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The term relativism belongs to philosophical views and is of many forms like Alethic relativism is the doctrine that tells us the truth is always relative to some particular frame of reference. Overall, relativity is all about the change in perception of different people at a different time in different frames of reference. A frame of reference is not a complicated concept. It is just something you decide is a fixed point or group of connected points. It is completely up to you. For example, when you look up at celestial objects in the sky, you fix the Earth as your frame of reference, and the Sun, Moon, etc seem to move across the sky. Everything is relative to something. People often drive their car real fast on highways, but it is not only the car that is moving. Earth itself is spinning on its axis at more than a thousand miles per hour. The universe itself is expanding. The universe is not only expanding but also the expansion rate is accelerating. Nothing is in absolute rest or absolute motion. Relativity is not just a science or Einstein or Newton or some kind of frustrating equation. Forget science. It’s midnight. You take your clock or darkness as the frame of reference.

You are reading this in the year 2020, probably the cursed year of the 21st century. Somebody will be reading this in 2021 or 2031 or whatsoever else. The time was even there when humans had no idea about numbers. You are eighteen years old that just meant the Earth has revolved around the Sun 18 times or so since the time you were born. The question that arises here is how to define time. Are the laws of physics constant in time? Does time exist? Does classical physics apply to the object moving at more than a thousand miles per second? Would length vary with speed? Is space homogeneous or isotropic? Your clocks run on batteries which make time slow for you as your batteries approach expiry date but not for me and somebody else with a brand new clock. You can reckon time independent of your psychological state.

Just for fun

Likewise, the directions (East, west, north, and south) are all possible because of the frame of reference. Does anything like west or north or south or east make sense to this universe? People usually relate the theory of relativity with its consequences but not the actual theory.

The concept of time and many more else will be explained soon. You are not going to tackle with displeasing maths here. If you come across a copy of Einstein’s original paper on relativity from 1905, neither maths nor vocabularies will perplex you. His writing was quite straightforward to read with equations mostly from algebra that would not be a bother for a typical high-schooler to nail it within a week or so. For Einstein, imagination was better than knowledge. Einstein had a highly visual understanding of Physics. This article is going to be fun and short and with a lot of images. Some sections can be skipped to make the article even shorter. I will let you know about the skippable sections.

Have a look at the image below showing very basic relativity that we have been familiar with it for ages.

This is relativity

Relativity is not difficult to grasp even in science. Relativity is the study of how different observers moving with respect to one another measure the same events. The theory of relativity is popular for accelerating/correcting the Newtonian relativity as well as intellectually explaining the theory of the structure of space-time. The theory of relativity is divided into special and general relativity and are two interconnected iconic theories by Albert Einstein. Special relativity was introduced first and is based upon the universal speed limit, while general relativity deals with the law of gravitation and its relation to other forces of nature, more like the geometric interpretation of gravity. This article is only going to explain special relativity.

Albert Einstein

The theory of relativity has characterized several relativistic phenomena like the relation between the law of physics and inertial frame of reference, the relation between matter(mass) and energy, time dilation, gravitational lensing, speed of light being constant, length contraction, and many more else. The theory of relativity refined the fundamental concept of space, time, matter, energy, and gravity. This theory plays quite a beautiful role in the study of astrophysics, cosmology, modern physics, quantum physics, astronomy, etc.

If the force of gravity attracts every object, then why is the universe expanding? Why is it so?

             Albert Einstein
                                (You can skip this).

Albert Einstein (14 March 1879 — 18 April 1955) was a German-born theoretical physicist. Einstein often transcended the kids of his age group in physics and mathematics. At the age of 12, he successfully taught himself algebra and Euclidean geometry (over a single summer) as well as discovered the proof of the Pythagorean theorem by his unaided efforts. He even started teaching himself calculus. He is the most admired to the general public for the world’s most famous equation or mass-energy equivalence; E = mc^2.

Einstein is also known for

At the age of 16 (in 1896), Einstein failed the entrance exam for admission enrollment in Swiss Federal Polytechnic School in Zürich. However, he obtained exceptional grades in physics and mathematics. Following the principal’s advice of polytechnic school, he attended the Argovian cantonal school (gymnasium) in Aarau, Switzerland, in 1895 and 1896 to complete his secondary schooling. At 17, he enrolled in the four-year mathematics and physics teaching diploma program at the Zürich polytechnic school. In 1900, Einstein passed the exams in Maths and Physics and was awarded the Federal teaching diploma.

Einstein’s view about schooling

Einsteins wanted to devote his life to learning and teaching. After graduation in 1900, Einstein spent around two disappointing years looking for a job that could appoint him as a professor. After a lot of unsuccessful attempts, he ended up employing himself as a patent examiner at the Swiss Patent Office in Bern. Einstein would often wrap up his work as soon as possible to contemplate the beauty of the physics of our universe. Einstein is by far the most important scientific figure of this century. His name is synonymous with genius now.

         History Of Special Relativity
                            (You can skip this).
        
Physicists have been studying relativity for more than four centuries back. The frame of reference is an essential part of relativity theory. For example, Unless you take something as the frame of reference, there will be no up, down, in, out, right, left, front, behind, near, far, center, outskirts, etc in space. Space hasn’t got any graduations or directions. Wherever you are in space, that is the center of the universe for you.

Galilean And Newtonian Relativity

Contrary to the popular myth, it wasn’t Einstein who coined the term relativity. Galileo Galilei and Sir Issac Newton developed the first correct version of classical relativity.

Galileo Galilei

Galilean invariance or Galilean relativity (1632) states that the laws of motion are the same in all inertial frames of reference. An inertial frame of reference is a system of coordinates that is stationary or moving at a constant speed relative to another frame of reference. He explained his principle taking the example of a ship traveling at constant velocity (uniform motion) on a smooth sea. As long as there would be uniformity in the motion of the ship (also sea), any observer below the deck could not be able to differentiate whether or not the ship was moving. You can try this up in the sky (airplane), down here in the land (trains, bus, etc), and even in seas and oceans (ships). Even though the train is moving (uniformly) at 600 miles per hour, there is no way to determine the state of you and train unless you sneak out of the window. Galileo postulated that there is no well-defined state of rest or motion.

Sir Issac Newton

In 1687, Newton came up with three laws of motion called Newton’s laws of motion. These laws completely changed the way physicists used to describe motion of ordinary objects to massive objects like planets itself. Newton’s first law of motion states that if the net force acting on a body is zero, then the state of the body remains unchanged. That means either the body is in rest or moving with uniform velocity. So, Galilean invariance states that Newton’s laws hold in all inertial reference frames. In this context, it is sometimes called Newtonian relativity.

