The Expansion of the Universe

Since the dawn of humanity, we have thought that the heavens are huge, but of constant size. We first knew that the stars move around, then that it is actually the Earth rotating on its axis. In the 18th century, the French astronomer Messier observed fuzzy objects that he didn’t know were galaxies. Only in 1923, Hubble conclusively proved that the Milky Way was not the entire universe. So while our understanding of the size of the universe expanded, we still thought it is constant or perhaps infinite. It took until the 1920s and 30s and again the brilliant observations of Hubble to show that the universe is expanding based on the red shift of galaxies. In 1998, observations made by the Hubble Space Telescope showed that this expansion is accelerating. Let’s attempt to understand Hubble’s experimental process and what the expansion of the universe means.

A diagram of the universe’s expansion with time. Credit: NASA.

From 1912 and 1922, Vesto Slipher showed that the light from many astronomical objects was red shifted, which was soon interpreted as galaxies moving away from the observer on Earth. The light emitted by stars lies on the electromagnetic spectrum and composed of waves. Due to the Doppler effect, when an object is moving away from you, the wavelengths you observe appear longer and stretched. Longer wavelengths appear more red, so that is why the term redshift. The amount of redshift is a function of velocity. In 1922, Alexander Friedmann developed a theoretical model of the expanding universe based on Einstein’s field equations. This model was confirmed in 1929 when Hubble measured the redshifts of various distant galaxies and their distances based on the apparent brightness of Cepheid stars in them. He found a groundbreaking linear relationship, which confirmed that the universe was expanding. This data was further improved upon by Hubble and Humason in 1931, after the determination of distances improved. This process showed the powerful achievements that parallel theoretical and experimental work can produce.

Hubble’s velocity vs. distance data from his original measurements. The almost perfect linear trend from 1931 is astonishing. Credit: Lumen Learning Astronomy.

Hubble’s equation for the redshift is v = H x r, where v is the velocity of recession, r is the distance and H is Hubble’s constant, which is the slope of the graph. The speed of expansion has been the center of debate in astrophysics, as more and more accurate measurements are made for H. The value is placed at around 67.8-74, with the consensus being at around 73. These values are still calculated by looking at Cepheids, but recently Freedman from the University of Chicago used a new technique and got a value of 69.8. Knowing a precise value for H can also help accurately determine the distance to distant galaxies based on how fast they are moving. Therefore, this debate is still raging and we will probably see the accepted value shift a little bit in future years.

The expanding universe has three possible shapes based on the Friedmann equations. The types are open, flat and closed. The open universe has a negative curvature, the closed one has a positive curvature and the flat one, as the name suggests, has zero curvature. These shapes are important as they determine the fate of the universe. With current technology we are able to see around 80% of the observable universe, and they agree with the flat universe. I will come back to the shape of the universe in another post.

The three possible curvatures of the universe. Credit: University of Oregon.

This was not the end of the story for the expansion of the universe. In 1998, two independent research teams observed distant supernovas using the Hubble space telescope. The hypothesis was that the universe should decelerate due to gravity, however they found that actually it is accelerating. This was later confirmed by analysing baryon acoustic oscillations. An explanation for this was dark energy, a new form of energy which acts against gravity and does not interact with electromagnetic forces. This is still a theoretical model and experimental confirmation is still yet to come. But the question of expansion is still as potent as it was in the 1920s.


Expanding universe. (n.d.). Sloan Digital Sky Survey.

Garner, R. (2019, May 17). Mystery of Universe’s Expansion Rate Widens With New Hubble Data. NASA.

Geometry of the Universe. (n.d.). UOregon Cosmology.

Jaggard, V. (2011, October 5). Physics Nobel Explainer: Why Is Expanding Universe Accelerating? Science.

Nature Editorial. (2019). How fast is the Universe expanding? Cosmologists just got more confused. Nature.

O.S. (n.d.). The Expanding Universe | Astronomy. Lumen Learning.

