The Photon Magazine #3 November 2020

NOVEMBER 2020 · ISSUE 3

photon A BRIEF HISTORY OF BLACK HOLES PAGE

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SPACE EXPLORATION (AND HOW TO MAKE IT MORE AFFORDABLE) PAGE

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SPACE: THE KNOWN AND THE UNKNOWN

ROGER PENROSE:

INTELLIGENCE CANNOT BE PRESENT WITHOUT UNDERSTANDING.

HOW WILL THE UNIVERSE DIE? PAGE 2 ENERGY PRODUCTION FROM BLACK HOLES PAGE 9

en ENGINE OF PROGRESS

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co DID YOU KNOW?

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A BRIEF HISTORY OF BLACK HOLES PAGE 5

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SPACE EXPLORATION

100 LAUNCHES AND MANY MORE TO GO

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THEORIES ON UNIVERSE EXPANSION PAGE 24

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LETTER FROM THE

EDITORS

Hello readers!

Welcome to the first Photon issue of 2020! In a year that has been filled with so much uncertainty and shock, it’s nice to know that the laws of physics are the one thing that remain constant (yes, don’t worry, at least the gravity bill has been paid this year). Over the past couple of months, we at the Photon magazine have explored realms of physics that some of us never knew existed, and we hope this issue might help you do the same.

And who knows, you might even find answers to questions you have been wondering about for ages. In honour of the one thing that will always be there no matter what we humans create on earth, we present to you the theme of this issue - Space: the known and the unknown.

May the Force be with you on your journey through this barely explored domain, and we hope you enjoy this issue!

The Editorial, Shrishti, Aanya, Siddhant

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HOW WILL OUR UNIVERSE DIE?

WE THINK WE KNOW HOW IT ALL STARTED. BUT HOW WILL IT ALL END? -MUKUL JHA

We think we know how it all started.

In 1929, Edwin Hubble proved that the universe was expanding by finding that galaxies were moving further away from us. If galaxies are moving away from each other, that must mean they started out much closer; as a singularity. The expansion of this high density state is believed to be the start of the universe, or the big bang.

But how will it all end?

First, we need to define ‘the end’.

When could we consider the universe to be officially ‘dead’? One view could be that the universe ends when we end. When all humans die out, we take the idea of the universe with us.

A more accepted definition is that the universe ends when nothing can happen anymore. This outcome could be caused by the maximisation of entropy. This refers to the second law of thermodynamics — “all closed systems tend to maximise entropy” — where entropy is the degree of disorder or randomness in the system. In this case, the universe is our closed system, in which all available energy will one day be spread out evenly between all matter.

How does this spread happen? Well, it happens every single time you, or anyone, or anything does something. The radiation of light from the sun, the supernovae of stars, the processing of this article by your brain. At its core, every action requires the transfer of energy. This transfer leads to the spreading out of energy, or the maximisation of entropy.

This end result (maximisation of entropy) seems convincing, but how do we get there?

There are many different speculations about how entropy could be maximised, but which one is correct? It all depends on gravity and dark energy.

In 1998, we discovered that the universe is expanding at an accelerated rate. However, we don’t know the cause. Our best solution? Give it an intriguing name: dark energy. Gravity is the opposite of dark energy. All matter in the universe has its own gravity. This opposes the expansion of the universe by pulling it inwards. In the end, it is the winner of this cosmic battle between gravity and dark energy that will decide the fate of the universe.

Possibility 1: Dark energy wins - the big rip!

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This means that the expansion of the universe will continue to accelerate forever. As of now, gravity is strong enough to hold galaxies and solar systems together even though the universe is expanding, but after a certain point, space may expand too fast for gravity to keep up.

First, galaxies and solar systems will be pulled apart as their gravity is too weak to hold them together. Then, smaller entities such as planets will be separated as well. This separation will continue until the atomic level, where electrons and quarks will be torn apart. Eventually, it will become impossible for particles to interact, which means nothing can happen anymore even though entropy might not be maximised. The universe will be ripped apart.

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Possibility 2: Gravity wins - Big Crunch/Big bounce!

Eventually, gravity will overcome the expansion caused by dark energy, and will become the dominant force affecting the size of the universe.

Everything will be pulled back together and black holes will devour all matter as they merge together.

Eventually, this black hole will devour itself, and the universe will revert back into a singularity. But there’s more! Depending on the nature of black holes, this new singularity could be identical to the one we had before the big bang.

This would mean that the universe operates in cycles, and countless big bangs and crunches happen throughout many repetitions of this cycle. Either way, entropy is maximised.

Possibility 3: A tie? Heat death Everything stays how it is right now. Dark energy and gravity will never fully overcome each other.

