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. 

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.  

What are Infra-red Radiations?

We all know that the sunlight consists of all those colours which are seen in a rainbow. These colours are: violet, indigo, blue, green, yellow, orange and red. Light from the sun travels in the form of waves which are known as electromagnetic waves. The different colours of light have different wavelengths. Our eyes are sensitive only to the wavelengths relating to the above seven colours. Apart from the wavelengths of these seven colours, the sunlight consists of radiations of other wavelengths also, but our eyes are not sensitive to them. Rays having wavelengths higher than that of red light are called infra-red rays and those lower than violet light are called ultraviolet rays. Both infra-red and ultraviolet rays are not visible to our eyes.

Spectral Lines.

Infra-red rays come not only from the sun but from every hot object. Burning wood and coal, electric heater-all produce these rays. These can be recorded on special type of photographic films made of infra-red sensitive materials. Whenever these rays fall on any material body they produce heat. They are very useful to us. 

Wavelength 

Wavelength of Infrared Radiation.

Infra-red radiations are being used for the treatment of several diseases. Special types of infra-red lamps are used for treating the pains of muscles and joints-especially for backpain. They are also used for heating rooms in winter.

Animals Pictures taken under IR Camera.

Infra-red radiations are being used for the guidance and control of missiles and other ballistic weapons. These radiations are also used for transmitting and receiving invisible signals. Molecular structures are studied with the help of these radiations. Impurities present in the materials can also be detected by these rays. 

Light, The Visible Reminder of Invisible Light ---John Green---