Breakthrough Starshot


The Starshot mission is tasked with reaching Alpha Centauri, the closest star system to Earth at 4.37 light years from the Sun. With current technology it would take 73,000 years to travel there, assuming travel at the speed of the Voyager (NASA). This project wants to use very small nano-probes attached to lightsails, which would be pushed by a beam of light from Earth. They propose that this way it would take just 20 years to reach Alpha Centauri. It would allow images of Proxima B, an Earth-like exoplanet orbiting Proxima Centauri, to be sent back to Earth and an analysis of the magnetic fields there. This approach could be more successful than an ordinary spacecraft, because the fuel would not run out. It would rely on a constant beam of photons instead of hydrazine, and the low weight of the sail would allow it to build momentum. A proof of concept LightSail 2 already flew in 2019, and it was a success.

A visualisation of the Starshot lightsail headed for Alpha Centauri.


One of the challenges to the project is developing a protective coating for the gram-scale Starchip. There would be numerous collisions with dust and particles in the interstellar medium, which would have a big impact on the probe due to its small size. They are considering using beryllium copper as a possible material, however there is still not a lot of research in this area. Another problem is cooling the light emitting device on Earth. The scale of the laser needed would be 100GW for the Alpha Centauri mission. Current lasers are 50% efficient, thus a lot of power would transform into thermal energy, which would need to be dissipated. They propose to use a conventional cooling system, however that would be tricky with the small optical instruments in the mirror. There is a whole list of problems here, which shows how many things still need to be addressed.  

Time frame

The team states that a seemingly impossible moonshot was already achieved, so they can overcome the technical challenges of this project. I think that the earliest this can happen is within 50 years, so just within our lifetimes. Nanotechnology is making tremendous leaps recently and the initiative has incredible financial support from Zuckerberg and Milner. The team is working on a 3 decade plan, however I think it will be pushed a bit longer than that. They expect to spend the first decade on the proof of concept, the second on constructing a prototype and the third on actually building the craft. I think that they should also account for about 10-20 years of additional research in lasers and nanotechnology before a prototype can be constructed. 

An image of Alpha Centauri from the Hubble Space Telescope. This system is composed of Alpha Centauri A (left), Alpha Centauri B (right), and a faint red dwarf Proxima Centauri.

If the project is successful, it could significantly advance nanotechnology and laser research. Developing a gram-scale device that contains a small camera, battery, processors and a transmitting device could be very important for medical applications in the future. Direct drug delivery that targets only specific cells, like cancer cells, would save many lives. Let’s hope that the Breakthrough Starshot goes well. Perhaps we might see its launch in our lifetimes, which would be breathtaking to witness.


F, J. (2016, April 14). Stephen Hawking, Mark Zuckerberg, Yuri Milner launch $100M space project CALLED Breakthrough Starshot. Nature World News.

Nanotechnology in medicine. Nanotechnology in Medicine | Nanoparticles in Medicine. (2019).,for%20earlier%20detection%20of%20disease.

NASA. (n.d.). The Nearest Neighbor Star. NASA.

Stirone, S. (2019, July 23). LightSail 2 Unfurls, next step toward space travel by solar sail. The New York Times.,-The%20Planetary%20Society&text=For%20centuries%2C%20it%20was%20only,laws%20of%20the%20planets’%20orbits.

Wall, M. (2019, May 29). Breakthrough needed? Starshot interstellar-flight project faces challenges. Space.

The Scale of the Universe

The size of the universe is incomprehensible by humans. One of the most fascinating experiences was playing around with the scale of the universe app made by Cary Huang. Seeing just how huge the Milky Way galaxy is made me feel small. I knew it was big, but not like that. Although, that app still does not convey the tremendous distances between objects in space. In this post, I will compile a list of the most interesting analogies and comparisons that help us understand just how big the universe is.

An image of the globular cluster NGC 6397, taken by the Hubble Telescope. This cluster formed 13.5 billion years ago and is one of the first clusters that has formed after the Big Bang. Credit: NASA.

Firstly, let’s start with something closer to home. This analogy was first brought into my attention by Vsauce. The International Space Station orbits 400km above the Earth’s surface, which is about the distance from New York to Vermont. Yet, if we take our planet to be a peach, the ISS would still be skimming the fuzz. Also, if you thought the sky was crowded with asteroids, try putting 5000 people in random places and make them find each other.