The universe will keep expanding and the transfer of energy will keep happening until entropy is maximised. All the energy in the universe will be spread out over countless lightyears and nothing will ever happen anymore.

The last stars and black holes will die out, leaving the universe cold and dead. This seems to be the most probable scenario at the moment.

The maximisation of entropy seems to be a common theme here. Therefore, if one of these possibilities is correct, time itself should end when the universe ends. How? Entropy is a quantity that goes hand in hand with time.

As “time’s arrow” moves forward, entropy increases. So what happens when entropy is maximised? What use does time have now? Well, nothing.

Time is rendered a useless quantity, so it ‘ends’ in a way.

Clearly, we don’t want all this to happen. To be frank, the end of the universe is so far away that calling it forever is acceptable, but what if I said you could help delay the death of the universe? How could you help, you say? Well, just do nothing. For entropy to be maximised, something needs to happen, but if you just don’t do anything, and just be lazy, you are technically delaying the death of the universe, albeit by an unimaginably insignificant amount of time.

A BRIEF HISTORY OF

BLACK HOLES WHAT EXACTLY IS A BLACK HOLE, HOW DO WE KNOW THAT THEY EXIST, AND WHY ARE THEY IMPORTANT? - SIDDHANT DOSHI On 6th October, the Nobel Prize in Physics for 2020 was awarded to Sir Roger Penrose, Prof. Reinhard Genzel and Prof. Andrea Ghez “for their discoveries about one of the most exotic phenomena in the universe, the black hole.” But what exactly is a black hole, how do we know that they exist, and why are they important?

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The idea of black holes dates back to 1783, when pioneering natural philosopher John Michell first proposed the idea of “dark stars”, stars so massive that even light would not be able to escape. His idea was that as light rays left the star’s surface, they would be slowed down by the gravitational influence of the star, and eventually fall back to the surface. Since no light would ever reach a distant observer, the star would be invisible. This idea initially excited the scientific community, however, subsequent evidence found in the early 19th century suggested that light was a wave, and it was unclear whether a light wave would be affected by gravity.

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However, it has since been found that this idea is not completely true and black holes don’t really behave that way. In order to describe what a black hole would really be like, we need to turn to the foundations of modern gravity. In 1915, Albert Einstein published his theory of general relativity, which presented the incredible notion that all mass and energy result in the curvature of space and time itself, and that gravity emerges from this curvature. Thus, the Earth revolves around the Sun as the Sun’s mass bends space itself, forcing the Earth to follow a curved path. This theory also established that light is indeed affected by gravity, as light too must follow the curvature of space.

The exact nature of the curvature caused by mass is described by Einstein’s Field Equations.

Only a few months later, German physicist Karl Schwarzschild discovered a solution to these field equations for a spherical mass.

However, he found that at what is now known as the Schwarzschild radius, the solution becomes “singular” or undefined as some of the terms in the field equation become infinite. This was the first hint at the possibility that objects like black holes could exist. It is now known that if an object’s size is less than or equal to its Schwarzschild radius, it is a black hole. For example, the Schwarzschild radius of Earth is about 9 mm, meaning that if you somehow manage to squish the Earth to about the size of a marble, you would get a black hole!

In 1958, David Finkelstein suggested that the Schwarzschild surface (the surface of a sphere with the radius being the Schwarzschild radius) is an event horizon, a region of space where the gravitational field is so strong that not even light can escape.

This creates a boundary, where nothing that takes place inside the event horizon can affect the outside universe. This, along with the discovery of pulsars, marked the beginning of the Golden Age of General Relativity. Before this, general relativity and black holes were regarded as scientific curiosities, and it was only then that they became mainstream subjects of research.

But by far one of the most significant discoveries was in the late 1960s when Penrose and Hawking proved that singularities (would appear in generic solutions to Einstein’s field equations. In other words, they proved that the formation of black holes is a robust prediction of general relativity, for which Penrose won the Nobel prize in 2020.

By this time, the theoretical description of black holes and their formation were mostly established. All that remained was to show that they did really exist by gathering experimental evidence. Since black holes by definition do not emit any electromagnetic radiation (apart from the hypothetical hawking radiation), there is no way to see them directly. There are however several indirect ways to observe them, the most prominent being their effect on surrounding stars and other matter.

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Several breakthroughs were made with regard to black holes in this golden age. In fact, it was in this period that the term “black holes” were first introduced and later popularised by theoretical physicist John Wheeler. The nohair theorem was postulated, which stated that any black hole can be described completely with only 3 properties – mass, electrical charge and angular momentum.

