We have three colored segment in this animation. Surprisingly the length of the longest one is always the sum of the length of the two smaller ones.
This is actually a very special case of Ptolemy’s theorem. The theorem gives a connection between the sides and the diagonals of a cyclic quadrilateral. In this case the length of the dashed lines is equal so the theorem can be simplified to the statement above.
A black hole is a concentration of mass great
enough that the force of gravity prevents anything from escaping it
except through quantum tunneling behavior.
To get out of the earth’s clutches, we need to travel at least at 11.2 km/s also called the escape velocity.
Similarly, since the gravitational strength of a black hole is so strong, the escape velocity ( if you intend to leave it ) exceeds the speed of light.
Where does it gets it’s gravitational powers?
To understand this, let’s do a thought experiment: What would happen if we compress earth to half its present radius without changing the mass density?
The gravity at the surface would be four times more because of the “inverse square law”. It gets stronger at shorter distances.
And now, say you keep on decreasing the radius even further, the gravity would just keep on spiking to phenomenal levels. This is the secret to the Black Holes extraordinary gravitational powers.
How are they even formed?
All stars follow a life cycle. I will elaborate on the life cycle in another post, since its kind of long. But this illustration from sciteachers would do for now:
Upon reaching a certain critical density, a star will collapse on its own weight. i.e Its radius will keep on decreasing and gravity swooping up at each stage untill it collapses to an almost infinitely small pinpoint.
And that’s how black holes are formed and why they have such a huge gravitational pull on Objects.
Important Note:
Hope you learnt something new about blackholes in this post. This is a series and we will dig deeper as we move down the line. As they say- tiny drops make a mighty ocean. Small baby steps at a time everyday and at the end we will attain colossal clarity! Have a good one.
A scanned copy of my complete list of derivatives. My professor offered this bonus assignment and told us the best one would receive a 110. I was really going for that 110!
1. Gravity as Thermodynamics Entropic gravity is a theory in modern physics that describes gravity as an entropic force - not a fundamental interaction mediated by a quantum field theory and a gauge particle, but a consequence of physical systems’ tendency to increase their entropy.
2. Loop Quantum Gravity According to Einstein, gravity is not a force – it is a property of space-time itself. Loop quantum gravity is an attempt to develop a quantum theory of gravity based directly on Einstein’s geometrical formulation. The main output of the theory is a physical picture of space where space is granular. More precisely, space can be viewed as an extremely fine fabric or network “woven” of finite loops. These networks of loops are called spin networks. The evolution of a spin network over time is called a spin foam. The predicted size of this structure is the Planck length, which is approximately 10−35 meters. According to the theory, there is no meaning to distance at scales smaller than the Planck scale. Therefore, LQG predicts that not just matter, but space itself, has an atomic structure.
3. Causal Sets Its founding principles are that spacetime is fundamentally discrete and that spacetime events are related by a partial order. The theory postulates that the building blocks of space-time are simple mathematical points that are connected by links, with each link pointing from past to future. Such a link is a bare-bones representation of causality, meaning that an earlier point can affect a later one, but not vice versa. The resulting network is like a growing tree that gradually builds up into space-time.
4. Causal Dynamical Triangulations The idea is to approximate the unknown fundamental constituents with tiny chunks of ordinary space-time caught up in a roiling sea of quantum fluctuations, and to follow how these chunks spontaneously glue themselves together into larger structures. The space-time building blocks were simple hyper-pyramids (four-dimensional counterparts to three-dimensional tetrahedrons) and the simulation’s gluing rules allowed them to combine freely. The result was a series of bizarre ‘universes’ that had far too many dimensions (or too few), and that folded back on themselves or broke into pieces.
5. Holography In this model, the three-dimensional interior of the universe contains strings and black holes governed only by gravity, whereas its two-dimensional boundary contains elementary particles and fields that obey ordinary quantum laws without gravity. Hypothetical residents of the three-dimensional space would never see this boundary, because it would be infinitely far away. But that does not affect the mathematics: anything happening in the three-dimensional universe can be described equally well by equations in the two-dimensional boundary, and vice versa.
There will be like 8,000 people doing awful drunken renditions of the Tchaik and Mendelssohn concerti but everyone loves them
That one tuba player who can somehow play the flightiest woodwind music
Someone who randomly shows up with a slide whistle and makes you cry over their performance of Barber’s Adagio
Also I’d love it if we could perform lieder this way, seriously. Can you imagine all the fun we would have singing along to Erlkönig the way people do to Journey? That would be so much fun.