Now for the solar system. If you imagine that the Earth is the size of a baseball on the homeplate of Nationals stadium in Washington D.C., Mars would be a block away from the fence. The edge of the solar system, the oort cloud, would be a halfway on the way to the Moon! The nearest star, Alpha Centauri, would be a little bit past the Moon’s orbit. I think we are starting to lose a sense of scale again, but how can you not. Remember, we started with a baseball for Earth. Feel free to make your own analogy. The user incoming on the nasaspaceflight forum suggests that the easiest way to do this is using a spreadsheet and picking an initial real life object to compare the size of Earth to.

Another one of my favourites is the toilet paper solar system. Try unrolling a roll of toilet paper and put the Sun on the first square. Mercury will be on the 3rd square, Venus on the 5th, Earth on the 7th, and Mars on the 11th. Now, time for a leap. Jupiter will be on the 39th, Saturn on the 72nd, Uranus on the 144th, and finally Neptune on the 225th. This really shows the astronomical (heh) difference in distance between the terrestrial planets and the gas giants. This is apparently a school activity for elementary school students, so if you want to try this with your younger siblings, it would be a wonderful learning experience for both of you.

An example toilet paper solar system. Credit:

One of the earliest examples of these size comparisons is the 1977 film Powers of Ten. It begins at a picnic in Chicago and zooms out all the way to billions of galaxies, and then zooms back in to the inside of a cell. The grainy quality makes the experience eerie and the score allows for a thoughtful reflection. Also, check out this beautiful diagram that compares gravitational wells made by different objects. Not only does it act as a size comparison of some of the planets, but also teaches the reader about gravitational wells and general relativity.

The comparison of gravitational wells. Credit: xkcd.

If you want to know more, check out this excellent size comparison of the universe video from Harry Evett. Also, if you have a powerful enough computer, I recommend playing Universe Sandbox. It’s a blast, which teaches you about our solar system and the properties of planets. I’ve been playing it for the last couple months, and in addition to blowing things up with sand grains travelling at the speed of light, I now understand how our solar system moves in the galaxy. Take a look at the steam page. Furthermore, the Charleston Lake Astronomical website provides a few additional analogies that you might find insightful. Take care!


Emspak, J. (2016, June 2). Does the Universe Have an Edge? Livescience.Com.

Episode 11: Toilet Roll Solar System. (n.d.). Institute of Physics.

Melina, R. (2017, August 4). International Space Station: By the Numbers. Space.Com.

Popova, M. (2017, March 29). Five Visualizations to Grasp the Scale of the Universe. The Marginalian.

The Scale of the Universe. (n.d.). Charleston Lake Astronomical.

The Formation of the Solar System

The solar system formed from a cloud of interstellar gas around 4.6 billion years ago. At some point, this cloud collapsed under gravity and the sun formed. The pressure in the center became so high that hydrogen atoms began fusing into helium, and the nuclear reactions that power stars begun. A solar nebula of gas began rotating around the Sun. From clumps of material in this disk, planets and Moons were formed. The exact process is a bit more complicated and there are three contrasting theories about the formation of our solar system. Let’s look at some of the details.

An artist’s rendering of the spinning accretion disk from which the Solar System formed. Credit: NASA.

The first model, which is referenced in most sources is called the core accretion model. It means that the cloud of gas collapsed under gravity to form the Sun. The gravitational potential energy was converted into thermal energy in the center of the solar system, which ignited nuclear fusion on our star. The solar wind swept lighter elements, such as hydrogen and helium from the inner regions of the solar system, leaving only rocks and minerals. Further away, the cooler temperature and the presence of hydrogen and helium allowed the gas giants to form, and their icy moons. This model makes sense when looking at our solar system, Mercury, Venus, Earth and Mars are rocky planets, Jupiter, Saturn, Uranus and Neptune are gas giants.

The most evidence for this model comes from looking at exoplanets. Stars with a greater proportion of elements other than helium and hydrogen have more giant gas planets in their planetary systems. Furthermore, the discovery of HD 149026, a star around which a giant planet was found, supported this hypothesis. It suggests that there should be more rocky planets than gas giants, which makes one optimistic about the search for extraterrestrial life.

Nonetheless, there are two major issues with the accretion model. Firstly, the tiny rocky planets during formation should have fallen into the Sun before reaching a stable orbit. Secondly, the gas giants would not have enough time to complete formation, before all of the gas would be swept away by solar wind. This discrepancy is on the order of several million years. To address these limitations, scientists have developed the disk instability model.