A ball dropped by a person sitting in a subway moving at uniform speed will follow the same laws of motion, whether the motion of the ball is observed in the reference frame of the subway or the reference frame of the Earth. However, the trajectory of the ball in each reference frame will vary according to the observer reference frame. Galileo outlined a series of transformations known as the Galilean Transformations which describe how the position and velocity of an object change between different inertial reference frames, based on the assumption that the time elapsed between two given events is the same in both reference frames.

Suppose, you are standing on pavement/sideways looking at a motionless car which is 1km behind you. Now the car starts moving.

You and car

If the person drives the car 3km forth or back, he says the car’s displacement is +3km or -3km respectively. That is a pretty obvious coordinate representation. Now you and the car are sharing the same position analogous to two ends of a perpendicular line drawn between two parallel lines. 

Car is approaching you

As the car passed you, you observed that it covered 60km within 30 minutes and 120km within an hour.

The car keeps on moving

So, you may come up with a simple equation for the car’s displacement with respect to you.

The equation derived by you

Since the car was 1km behind you, his displacement with respect to you would be 61km within 30 minutes and 121 km within an hour. By analyzing your position and the car’s initial position, we can generalize it with a simple combined equation. This is what we call Galilean Transform Equation.

Combined equation
Galilean transform equations

In other words, Galilean transformation equations deal with the concept that space and time are absolute. Classical relativity can explain the Physics behind the body moving at low velocities(like everyday motion on Earth). Galilean relativity didn’t seem to be valid for electricity and magnetism represented by Maxwell’s equations (will come soon). Speed is given by distance traveled (space) upon duration (time). The speed of electromagnetic disturbances couldn’t be explained just by Galilean relativity. It was as if speed could affect the length, mass, and time depending on the relative motion of the observer. The clocks of two people would agree if they were at rest with respect to each other but not if they were in motion. But according to Galilean transform, length, time, and mass are independent of the relative motion of the observer. In the Galilean transform, nothing was constant (not even light). The speed of light was also supposed to be dependent upon the relative motion of the observer. It turns out that the speed of light is always constant in special relativity, regardless of what frame of reference you prefer. The constant nature of the speed of light seems to fail the notion of the classical interpretation of space and time. The Galilean transformation was replaced by the Lorentz transformation. First of all, let us get to know about how electricity, magnetism, and light were proved as the different manifestations of the same phenomena.

Ether And Wave Nature Of Light

In the 1660s, an atomist named Pierre Gassendi (1592–1655) proposed a particle theory of light which was published posthumously. That means light is made up of the finest particles. Newton’s curiosity about Gassendi’s work eventually directed him to hypothesize that light was a stream of particles or corpuscles which were emitted in all directions from a source. He also surmised that the corpuscles moved with equal speed concerning the absolute reference frame. Newton’s idea was that if the light was supposed to be a wave, then it should bend around obstacles rather than propagating in a straight line as waves were theorized to be bent around obstacles then. The particle theory of light managed to explain phenomena like reflection, but it turns out to be a bit puzzling in the case of refraction. He speculated about the polarization of light and inferred that it was due to the particle theory of light, making him the first person to qualitatively explain the Polarization of light. But other thinkers that followed, interpreted the wave theory of light as evidence that could explain polarisation most scientifically. The wave theory of light did explain convincingly the polarization of light. Newton’s corpuscular theory of light was accepted by many scientists, in spite of the fact that it couldn’t demonstrate a few optical phenomena like interference. Some physicists were against the particle nature of light. They put forward a fact — all the optical Phenomena that light possessed were due to wave nature.

Corpuscles

Previously, it was thought that all waves needed a medium for its propagation, pretty similar to water waves that need water for propagation or sound waves that need air for propagation (We now know that no transmission medium is required for electromagnetic radiations like light itself). So, the physicists at that time came up with a concept of Luminiferous aether or just ether that acts as a medium to travel light through the vacuum of space. In the 17th century, Robert Boyle was a proponent of an ether hypothesis. Luminiferous aether or just ether was a hypothetical medium for the propagation of light (or electromagnetic radiations). It had to have some strange properties:
• Invisibility, of course.
• It was massless.
• It filled all of the space.
• High rigidity, so light could travel so quickly through it.
• It had no drag on objects moving through it: the Earth isn’t slowed down in its orbit.

In 1690, Dutch physicist Christiaan Huygens hypothesized that light was a wave propagating through luminiferous aether or ether. However, Christiaan illustrated that wave as a longitudinal wave. But this didn’t work out to explain the phenomenon like polarisation accurately. The polarization of light proved that light is a transverse wave.

Polarization of light
Wave

In the early 1800s (1801–1803), English physicists Thomas Young made a remarkable contribution to the wave theory of light through his brilliant experiment called the double-slit experiment.

Thomas Young

Young’s experiment was based on the water waves or ripples. When the surface of calm water was disturbed at two separate points (Opposing water waves created), waves either added up (reinforced) or destroyed each other. You can try this.

Water surface disturbed at two points
Interference pattern on water surface

Wherever the crest of one meets another, they add up creating larger waves, while the meeting of crest and trough provokes the waves to cancel each other producing a flat surface in that area. 

Wavelength, Crest, and trough

One of the key aspects of the double-slit experiment was to measure the wavelength of light. The ordinary light sources (candles, lamps, etc) can’t act as a coherent source of light. Young set up his experiment so that a single beam of light from the sun (as a coherent source of illumination) entered a darkened room through a small pinhole in a window shutter. A mirror was used to direct the pinhole beam horizontally across the room. This beam of light was then split into two by placing a piece of card in its path, resulting in the partial beam of light passing through the left and right side of the card. Now the light waves from these two sources (the right and the left side of the card) can be considered as two coherent sources of light as they both emerged from the Same source i.e. sun. Young observed that the overlapping of the two waves created interference patterns. He showed that light added to light could produce more light—or, most surprisingly, darkness. The interference pattern was then projected onto a screen. By applying maths on certain parameters, Young measured the wavelength of light. The point was that if the light was composed of classical particles, it shouldn’t create interference patterns. One would expect to see classical particles pattern corresponding to the size and shape of the apparatus used rather than an interference pattern.

(In the original experiment performed by Young, there was no use of slit. Now, the technologies are advanced enough to produce a coherent source of light, and many more else like by preferring a laser beam as the source of light, a carbon-coated glass slide with two closely spaced etched slits can replace the paper card, etc. (The modern double-slit experiment is based on the advancement of Young’s interference experiment and makes a significant contribution to the concept of wave-particle duality). Young’s radical ideas about the nature of light weren’t appreciated well enough for some years.

Young’s work was afterward appreciated by the work of Augustin-Jean Fresnel (1816) and was able to explain the interference and polarisation phenomenon satisfactorily. So, it was believed that light propagates as a transverse wave within an elastic medium called luminiferous aether or ether. Thomas Young has been known as “The last man who knew everything”.

