Why Light Bends by Gravity?

Introduction to General Relativity:

The Equivalence Principle

Einstein's theory of General Relativity builds on the Equivalence Principle, which states that the effects of gravity are indistinguishable from the effects of acceleration. This principle implies that a uniform gravitational field is locally equivalent to an accelerated frame of reference. 

Einstein's Field Equations

The heart of General Relativity is encapsulated in Einstein's field equations:

where:

• is the Ricci curvature tensor,
• is the Ricci scalar,
• is the metric tensor,
• is the cosmological constant,
• is the gravitational constant,
• is the speed of light,
• is the stress-energy tensor.

These equations describe how matter and energy influence the curvature of spacetime.

Spacetime Curvature and Geodesics:

Metric Tensor

The metric tensor gμν​ defines the geometry of spacetime. In the presence of a massive object, this tensor describes how distances and times are measured differently compared to flat spacetime.

Geodesics

In curved spacetime, the path that light follows is called a geodesic. Mathematically, a geodesic is the curve that minimizes the spacetime interval:

Light Bending.

Gravitational Lensing:

Bending of Light

When light passes near a massive object, its path bends due to the curvature of spacetime. This bending can be calculated using the lens equation:

where:

• is the observed position of the lensed image,
• is the true position of the source,
• is the deflection angle,
• is the distance between the lens and the source,
• is the distance to the source.

Deflection Angle

The deflection angle α can be derived from the Schwarzschild metric for a point mass M:

where, b is the impact parameter, the closest approach of the light ray to the massive object.

Historical Verification:

1919 Solar Eclipse

The first observational confirmation of light bending by gravity was made by Sir Arthur Eddington during the solar eclipse of 1919. Eddington measured the positions of stars near the Sun and found them to be shifted, confirming Einstein's prediction. 

Types of Gravitational Lensing:

Strong Lensing

Occurs when the alignment of source, lens, and observer is very close, resulting in multiple images, arcs, or Einstein rings.

Weak Lensing

Involves slight distortions in the images of background objects. This type is used to study the distribution of dark matter.

Microlensing

Causes temporary brightening of a background star when a smaller object like a star or planet passes in front of it. This technique is often used to detect exoplanets.

Mathematical Representation and Calculations:

Deflection Angle in a Weak Field

For weak gravitational fields, the deflection angle α is small, and the bending can be approximated using linearized gravity.

Exact Solutions

For strong fields near black holes or neutron stars, exact solutions to Einstein's field equations are required. The Schwarzschild and Kerr metrics are commonly used for these purposes. 

Applications and Implications:

Astrophysics

Gravitational lensing is used to study distant galaxies and quasars, revealing information about their mass and structure.

Cosmology

By observing the lensing of distant objects, scientists can map the distribution of dark matter and study the expansion of the universe. 

References and Further Reading:

1. Einstein, A. (1916). The Foundation of the General Theory of Relativity. Annalen der Physik, 354(7), 769-822.
2. Carroll, S. M. (2004). Spacetime and Geometry: An Introduction to General Relativity. Addison-Wesley.
3. Weinberg, S. (1972). Gravitation and Cosmology: Principles and Applications of the General Theory of Relativity. Wiley.
4. Misner, C. W., Thorne, K. S., & Wheeler, J. A. (1973). Gravitation. W. H. Freeman.
5. Schneider, P., Ehlers, J., & Falco, E. E. (1992). Gravitational Lenses. Springer-Verlag.
6. Dyson, F. W., Eddington, A. S., & Davidson, C. (1920). A Determination of the Deflection of Light by the Sun's Gravitational Field, from Observations Made at the Total Eclipse of May 29, 1919. Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, 220(571-581), 291-333.  

How are Tides Formed?

Tides:

Tides are the regular rise and fall of sea levels caused by the gravitational forces exerted by the Moon and the Sun, as well as the rotation of the Earth.

The Basics of Tides:

Gravitational Pull: The Moon’s gravity pulls on the Earth's water, creating a bulge of water on the side of the Earth facing the Moon. This bulge is the high tide.

Centrifugal Force: As the Earth and the Moon orbit around a common center of mass, a centrifugal force is generated. This force causes another bulge on the opposite side of the Earth, creating a second high tide.

Types of Tides:

High Tide: Occurs where the water is bulging due to the gravitational pull of the Moon and the centrifugal force.

Low Tide: Occurs in areas between the high tides, where the water level is lower.

The Role of the Sun:

The Sun also exerts a gravitational pull on the Earth's waters, but it is less significant than the Moon's pull because the Sun is much farther away. However, the Sun's gravity can either enhance or diminish the effects of the Moon's gravity:

Spring Tides: When the Sun, Moon, and Earth are aligned (during full moon and new moon), their combined gravitational forces create higher high tides and lower low tides. These are known as spring tides.

Neap Tides: When the Sun and Moon are at right angles to each other (during the first and third quarters of the moon), their gravitational forces partially cancel each other out, resulting in lower high tides and higher low tides. These are called neap tides.

The Tidal Cycle:

Semi-Diurnal Tides: Most coastal areas experience two high tides and two low tides every 24 hours and 50 minutes. This is because it takes about 24 hours and 50 minutes for the Earth to complete one rotation relative to the Moon.