A comparison of the Core Accretion Model and the Disk Instability Model. Credit: dherna98.

This model states that clumps of gas were already forming in the earliest stages of the solar system’s life. This allowed them to create stronger gravitational field and trap the escaping gases. They were able to reach the critical mass to become a planet in as little as 1000 years, which is a blink of an eye on the cosmic scale.

The third model is pebble accretion, which has gained traction this decade. It differs from the previous two models by stating that the planets formed even faster, by collecting smaller fragments of other bodies that were forming. The main issue in these models is time, and it seems that formation of planets from a collection of small pebbles would achieve this the fastest. The best theory will be verified with more precise computer simulations and exoplanet observations, as telescope technology improves.

Let’s end this discussion with examining how the solar system continued forming. Especially, how did Earth get its immense amount of water? The mainstream theories for a long time claimed that water came from comets, since the Earth was too warm to accrete ice from the gas cloud. However, flybys of the Halley’s comet and the Rosetta satellite showed that the ice composition on these bodies is different than ice on Earth. Another potential source remains asteroids from the asteroid belt, yet that claim still remains to be verified. In accord with pebble accretion, another theory states that the Earth formed quickly enough that it could accrete water molecules before it was too hot. As you can see, the formation of the solar system is closely linked with other mysteries of life.


Czekala, I. (2011, March 11). Review Article: Protoplanetary Disks and Their Evolution. Astrobites.

Dherna98, A. (2017, May 6). How solar system was formed. Joliet Junior College – Astronomy 101 Class Blog.

Our Solar System. (n.d.). NASA Solar System Exploration.

Savagekt, S. (2014). disk instability. Planet Hunters.

Tillman, N. T. (2017, February 1). How Did the Solar System Form? Space.Com.

The Apollo 11 Story

Neil Armstrong’s words when he touched down on the Moon “That’s one small step for man. One giant leap for mankind.”, are probably the most famous in the history of space exploration and in the 20th century as a whole. The Apollo 11 mission, which launched from Cape Canaveral on July 16, 1969, has been a milestone in human history. It has been covered in countless documentaries, movies, books and articles. Let’s create a timeline of the events of July 1969, to see how exactly was this wonderful feat achieved.

Buzz Aldrin setting up the solar wind experiment on the Moon. Credit: NASA.

The Apollo program was initiated during the space race of the cold war, when the Soviet Union and the United States were trying to prove their military and technological might by exploring space. The Soviets got a head start by putting Yuri Gagarin and Sputnik into orbit. As a response, in a 1961 speech president Kennedy made a statement saying “I believe this nation should commit itself to achieving the goal, before this decade is out, of landing a man on the moon and returning him safely to Earth.” This launched the decade long quest to put a man on the moon.

The road to July 1969 was not easy. In 1967, there was a fire during testing and three astronauts died. The research continued and Apollo 8 took the astronauts in orbit around the Moon in December 1968. There were several other missions that tested the lunar module and other vital equipment, mostly in Earth orbit. Then in July everything was ready to launch.

At 9:32 a.m. the huge Saturn V rocket lifted off from Cape Canaveral on July 16th. On board were Neil Armstrong, Michael Collins and Buzz Aldrin. After three days, the ship got into orbit around the Moon. On the 20th of July, the lunar landing module called the Eagle, manned by Aldrin and Armstrong, separated from the main orbiter. Two hours later, the Eagle began descending and at 4:17 p.m men have landed on the Moon on the Sea of Tranquility.

At 10:39 p.m, the impatient Armstrong decided to step out of the lunar module with the television camera that was broadcasting his steps live. At 10:56 p.m, Armstrong stepped of the ladder and spoke his famous quote. A few minutes later, Aldrin joined him. They spoke with president Nixon on the phone, planted the flag and took pictures. They conducted tests on solar wind, collected numerous samples of lunar soil and deployed the Laser-Ranging Retroreflector and the Passive Seismic Experiment Package. Just two hours later, the astronauts returned to the lunar module to sleep and prepare for launch. In total, the two astronauts spent 21 hours and 36 minutes on the Moon, including sleep.

