Into the Unknown: Black Holes and Beyond
Abstract — This article looks into the concept of black holes. By using the way light behaves in general relativity, together with the concepts of gravity, we are able to unravel the origins and workings of black holes. With this foundation in place, we can begin to explore the black hole’s implication which includes concepts such as wormholes and time travel, often depicted in sci-fi movies.
I. Introduction
Welcome to the very second part of my Quantum Physics series. If you require a solid understanding of Quantum Mechanics and the Theory of Relativity, be sure to check out part 1 here.
My article is made out of the following sections. These are:
1) The Origin of Black Holes
2) Wormholes and Time Travel
3) The Problems with Sci-Fi
II. The Origin of Black Holes
Physicist Sir Robert Penrose, the father of Quantum Gravity, showed that a star collapsing under its own gravity is trapped in a region whose surface eventually shrinks to zero size. And, since the surface of the region shrinks to zero, so does its volume. All the matter in the star will be compressed into a region of zero volume, so the density of matter and the curvature of space-time becomes infinite. That region, the center of the black hole, is known as a singularity.
A star that was sufficiently massive and compact would have such a strong gravitational field that even light could not escape. The light emitted from the surface of the star would be bent and pulled back by its own gravitational attraction.
The formation of a black hole becomes more intuitive once we understand the life cycle of a star. Stars begin their lives as dense regions of gas and dust called molecular clouds. These clouds undergo gravitational collapse due to their own mass and gravitational attraction, leading to the formation of a protostar — a hot, dense core surrounded by a rotating disk of gas and dust. As the protostar continues to accrete matter from its surrounding disk (atoms of the gas collide with each other more and more frequently and at higher speeds), it heats up and becomes increasingly luminous. Eventually, when the temperature and pressure at its core are high enough, nuclear fusion reactions ignite, primarily converting hydrogen into helium. The protostar enters the main sequence phase. The main sequence phase is the longest stage in a star’s life cycle, during which it steadily fuses hydrogen into helium in its core. The energy released from these fusion reactions counteracts the inward pull of gravity, maintaining the star’s stability and preventing further collapse. The star remains in this phase for the majority of its lifetime, with heat from the nuclear reactions balancing the gravitational attraction.
Stephen Hawking puts this concept succinctly:
“It is a bit like a balloon — there is a balance between the pressure of the air inside, which is trying to make the balloon expand, and the tension in the rubber, which is trying to make the balloon smaller.”
As a main sequence star exhausts its hydrogen fuel, its core contracts and heats up, while its outer layers expand and cool. This results in the star swelling in size and becoming a red giant (for low to medium-mass stars) or a red supergiant (for high-mass stars). During this phase, the star may undergo further fusion reactions, such as helium fusion, in its core. Ironically, the more fuel a star starts off with, the sooner it runs out. More massive stars will heart up more to balance out its gravitational attraction, resulting in faster fuel usage.
When the star becomes small, the matter particles get very near to each other, and according to the Pauli Exclusion Principle, they must have very different velocities. This makes them move away from each other and tends to make the star expand. A star can therefore maintain itself at a constant radius by a balance between the attraction of gravity and the repulsion that arises from the exclusion principle.
Yet, there is a limit to the repulsion. The theory of relativity limits the maximum difference in the velocities of the matter particles in the star to the speed of light. This means that when the star got sufficiently dense, the repulsion caused by the exclusion principle would be less than the attraction of gravity. This mass is known as the Chandrasekhar Limit. It describes the maximum mass that a white dwarf — a remnant of a low to medium-mass star — can attain before gravitational collapse leads to further compression into a black hole.
Chandrasekhar Limit: A Layman Explanation
Imagine a white dwarf as a stellar ember, a remnant left behind after a star similar to our Sun exhausts its nuclear fuel and sheds its outer layers. Despite its small size — about the size of Earth — a white dwarf is incredibly dense, with matter tightly packed together. As more mass is added to a white dwarf, its gravity increases, squeezing its atoms closer together. At some point, if the white dwarf’s mass exceeds the Chandrasekhar Limit, the inward pull of gravity overwhelms the resistance provided by electron degeneracy pressure — the quantum mechanical pressure exerted by electrons — and the white dwarf collapses under its own weight.