General solutions for rotating and charged black holes were found

by Roy Kerr and Ezra Newmann respectively. Stephen Hawking even showed that black holes can emit radiation in what is now known as Hawking radiation.

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In 1974, 2 astronomers Bruce Balick and Robert Brown discovered a powerful radio source while observing the centre of the Milky Way with radio telescopes. They named it Sagittarius A* (abbreviated Sgr A*). Astronomers subsequently measured infrared radiation from the region and found that Sgr A* was at the centre of a large and dense cluster of stars.

However, despite the mounting evidence, it was still difficult to show conclusively that the object was a black hole.

In the early 1990s, two independent teams led by Professors Reinhard Genzel and Andrea Ghez respectively studied the infrared radiation coming from the Sgr A* region. Since measurements are often blurred due to turbulence from Earth’s atmosphere, they took several short-exposure shots and merged them to produce the final images. Furthermore, the long observation time made the use of space telescopes unfeasible.

Both teams studies in detail the distances, speeds and orbits of stars in the central cluster for many years, and finally published their results in 2008 that provided conclusive evidence that Sgr A* was a supermassive black hole in the centre of the Milky Way with an estimated mass of 4 million times that of our Sun. Both Reinhard Genzel and Andrea Ghez shared half the Nobel Prize for Physics 2020.

Since then, scientists and astronomers have significantly improved their experiments and introduced new methods for detecting the presence of black holes. On 14 September 2015 the LIGO (Laser Interferometer Gravitational-Wave Observatory) and Virgo observatories made the first detection of gravitational waves from the merger of 2 black holes, first postulated by Einstein over a hundred years ago. Just a few years later, on 10 April 2019, the first picture of a black hole was taken using the Event Horizon Telescope.

All these breakthroughs have shown beyond reasonable doubt that black holes are indeed very much real, beasts though they may be.

Energy Production from Black Holes - Dev Sahu A (not so brief) introduction Black holes are formally defined as a region in space-time in which gravity becomes so strong that nothing can escape, not even light waves. They are formed specifically at the time of death of a supermassive star that has a core with a mass exceeding 3 solar masses (Msun). This usually takes place in phenomenal explosions called supernovae. These happen when the energy produced by nuclear reactions in a star’s core is no longer sufficient to counteract the gravitational force exerted by the mass of the star itself. When this happens, the core collapses into an incomprehensibly tiny region called a singularity, thereby forming a black hole.

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This naturally begs the question: is it even possible for particles with wave

properties, such as a fixed wavelength, to be compressed into almost nothing? Yes indeed! Because particles have wave properties, including wavelength, it is possible to compress this wavelength with sufficient energy. The tremendous energy liberated by the gravitational collapse of a star is more than enough to be able to compress the wavelength of the particles to almost nothing. The limit at which this occurs is 1.4 Msun (solar mass) and is called the Chandrashekhar limit, named after the scientist who discovered it. This means that stellar cores that weigh above 1.4 Msun suffer gravitational collapse at the time of the star’s death. Stellar cores with masses between 1.4 and 3 Msun collapse to form neutron stars, while cores with masses above 3 Msun collapse into black holes.

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Black holes are divided into 2 regions: the singularity and the event horizon. The singularity contains all the mass of the black hole. The event horizon is a kind of boundary that surrounds it. At the event horizon, the escape velocity required is equal to the speed of light (3×108 ms-1), which is unattainable for objects with mass (including us). It is for this reason that the event horizon is sometimes called the point of no return. The distance of the event horizon from the singularity is given by the formula v2 =2Mr, where v is the escape velocity (in this case, the speed of light), M is the mass of the black hole, and r is the distance between the event horizon and the black hole. 2Mr simply denotes the space-time curvature produced by a mass M at a distance r (for more, do check out the Schwarzschild solution to Einstein’s field equations - explained on page 6).

In layman’s terms, nothing can escape from a black hole, not even energy in the form of photons which travel at the speed of light.

Therefore, is it really possible for us to even theoretically extract energy from black holes? Short answer: yes.

Long answer: it is possible to do so because of one reason– some black holes spin.

Why do black holes spin?

Whether or not a black hole is a Kerr or Schwarzschild black hole - that is, whether it spins or not - depends on the star from which it was formed. If that star was spinning (which most stars do), then so does the black hole. This is because the law of conservation of momentum tells us that it must keep on spinning. The angular momentum of any object, including celestial bodies, is given by (more math, but somewhat inevitable) L =mvr, where m is the mass of the object, v is its velocity, and r is the radius from the axis of rotation to the outermost point.

