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.  

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. 

Nicolaus Copernicus's: Revolutionary the Mind

    On February 19, 1473, in Toruń, Poland, Nicolaus Copernicus—the man who dared to change the centre of the cosmos from Earth to the Sun—was born. Though his life was filled with many varied hobbies and endeavours outside of space exploration, his revolutionary work in astronomy permanently changed our knowledge of the universe.

    Copernicus was raised in a secure and intellectually stimulating atmosphere because his parents were merchants and clergy. Following his father's premature death, Lucas Watzenrode, his uncle, assumed responsibility for his upbringing and education. Prominent clergyman Watzenrode sent Copernicus to study at the University of Kraków in 1491 to make sure he had the greatest education possible. Here, Copernicus was introduced to the complexities of philosophy, astronomy, and mathematics, which stoked his interest in astronomical occurrences.

Copernicus.

    In order to further his education at the University of Bologna in Italy in 1496, Copernicus moved there and resided with the well-known astronomer Domenico Maria Novara. Copernicus's criticism of the geocentric model of the universe—which put Earth at its center—was greatly affected by this mentorship. He pursued further education at the University of Padua, where he studied law and medicine. Later, the University of Ferrara awarded him a doctorate in canon law.

    The widely accepted geocentric model promoted by Claudius Ptolemy was boldly replaced by Copernicus's heliocentric theory. For centuries the accepted wisdom in astronomy was the Ptolemaic system, with its intricate epicycles and deferents. In his more straightforward theory, Copernicus put the Sun at the centre of the cosmos, with Earth and the other planets revolving around it. In 1543, the year of his death, he released his ground-breaking treatise, De revolutionibus orbium coelestium (On the Revolutions of the Heavenly Spheres), which laid forth his thesis.

    A heliocentric cosmos was not just a scientific theory; it was a significant departure from the previous worldview that was influenced by religious and scientific beliefs. Copernicus waited years to reveal his findings because he was worried about what might occur. When he did, many were curious about his views but also opposed to them. With the help of later scientists like Johannes Kepler and Galileo Galilei, the heliocentric theory took decades to become widely accepted.

    Although being mostly recognised for his contributions to astronomy, Copernicus was a true Renaissance man with a wide range of skills and passions. He oversaw the financial and administrative matters of the Frombork (formerly Frauenburg) cathedral chapter while serving as a canon. In addition to controlling the grain supply and keeping an eye on the finances, he also practiced medicine. His medical expertise was especially wanted during plague and other disease epidemics. In addition to his work in mathematics, Copernicus wrote a treatise on the value of money and the depreciation of currency. His understanding of the economy was predicted and reflects his wide-ranging intellectual interest.

Helio-Centric Model.

Astronomer and Artist: Copernicus was not only a skilled mathematician and scientist but also an amateur artist, producing illustrations of his astronomical theories in the form of drawings and diagrams.

Astronomical Tools: In order to make accurate observations of the sky, he built his own astronomical equipment, such as an armillary sphere and a triquetrum.

Delayed Fame: Copernicus's contributions took time to become well-known. His heliocentric concept was not fully understood until much later, thanks to the efforts of other astronomers and the invention of the telescope.

Deathbed Publication: It is reported that Copernicus saw the result of his life's labours before he passed away, as he was given a copy of his published De revolutionibus on his deathbed.

    The legacy of Nicolaus Copernicus is evidence of the value of curiosity and the courage to go against conventional wisdom. In addition to changing astronomy, his heliocentric theory cleared the path for the scientific revolution, which altered our understanding of the cosmos and our place in it. His biography serves as a reminder that genuine innovation often requires having the courage to see past conventional wisdom and journey into unknown spaces.

"To know that we know what we Know, and to know that we do not know what we do not know, Chat is true knowledge." -N. Copernicus.

Particle Nature of light: Einstein's Explanation.

 Particle Nature of light: Einstein's Explanation.

Einstein extended Planck's quantum concept to explain the photoelectric effect in 1905. According to Einstein, the energy in light is not spread out over wavefronts but is concentrated in small packets or energy quanta. Therefore, light (or any other electromagnetic waves) of frequency v from any source can be considered as a stream of quanta and the energy of each light quantum is given by E=hv.
[1] 

He also proposed that a quantum of light has linear momentum and the magnitude of that linear momentum is p=h/c. The individual light quantum of definite energy and momentum can be associated with a particle. can behave as a particle and this is called photon. Therefore, photon is nothing but particle manifestation of light.

Light is made up of particles called Photons.

Characteristics of photons:

According to particle nature of light, photons are the basic constituents of any radiation and possess the following characteristic properties:

i) The photons of light of frequency v and wavelength & will have energy, given by E=hv= hc/λ

ii) The energy of a photon is determined by the frequency of the radiation and not by its intensity and the intensity has no relation with the energy of the individual photons in the beam.

iii) The photons travel with the speed of light and its momentum is given by hhv P=h/λ =hv/c

iv) Since photons are electrically neutral, they are unaffected by electric and magnetic fields.

v) When a photon interacts with matter (photon-electron collision), the total energy, total linear momentum and angular momentum are conserved. Since photon may be absorbed or a new photon may be produced in such interactions, the number of photons may not be conserved.... 

“Matter is Energy… Energy is Light…We are all Light Beings” —Albert Einstein.

  

Story of X-Rays.

 X-rays, like the light are electromagnetic radiations and are not visible to the eye. Their wavelengths are smaller than those of the visible light. They are high energy rays. That is why they have high penetrating power. They can pass through the flesh of our body. They travel with the velocity of light. 

X-Rays image of the human hand.

These rays were discovered by Prof. Wilhelm Conrad Roentgen in 1895. They are sometimes called 'Roentgen rays' also. They were called X-rays (X-means unknown) because these were not known earlier. For this wonderful discovery Prof. Roentgen was awarded the first Nobel Prize of Physics in 1901 .

Wavelength of the Electro-magnetic waves.

The apparatus used for producing X-rays is called 'X-rays tube'. This tube is made up of hard glass and is fitted with two electrodes which are connected to high voltage D.C. source. The electrode connected to the negative terminal is called cathode and the one connected to positive terminal is called anode. Low pressure is created inside the tube by pumping out air from it. When high voltage is applied between the electrodes, electrons emerge from the cathode and hit the 'anode' or the 'target'. As a result the X-rays come out of the tube. 

X-rays are very useful for us. They can pass through substances like wood, paper, skin, flesh etc. but are absorbed by bones, iron,lead etc. Doctors make use of X-rays to detect the dislocations and fractures of bones. They are also used to examine the diseases of lungs and presence of stones in kidneys and gall bladder. X-rays are allowed to fall on the body part to be examined and a photograph is taken on the photo film kept behind that part. In this film the portion of bones appears grey. From these X-ray photographs, the disease and defects are located easily. 

X-rays are also used in treating cancer. With the help of these rays, gold and other valuable gems hidden in the body are detected easily. They are also used to detect cracks and bubbles in the iron bars used for constructing bridges and buildings. They are used to study the structure of crystals. With these rays, it is very easy to distinguish between natural and synthetic diamonds.