Diurnal Tides: Some areas experience only one high tide and one low tide each day.

Mixed Tides: In some locations, there are two high tides and two low tides of different heights each day.

Factors Affecting Tides:

The Shape of the Coastline: Coastal shapes can influence how high or low tides are. Narrow bays, inlets, and estuaries can experience much higher tides than more open coastlines.

Ocean Basin Topography: The depth and shape of the ocean floor can affect tidal ranges. Shallow areas can amplify the effects of tides.

Earth’s Rotation: The rotation of the Earth also affects the timing and height of tides, creating complex tidal patterns.

Tidal Effects and Uses:

Intertidal Zones: The area between high and low tide marks is called the intertidal zone. This area is rich in marine life and is crucial for many ecosystems.

Tidal Energy: Tides can be harnessed to generate renewable energy. Tidal power plants use the movement of water caused by tides to produce electricity.

Navigation and Fishing: Knowledge of tides is essential for navigation and fishing. Ships must account for tides when entering and leaving harbours, and many marine species rely on tidal cycles for breeding and feeding.

Tides are a fascinating natural phenomenon influenced by the gravitational pull of the Moon and the Sun, the rotation of the Earth, and the shape of coastlines and ocean basins. They play a crucial role in marine ecosystems, human activities, and even renewable energy. Understanding tides helps us appreciate the intricate connections between celestial bodies and our planet’s oceans! 

The Toughest Predators Ever: Tyrannosaurus Rex.

    Tyrannosaurus Rex was one of the most ferocious creature to ever roam the Earth. With a gigantic body, keen teeth, and jaws powerful enough to smash a vehicle, this renowned carnivore controlled the forested river valleys of western North America during the late Cretaceous period, 68 million years ago.

    T. Rex is a well-known Tyrannosaur, yet our understanding of him is continually changing. Improved technologies, including as biomechanical modelling and x-ray imaging, have helped scientists obtain a better understand of how this apex predator lived.

    Tyrannosaurus rex, which means "King of the Tyrant Lizards," was designed to take control. This dinosaur's massive body covered up to 40 feet—roughly the length of a school bus—from its nose to the tip of its powerful tail. T. rex, weighing up to eight tonnes, raised headfirst across its territory with two powerful legs. These dinosaurs most likely hunted living animals and collected cadavers, and they occasionally ate one another.

    Tyrannosaurus rex had a good sense of smell, which helped it find its prey. While scientists have long known that this dinosaur's brain was dedicated to scent processing, current research has revealed that T. rex has nearly as many genes encoding its olfactory receptors as a house cat does today. This strong nostrils most likely helped T. rex find mates and identify other predators.

    The head of a Tyrannosaurus dinosaur was very terrifying. This ruthless carnivore was designed to crush through its prey, with a hard cranium that allowed it to concentrate all of its muscle power into a single bite, making a up to six tonnes of pressure. This dinosaur utilised its 60 hooked teeth, each about eight inches long, to puncture and hold flesh before throwing it into the air and eating it whole. To protect from overheating while crushing prey with its powerful jaws, the gigantic animal developed openings in its head to keep its brain cool, similar to those found in alligators.

Tyrannosaurus Rex.

    Tyrannosaurus rex, a ferocious dinosaur, had tiny arms that biologists debated. Some believe they were evolutionary leftovers or served non-predatory purposes, while others argue they were evolved for "cruel cutting" in close quarters. Considering their powerful thighs, these dinosaurs could only walk at 12 miles per hour, which scientists believe would have fractured their feet if they travelled faster.

    Tyrannosaurus rex, a dangerous predator with a life expectancy of 28 years, suffered a growth rise during its adolescent years. A 2020 analysis of Nano Tyrannus fossils found that the bones belonged to a young T. rex rather than another species. This shows that Tyrannosaurus rex's growth rate varied as it aged, and that it could slow down when food was limited. Despite its advantages, T. rex was unable to equal the 66 million-year-old catastrophe that killed three-quarters of all species on Earth. This catastrophe occurred when an asteroid or comet collided with Earth, destroying Tyrannosaurus rex and other non-avian dinosaurs and marking the end of the Cretaceous epoch. 

The Photoelectric Effect.

    A process known as the photoelectric effect occurs when a substance, usually a metal, absorbs enough light to cause electrons to be expelled from its surface. This phenomenon made a fundamental contribution to the advancement of contemporary physics and offered vital data in support of the quantum theory of light. 

Scientific Principles:

Photon Concept:

• Light consists of particles called photons, each carrying a discrete amount of energy determined by its frequency (E=hv), where "h" is Planck's constant and "v" is the frequency of the light.

Energy Threshold:

• For electrons to be ejected from a material, the energy of the incident photons must exceed a certain minimum value known as the work function (ϕ) of the material.

Electron Emission:

• When a photon hits the material, its energy is transferred to an electron. If the energy is greater than the work function, the electron is emitted from the surface with kinetic energy given by Ek=hv−ϕ.