When r decreases, the law of conservation of momentum tells us that v increases. Thus, when supermassive stars collapse to form black holes, their radius shrinks to practically zero, which means that black holes are spinning incredibly fast. This rotation of black holes has another effect. When black holes rotate, they drag the fabric of spacetime with it, transferring some of its angular momentum to that region.

This is known as frame-dragging or the Lense-Thirring effect, and the region created by it is called the ergosphere.

Because the ergosphere is located outside the event horizon and it contains some of the rotational energy of the black hole, it is possible for an object to return from it with more kinetic energy than it entered the ergosphere with.

Sir Roger Penrose, one of the recipients of the 2020 Nobel Prize in Physics, conceptualised a process by which we might achieve this. For this reason, it has been named the Penrose process.

Penrose Process

Penrose theorized a process by which a future civilisation may sustain itself by positioning itself around a suitable black hole. This civilisation might then launch rockets into the ergosphere. Inside the ergosphere, the rocket could then split into two parts. If carefully executed, one part would fall beyond the event horizon, while the other would take on some of the rotational energy of the black hole and return from the ergosphere with increased velocity.

This entire process obeys the laws of black hole mechanics and would result in a slight decrease in the angular momentum of a black hole, which corresponds with the energy extracted. This process can be repeated over and over again until the black hole eventually loses all of its angular momentum and stops spinning, turning into a Schwarzschild black hole.

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The maximum theoretical amount of energy that can be extracted in this manner is equivalent to 29% of the mass-energy of the black hole. However, converting the kinetic energy of the rocket to other forms of energy could pose potential problems.

A more practical approach to the Penrose process would be the use of electromagnetic radiation.

Instead of launching a rocket, the future civilisation would construct a giant spherical mirror around a black hole, with the reflecting surface facing inwards. This mirror would also have windows which can be opened from outside. The window would be then opened and electromagnetic waves would be fired inside.

These electromagnetic waves would then be reflected around the black hole by the mirror. Some of them would pass through the event horizon, never to return, but the majority would simply pass around the black hole in the ergosphere, thereby taking on some of the rotational energy of the black hole, amplifying and growing exponentially stronger.

This phenomenon is real and is called superradiant scattering. Another window could be opened and the energy of the amplified electromagnetic waves could be harnessed for various purposes.

Producing energy from black holes would be, if perfected, our most efficient method of energy generation, and is therefore the most likely method of energy production for future civilisations.

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Poster by: Disha Saraogi

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Enceladus, one of Saturn’s smaller moons, reflects 90% of the Sun’s light.

There are more stars in space than there are grains of sand in the world.

Pluto is smaller than the USA.

LAUGHS CAN'T BE HEARD ON SPACE GOOD THING WE'RE ON EARTH! What is an astronaut's favourite key on a keyboard?

The space bar!

I’m addicted to space jokes, but someday I’ll overcomet.

Why did the alien throw beef on the asteroid?

He wanted it a little meteor!

SPACE EXPLORATION (AND HOW TO MAKE IT MORE AFFORDABLE) Arushi Kolluru

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The dream of floating in the beauty of space is currently out of reach for those who aren’t astronauts or billionaires.

There are, however, several concepts that could help make space exploration for the common person a possible reality.

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The Space ElevatorIn present times, a rocket requires enough fuel to move upwards and sideways to overcome the force of gravity and reach the orbit. This results in the excess fuel adding more weight to the rocket’s mass, making it unable to carry heavier goods or people.

Therefore, rockets burn a huge amount of fuel to get a small weight of cargo into space. This immense cost is one of the major limitations of human spaceflight.

A Space Elevator, however, uses much less fuel, as it taps into the energy of the Earth’s rotation to give the cargo enough of a ‘boost’ to reach the orbit. It also drastically reduces the cost of sending cargo into space to less than 2% of the current amount. This means that it would take a mere $200 to transport 1kg of payload into space.

The manufacture of a Space Elevator is currently restricted to the realm of science fiction. But various comprehensive studies of this piece of technology and its variants have been done with varying levels of professionalism.

There are 4 main components of the standard Space Elevator- The tether, climber, anchor and counterweight.

The tether and the climber form the elevator components which will extend outwards from the surface of the Earth to the counterweight, positioned in space. The anchor will hold the tether to the surface of the Earth.

The tether is like a tightrope; drawn taut, it will connect the anchor on the ground to the counterweight up in space. The climber will act as a regular elevator carrier, moving up and down the tether, transporting rockets, cargo and probes into orbit. The anchor would pin the tether to the Earth and maintain stability at the ground level. The counterweight, situated at the top, would hold up the tether and maintain balance on the upper end of the Space Elevator. The counterweight is vital in supporting the tether and holding it up with the use of tension. The counterweight would serve as not only a launching point for all space missions but could also be used as an International Space Station and point of experimentation.