Light, A Electromagnetic Wave

In 1831, Michael Faraday discovered electromagnetic induction. The process of production of current or induced emf in a coil (electric field), whenever there is a change in magnetic flux (magnetic field) linked with coil or just relative motion between coil and magnet is called electromagnetic induction.

Electromagnetic induction

Faraday also provided the base for the concept of mutual induction. Faraday’s immense achievement was introduced when he wrapped two insulated coils of wire around an iron ring. He discovered that upon passing a current through one coil, a momentary current was induced in the other coil. This phenomenon is now known as mutual induction.

Mutual induction

Thus, Faraday concluded that a change in the magnetic field could produce an electric field. That was later termed as Faraday’s law which will come up soon. He also conceptualized that magnetism could affect rays of light.

Michael Faraday

Michael Faraday was such an adorable English scientist that even Albert Einstein kept a picture of Faraday on his study wall, alongside pictures of Issac Newton and James Clerk Maxwell.

The mathematical framework of Michael Faraday’s work was pioneered by Lord Kelvin in 1845, where he described that electric induction takes place not due to incomprehensible action at a distance but of the dielectric or intervening medium. That led Faraday to discover Faraday’s effect (the rotation of the plane of polarisation or just plane of vibration of a light beam by a magnetic field) in the same year. Faraday successfully managed to relate light, magnetism, and electricity all at once.

Lord Kelvin

James Clerk Maxwell studied Michael Faraday’s work and presented a simplified model of Faraday’s work of the 1860s. In 1861, Maxwell came up with a mathematical model of Faraday’s work, Lord kelvin’s work as well as all of the current knowledge and reduced them into twenty mathematical equations. Those twenty equations were, later on, summarized down to four equations by Oliver Heaviside (in the 1870s) known as Maxwell’s equation. Maxwell’s equations have been addressed as the “second great unification in physics” after the first one by Sir Issac Newton. He is honored with the same brilliance as Einstein and Newton possess in the scientific community. Those four equations are described below briefly. No need to worry about maths. I will just explain the true meaning and application behind these equations. All the modern electrical appliances and technologies make huge implications of Maxwell’s equation.

Maxwell’s equation

01. Gauss law.

Gauss Law

This equation tells us how electric charges create an electric field and even allowing us to measure the strength of the electric field emanating due to electric charge, based on the concept developed by Carl Friedrich (German mathematician).

Permittivity of free Space

Constant is the property of vacuum of space which acts as the resistance of free Space against the formation of the electric field.

02. Gauss’s law for magnetism

Gauss’s law for magnetism

This tells us that there will be no magnetic monopoles. A magnet can never be monopoles because magnetic lines of force are always in a loop, in essence, magnetic lines of force distributed outward is always equal to inward. You can’t have a magnet with just the North Pole or the just South Pole by itself. Although you cut the magnet’s North end or south end, you won’t get monopoles. Instead, you will get two smaller magnets with two poles.

No monopoles

03: Faraday’s law

Faraday’s law

We have been familiar with this law earlier. It tells us that if you change the magnetic field with times, the electric field will be generated, i.e., electromagnetic induction.

04: Ampere’s law

Ampere’s law

This law explains that moving charges or moving electric fields can generate a magnetic field. In other words, two Current carrying wire can attract each other. The first term of the right-hand side deals with moving charges, while the second term of the right-hand side deals with moving electric field. Well, the second term was Maxwell’s addition to Ampere’s law.

Besides these, numerous physicists made important contributions to Maxwell’s theory like Hendrik Lorentz, Joseph John Thompson, Oliver Heaviside, etc.

Einstein appreciated Maxwell

In 1864, Maxwell made a revolutionary statement that light itself is an electromagnetic disturbance and its propagation must follow electromagnetic laws. Light, electricity, and magnetism are the different manifestations of the same phenomenon. He proposed that light is an undulation in the same medium (aetherial medium) that is the cause of electric and magnetic phenomena. Maxwell found that electromagnetic disturbance always traveled at a particular speed, regardless of how shorter or longer the wavelength might be. He calculated the speed of electromagnetic disturbances using his maths and equations and noticed that the speed was very close to the best available measurement of the speed of light. Well, the speed of light is not only about light but of all the electromagnetic disturbances.

Equation to calculate the speed of light

If the speed of electromagnetic disturbances equal to the speed of light, then light itself must be electromagnetic disturbances. That’s what Maxwell proposed. He demonstrated that light is a wave with both oscillating electrical and magnetic components i.e. electric field and magnetic field. Maxwell calculated the speed of electromagnetic waves to be 186,000 miles per second. There was a point in time when Maxwell was the only person in the world to realize this. He couldn’t prove experimentally at that time. Maxwell’s Laws predicted a constant speed of electromagnetic disturbances in the vacuum.

More generally, he predicted the existence of electromagnetic radiation. Since speed is relative, thereby, light must be relative to something, and that something was supposed to be ether. Maxwell’s theory suggested that it should be possible to experimentally determine motion relative to the aether. However, Maxwell’s theory failed to explain the accurate concept and mechanism and motion relative to the aether.

James Clerk Maxwell

Aether-Wind, Theory Of Ether

The concept of the luminiferous aether was itself strange and mysterious to scientists of that time. Light rays and radio signals were waves in this ether just as sound is pressure waves in air. Ether was the inevitable consequence of the concept that wave always required a medium for its propagation. Some scientists argued with the concept of stationary aether (Partial drag between matter and ether), while some believed contrary to them. 

Water dragging

When a ship moves through the water, it drags a “boundary layer” of fluid along with it. Was it possible that the Earth in its orbit was somehow “dragging” some ether along?  This ideology is called frame-dragging. Frame dragging was an attempt to explain the Stellar aberration. According to stationary ether theory, light traveling through a moving medium would be dragged along by the medium. Augustin-Jean Fresnel began to propound the idea of stationary aether, meaning that aether is partially dragged with a certain coefficient due to relative motion between matter and aether.

Augustin-Jean Fresnel

In 1845, some physicists like George Gabriel Stokes encouraged the concept that aether was entirely dragged by matter but changeable for rapidly moving bodies and slow-moving bodies. According to this theory, aether is rigid for faster bodies and fluid for slower bodies. Therefore, Earth could move through it fairly freely, but it would be rigid enough to transport light. This theory was proved wrong in 1851 by the Fizeau experiment. 

Fizeau experiment was a special interferometer arrangement to detect a dragging effect — relative speed of light in moving water. This experiment was performed by French physicist Hippolyte Fizeau in 1851.

Fizeau experiment

The light of the source is split up into two beams using a halve way mirror (50% light transmitted, 50% reflected) in such a way that one beam travels with the flow of water and another beam against the flow of water. Water is flowing with speed V. The two rays unite at the interference detection point, where they produce the interference pattern.