The Eagle lunar module in orbit around the Moon. Credit: NASA.

Around 1 p.m. on July 21, the Eagle took off from the lunar surface and rejoined with the command module in orbit. Then, the astronauts began their journey home and splashed down in the Pacific ocean on July 24th. In total, there were 5 more missions to the Moon. The last people to be on the Moon were Eugene Cernan and Harrison Schmitt in December 1972.

If you want to learn more, I recommend this inspiring video from Vox. Also, the original broadcast gives me chills. Please feel free to explore this fantastic Apollo 11 image gallery courtesy of NASA.


Apollo 11. (n.d.). National Air and Space Museum.

Apollo 11 | History, Mission, Landing, Astronauts, Pictures, Spacecraft, & Facts. (2009). Encyclopedia Britannica. Editors. (2018, August 23). 1969 Moon Landing. HISTORY.

NASA. (2019, May 15). Apollo 11 Mission Overview.

Cosmic Microwave Background

Cosmic microwave background radiation (CMB) is the leftover radiation from the Big Bang and serves as a source of evidence for it actually happening. It is extremely cold at just 2.725 Kelvin, so emits blackbody wavelengths in the microwave part of the electromagnetic spectrum. It was discovered in 1964 by Arno Penzias and Robert Wilson, who won the 1978 Nobel Prize in physics alongside Pyotr Kapitsa, a pioneer in low temperature physics. Let’s look at where it comes from and how it was detected.

A map of the cosmic microwave background taken with the Planck satellite in 2013. Credit: ESA.

When the universe first formed, it was incredibly hot at around 273 million Kelvin. This was so hot that any potential atoms that could have formed were broken into protons and electrons, a sort of hydrogen plasma. The photons of light hit the electrons and scattered in random directions. After 380,000 years, the universe cooled and hydrogen atoms formed. These could no longer scatter photons through Thomson radiation, so the universe became “transparent” and light travelled in straight lines.

The cosmic microwave background allows us to see the universe as it was only 380,000 years after its formation. This radiation is mostly uniform, but there are fluctuations based on the early stages of galaxies and stars, which are visible with the color changes on the map. Furthermore, these fluctuations tell us more about how the Big Bang happened.

Scientists are also looking for evidence of the faster than light inflation of the universe right after the Big Bang. The model is theoretically sound and could be confirmed by examining the polarization of the CMB. Moreover, it can be used to study gravitational waves.

The story of its detection is one of luck and inspiring collaboration. The CMB was first theoretically predicted in 1948, by Gamow, Alpher and Herman. In 1965, researchers at the Bell Telephone Laboratories were constructing a new radio receiver. They were constantly bothered by a certain noise, which was coming from the sky. At the same time, a team at Princeton led by Robert Dicke was trying to detect the cosmic microwave background. The two groups heard about each other’s work, and Dicke realized that this unaccounted for noise was due to the CMB. The group swiftly published their results in the Astrophysical journal and the Big Bang theory became the new paradigm.

The Holmdel Horn Antenna that was used by the teams to detect the CMB. Credit: Bell Labs.

The cosmic microwave background is an ancient artefact from the Big Bang. Its an inspiring story about an accidental discovery. The resolution of our maps is getting better and better with each decade, so we can reasonably expect that it will be the key for future research about the Big Bang. If you want to learn more about the CMB and its discovery, check out this video from Khan Academy.


Decoding the cosmic microwave background. (2018, July 27). Astronomy.Com.

Howell, E. (2018, August 24). Cosmic Microwave Background: Remnant of the Big Bang. Space.Com.

Unfortunate pigeons and the search for a theory of everything. (2013, August 8). Early Universe @UCL.

Williams, M. (2018, September 8). What is the Cosmic Microwave Background? Universe Today.

The Fermi Paradox

At first glance it seems that our civilisation is quite special. We exist in a habitable zone on a planet with large bodies of water and oxygen. Unlike the dinosaurs, we have not been hit by a major asteroid 67 million years ago. This supposed uniqueness gave rise to many religions and philosophies. I would even argue that it lead to solipsism, or the idea that everything exists only in the mind. Yet, it turns out that we might not be so special after all.