Intensity Independence:

• The number of ejected electrons depends on the intensity of the light, but the energy of the ejected electrons depends only on the frequency of the incident light.

Historical Development

Heinrich Hertz (1887):

    While researching electromagnetic waves, the photoelectric effect was discovered. Hertz noted that sparks may jump across metal electrodes more readily in the presence of UV light, but he did not investigate the underlying mechanism.

Wilhelm Hallwachs (1888):

    It was discovered that a negatively charged zinc plate would lose its charge when light fell on it, offering preliminary proof for the photoelectric effect.

J.J Thomson (1899):

    Photoelectrically released electrons' charge-to-mass ratio was measured, and it was determined that these particles were identical to those seen in cathode rays.

Albert Einstein (1905):

    Used the quantum theory to provide a theoretical justification for the photoelectric effect. According to Einstein's theory, the energy of the quanta—later referred to as photons—in light is proportional to the frequency of the light. He was awarded the 1921 Nobel Prize in Physics for this achievement.

Robert Millikan (1916):

    Millikan's work, which involved precise tests to validate Einstein's theory, cleared the air for the linear relationship between the frequency of incident light and the kinetic energy of released electrons. Millikan was first sceptical of the hypothesis.

Impacts:

Quantum Theory of Light

    The photoelectric effect provided evidence in favour of the fundamental tenet of quantum mechanics—that light possesses both wave and particle characteristics.

Useful Applications:

   Numerous technologies, such as photovoltaic cells (solar panels), photomultiplier tubes, and photoelectron spectroscopy, rely on the principles underlying the photoelectric effect.

   One of the key ideas in comprehending how light and matter interact, bridging the gap between classical and quantum physics, is the photoelectric effect. 

The Brief History of The Sun.

The Sun:

The Sun is the star at the centre of our solar system. Its gravity holds the solar system together, keeping everything from the - biggest planets to the smallest bits of debris - in its orbit.

Heat and light are produced by nuclear events that occur deep beneath. In order to produce this energy, The Sun has been using four million tonnes of hydrogen fuel each second since its formation, or around 4.6 billion years ago.

Solar Flares:

A solar flare is a massive eruption that occurs on the Sun when energy that has been trapped in "twisted" magnetic fields- which are typically found above sunspots, Chromosphere -is suddenly released.

They may heat materials to millions of degrees in a matter of minutes, resulting in a burst of radiation that includes: radio waves, X-rays, and gamma rays.

Sun Spots:

Sunspots are areas where the magnetic field is about 2,500 times stronger than Earth's, much higher than anywhere else on the Sun. Because of the strong magnetic field, the magnetic pressure increases while the surrounding atmospheric pressure decreases.

This in turn lowers the temperature relative to its surroundings because the concentrated magnetic field inhibits the flow of hot, new gas from the Sun's interior to the surface.

Sunspots tends to occur in pairs that have magnetic fields pointing in opposite directions.

Why Sun Spots are Dark?

The sunspots are large concentrations of strong magnetic field. Some energy is partially prevented from passing through the surface by this magnetic field.

As a result, sunspots experience a lower surface temperature than other areas of the surface. It appears darker when the temperature is lower.

Coronal Mass Ejections (CMEs):

Coronal mass ejections (CMEs) are large expulsions of plasma and magnetic field from the sun's atmosphere the corona.

Compared to solar flares bursts of electromagnetic radiation that travel at the speed of light, reaching Earth in just over 8 minutes.

Formation of CMEs:

The more explosive CMES generally begin when highly twisted magnetic field structures (flux ropes) contained in the Sun's lower corona become too stressed and realign into a less tense configuration - a process called magnetic reconnection.

Near Earth CMEs Effects:

Auroras:

The CMEs causes stunning light displays known as auroras, visible in the polar regions of the earth.

Geomagnetic Storms:

CMEs can cause significant disturbances in Earth's magnetosphere, leading to geomagnetic storms which are; Satellite Operations, Power Grids, Communication Systems.

Radiation Hazards:

It Increases radiation levels at high altitudes, especially near the poles.

Preventing & Monitoring:

SPACE WEATHER FORECASTING:

To provide early alerts of possible CMEs, organisations such as NASA and NOAA's Space Weather Prediction Centre (SWPC) track solar activity.

AID:

Continuous monitoring and improved prediction models are essential to prevent the bad impacts of CMEs.

How to Find the Sun Spots Area:

To find the area of sunspots, I use the manual formula to calculate the area of the sunspots.

As = ((Af x n) / cos (B) x cos (L))

Where,

As - Area of the sunspot,

Af - Area factor constant for the solar chart image (i.e., 63.66),

n - Number of grid sares occupying the sunspot,

B- Heliographic latitude,

L - Angular distance of the sunspot from the solar disk centre.

The physical unit for the calculated area is a millionth of a hemisphere (MHS). 

Solar Cycle:

About every 11 years, the Sun's magnetic field gradually changes polarity, a process known as the solar cycle. This reversal causes changes in solar activity.

The solar cycle has been observed and recorded since the mid-18th century, with the current cycle being Solar Cycle 25. 

 "Sun, in fact, is the center of the universe" -Nicolaus Copernicus.