Refraction

The refraction index of glass is 1.5 which just means that light travels 1.5 times rapidly in a vacuum than it does in a glass.

To calculate the speed of light in water or a given medium, one measures the speed of light through water or given medium and the speed of water or that medium. The addition will result in the speed of the beam of light.

Let us assume that the refraction index of water is n, and the speed of light in water is w.

W = c/n

According to the stationary ether model, the concept/hypothesis of frame-dragging or dragging effect was unavoidable. Considering this model, the speed of light in water could be interpreted in two ways, i.e., while light travels along with water, while light travels opposing the flow of water.

(I) While light travels along with water

(II) while light travels against water

And by studying the interference pattern, Fizeau calculated the speed of light with respect to the speed of the water.

The drag coefficient of Fresnel is
(1 – 1/n^2)

The outcome of this experiment perturbed physicists greatly. This experiment confirmed the dragging effect but didn’t satisfy physicists, cause the experimental dragging effect measurement was annoyingly less in magnitude than the expected/theoretical one. It was a very pressing issue. But that was scientific enough to refuse Gabriel’s theory of ether. Moreover, Gabriel’s theory couldn’t explain the concept of stellar aberration.

In 1881, Albert A. Michelson tried to measure the relative motion of matter (Earth) and ether. This is known as aether-wind. He didn’t find any relative motion, thereby, he went against the Fresnel theory of ether. Lorentz in 1886 disagreed with Michelson saying that his maths and accuracies were absurd. That made Michelson, perform a repetition of the experiment along with Edward W. Morley. This is called the Michelson—Morley experiment.

Edward W. Morley

Michelson–Morley Experiment

The results of the Michelson–Morley experiment discombobulated the Physicists of that time. The experiment was completely against expectancy leading to nothing but several other conjectures and theories. The experiment was performed between April and July 1887 at the Case Institute in Cleveland, Ohio, by Michelson and Morley with larger accuracy.

Albert A. Michelson

Since the complete drag of ether by matter was rejected by the Fizeau experiment, the partial drag/stationary ether was accepted which coined the existence so-called term “aether-wind”. The experiment aimed to detect the relative motion of matter and luminiferous ether by intellectually considering two beams of light at the right angle to each other, and Earth’s movement as their major experimental apparatus. Earth orbits around the sun at the speed of 108,000 Km/hr or 30 Km/s.

Michelson-Morley experiment

Michelson and Morley built a Michelson interferometer which mainly consists of a light source, a half-silvered glass plate, two mirrors placed at the right angle to each other, and a detector. Light from the source hits a half-silvered glass plate which causes half of the light to bounce off vertically, and the other half going through it. Because two mirrors are placed at equidistant from the half-silvered mirror, the two perpendicular rays of light will again bounce back to the half-silvered glass. Meanwhile, the half-silvered glass will again reflect and transmit these rays of light causing them to reunite at the detection point. At the detector, the interference pattern (either constructive or destructive) is observed because of the overlapping of two waves.

If there was a luminiferous ether, then these light waves traveling in orthogonal direction should be going at different velocities depending on the direction of ether-wind. If light waves were traveling along with the direction of ether, it should be going faster and vice versa, similar to the boat traveling along with current always moves faster. No matter how they rotated or arranged their apparatus, they always received the same interference pattern. Michelson and Morley were able to measure the speed of light by examining interference fringes between the light which had passed through the two perpendicular arms of their apparatus.

Earth and the aether are in relative motion. As the Earth rotates on its axis and orbits around the sun as well, it will move through the ether resulting in the divergent in the speed of two-beam of light. Although ether was believed to unmoving and static, the speed of wave was thought to be speeding up or slowing down if they travel the same or opposite direction of the Earth’s movement respectively. But the result yielded was negative, no daily or yearly difference between two beams of light was found. It was as if light always traveled at the same speed relative to you, no matter how the Earth was moving.

That was the time when the concept of ether-wind was kind of divided into two possibilities: either this ether isn’t having an effect on speeding up or slowing down of light waves or there’s no ether. A series of experiments were performed in different years. Now it has been proved that there is no existence of ether, light doesn’t need a medium to propagate. However, the most famous failed experiment revolutionized Physics. Einstein once wrote, “If the Michelson–Morley experiment had not brought us into serious embarrassment, no one would have regarded the relativity theory as a (halfway) redemption.

Length Contraction And Slowing Down Of The clock

The Irish physicist George FitzGerald and the Dutch physicist Hendrik Lorentz had the solution for the negative result of the Michelson-Morley experiment. They suggested that bodies moving through the ether would contract and that clock would slow. The concept of the contraction was coined by George FitzGerald in 1889, the shortening of an object along the direction of its motion relative to an observer, and it was thereafter independently developed by Hendrik Lorentz. It is also called Lorentz–FitzGerald contraction (hypothesis).

Hendrik Lorentz

Lorentz comprehended the stationary ether hypothesis proposing that electrostatic fields in motion were deformed, i.e., because of the electrons in materials (interferometer and everything else), the interaction between electrons and ether might cause the shrinking/contraction of materials by a certain amount in the direction of motion but not in the transverse direction. On further development, Lorentz found that clocks moving through the ether should run slow too by a certain amount. Lorentz made the substitutions into Maxwell’s equations which are now known as Lorentz transformation. Thus, the shrinking and slowing down of the clock would be in such a way that one would get a constant speed of light, regardless of how fast one was moving with respect to the ether. That made physicists replace Galilean transformation equations with Lorentz transformation equations. Lorentz transformation idea was pretty wacky. According to this transform, space and time are not absolute. That means the length, time, and mass are dependent on the relative motion of the observer. This transform also clarified that the speed of light in a vacuum is constant and independent of the motion of the observer or the source.

George FitzGerald

However, we can’t observe this phenomenon in our daily life because the speed is quite low, relatively it will bring us back to classical relativity. Lorentz did not interpret or utilize his equations in the same way that Einstein did. The main difference between the relativity of Einstein and the relativity of Newton is that the laws of transformation connecting the coordinates and times between relatively moving systems are different, Lorentz transform.

Lorentz transformation equations

Poincaré’s Principle Of Relativity

Lorentz’s farcical hypothesis was not accepted by many physicists. Lorentz’s ideas were thought of as the extrapolation of a false Science which was invented just to disprove the ether-wind. Neither in a philosophical sense nor in a scientific sense that was acceptable. But Lorentz turns out to be right. It was the French mathematician Henri Poincaré who proposed that there is no way to determine absolute velocity, in essence, the law of nature itself does not allow us to discover ether-wind by any experiment. His point was that the complete conspiracy is itself a play/law of nature. Poincaré’s principle of relativity states that The laws of physics should be the same in all reference frames which move in uniform motion with respect to one another.