There are billions of main sequence stars that are very similar to the Sun in our galaxy. A portion of these stars has Earth-like planets orbiting them at a habitable zone distance. A lot of these stars are older than the Sun, so civilisations would have developed there long before us. If so, they likely would have developed interstellar travel. Even with our current technology, you could traverse the galaxy in a few million years. So, where is everybody?

There are a ton of explanations of this paradox. One of them states that civilisations are very far away from us and we have not listened for long enough. Humans are not an old species by cosmic standards, and radio telescope technology has existed only since the 1930s. We have received the famous Wow! message in 1977, which some people claim to be evidence of aliens. While there are many hypotheses for its origin, we still don’t agree upon one. What’s interesting is that the frequency 1420 MHz is restricted only for astronomical use. Therefore, it is unlikely that this was a commercial or military signal. However, I believe that if aliens tried to make contact, they would’ve done it more than once.

The Wow! signal was detected by the astronomer Jerry R. Ehman at the Ohio State University‘s Big Ear radio telescope.

Another explanation is that advanced civilisations don’t last long enough to talk to each other. We have come close to nuclear annihilation in the Cuban missile crisis just 25 years after the first radio telescope was developed. Perhaps, civilisations self-destruct before discovering rapid methods of interstellar travel. The knowledge of radioactive processes is crucial for harvesting large amounts of power needed for a complex society. The creation of bombs follow almost immediately. Furthermore, climate change could be the destroyer of civilisations. We suspect that the chemical composition of planets that sustain life is similar to that of Earth. Therefore, using coal and oil as fuels is a straightforward choice that leads to greenhouse gas emissions.

Destruction could also come from space. Large asteroid impacts, like the meteor that wiped out the dinosaurs 66 million years ago, happen approximately every 100 million years. That gives fairly little time for civilisations to exist, since evolution needs a lot of time to happen. Nonetheless, assuming sustainable exponential growth, a lucky society could easily get tremendous communication capabilities within a million years.

One of the coolest ways, in which we have tried communicating is the Golden Record. They are two records launched on the Voyagers in 1977. The selection of what to put on the record was directed by Carl Sagan at Cornell. It has a ton of images of natural life, recordings of brainwaves and English voices. They are inspiring messages in a bottle thrown into the dark cosmic ocean. Perhaps, they will be the only thing left from our civilisation.

The Golden Record. The spacecraft are not heading towards a particular star system, however Voyager 1 will pass within 1.5 light-years of Gliese 445 in about 40,000 years.


Koehrsen, W. (2019, February 4). Predicting the frequency of asteroid impacts with a poisson processes. Medium.

NASA. (n.d.). Voyager – the Golden Record. NASA.

Wikimedia Foundation. (n.d.). Fermi paradox. Wikipedia.

Wikimedia Foundation. (n.d.). Voyager golden Record. Wikipedia.

Hawking Radiation

Black holes are regions of space with such a strong gravitational field that nothing, even light, can’t escape. They were a theoretical construct from the theory of general relativity, and only observed in April 2019. In the 1970s, questions arose if black holes had entropy and a temperature. The results of Bekenstein, Starobinsky, Hawking and Zeldovich showed a beautiful connection between quantum mechanics and general relativity and completely changed our understanding of black holes. Let’s examine what Hawking radiation is.

The equation for the temperature of a black hole on Hawking’s grave. Credit: Westminster Abbey.

When matter falls into a black hole, it cannot go back out into the universe, which should break the second law of thermodynamics. This law states that entropy, or the measure of disorder, should always increase. It makes intuitive sense, the longer you live in your apartment without cleaning it, the messier it will become. A black hole is kind of like throwing your messy clothes and dirty dishes outside the window, increasing order and decreasing entropy.

In 1972, a Princeton student Jacob Bekenstein, showed that this paradox could be solved if the event horizon increased when matter was consumed. At the same time on the other side of the Atlantic ocean, Hawking began doubting Bekenstein’s solution. Entropy is strongly connected with thermal energy, so this expansion of the event horizon would also mean that a black hole had to emit radiation.

To find out more, Hawking visited Starobinsky and Zeldovich who were simultanously working at this same problem. They convinced him that rotating black holes could emit radiation. Hawking attempted to disprove Bekenstein, but at the same time showed that rotating and non-rotating black holes do emit radiation. This was different from the regular black-body radiation that every object emits, but it still meant that black holes were losing mass.