For low to medium-mass stars, the red giant phase culminates in the shedding of its outer layers into space, forming a glowing shell of gas known as a planetary nebula. The remaining core, composed of degenerate matter, becomes a white dwarf — a dense, earth-sized remnant that gradually cools over billions of years.
For high-mass stars, the end of their lives is marked by an explosion known as a supernova to reduce their mass below the limit and to avoid gravitational collapse. This explosive event releases an immense amount of energy and synthesizes heavy elements, enriching the surrounding interstellar medium with new materials. In some cases, the core left behind after a supernova may collapse further, depending on its mass. For cores with masses below about 1.4 times that of the Sun (the Chandrasekhar limit), electron degeneracy pressure can support the core against further collapse, resulting in the formation of a neutron star — a dense remnant composed primarily of neutrons.
For cores with masses exceeding the Chandrasekhar Limit, gravitational collapse continues unabated, leading to the formation of a black hole — a region of spacetime where gravity is so intense that nothing, not even light, can escape its gravitational pull. This was hypothesized by Robert J. Oppenheimer (although he did not complete this phenomenon as he was closely involved in the atomic bomb project during World War 2). He believes that the gravitational field of the star changes the paths of light rays in space-time from what they would have been had the star not been present. Light bends at the surface of the star. As the star contracts, the gravitational field at the star’s surface gets stronger and light bends inwards by a greater amount. Eventually, the star’s gravitational field is so strong that light can go no longer escape. Nothing can travel faster than the speed of light. Therefore, it is logical to believe that nothing can escape since everything is dragged back by its gravitational field. This is a black hole. Its boundary is known as the event horizon and it coincides with the paths of light rays that fail to escape from the black hole.
III. Wormholes and Time Travel
The idea of wormholes and time travel can only happen if we are able to travel faster than the speed of light (star wars hyperspace maybe?)
Therefore, wormholes and time travel are purely theoretical, given our level of technology today. Wormholes essentially warps space-time so that there is a shortcut between two events in the space-time axis. It is a thin tube of spare-time which can connect two nearly flat regions far apart.
There are two main types of wormholes:
- Traversable Wormholes: These are wormholes that, theoretically, could be traversed by matter or light. Traversable wormholes would require exotic forms of matter with negative energy density to stabilize their structure and prevent them from collapsing under their own gravitational forces. While such exotic matter has not been observed, it is allowed by the equations of general relativity.
- Non-Traversable Wormholes: These are wormholes that exist only on paper and cannot be traversed by matter or light. Non-traversable wormholes may still provide valuable insights into the mathematical properties of spacetime and the behavior of gravitational fields.
Time travel arises from the concept of wormholes connecting different points in spacetime, including points in the past and future. If a traversable wormhole were to exist and were stable enough to allow passage, it could potentially serve as a conduit for traveling to different points in time as well as space.
Assuming a wormhole links from A to B, we can infer that an observer moving towards B should be able to find another wormhole that enable him to get from B to A before the travel from A to B even happens. Einstein and Nathan Rosen jointly proposed the concept of wormholes known as the Einstein-Rosen Bridge.
In regions of spacetime where matter or energy is concentrated, such as near massive objects like stars or black holes, spacetime becomes curved. This curvature affects the paths of objects moving through spacetime, causing them to follow trajectories influenced by gravity. In the vicinity of a highly curved region of spacetime, such as near a black hole or within the interior of a traversable wormhole stabilized by exotic matter, spacetime may become sufficiently warped to create a narrow “throat” or tunnel-like passage. The Einstein-Rosen Bridge effectively connects two separate points in spacetime, allowing for a shortcut between them. For example, one end of the bridge might be located near a massive object in one part of the universe, while the other end could be situated in a distant region of space or even in a different point in time. In theory, if the Einstein-Rosen bridge were stable and traversable, matter or energy could pass through it, effectively traveling from one point to another without having to travel through the intervening space. This could potentially enable rapid interstellar travel or even time travel, depending on the properties of the wormhole.