Henri Poincaré

Gedankenexperiment(German: “thought experiment”)

It was the thought experiment that Einstein came up with at the age of 16 (late 1895 to early 1896), where he imagined chasing after a beam of light while traveling parallel to that beam of light with the speed equals to the speed of light. Following the relativity of classical Physics, then Einstein should have seen that beam of light moving at a relative speed of zero. That would violate the laws of electromagnetism, i.e., Maxwell’s equation. That means Einstein could be able to see the electromagnetic field at rest or say frozen light waves. But Maxwell’s equation showed that electromagnetic disturbances(ripples in the field) or electromagnetic waves(like light) always travels with the speed of 3 × 10^8 m/s. Nothing in the theory allows a light wave to have a speed of zero(literally, zero exception).

The scenario became even worse. According to classical mechanics, the same laws apply to all observers. But the case varies here: if a fixed observer sees light as having a speed of 3 × 10^8 meters per second, whereas an observer moving at the speed of light sees light as having a speed of zero. This clearly states that the laws of electromagnetism depend on the observer. The thought experiment contradicted both Newtonian relativity as well as Laws of electromagnetism.

Einstein struggled 10 years longer for the search of the best scientific answer to his thought experiments which led him to a series of other thought experiments.

A Moving Train And The Light Beam’s Speed, A Thought Experiment

In the year 1904, Einstein showed up with an amazing thought experiment that might seem improbable at first glance but is true and real. Einstein made strenuous efforts to figure out the issue of Maxwell’s equation in his previous thought experiment. He started thinking of a radical idea; What if Maxwell’s equation or rather the speed of light is always constant. The notion was quite simple and was the only way to reconcile Maxwell’s equations with the principle of relativity.

It doesn’t matter whether the light source approaches you, leaves you, or how fast the source is going, you will always measure that beam’s velocity to be 186,000 miles a second. Einstein would never see the stationary, oscillating fields because he could never catch the light beam. Einstein elucidated this with another thought experiment — Imagine firing a light beam along a railroad embankment just as a train roars by in the same direction at, say 2,000 miles a second. Someone standing on the embankment would measure the light beam’s speed to be the standard number, 186,000 miles a second. But someone on the train would see it moving past at only 184,000 miles a second. If the speed of light was not constant, Maxwell’s equations would somehow have to look different inside the railway carriage, Einstein concluded, and the principle of relativity would be violated.

However, the conflict between relativity and Maxwell’s equations wasn’t settled yet. Despite his best endeavors, nothing satisfied him. But then, on a beautiful morning in May 1905, he was walking to work with his best friend Michele Besso, an engineer he had known since their student days in Zurich. They were discussing Einstein’s dilemma, as they often did. And suddenly, Einstein saw the solution. He worked on it overnight, and when they met the next morning, Einstein told Besso, “Thank you. I’ve completely solved the problem.”

Lightning And A Moving Train, A Thought Experiment, May 1905

The consequence of this thought experiment reflects the discrepancies of time between observers in relative motion, i.e., Even though two events happen simultaneously from the interpretation of one observer, the clock of one observer may vary from the interpretation of the other observer. Alluringly, both observers can be right. Einstein later adorned his preposterous idea with another thought experiment.

Imagine you’re seated in the middle of the train, while your friend is standing outside on the platform as the train roars by. As the midpoint of the train passes by your friend on the platform, he sees each end of the train is struck by a bolt of lightning, one on the front and one on the rear. Because the lightning strikes traveled the same distance from your friend’s eyes, he correctly says that they happened simultaneously.

He also predicts that you are closer to the bolt of lightning that the train is moving toward. That means you will notice the front strike before the rear strike as the rear strike is moving away from the train. Meanwhile, you are on the train sitting at its exact midpoint. From your perspective, the light from the two strikes also has to travel equal distances, and you will likewise measure the speed of light to be the same in either direction. But the train is moving. So, you do notice that the flash from the front before the flash from the rear exactly as your friend predicted.

Now, Whose interpretation is correct; either you on the train or your friend on the platform? Einstein tells us that they both are correct within their own frame of reference. In short, Einstein realized, simultaneity doesn’t exist but is rather relative. This thought experiment showed that time moves differently for someone moving than for someone standing still in essence events that are simultaneous for one observer may not be for another. Time and space are relative. This is the cornerstone of special relativity.

Thus, Einstein rejected the possibility of ether claiming that there is no absolute frame of reference that aether could be theorized, i.e, the ether hypothesis was abandoned as being unnecessary in terms of Einstein’s assumption that the speed of light, or any electromagnetic wave, is a universal constant. Special relativity simply doesn’t require ether. And in 1905, Einstein introduced his special theory of relativity that completely changed the way physics was interpreted back then. Well, it is true that relativity was even before Einstein, but it was only Einstein who solved the puzzle between classical relativity, ether, clash with Electromagnetism, etc, thereby revolutionizing the world of physics.

Special Relativity

The special theory of relativity or special relativity is the theory of the structure of space and time proposed by revolutionary physicist Albert Einstein in the year 1905. It is called special relativity because it applies to specific circumstances only. We will be discussing it soon. Although special relativity has got some limitations, it explains the unexpected nature of reality. This theory is basically the improvement in Galilean transform and theory of motion giving us the actual explanation of how motion, space, time, and mass are interrelated to each other through Lorentz transform. The concept of classical relativity inexplicably seems to fade away considering the special relativity point of view. Special relativity has gained fame among the people outside of science background just with a simple equation:
E = m × c^2, the incomplete equation. Here in special relativity, we will be dealing with some fascinating phenomena that we may not encounter or rather unnoticeable in our ordinary life. Nevertheless, Classical mechanics and relativity are quite good approximations for large and slow-moving objects. Otherwise, we could not use classical physics to launch satellites. In the classical limit (objects larger than submicroscopic and moving slower than about 1% of the speed of light), relativistic Physics becomes the same as classical Physics.

Special relativity is compromised of just two postulates:

1. The laws of physics are the same for all inertial frames of reference (not moving or moving at a constant velocity or non-accelerating).

This was the part of Newtonian/Galilean relativity pioneered by Galileo Galilei. This had been proposed by Henri poincaré as well. To this, Einstein added his second postulate:

2. The velocity of light in empty space/vacuum is the same in all reference frames, and is independent of the motion of the emitting body or regardless of the motion of the light source or observer.

But the thing to be noted here is that the velocity of light can vary under the influence of matter. The velocity of light in glass is lesser than the velocity of light in a vacuum. That’s because the interaction of light with material generates a second wave that combines with light, superimposing each other, the resulting combined new wave moves slower than the actual speed of light.

