Kurzgesagt – In a Nutshell
Sources – Interstellar War
Thanks to our expert:
Dr. Luke Campbell
Pacific Northwest National Laboratory
– The Smorpians disagree. They reside on a planet around the orange dwarf star HD 40307, 42 lightyears away. Smorpian civilization developed earlier than Humans and they have much better technology.
The Smorpians are fictional aliens we’ve positioned on the potentially habitable super-Earth planet discovered around star HD 40307. It is a K-type orange dwarf with 77% of the Sun’s mass and 23% of its brightness. We can find it in the Pictor constellation, 42 lightyears away.
#Mikko Tuomi et al. (2012): Habitable-zone super-Earth candidate in a six-planet system around the K2.5V star HD 40307
https://arxiv.org/abs/1211.1617
Quote: “We show that Doppler measurements can be filtered for activity-induced signals if enough photons and a sufficient wavelength interval are available. If the signal corresponding to HD 40307 g is a genuine Doppler signal of planetary origin, this candidate planet might be capable of supporting liquid water on its surface according to the current definition of the liquid water habitable zone around a star and is not likely to suffer from tidal locking. Also, at an angular separation of ∼ 46 mas, HD 40307 g would be a primary target for a future space-based direct-imaging mission.”
Consider how little time it took for humans to go from steam engines to supercomputers relative to how long our species has existed: 250 years vs 200,000-300,000 years, or 0.1%. If an alien species like ourselves evolved just 0.1% earlier, then it might have a technological edge over humanity as large as the gap between steam engines and supercomputers!
– They recently built a Dyson Swarm around their star, which gives them near limitless energy.
A Dyson Sphere is a hypothetical megastructure that would enclose an entire star and extract its energy to power an advanced civilization. A Dyson Swarm is the most realistic version of that idea: a huge number of power satellites in separate orbits around a star, each collecting light and converting it into laser beams to send it to the civilization that built them.
#Stuart Armstrong and Anders Sandberg (2012): Eternity in six hours: intergalactic spreading of intelligent life and sharpening the Fermi paradox, Future of Humanity Institute
http://aleph.se/papers/Spamming%20the%20universe.pdf
Quote: “The most realistic design for a Dyson sphere is that of a Dyson swarm ([Dys60,
San06]): a collection of independent solar captors in orbit around the sun. [...] The lack of perfect efficiency isn’t an issue either, with 3.8×10^26 W available. And the advantages of Dyson swarms are important: they don’t require strong construction, as they will not be subject to major internal forces, and can thus be made with little and conventional material.”
We have a video on the topic!
#How to Build a Dyson Sphere - The Ultimate Megastructure
– Interstellar war is hard though. Frontlines, tactics and logistics are meaningless at these scales. It is also fought across time: decades will pass between firing a weapon and learning whether it hit or not.
This is a consequence of the limited speed of light. Light carries information but only travels at around 300,000 km/s. So learning about an attack or coordinating a response on short timescales - what we call tactics - is impossible. Also, weapons that can cross interstellar distances are able to touch every part of an enemy’s territory. So there are no ‘frontlines’ which separate regions at risk from war from regions which are safe: everything becomes a battlefield.
The modern conception of strategy, operations and tactics:
#USAF College of Aerospace Doctrine, Research and Education (1997): Three Levels of War, Air University Press
Quote: “Modern military theory divides war into strategic, operational, and tactical levels”
An explanation on how the speed of light and the speed of information are related:
#RP-Photonics, Causality (retrieved 2023)
https://www.rp-photonics.com/causality.html
Quote: “Causality is one of the most fundamental principles of philosophy, physics, and other sciences. It is essentially the attempt to make sense of observations by linking events (effects) to other events (causes) and explaining the mechanisms behind these relations.
A fundamental requirement for causality is that a caused effect can not occur before the cause. Within Einstein's theory of relativity, causality requires a more stringent restriction: the time between cause and event must be at least the time which light propagating in vacuum needs to get from the location of the cause to the location of the event. In short, no signal can propagate faster than light does in vacuum.”
– Sending an invasion fleet is futile: even if the Smorpians travel at a large fraction of the speed of light, the journey to Earth would take decades or even centuries and humans would have plenty of time to prepare.
The fastest probes we plan to send to other stars would travel at 25% of the speed of light. It would be done by using very powerful laser beams to push probes reduced to ‘wafers’ of just 1 gram.