A Space Elevator on the Earth, is, however, a far-fetched dream at present. For starters, a difficulty in the creation of a Space Elevator is that the initial building cost of a Space Elevator is at least $20 billion. This would make Space Elevators the single largest one-time investment in the space exploration sector. Even if we are to acquire the necessary funds for such a massive project, there lie problems with the components, materials, installation and possible hazards.

In terms of materials and components, the tether is the most difficult main component to acquire and make. The tether needs to be light, affordable, resistant to damage, strong and able to withstand the effects of radiation, weather and atmospheric corrosion. No material that we currently know of and can produce has the stability and resistance that we require. Although graphene and diamond nano threads are possible options, they too might not prove to be put to the task. Moreover producing enough length (nearly 40000 km) of the tether will prove to be a near-impossible task.

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With regards to installation, the tether needs to be either launched into space from Earth or lured down to the ground from the Space Station, both difficult and time-consuming processes. To build a Space Elevator on the Earth, we still have several major technological hurdles to overcome.Most of all, however, a Space Elevator, in case of a malfunction, would cause great loss of property and finance. If the tether were to break, there would be catastrophic results. We need to get it right the first time if we want to keep the Earth safe.

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These difficulties do not reduce the benefits of Space Elevators in any way. However, to keep ourselves out of direct harm and to make do with the materials currently available to us, we should consider making a Space Elevator on the moon. The moon’s gravity is much weaker than the Earth’s. Therefore a flimsier, existing and more widely available material can be used, while also decreasing the overall required length of the tether. Weaker materials like kevlar could be used. Moreover, stronger self-healing fabrics and fibres like the famed wolverine cloth could be put to use to drastically reduce or eliminate the possibility of a tear in the tether. Installation would also be easier to accomplish on the moon’s surface and it would give us the necessary experience to, one day, build a Space Elevator on Earth.

Despite all the challenges, the payoff of having a Space Elevator would be immense. A fully functioning and properly utilised Space Elevator might be the first step in humanity’s journey to becoming a space-faring civilisation.

That goal, however, has a long way to go. Having a properly utilised Space Elevator situated on the moon would require far more regular trips to and from the moon, making it the launchpad for rockets and probes headed to other planets. Humanity is currently far from that stage of sophisticated development and expansion in space. Moreover, the setup on the moon would require a considerable number of human trips to our natural satellite.

According to me, such technology is truly revolutionary and will mark the beginning of a new era of human civilisation. The era will consist of planetary exploration, asteroid mining and colonisation of planets, but it cannot begin today.

Visits to the moon need to rise along with the visits to other planets in our solar system if we wish to make effective use of our Space Elevator. Superior technology needs to increase in availability and be used more often. For now, Space Elevators are a possible plan for the future at most, but a highly beneficial plan at that! Space Elevators could be our future gateway to becoming an interplanetary and technologically advanced civilisation.

100 LAUNCHES AND MANY MORE TO GO A Brief History of SpaceX

- Varun Satish

with the future of the company riding on the success of the fourth. Needless to say, the fourth and final launch of the Falcon 1 succeeded, making SpaceX the first privately owned company to launch a liquid-propellant rocket into orbit.

Initially attempting to set up a small scale greenhouse on Mars, Musk faced resistance when he attempted to purchase refurbished Intercontinental Ballistic Missiles from Russian Companies. Rather than admit defeat, Musk set up SpaceX with the intention of building affordable rockets and launching satellites at a low price. With the first headquarters established in El Segundo, California, Musk and his team set out to build and launch the Falcon 1.

With the success of the Falcon 1, SpaceX moved onto developing the Falcon 9 rocket and the Dragon capsule, a cargo spacecraft that would resupply the International Space Station (ISS).

In 2010, the Falcon 9 V1.0 was up and ready with its first launch attempt from Cape Canaveral Air Force Station in Florida. Through the Dragon Spacecraft and the Falcon 9, SpaceX achieved many firsts, including becoming the first privately funded company to send a spacecraft to the ISS. But going into 2015, they would attempt their most daunting task yet.

By 2008, the Falcon 1 had launched and failed three times,

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In 2001, Elon Musk tried to buy some Russian Missiles to send some plants to Mars. Less than a year later, he founded the company that would become the world’s first privately funded company to send humans to space.

More recently, SpaceX tested the crew version of the Dragon spacecraft as a part of the Commercial Crew Program.

SpaceX is one of two companies, the other being Boeing, that won contracts to develop spacecraft to send humans to space. Since the last Space Shuttle Launch in 2012, the United States has had no way of launching astronauts from American soil and has had to rely on the Russian Space Agency.