An inertial frame of reference is a reference frame in which a body at rest remains at rest and a body in motion moves at a constant speed in a straight line unless acted on by an external/outside force. The first postulate is nothing like weird quirks of physics. Let us say that you drop a ball from an airplane flying with half of the speed of Earth’s rotation at a constant altitude and speed. That ball would fall straight down. Now repeat the same experiment on the surface of Earth. You will again find that ball falling straight down to the ground. Literally, there’s no experiment that you could perform to tell whether or not the airplane was moving. The laws of physics are the same for the person outside on the surface of Earth and inside the airplane as well. But right after you see the clouds from the window, you can tell the plane is moving. Not so fast! When you experience turbulence or during takeoff (the motion is non-uniform), you can determine the state of motion, implying that special relativity will be no longer valid. The wonderful outcome of this postulate is the famous equation: E = m × c^2, Energy equals mass times the speed of light squared.

The second postulate unfolds something peculiar about the behavior of light. Maxwell’s equations(the laws of electromagnetism) predicted that light or any other electromagnetic wave travels at a particular speed, i.e., c = 3 × 10^8 m/s in a vacuum, but he did not specify the frame of reference in which light has this incredible speed. Meanwhile, Newton’s laws, where the velocities are the simple vector addition. The vector addition would contradict Maxwell’s equations because of the possibilities of the stationary electromagnetic wave relative to the observer. It is recommended to have a look at the Gedankenexperiment. You can find this right above (in the history of special relativity).

So, this draws to only conclusions that either Maxwell’s equations are wrong (Speed of light is not constant) or an object with mass can never travel at the speed of light. Einstein later illustrated that the vector addition is not valid for the speed of light,  meaning that Maxwell’s equations are correct. That means light always travels at the same speed in a vacuum. This also produces another statement that the object with mass can never travel at the speed of light. Young Albert simply realized that something else would have to change rather than the speed of light. What if the clock itself slowed down. This thought blew his mind. Einstein thus introduced the relativity of simultaneity and time dilation.

If you are standing still on Earth, you will calculate the speed of light to be simply 3 × 10^8 m/s.

Even though you are in a super-fast rocket moving with a speed of 99% of the speed of light, you will still measure the speed of light to be 3 × 10^8 m/s. 

Relativity Of Simultaneity And Time Dilation

The speed of light is the fundamental laws of physics. This is the speed limit/universal speed limit. The speed of light remains constant for every inertial reference frame. It doesn’t matter how hard you speed up your machines, you will never catch the speed of light.

Our clocks have been improving further and further throughout the ages. We use clocks to determine the interval between two events. And of course, all clock measures the same time. No matter whether you are inside the moving Subway or outside the platform. They both will measure the same time. What exactly is time? And the straightforward answer is that the physicists still have no idea. Physicists do know some strange properties of time like relativity of simultaneity, time dilation, etc. The relativity of simultaneity tells us that time is not absolute but is dependent on the observer’s perspective. The clocks are not absolute because of the constant nature of the speed of light. Two events happen at the same time at a different spatial position may happen at a different time when viewed from a moving relative to others. In other words, two people moving relative to each other will not agree with the simultaneity of the same event depending on their frames of reference.

Time can vary with relativity that has nothing to do with your Physiology, nothing with your psychology. But the physics of the universe. Imagine bouncing a tennis ball. You dropped it and catch it again. Let’s say you drop it and takes a second to bounce. In that one second Earth has traveled 80 miles or so in the space around the sun. The question is; Did the ball return to the same space or not? According to your perspective, the ball did return to the same position. But from the perspective of someone watching the Earth, that ball traveled all the away around the sun. This concludes that there is no absolute space and time. Everything is just relative to each other.

Relative of simultaneity is the reality. It is not like the audio illusion or optical illusion. Albert Einstein expressed this scenario with his thought experiment. You can read this thought experiment (Lightning And The Moving Train) right above (in the history of special relativity). Measurements are the essential core of experimental physics.

Time Dilation

Time dilation is the phenomenon of the slowing down of a clock as determined by an observer who is in relative motion with respect to that clock. In other words, time is slower for an observer who is moving relative to another observer. The faster the relative velocity, the greater the time dilation between one another.

Imagine you are in a spaceship moving constantly at 96% of the speed of light, say it V. Inside the spaceship, you installed some apparatus in such a way that light is bouncing between two mirrors separated by height h (see image below). As the light hits one mirror, the clock gives out a tick.

Let us say that for one complete bounce (distance equals to 2h), the time taken is T. And the speed of light is c.

But for an observer on the Earth, instead of just going up and down, the light makes a zigzag motion.

You Versus an observer on Earth

That means a person on the Earth sees the light follow the longer path 2s and take a longer time T’. Geometrically, it gives out a triangle. Here the spaceship is moving with velocity V.

Using Pythagorean theorem, distance (s) is found out to be,

Time (T’), for an observer on Earth is

Squaring the above equation on both sides,

Squaring the time (T) on both sides,

Substituting the value of T and s on T’

As we know, T = 2h/c. So, by doing further maths, we will get the time dilation equation(T’).

Time Dilation equation

Proper Time (T) measured by you inside a spaceship is lesser than that measured by an observer on Earth (T’). Therefore, the clock slows down for you relative to an observer on Earth. A person on Earth sees time dilate for a spaceship moving relative to the Earth. It’s not just the mechanical feature of your clock, but every biomechanics would slow down like cellular, metabolic activities, and so on.

At low velocities or rather mathematically, special relativity approach to classical relativity, minuscule time dilation. Mathematically, if the magnitude of v is extremely small, then elapsed time T and T’ will be the unnoticeable, quite small relativistic effect. Well, time dilation even takes place at low velocities. If an airplane goes around the Earth, then clock on ground and clock on airplane will show discrepancy, a few billionth of a second. It has actually been performed with ultra precise clock (like atomic clock), and the discrepancy satisfies the time dilation equation. For smaller relativistic effect, you just need to have an instrument that could detect every minor change.

Likewise, Some Muons produced by cosmic ray particles travel near the speed of light. The muon’s half-life as measured from our frame satisfies the above equation. That means the faster the muon moves, the slower it decays. There are so many experiments that have confirmed time dilation.

Because of the high speed of satellite orbiting around the Earth, they posses relativistic effect and can show discrepancy in time. That’s why, the satellite clocks are programmed with correction factor to account for relativistic effect and remain in sync with Earth. Otherwise, your GPS and many other devices will not be accurate.

Satellite orbiting the Earth

  TIME DILATION (THE SIMPLEST EXPLANATION)

Imagine the same scenario once again that you are inside a spaceship, where the light is bouncing between two mirrors separated by distance h (say h = 3m). Let’s say that speed of light(c) is just 6 m/s. Your measurement of time (T) for a single bounce will be 2 seconds.

