstein showed that mass is not an absolute and unchanging quantity. Albert Einstein introduced the idea of mass variation, which tells us that as an object moves at higher speeds, its observed mass increases compared to its mass when at rest. This phenomenon is called relativistic mass.

Imagine you have an object with a certain mass, say a baseball. When the baseball is at rest, it has a specific mass, let's call it "m₀", which is its rest mass. However, when this baseball starts moving very fast, close to the speed of light, its observed mass, which we call "m" (relativistic mass), increases. The faster it moves, the larger its observed mass becomes.

m = m₀ / √(1 - v²/c²)

In this equation:

m is the relativistic mass of the object (mass observed at a certain velocity).

m₀ is the rest mass of the object (mass at rest).

v is the velocity of the object.

c is the speed of light in a vacuum.

Hence if an object moves with the speed of light then the mass becomes infinity and also in order to move such an object infinite force is required which is practically not possible so that’s why no mass can travel with the speed of light only photons can travel with the speed of light because they are massless particles. If you have an observer on Earth (stationary observer) watching a spaceship zooming past at a high speed, the observer on Earth will see the spaceship's relativistic mass increase. But from the perspective of the person inside the spaceship (moving observer), their own mass remains constant. They would measure their mass to be the same value they would measure when at rest. Only the person in the other frame of reference will observe that mass is increasing.

Verification:

Now let’s discuss the verification of the special theory of relativity. One of the classic experiments that confirmed the phenomenon of time dilation is known as the "Hafele-Keating Experiment." It was conducted in 1971 and involved flying atomic clocks on commercial airliners. The experiment was a crucial verification of the time dilation effect predicted by the Special Theory of Relativity. The main goal of the experiment was to observe and measure the effects of time dilation on atomic clocks as they traveled at high speeds relative to the Earth's surface. Scientists from the U.S. National Institute of Standards and Technology (NIST) installed four highly accurate cesium atomic clocks in two commercial airliners. The planes, one traveling eastward and the other westward, flew around the world on regularly scheduled flights. The eastward-bound plane traveled around the world in the same direction as Earth's rotation, effectively increasing its speed relative to the Earth's surface. The westward-bound plane traveled in the opposite direction, reducing its speed relative to the Earth's rotation. During the flights, the atomic clocks on the planes were compared with identical atomic clocks that remained stationary at NIST laboratories. According to the Special Theory of Relativity, the clocks on fast-moving planes should experience time dilation, causing them to run slower compared to the stationary clocks on the ground. After the flights, the clocks were compared, and the results matched the predictions of time dilation. The clocks on the planes, especially the eastward-bound one traveling faster than the westward-bound one, showed a measurable time difference compared to their stationary counterparts. Hence, proved the phenomenon of time dilation.

One of the key experiments that indirectly verified mass variation (relativistic mass increase) as predicted by the Special Theory of Relativity is the "Particle Accelerator Experiments." Particle accelerators are powerful machines used to accelerate subatomic particles, such as protons or electrons, to extremely high speeds, approaching a significant fraction of the speed of light. Particle accelerators were developed to study the behavior of subatomic particles at high energies and speeds. These machines use electromagnetic fields to accelerate charged particles to nearly the speed of light before colliding them with other particles or targets. As particles approach the speed of light in these accelerators, relativistic effects become significant. One such effect is relativistic mass increase, where the observed mass of a particle increases as it moves at higher speeds. As a particle accelerates and gains kinetic energy, its relativistic mass increases. That proved the phenomenon of mass variation. The experimental data aligned with the predictions of Einstein's theory.

Applications:

Now let’s discuss the applications of the Special theory of relativity. There are many applications.

Ø GPS (Global Positioning System): The accuracy of GPS relies on the precise synchronization of satellite clocks with receivers on Earth. Since the satellites are moving at high speeds relative to Earth's surface, they experience time dilation, which, if left unaccounted for, would introduce significant errors in GPS calculations. The Special Theory of Relativity's time dilation corrections are crucial to ensuring the accuracy of GPS navigation.

Ø Particle Accelerators: Particle accelerators, like the Large Hadron Collider (LHC), accelerate subatomic particles to near the speed of light. As these particles approach the speed of light, they gain significant relativistic mass, making them more energetic and leading to high-energy collisions that help scientists study the fundamental nature of matter.

Ø Electromagnetism: The theory has implications for electromagnetic phenomena. For example, the relativistic correction factor comes into play when charged particles move at high speeds in electric or magnetic fields, impacting their behavior and radiation emissions.

Ø Astrophysics: The theory is applicable in astrophysics, where objects like stars and black holes approach the speed of light or exist in strong gravitational fields. Special relativity plays a role in understanding phenomena like the behavior of particles near black holes and the energy emitted from stars.

 

In conclusion, the Special Theory of Relativity, proposed by Albert Einstein in 1905, has significantly impacted our understanding of the universe. Its postulates about the constancy of the speed of light and the equivalence of inertial frames of reference have been verified by numerous experiments. The theory's consequences, such as length contraction, time dilation, and mass variation, have been confirmed in various ways, solidifying its scientific validity.

Furthermore, the Special Theory of Relativity finds practical applications in modern technologies, from GPS navigation to particle accelerators. It has revolutionized our perspective of space, time, and motion, challenged classical notions, and shaped our fundamental understanding of the universe. As one of the most celebrated and tested theories in physics, the Special Theory of Relativity remains a cornerstone of modern physics, paving the way for further discoveries and advancements in the field.