However, in May of 2020, SpaceX launched astronauts Bob Behnken and Doug Hurley to the ISS, becoming the first privately owned company to send humans to space.

In 2018, SpaceX set another set another first by becoming the first private company to launch an object into orbit around the sun.

Using the newly developed Falcon Heavy, SpaceX launched Elon Musk’s Cherry Red Tesla Roadster into orbit as a test of the new rocket. The Falcon Heavy also became the most powerful operational rocket since the Saturn V from the Apollo era.

With 100 successful launches and many firsts, SpaceX has an exciting future ahead, to say the least. As of the time of writing, SpaceX is developing a new rocket called Starship with the intention of sending humans to Mars.

Simultaneously, they are also expanding their Starlink network of satellites to provide a low latency internet across the world.

From when they began to today, the mission of SpaceX has always been to revolutionise the industry and provide services of the highest quality.

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Starting in 2014, SpaceX began to test the vertical launching and landing of a rocket. They started with a prototype, aptly named ‘Grasshopper’. After numerous attempts, SpaceX finally transitioned to testing this method on rockets used for launches themselves. Following many huge explosions, they finally landed a rocket on the 21st of December 2015 at Landing Zone1, Kennedy Space Centre, another first in the industry.

Less than five months later, they followed this by landing a rocket on their Autonomous Spaceport Drone ship ‘Of Course I Still Love You’.

Engine of Progress

By Rohan Doddavaram

Science fiction works “discovery” and “exploration”

of

tend to be common, since not only do they sell well, but they also have plot lines that are easy to think of, with both authors and readers living vicariously through the exploits of some dashing, square-chinned spacefarer. It’s effectively the same trope as say Indiana Jones or any others of that ilk: exploration, discovery, and adventure. What makes them different is the fact that rather than filling us with nostalgia for the past, as Indy’s shenanigans in the Yucatan typically do, they fill us with something more of an optimism for the future: we know most of the places that probably exist on the Earth, except of course, wherever it is my socks seem to keep vanishing. On the other hand, space seems like a virgin frontier, untouched and unspoiled. Of course, my only hope is that we won’t treat the Universe with the same callousness we seem to have no qualms about treating the Earth with.

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The idea of exploration is definitely one that has driven human discovery throughout the ages. Of course, the scale and significance of these discoveries varies slightly between voyaging the Pacific in a canoe as the Samoans did, and what a lot of you do to the effect of “ooh how about we order a banana milkshake not a chocolate one with our vanilla tea cake”. To be fair, not many of us reading this are going to be discovering a new planet. On the other hand, quite a few of us have likely read (or encountered) a work of sciencefiction in our lifetimes.

A key component of these works is this very spirit of exploration that is emblematic of the human spirit to explore, expand (this part is good), exploit, and exterminate (these two not so much).

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However, although the plot lines of these novels/films/musicals (yes, there are a few - do not watch them) remain fairly consistent with the classic adventure story, the methods of exploration can differ greatly from book to book to film to unfortunate musical (I’m so sorry, Tim Fitzsimmons). I’m talking of course about the feature of Star Wars and Star Trek that were (at least to me) by far the most intriguing and memorable of the entirety of the franchises: the spaceships, which have stuck with me more than the characters or the (mediocre) world-building, if only for my preternatural love for shiny, fastmoving objects.

What’s really interesting about the ships is their means of propulsion.

Aeroplanes have turbo-fans or turboprops.

Cars have the ubiquitous internal combustion engine. Ships and helicopters have gas turbines. But is there really one convenient “ideal motor” that we can attribute to spaceships? True, rocket engines are what’s commonly used, but that’s more out of the limits imposed upon us by our technology than any optimisation.

It turns out that there are, in fact, several. Now the incredibly talented Professor Michio Kaku does the topic far more justice than I ever could in his fantastic book Physics of the Impossible. I will nevertheless endeavour to give it a fair go.

The two means of propulsion that strike the best balance of ludicrously cool SF fantasy and practical, pragmatic science fact are the Bussard ramjet and the putative “laser sail”, more properly known as directed-energy propulsion.

Now directed-energy propulsion is the far less exciting one, at least in my opinion. It is also, however, much more feasible. Like most rocketry, it is derived primarily from fairly basic principles, in this case, like so many others, Newton’s Third Law of Motion, which states that every action has an equal and opposite reaction. A general rule of thumb that’s useful to remember when working with rockets is that exhaust velocity is proportional to the square root of exhaust temperature.

The effect of this is that rockets are fundamentally inefficient machines, with huge amounts of energy needed to get a projectile up to speed and out of orbit. This is a factor of the working mass: the mass against which force acts to accelerate an object. With rockets, most of this is fuel needed to get up to speed, and which is quickly burned off, hence the inescapable Tsiolkovsky equation.

