General Theory of Relativity
The General Theory of Relativity requires immense power of visualisation. One needs to visualise the graphs and figures along with reading...
General Theory of Relativity
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| Depiction of Space-Time Cited from LIGO Caltech |
Hello Readers!
The Theory of Relativity is one of the most influential works in the history of science. It led to a huge paradigm shift in understanding fundamental forces in the universe.
The end goal of this post is to provide you with an interpretation of General Relativity's fundamental concepts.
Space-Time
In a two-dimension graph, we have a dependent variable and an independent variable. The former occupies the y-axis or the vertical axis and the latter is shown as the x-axis or the horizontal axis.
In a distance versus time graph, distance is the dependent variable that changes, and time is the independent variable, that moves on unperturbed. This is agreed upon in classical mechanics.
However, Einstein stated that time may not be independent. That is, different regions of space may experience different values of time. Space and Time are relative to each other.
Therefore, it is necessary to integrate space and time into a single medium affected by the fundamental forces. He named it Space-Time.
The Space-Time continuum is a fourth-dimensional object because it contains three dimensions of space and one dimension of time. Therefore, human minds cannot comprehend it. The best we can do is visualize it as a two-dimensional rubber sheet, as seen in the image above.
Any object such as the Sun, the Earth etc. produces a dent as shown above in space-time. This causes the normally uniform straight space-time to have a curvature.
Gravity is a weak force, and given the vast distances between two bodies, like the Sun and Jupiter, it is unrealistic to expect it to pull them together directly. The continuum provides a medium where gravity is exerted physically on other bodies.
Gravity
Einstein noted that gravity never existed. It was simply an illusion created by the effects of space-time.
How can this be? Newton is said to have discovered gravity and drafted an equation for gravitational force. How can gravity be nothing?
Imagine you are travelling on an extremely huge circular racing track. You feel that you are moving in a straight line, but given the shape of the track, you reach where you have begun earlier. Therefore, your motion's direction is determined by the path's shape.
In the universe, an object travels in a straight line through uniform space-time, owning to Newton's First Law. However, when it enters curved space-time, such as that surrounding Earth, its path bends towards the Earth, and the object follows that trajectory. This deviation from the actual trajectory of the object over time causes it to impact the Earth.
We interpret this as gravity pulling the object towards Earth.
If you're confused, try reading again and visualize it carefully.
Curved space-time also has other effects. It can influence the path of light rays themselves.
Consider that the light of a distant galaxy is travelling towards Earth. Another galaxy exists which is closer to us. Since the second galaxy has a lot of mass, it creates a massive dent in space-time. The light rays from the first galaxy change their path due to the curvature. This produces an image in which the farther galaxy appears ring-shaped around the closer galaxy. This is known as the Einstein Ring.
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| An Einstein Ring Cited from Sky News |
Einstein Rings are most commonly found in simulations of black holes, where the backdrop of stars appears to curve around the object.
Einstein's Happiest Thought
Einstein discovered that a person falling from a height and an astronaut floating about in space experienced the same conditions! He expressed that this was his happiest thought.
Any object moving in a straight line through space-time is said to have an Inertial Frame of Reference, meaning that it moved inert or unchanging relative to other objects.
A worker who cleans the windows of a building once fell to earth along with his tools. He observed that all his tools fell with him at the same velocity and remained at the same place relative to him. He felt like an astronaut drifting about in space in his spacecraft. He was in uniform, straight space-time and had an inertial frame of reference.
But how could this be? The Earth clearly has curved space-time all around it.
Let us envision a three-dimensional graph with two dimensions of space and one dimension of time. Since time is dependent on space, let it be on the y-axis. Now, a spacecraft moves in a straight line but circles the Earth due to the curvature of space-time. This happens over time, so it appears to trace a helical shape.
Most importantly, the Earth is moving upward in space-time. Every object in contact with the Earth's surface accelerates upward at 9.81 meters per second squared. Since space-time is not a physical medium, we are not moving upwards in space but in time.
The worker who "fell" is not in contact with the Earth. He sees the building accelerating past him and the ground rushing to meet him. Similar to the interpretation of the curvature of the invisible medium as gravity, we feel like we are falling towards the Earth.
It is incredible how such a complex theory evolved in a person's mind. Despite scepticism in the scientific community, many supporting proofs emerged with advancing technology. These included the discovery of Black Holes, gravitational waves and more.
For information on unearthing black holes, check out Discovery of Black Holes. For additional scientific content, see Time Travel Paradoxes.
If you enjoy reading about achievements in astronomy, explore Apollo 11, Spacecraft: Exploring our Planets and James Webb Space Telescope.
This is where I will conclude my post.
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Thank you for reading
Aditya VN Kadiyala
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