Gravitational Lensing-II
“The greatest enemy of knowledge is not ignorance; it is the illusion of knowledge.”-Stephen Hawking.
As rightly said by Stephen Hawking, nothing is more dangerous than half-baked knowledge. In the last post on gravitational lensing, we gave a brief overview of what gravitational lensing is and its types and discussed a few cases like Einstein's ring, the Einstein cross, etc. Gravitational lensing is a very important astronomical/cosmological tool that helps us detect distant galaxies, clusters, and exoplanets, to name a few.
If we go back in history, around the 1660s, Newton predicted the idea of gravity as a force and rest as we read in books the famous Newton's laws and
where F is the force acting on anybody, and d is the distance between the two attracting bodies
Now Newton’s deflection can be calculated with mass M with impact parameter b, then the observed deflection is seen as
where G is the Gravitational constant i.e.,, 6.67x10^(-11) m³/kg s², M is the mass of the concerned body, b is the impact parameter, and c is the speed of light, i.e., 2.998x10⁵km/s
This calculation was made with the assumption that gravity bends the light. A German Mathematician Soldner ( 1801), neglected the local curvature of space-time around massive objects. His calculation gave the angle of deflection \tilde\alpha
It was observed later that his results gave half of the time deflection.
Now wait! So we know the deflection in the path of light is due to gravitational field, so gravity is a force? This statement might haunt physicists (but being a mathematician myself I care more about the numbers). But no,in 1915 Einstein proposed gravity as a curvature of space time due to unequal distribution of mass(ie in simple words a bulge in the space time cloth(which isn't a 3d fabric, though for simplicity in understanding you may think one but it isn't, keep in mind!) which causes masses to move in geodesic lines) in this theory of General Relativity.
Now lets take a brief moment and understand these notions as quick as possible.
Newtonian: space and time are absolute and independent for any matter.
Special relativity: space and time are unified, and depends on motion of observers (like relative orientation of an object depends on rotation of observers).
General relativity: space and time can be curved by objects(specifically by the gravitational field they create)
From these theories we might come to the notion of Quantum gravity which is still a conjecture. (If Im being honest im also trying to understand so widh this girl some luck and if im able to deduce I would love to talk on these.So now that we briefly know the underlying concepts lets go back to lensing again!
Einsteins' equivalence principle (and predictions were made on the complete set of General Relativity(GR) equations) showed a problem in the previous results. Contrary to Newton’s idea of gravity, Einstein theoretically showed space as a fabric in 3+1 space-time (3 space coordinates over changing the time), so masses form a curvature. The heavier the mass, the more its curvature will be. (a reminder the notion of Light stays as it is. light moves in a straight path; more specifically, the space-time fabric bends due to the masses bending the path of light (we can say light moves straight in the curved path and hence gets curved).
The anomaly in prediction was rectified, and GR predicted the deflection to be twice as big.
Eddington, in 1919, proved this prediction of Einsteins' result, showing a deflection of 1"75' by observation. On May 29, 1919, this English astrophysicist and other astronomers observed a long solar eclipse from two different locations: Príncipe, an island off the coast of West Africa, and Sobral, a town in Brazil. They observed a star that was supposed to be behind the massive Sun but turned out to be visible with an angle of deviation of 1"65'. Hence verifying Einstein’s deflection(almost).
While lensing, an object is seen to produce multiple images at a time (it is due to the multiple paths of light). This phenomenon is called image splitting. Later, in 1937, Fritz Zwicky, a Swiss astrophysicist, predicted that this image splitting due to the lensing effect is about 1%.
Zwicky spent a significant amount of time from 1961–67 cataloguing and studying all of the galaxies he had, allowing him to produce a six-volume “Catalogue of galaxies and clusters of clusters of galaxies.”
Another significant discovery resulting from his observations of galaxies was a hypothesis on dark matter, which he termed, first as “Dunkle Materie.” He discovered a gravitational anomaly while studying the Coma galaxy cluster: an abnormal rotating velocity of bright or regular matter (approximately 400 times the predicted one) compared to the projected gravitational force this regular matter would create within the cluster. This disparity clearly suggested the presence of another sort of matter, which would be unseen but would also contribute to gravitational attraction. Although Zwicky’s proportions were eventually shown to be incorrect, he correctly deduced that the vast bulk of the substance was “dark.”
We will discuss this in detail as it demands more talk on the dark matter, which isn't the subject of today's discussion. But again, Gravitational lensing is a very useful tool for observing dark matter, but its details won't be discussed in this part. In the next part, I will focus more on the gravitational fields and the lensing equation. (I know I promised to be covered in this part, but it was pretty long, so I'm saving it for the following parts!!)
Keynotes:
- Newton's form of gravity was canonical; it was revolutionary because it was the first mathematical theory to represent force between two masses.
- One of Einstein’s motivations for proposing general relativity was his work on special relativity. He postulated that there is a “universal speed limit,” the speed of light, which is the maximum speed that any object could have. In Newton’s theory, the force of gravity is transmitted instantaneously. If the Sun moves, the Earth experiences the change immediately. This clearly violated Einstein’s speed limit and sent him searching for a better understanding of gravity.
- When masses move, they change the fabric of spacetime around themselves, causing other masses to move in turn. A mass in orbit is not being held by force but is actually following the shortest path (called a geodesic) through a warped spacetime.
- Einstein described the geometry of spacetime in the Einstein tensor, a four-by-four matrix that combines the three dimensions of space with time (hence the name). That geometry (G_μv) depends on the mass and energy (T_μv) in a given region of spacetime according to the Einstein field equation: G_μv=(8πG/c⁴)T_μv.
For Understanding Gravitational Lensing, I've gone through books like
- Introduction to Cosmology by Barbara Ryden
- Dynamics and Astrophysics of Galaxies by Joe Bovy
- lecture notes on GR and SR by the Hong Kong University of Science and Technology
- Gravitational Lensing: Strong, Weak andMicro Saas-Fee Advanced Course 33, Swiss Society for Astrophysics and Astronomy (Edited by G. Meylan, P. Jetzer and P. North)
- WSU lectures on gravity and special relativity.
The list is not exhaustive!