On the other hand, laser sails make use of the radiation pressure of light (specifically lasers) to push a spaceship, so both fuel and reaction mass (propellant mass) drop to zero.

The spaceship bears what is for all intents and purposes a large reflective membrane which functions as a sail, and laser light is beamed onto it from a stationary power plant on the ground. The simplest way to think of this is a conventional ship’s sail, except that the force of wind is replaced by the radiation pressure exerted by light. This isn’t necessarily a very fast means of getting from A to B, but it functions indefinitely due to the absence of fuel, and can work well for generation ships or probes.

These are pretty basic introductions to what is a fascinating and rapidly-growing field, and I don’t expect it to do anything but spark an interest in you for science, and astrophysics in particular. But to me, it just goes to show what we can do with our spirit for adventure, when our minds are really put to it. Maybe you can’t go to Saturn for a vacation. But it’s the little things that count. Maybe take the lessbeaten road to school tomorrow.

Maybe learn a new language and visit a new country. And hey, buy the banana milkshake. You’ll like it, I promise.

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The Bussard ramjet is the one that really gets me excited.

It uses a massive electromagnetic field to attract protons (H+ ions) into a “scoop” or inlet.

The speed of the spaceship forces the ions, now atoms, closer together in a narrower and narrower magnetic field, until boomthermonuclear fusion occurs, outputting vast amounts of energy. Since the idea’s inception in the 60s, refinement and the use of the CNO fusion cycle rather than the typical proton-proton chain have projected speeds of up to 500,000 m/s: remember that this is a constant speed, unlike a plane in our atmosphere which must constantly output thrust to maintain its velocity, and also that this is done without fuel.

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Theories on the Expansion of the Universe - Arushi Kolluru, Aryan Kaul, Chakradhar Reddy, Dhruv Agarwal

The theories behind the “space” occupied by the universe have evolved throughout the years.

Scientists have puzzled over whether the size of the universe is constant, shrinking or expanding at an accelerated rate. Our quest for knowledge about the universe never ceases as we try to grasp what the seemingly infinite expanse we know as the universe really is.

FRIEDMANN'S EQUATIONS AND CRITICAL DENSITY One way to measure the rate oF expansion in the universe is to use the Friedmann equations:

Where ρ is the average density of the universe at that moment, and a' is the rate of change of a. Hubble’s constant (the current rate of expansion) is given by

Where k is the constant that defines the geometry of space and influences the value of π. If k = 0, pi is constant. If k > 0, the value of π falls and if k is < 0, the value of π rises.

These different geometries can perhaps be best understood through a two-dimensional analogy.

A universe with k = 0 is flat and homogenous in all directions. A universe with k > 0 is analogous to the surface of a sphere. If you go far enough in any direction, you will end up back where you started. The universe is finite, but has no edge.

Two lines that start off parallel will ultimately converge in this scenario.

A universe with k < 0, on the other hand, is analogous to a saddleshape. The universe is infinite and lines that start off parallel tend to diverge.

Critical density is the value at which the universe is at balance, and expansion is stopped. This value is estimated as 9 x 10^(-27) kg/m³ and it is calculated when you take the matter-energy density of the universe and divide it by the matterenergy density of the universe that is required to achieve that balance.

If the density is larger than this, we live in a “spherical”, finite universe, while if the density is smaller than this critical value, we live in a saddleshaped, open universe. Because this critical density is so important, the average density of various components of our universe is often quoted as the ratio to this critical density:

HUBBLE'S LAW Edwin Hubble, who is famous for his Hubble’s law, Hubble’s ‘constant’, and the quite unrelated Hubble telescope, was one of the greatest contributors to affirming the theory of the ever-expanding universe. It is also based on his discovery of redshift. The Doppler effect and the red shift are used to measure the motion of other stars and galaxies relative to the earth.

A red shift is a phenomenon where electromagnetic radiation from an object undergoes an increase in wavelength. This is mainly due to stars and galaxies moving away from a fixed point, which is usually taken as the earth. This red shift is further proven by the Doppler effect, which states that objects emit waves of higher frequency (lower wavelength - bluer shifts) when they are moving towards the earth, and waves of lower frequency (higher wavelength - redder shifts) when they are moving away from the earth. This value of the red shift can also be determined by using the formula:

z = red shift

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Expanding on this formula, we can also find the velocity of the stars/galaxies moving away from us using the value of their red shift.

This can be calculated by using the formula v=cz where v is the velocity of the object, c is the speed of light and z is the redshift. Figure 1.1 represents the wavelengths and the element that their photon emissions represent.