Here comes the beautiful part. This radiation is due to pairs of virtual particles appearing at the event horizon. These are a particle and an antiparticle pairs, which arise due to fluctuations in the quantum field. Normally, they would be annihilated soon after their creation, nonetheless sometimes a black hole consumes one of the particles and the other flies off into space. This causes the black hole to lose the mass equivalent to that one particle. It is a complicated process governed by loads of equations so read about it here in more detail.

A diagram of Hawking radiation. Credit: Areeba Merriam.

This radiation happens at a tremendously slow rate, relative to the size of the black hole. For many of them, the time taken to disappear due to Hawking radiation is orders of magnitude higher than the remaining lifespan of the universe. The time taken is proportional to mass cubed. For a black hole with the mass equivalent to the mass of our sun, which is tiny in black hole terms, the time taken is already greater than the lifespan of the universe.

The formula for the time taken for a black hole to evaporate, where M is the mass of the black hole and M dot is the mass of our sun.

Unfortunately, this radiation is too faint to be observed experimentally with current technology. There have been attempts to simulate this radiation with a white hole event horizon, yet the experimental results were not replicated and the conclusions remain inconclusive.

If you want to learn more, I strongly recommend reading the chapter Black Holes Ain’t So Black from A Brief History of Time by Stephen Hawking. It’s a fantastic explanation with a lot of diagrams from one of the people who discovered it. Also, check out this video from PBS SpaceTime.


Merriam, A. (n.d.). Hawking Radiation of Relativistic Particles from the Horizon of Black Holes. Medium.

S.A. (n.d.). What Is Hawking Radiation? ScienceAlert.

Spindel, R. (2011). Hawking radiation. Scholarpedia, 6(12), 6958.

A Brief History of Time

A Brief History of Time was originally published in 1988 and remains a bestselling introduction to cosmology and astrophysics. It was one of the first books I read on the subject and it immediately inspired me to find out more. It leaves the reader feeling both dumber and smarter at the same time, since it teaches a tremendous amount in just 256 pages, but also shows how little we know. The ontological discussions on the existence of God and the beginning of the universe bridge the gap between cosmology and philosophy, and personal stories about research on Hawking radiation make the concepts feel very human. The author, Stephen Hawking, has sadly passed away in March 2018, but the lessons he conveyed in this book over 30 years ago remain lucid and timeless. There is a running joke of how many people actually finish or understand the book, but no matter what it is worth at least skimming through as it offers a lot of insight into cosmology.

Stephen Hawking (1942–2018) was a British cosmologist at the University of Cambridge. He was born on the 300th anniversary of the birth of Galileo, which he was very proud of. At age 21 he was diagnosed with ALS, despite which he continued pursuing his PhD and studying. His life was portrayed in the 2014 movie The Theory of Everything. Credit: Santi Visalli.

One of my favourite chapters is the first one, titled Our Picture of the Universe. It functions as a phenomenal introduction. It is a brief overview of the important discoveries in astronomy, such as the heliocentric model of Copernicus and Hubble’s discovery of the expanding universe. It is told in parallel with philosophical developments about the beginning of time, summarising the ideas of Kant and St. Augustine. Hawking discusses the philosophy of science and the fact that we can never prove anything. Finally, it ends with our pursuit for the theory of everything, which would bridge the gap between general relativity and quantum mechanics. This chapter provides a scientific lens for looking at the rest of the book, which makes the ideas more accessible.

Another great chapter is Black Holes Ain’t So Black. Through phenomenal diagrams and great storytelling the author discusses his journey to discover that black holes radiate heat and eventually die. It’s the single best explanation of Hawking radiation I have seen, maybe since it comes from the one who discovered it. Some of the developments are difficult to wrap your head around, but with the help of Wikipedia and PBS on YouTube you can get a phenomenal grasp on why exactly black holes radiate and what entropy of black holes is.

A Brief History of Time is a classic text in non-fiction cosmology. You will learn about all the thorns that trouble cosmologist to this day, and you will know how cosmological research is conducted. It’s also fantastic to reread, which I am doing right now. Do yourself a favour and buy the most recent 2016 edition, as it offers a fantastic update about the book’s reception both from 2016 and 1996, and also discusses the research developments since 1988.