IV. The Problems With Sci-Fi
We all probably watched the film interstellar and saw the main character, Cooper, sacrificing himself by jumping into the heart of the black-hole to give others enough momentum to escape its gravity. At the heart of the black-hole, Cooper finds a tesseract (a representation of 5 dimensions in space where time is a physical dimension). By manipulating space-time, Cooper is able to give his daughter the knowledge for past Cooper to start the mission to the other planets in the first place.
Is this even possible? Let us first answer if it is even possible to catapult yourself into a black hole. The barrier of entry into the black hole itself is super difficult, maybe even impossible. Angular momentum can become near relativistic the closer you are to the black hole, requiring you to shed momentum before you can descent further. The event horizon is doing just that. It is spinning so fast to shred momentum to fall deeper but the friction involved has turned it into a bright plasma instead. Light is also bending inwards at the event horizon, so you can imagine how hot it will be. We will probably vaporize at the start.
However, assuming you survive the plasma. You will experience the problems of gravity. Since there is no concept of absolute time, each observer has his own measure of time. Suppose Cooper falls straight into the black hole and we were viewing him from the space ship, we will see the image of his body freeze on the event horizon before gradually turning invisible. This is due to light being stretched due to the extreme distortion of space time, its wavelength increases, becoming more red-shifted until he disappears. For Cooper on the other hand, depending on his angle of entry, would start to feel the gravitational force from the black hole. Gravity gets weaker the farther you are from the star, so the gravitation force on Cooper’s feet would be greater than the force on his head. This difference in the forces would stretch him like spaghetti and tear him apart before the star had contracted to the critical radius at which the event horizon formed. He will snap in half and the gravitational forces will overcome the bonds between his own molecules. This process, known as spaghettification, will continue until he becomes a stream of molecules into the Black-Hole’s heart. Yikes, that is not a very pleasant death!
What about wormholes? Despite having the theory and mathematics behind them, we do not have the means to make them. The first problem is the creation of a wormhole as it requires backward time travel. It leads to a whole lot of paradox which can destroy reality. A famous paradox of time travel is known as the Grandfather’s Paradox which violates causality.
Grandfather’s Paradox: A Layman Explanation
Suppose you travel back in time and prevent your grandfather from meeting your grandmother, thus preventing your own birth. If you were never born, how could you have travelled back in time to prevent their meeting in the first place? This paradox highlights the apparent contradiction that arises when contemplating changes to the past and the potential for causality violations.
Stephen Hawking addresses this paradox and related issues by proposing a principle that safeguards the consistency of causality within the framework of general relativity known as the Chronology Protection Conjecture. Hawking suggested that the laws of physics might inherently prevent the formation of closed time-like curves — paths through spacetime that loop back on themselves and allow for time travel to the past — in the first place. These barriers could take the form of incredibly high energies or other physical phenomena that make it impractical or implausible to travel back in time.
Secondly, travelling through wormholes is not practical as the throat of the wormhole is not sustainable. We believe that the wormhole is unstable under the influence of gravitational forces. As matter passes through the wormhole, the throat would experience significant stresses and strains, potentially leading to its collapse or deformation. The only way to make it sustainable to through the form of negative mass where it possesses gravitational repulsion rather than attraction. By placing negative mass at the throat of a wormhole, it could potentially counteract the inward pull of gravity via opposing curvature, stabilizing the structure of the wormhole and preventing its collapse. Negative mass would introduce exotic conditions that defy conventional physics, making it more difficult. We have also never found negative mass and we have no idea how to make it.
V. Final Thoughts
From the origins of black holes in the collapse of massive stars to the possibilities of wormholes and time travel, the study of black holes opens doors to both scientific inquiry and speculative imagination. Yet, as we dig deeper into its speculative fiction, we encounter the limitations and challenges in wormholes and time travel. While the mathematics may suggest the existence of traversable shortcuts through spacetime, practical considerations and theoretical barriers remind us that it is highly not plausible for it to ever happen.
References
[1] The Problem With Interstellar’s Black Hole that Everyone Ignores — Astrum
[2] The Particle Problem in the General Theory of Relativity — 1935 Einstein, Penrose
[3] A Brief History of Time — Stephen Hawking