For an observer on Earth, the light has traveled more distance because the spaceship itself is moving. Let us call that distance(s) to be 12m. According to 2nd postulate, the speed of light is the same for all reference frames. So, an observer on the Earth will measure the time(T’) to be 4 seconds.

A short video of Professor Brian Cox explaining time travel

The Twin Paradox Is A False Paradox

Let us make the use of time dilation equation in the previous scenario, where you were traveling in a spaceship constantly with 90% of the speed of light or 0.9c. Let us suppose you explored interstellar space at the age of 60 for 6 months and then traveled 6 months back. How long would that be for your twin brother on Earth?

So, that would be 2.29 years for your twin on Earth, while it was just a year for you. You are 2.29 years younger than your twin brother on return. Your biological clock has been slowed down in comparison to your twin brother.

The paradox arises with inertial reference frames. According to your twin on Earth, you traveled quite fast to interstellar space for a year long. That implies that you should have aged less. But to you in the ship, it was the Earth that sped away and came back a year later. That implies that your twin brother on Earth should have aged less. This makes the case quite spooky as if there was no answer whether or not you would be younger than your twin on return.

The crux of the matter is that it was the spaceship that was performing all the accelerating and decelerating, making it a non-inertial reference frames as your twin on Earth didn’t experience this acceleration and deceleration. We know that special relativity is only applicable for an inertial frame, meaning that non-accelerating or rotating. This paradox holds no longer the meaning of special relativity. So, we must consider Earth as our inertial reference frame, and you for sure will be younger than your twin on Earth.

Lorentz contraction

The speed has got an uncanny ability to fail the notion of absolute time. Speed means the distance covered within a certain duration. Does that mean speed could also fail the notion of absolute space? Yes. The speed of an object does fail the notion of absolute space. In special relativity, physicists call this phenomenon Lorentz contraction or Lorentz–FitzGerald contraction. Length Contraction is the phenomenon of shrinking of an object moving relative to the observer’s frame. In other words, the moving object length is contracted, making that length shorter than the proper length. Proper length is the distance between two points measured by an observer at the object’s rest frame, the observer is at rest relative to both points. This is also called the rest length.
               (Length contraction takes place only along the direction of motion).  

Imagine you are on the platform, wanting to measure the length of the moving train. You come up with a brilliant idea to measure its length using just a single equation in essence speed. As the train’s front races by, you turn on your stopwatch and paused your stopwatch as the train’s rear portion races by you. You already know that the speed of the train is v. So, you performed simple maths and calculated the length of the moving train.

Length(L) = distance = Speed (v) × time (T)

Length (L) and time (T) is according to your perspective. For a person inside the train, the clock slows down and is given by time dilation equation. T’ represents the time for an observer inside the train.

Now you will substitute the value of T in your original equation of length.

For an observer inside the train, the length is represented by l and is given by v × T’.

Equation: Length contraction

Hence, the length according to you(L) is lesser than the length according to an observer(l) inside the train along the direction of motion. If the train is moving with 90% of the speed of light, then its length will be shrunken according to your perspective,

Let’s say that l = 100 m, then L = 43.5 m.

This is not just a mathematical fantasy but also has been proven several times. The LIGO gravitational wave detectors are sensitive to changes in distance as small as less than 0.1% the width of a proton. Did you know that electromagnet works because of Lorentz contraction? How?

Relativistic Velocity addition

Velocity is relative in classical physics and Modern physics as well. If you are driving your car with a speed of 90 km/hr, then this speed is simply with respect to the ground/Earth. In classical Physics, the relative velocity is given by the vector sum. The velocity-addition equations signify the velocity of a moving body under different frames of reference. The velocity-addition is pretty intuitive in the case of classical physics.

If the police car chases a robber at A m/s and that robber is running away from that car with a Velocity of B m/s (Velocity with respect to the ground), then the speed of approach by police is given by (A – B) m/s.

Now the robber is exhausted and decided to surrender. He started running toward the police car with B m/s, then the relative speed of approach is (A + B) m/s now.

What if we replace a police car with a beam of light having Velocity C m/s. Just in case if the robber runs away from a beam of light, then velocity-addition will result (C – B) m/s. If he approaches that beam of light, then net Velocity will result in (C + B) m/s.

(C + B) > C, this violated the second postulate of special relativity. We can see that the magnitude net Velocity exceeds the magnitude of speed by light which can’t be possible. Einstein reconciled this with flaw through Lorentz transform equations. Einstein suggested that the Classical velocity combination goes for low velocities only but can’t account for the higher Velocity. Meaning that the equations need some corrections, correction factors.

While approaching
While running away

C stands for the speed of light. According to Einstein, the combined speed will follow the above equations rather than simple addition and subtraction. Let’s say that you are approaching each other with 3/4 c. Classical relativity will result you net Velocity ( 3/4 + 3/4) c = 3/2 c > c. For higher velocities, we will follow the above equation.

Again if we apply these equations to lower Velocities, it will lead us back to classical relativity.

Relativistic Doppler shift

Light is a transverse wave. Sound is a longitudinal wave. Every wave follows the phenomenon called the Doppler Effect. It is named after the Austrian physicist Christian Doppler, who described the phenomenon in 1842.

Let’s get started with a quick story. You are quietly exploring the countryside on a gloomy evening, visualize it. Suddenly, a car is approaching you with its headlights on and with head-splitting noise blaring from the engine. As the car keeps on moving, after a while, your intuition will tell you that the pitch is getting lower, making you feel soothed. While during the approach, the sound was like a pain. This apparent change in frequency due to relative motion between you and the source of sound(or any wave) is Doppler Effect. Meanwhile, the frequency was the same all the time in the driver’s context. The same storyline goes with light too. If you observe the star from the astronomical observatory, the intensity of light will increase or decrease depending upon the star approaching or receding your observation. The Science behind Doppler Effect is that when the source of waves is approaching you, successive wave crest has to travel less distance and takes less time to reach you as compared to the previous one, causing an increase in the frequency.

Despite the speed of light never increase or decrease with relative Velocity, the frequencies and wavelengths do change. The relativistic Doppler effect is the change in frequency and wavelength of light, caused by the relative motion of the source and the observer. The relativistic Doppler Effect includes time dilation, the implication of special relativity.

You will often get to hear the word redshift by astronomers to determine how far away the stars are. Light waves are able to be compressed or stretched just like sound, but in this case, the color is changed, in sound, it corresponds to frequency. The wavelength of blue is shorter than the red. When an object in space approaches us, the light waves are compressed into higher frequencies and get shifted to the shorter wavelength, resulting in a blue shift. When the object in the space is moving away from you, the light waves are stretched into lower frequencies and get shifted to the longer wavelength, resulting in redshift. The universe is expanding which causes the Doppler Effect. The further away the galaxies are, the more redshifted it will be. Since these motions are relative, so instead of using classical Doppler shift, the relativistic Doppler shift is applied and is given by.