Hawking, S. (1998). A Brief History of Time (10th Anniversary ed.). Bantam.

Hawkins, D. (2018, March 14). What made Hawking’s ‘A Brief History of Time’ so immensely popular? Washington Post.

Tillman, N. T. (2018, March 14). Stephen Hawking biography (1942–2018). Space.Com.

The Death of the Universe

In the previous post I have talked about the most probable cause for the creation of all reality, the Big Bang. As we know, all things that exist will (probably) die, and the same goes for the universe. In this post I will talk you through some of the most prominent theories and also make a case for optimistic nihilism, so you don’t kill yourself immediately after reading this.

I will provide a brief description of the few leading theories, but keep in mind these are likely to change as research into dark energy progresses. I will be leaving out the simulation theory or an infinite universe, as they deserve a separate article and are not seriously considered by many physicists. Also, don’t dismiss this subject because of its depressing nature, it is a really important field, which helps us learn more about the box, in which we are all stuck. Memento mori!

Dante’s Inferno. Credit: Gustave Dore.

Let’s begin with the mostly agreed with theory, the heat death. Frankly, it is quite boring and uneventful when compared to others, but it’s the best one that scientists have come up with. We assume that we know two things, the universe is expanding at an accelerating rate and the universe is flat (you can read more about these in the sources below). We also know that there is a finite amount of matter in existence. Stars can only burn for a set amount of time, at some point they will all run out of fuel and either become black holes, or get consumed by black holes. This is predicted to happen in around 100 trillion years, a massive amount of time. Black holes are also mortal, due to Hawking radiation they decay as virtual particles form on the event horizon. In this process the universe will cool and approach absolute zero, or else maximum entropy, which would mean that no particles would be moving and the universe would stop existing. How chilling. I am really not going into much detail here, so check out the sources below if you want to know more.

Next up is the Big Rip, something I was really interested in when I was younger. Imagine you are holding a big, flat piece of pizza dough, and you stretch it out as much as you can. At first it holds up pretty well, but as it gets longer and longer, at some point it breaks. Now imagine everything in the universe is a piece of pizza dough. At first it expands and it seems fine, but remember that the expansion rate of the universe is increasing. Therefore, at a certain point in the future, all of matter would be ripped apart and disintegrate into unbound elementary particles and radiation. And as the expansion rate approaches infinity, the universe would go back into being a singularity. Much cooler than the heat death, don’t you think?

Now here are two more hopeful theories, although not as likely, the Big Crunch and the Big Bounce (cool names btw). Some physicists argue that the expansion of the universe cannot go on forever, and at some point everything will contract back into a singularity. I would compare this to a rubber band, which is not a very precise analogy, yet works in this context. You stretch out the rubber band, and at some point you let go, which makes it revert back into its original shape. Now this is optimistic, because as with a rubber band, the Big Bounce argues that this could happen indefinitely. What I mean is that the universe could begin again from the aforementioned singularity, experience another Big Crunch, and constantly oscillate between the two states like a pendulum. Sounds amazing, but we will be dead way before any of this happens, and even if we lived long enough, the gravitational forces needed to pull the universe back together would instantly obliterate us.

The Ancient of Days. Credit: William Blake.

Why am I even talking about this? The sun will kill us long before the universe will even be able to conceptualize its own death. I probably exaggerated with the “killing yourself” in the introduction, but think about it. Everything you create, even if you get it far away from global warming, wars, the sun etc. ; everything will be gone at some point. Even reality, even the whole freaking universe, so your death will not be so special at all. The fear and nihilism are all logically correct, yet why not make the best out of what you have? You are not special, nothing is, and the only thing that we can do better than a dog, a tree or a cloud is to learn about things. Even if the pursuit of knowledge is pointless, it is the only reasonable thing to do, so it’s better to take the red pill and see the tragedy of the universe, than to die as a blind man in Plato’s cave.

Sources for further reading:


Timeline of the heat death:

For pessimistic nihilists:

Good article summarizing my main points:

Mathematical explanation of entropy and the heat death (video):