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Figure 1.1

Using the concept of redshift and his observation of the motion of galaxies, Hubble derived a law which states that the recession velocity of a celestial object is proportional to its distance from the observer. This means that the farther away an object is, the faster it will be moving away from us.

Hubble’s constant is the proportionality constant for this relation, and was found experimentally by comparing the velocities of objects with respect to their distances. Like mentioned before, the value of the Hubble’s constant can be found using the equation

The Hubble’s “constant” is a misnomer considering the fact that this value has been shown to vary through the decades. As of 2019, the value of H0 is stated to be 73.9 km per second per megaparsec.

To put this in layman terms, a galactic body in space, one megaparsec away from the observer, is moving away at a velocity of 73.9 km per second.

Recessional velocity = Hubble's constant x distance Using this formula regarding recessional velocity - which is the velocity at which other objects are moving away from you - it can be argued that the farther away something is away from us, the faster it is moving away from us, which can be seen in figure 1.2.

Figure 1.2

Therefore, wherever you are in the universe, everything is moving away from you at a velocity proportional to its distance from you. This is conclusive evidence for the expansion of the universe.

INFLATION THEORY Inflation theory, proposed in 1980

by American theoretical physicist Alan Guth, endures as the most probable theory to explain the primitive universe and its inevitable annihilation. This theory stands on the pillars of the observations of other legendary physicists like Alexander Friedmann, Edwin Hubble, and Albert Einstein. It states that in the very early universe, the universe experienced a period of explosive expansion that lasted from around 1036seconds to10-33seconds after the Big Bang, going from about a billionth the size of a proton to the approximate size of your palm. It is essentially the â&#x20AC;&#x153;Bangâ&#x20AC;? in the Big Bang. One of the main motivations for this theory was the homogeneity of the universe that was observed on large scales, something that the conventional Big Bang theory was unable to explain.

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The concept of homogeneity of the universe indicates that the same objects are visible to observers at different locations in the universe.

Upon observation, it is evident that the universe is not homogenous at the local level; the difference in material density amongst Earth and outer space is massive. On scales of thousands of light-years, it is still observed to be irregular; some galaxies are dense whereas some are wisps of stars and nebulae.

Galaxies themselves are gathered into groups and clusters, which form superclusters, separated by voids.

Yet, there is no solid evidence of the principle of uniformity. On larger scales still, cosmic objects seem to blend into a smoother space.

Surveys that probe billions of light years for quasars and similar celestial bodies do find a very uniform distribution, as observed in Figure 1.3. The cosmic microwave background (CMB) is another key example of uniformity, as it shows that the maximum temperature difference between any 2 points in space is no more than 0.00001 degrees Kelvin, which is an immeasurably tiny amount.

Therefore, on greater galactic scales, the universe does appear to be homogeneous.

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Figure 1.3

Inflation theory allows us to explain this homogeneity by suggesting that during the early universe, electromagnetic radiation had time to convey information across the then tiny universe, before inflation kicked in to smooth out any further irregularities.

ANNIHILATION OF THE UNIVERSE Until recently, it was thought that the expansion of the universe was slowing down due to the influence of gravity. However, it is now known that the universe is expanding rapidly - at an accelerated rate. This was a highly surprising discovery, as it implied that there existed an unknown force that was able to counteract the gravitational influence of all matter in the universe. This has been attributed to dark energy, a mysterious component of our universe, hypothesised to be the driving force in expansion.

However, it is opposed by another strange and relatively unknown phenomenon: dark matter. From the constantly decreasing viscosity of the universe and the gradually fading luminosity, it can be inferred that the gravity of dark matter is reducing as it is the force keeping the expansion of the universe in check. This leads us to three different catastrophic scenarios of the conclusion of space-time: Big Crunch, Big Rip, and the Great Freeze - which you can take a look at on page 2.

As researchers at LIGO, CERN and many other reputed organisations of the world have been aiming to gather stronger experimental evidence in favour of these models, scientists strive to create even more accurate theories to understand the true nature of the universe.

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PHOTON NOVEMBER 2020

03 Editors-in-Chief Shrishti Kulkarni / Aanya Pratapneni / Siddhant Doshi Correspondents Mukul Kashyap Jha / Disha Saraogi / Arushi Kolluru / Varun Satish / Dev Sahu / Rohan Doddavaram/Physics Club (Arushi Kolluru / Aryan Kaul / Chakradhar Reddy / Dhruv Agarwal) Design Consultant Samika Sivaraman Visit our website at: thephotonmagazine.com Follow us on Instagram: @thephotonmag Email us at: thephotonmag@gmail.com