Here V is the relative velocity of the source to the observer, and c is the speed of light as usual. The velocity V is positive for motion away from an observer and negative for motion toward an observer.

Suppose a galaxy is moving away from the Earth at a speed of 0.72c. It emits radio waves with a wavelength of  0.525m. What wavelength would we detect on the Earth?

As it is moving away from the Earth, the redshift will take place which turns out to be 1.30m, redshifted from the original wavelength of 0.525m.

Relativistic momentum

Concerning classical physics, momentum is simply the product of mass and Velocity.  Momentum is an essential aspect to figure out the physics behind work, energy, etc, and how they are conserved. Newton’s 2nd law is stated in the terms of momentum, i.e., the rate of change of momentum is directly proportional to the force applied. In Classical physics, momentum is always conserved (invariant), in essence, when the net external force is zero. The first postulate of relativity states that the laws of physics are the same in all inertial reference frames. This means that the conservation law needs to hold in any frame of reference. Does the law of conservation of momentum hold the meaning of that postulate at high velocities? Relativistic momentum does conserve. It turns out that the Classical definition of momentum is not adequate to describe the momentum of a body moving with pretty high velocity, so in special relativity, momentum has a relativistic effect.

Relativistic momentum (p) is a classical momentum multiplied by the relativistic factor γ.

Relativistic momentum
Relativistic factor

where m is the rest mass (mass of the object in its rest frame) of the object. Note that u is the velocity of the object in a reference frame, not the velocity of a reference frame relative to another (u is used for Velocity to distinguish it from relative velocity v  between observers). This means only one observer is being considered here. With p defined in this way, the total momentum is conserved whenever the net external force is zero, just as in classical physics. The relativistic momentum becomes the classical or non-relativistic momentum at low velocities because γ is very nearly equal to 1 at low Velocities. Mathematically, to get a gamma (Y) value equals 1.01, you need the velocity incredibly faster, fast enough to circle the Earth at the equator in just a single second. If a body moves with Velocity 30% of the speed of light or 0.3c, then gamma will correspond to the magnitude of just 1.049.

Even at 90% of the speed of light, the value of gamma will be just 2.29. As one approaches the speed of light, however, relativistic momentum becomes infinite, while Newtonian momentum continues to increases linearly.

Graphical representation

Relativistic Energy

You may have been familiar with the first law of thermodynamics or simply the conservation of energy — energy is conserved. Classically, we also have the law of conservation of mass. Special relativity tells us that mass is the form of energy and can be converted into energy and vice versa. There is two kind of mass in special relativity — Invariant mass (rest mass), and relativistic mass (Hang on! I know what you are up to). Energy and (inertial) mass are inextricably linked by Einstein’s famous formula.

                 TOTAL ENERGY
                
The first postulate of special relativity states that the laws of physics are the same in all inertial frames. Does the conservation of energy still valid in special relativity? Einstein showed that the law of conservation of energy is valid relativistically. If we define energy to include a relativistic factor, the total energy is represented by an equation:

Total energy equation

Where C is the speed of light, m is mass, and v is the velocity of the body (mass) relative to an observer. If an object Velocity approaches toward c, the magnitude of gamma(Y) gets higher and higher, resulting in an enormous increase in energy. But this doesn’t mean that mass is increased too. As Velocity increases, the mass shall increase too. No. This is just a popular misconception that has been around us for decades. We will get back to it sooner. However, the equation itself has a couple of limitations:

1. It only makes sense for a particle with Mass. Massless particles like photons are not convenient to imply this equation.

2. It deals with Velocities less than the speed of light only. 

                       REST ENERGY

If a body is stationary, then V= 0. That implies Y= 1. This is what we call rest energy (Eo). So, Rest energy is given by

This is the equations that let you calculate the energy of the body at rest. Contrary to popular culture, this equation is not valid for a kinetic object — for special cases only. That means the object must not (Shouldn’t, wouldn’t) move with respect to you. Thus,  this also implies that mass can be converted into energy and vice versa. A body of mass 9 grams or 9 × 10^-3 kilograms has the rest energy 81 × 10^13 Joule. Rest mass is also called invariant mass. The rest mass is a fundamental physical property that remains independent of momentum, even at an extreme speed approaching the speed of light (i.e., its value is the same in all inertial frames of reference); while the relativistic mass is dependent on the velocity of the observer. The most practical implications of conversion of mass into another form of energy are performed by Nuclear power plants. Just a few grams of nuclear fuels can produce a tremendous amount of energy. But there’s no anything like relativistic mass. Physicists dislike this concept. There’s only one mass and also that doesn’t increase with an increase in Velocity. Does that mean an object with mass can travel at the speed of light? No, it doesn’t, can approach the speed of light, but never exactly the speed of light. The most heard explanation for “why an object can’t travel faster than light?” is that your mass increases as you get faster, so you need more kinetic energy to get a little bit faster, but then you get heavier, so you need more kinetic energy…. and so on and so on, until you need an infinite amount of energy. That’s a pretty bizarre concept. What in the world is that wrong?

We have another equation that applies to both kinds of motion (kinetic as well). That can even fulfill the limitation of our previous equation, in essence, explains the energy of a particle with and without mass.

Relativistic Energy and Momentum Relation

m stands for rest mass and is the only mass.

Momentum is basically the motion of the particles.

Let us suppose that an object has zero momentum, then our equation will be

Now let us suppose that a particle is massless like photons, then our equation will be

So, for a massless particle, E = M × C^2 is simply pointless. Light has no mass. That is to say light has no rest mass. you cannot bring a photon to a halt and measure its mass.

It’s outrageous that even Physics students sometimes get this wrong. In reality, kinetic energy in special relativity doesn’t work the same way as it does in classical Physics. The actual reason that you can’t achieve the speed of light is because this is the real equation for kinetic energy.

When V approaches, exactly c, the kinetic energy goes infinity, undefined. Meaning that V = c is not a physical speed for a thing with mass.

We have the most famous Equation, and it looks like this.

If we define mass to be (see image below), it can neatly fit with the concept.

Not so fast! What about kinetic energy. If you plug that moving mass ideology into the classical definition of kinetic energy, then it will result you this

T stands for kinetic energy.

This is very very poor science. This is wrong, and a great example of why the ‘moving mass’ doesn’t make things intuitive! That’s it — no changing mass. We have only one mass and that doesn’t change, but the kinetic energy simply follows a different formula than you intuitively expect it to. Our universe works this way. Astrophysicists Neil DeGrasse Tyson once said that the universe is under no obligation to make sense to you. If some massive heavenly bodies hit Earth, then it’s not the fault of our universe.


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