#Philip Lubin, A Roadmap to Interstellar Flight (2016), JBIS vol 69
https://arxiv.org/pdf/1604.01356.pdf
Quote: “We propose a roadmap to a program that will lead to sending relativistic probes to the nearest stars and will open up a vast array of possibilities of flight both within our solar system and far beyond. Spacecraft from gram level complete spacecraft on a wafer (“WaferSats”) that reach more than 1/4c and reach the nearest star in 20 years”
If the Smorpians and their advanced technology can propel whole spaceships to that speed, then they could send an invasion fleet to Earth in around 168 years. However, that’s like setting out to conquer the world of 1855 and arriving to find the nuclear-armed modern militaries of 2023. And it gets worse: the information the Smorpians would have on Earth would be 42 years older than that. The last observations they would get from our planet before launching the fleet would be from 1813, a year where Napoleon was fighting with wooden ships and flintlock rifles. An invasion fleet armed to defeat that level of technology would be wholly inadequate for what we have today.
– If you want to learn more about the mind numbing problem of war between alien civilizations, we made a video about it –
#Why We Should NOT Look For Aliens - The Dark Forest:
https://www.youtube.com/watch?v=xAUJYP8tnRE
– As an advanced technological civilization, the Smorpians harness the energy of their star by surrounding it with billions of solar power satellites. This Dyson Swarm collects 1% of the star’s energy output: a million billion billion watts. 50 billion times more than all Humanity generates.
1% is a plausible figure for how much starlight a Dyson Swarm would collect and be able to convert into useful power. 10% would lead to major climate disruption for the Smorpian’s home world, as the reduced sunlight reaching the planet would lower its temperature drastically. 100% would require a solid shell with all the problems that would entail, like completely cutting off sunlight from the planet and requiring super-materials to build without collapsing.
It’s also a figure within the range considered plausible in this paper:
#Jack Smith, Review and viability of a Dyson Swarm as a form of Dyson Sphere (2022), Physica Scripta, Volume 97, Number 12
https://iopscience.iop.org/article/10.1088/1402-4896/ac9e78
Quote: “Efficiency of the Dyson Swarm ranges from 0.74–2.77% of the Sun's 3.85 × 10^26 W output, with large potential for growth as both current technologies improve, and future concepts are brought to reality in the time before and during the swarm's construction.”
Our Sun’s total power output is 3.8 x 10^ 26 Watts. HD 40307 is only 23% as bright, so its output would be 0.87 x 10^26 Watts. 1% of that figure is 8.7 x 10^23 Watts, which we’ll round up to 10^24 Watts. That’s equivalent to 8,760,000,000,000,000 TWh per Earth year.
#Mikko Tuomi et al. (2012): Habitable-zone super-Earth candidate in a six-planet system around the K2.5V star HD 40307
Human civilization has a primary energy consumption of 160,764 TWh per year. It translates to an average power of 18.3 Terawatts. The Smorpian Dyson Swarm would be producing over 50 billion times more than that.
#Global direct primary energy consumption, OWID (retrieved 2023)
– What if all the power of the Dyson Swarm, all those satellites were used to create a star laser? Like any laser, the bigger it is the longer its range. Human-built lasers use small mirrors to focus, so they have short ranges. The Smorpians could turn their entire Dyson Swarm into a collective focusing element a million kilometers wide. The Star-Laser has an insane range as a result: enough to focus on target Earth from a distance of over 2 million lightyears.
The power satellites in a Dyson Swarm collect sunlight and convert that energy into a laser beam they can send to their home planet or wherever it is needed. Each satellite can be considered a separate laser emitter. A large number of emitters can synchronize their beams to produce a single larger beam. So with very careful timing and spacing, they can all work together to form a single phased array laser.
We have managed to engineer thousands of emitters to work together in a phased array laser.
Phased array for light:
#Jie Sun et al., Large-scale nanophotonic phased array (2013), Nature volume 493, pages195–199
https://www.nature.com/articles/nature11727
Quote: “Here we report the demonstration of a large-scale two-dimensional nanophotonic phased array (NPA), in which 64 × 64 (4,096) optical nanoantennas are densely integrated on a silicon chip within a footprint of 576 μm × 576 μm with all of the nanoantennas precisely balanced in power and aligned in phase to generate a designed, sophisticated radiation pattern in the far field.”
A phased array made out of a Dyson Swarm would be very difficult but also technically possible. The result is also called a ‘Nicoll-Dyson Beam’. Little has been written about it outside of science fiction contexts:
#Nicoll-Dyson Beams, Encyclopedia Galactica (retrieved 2023)
https://www.orionsarm.com/eg-article/48fe49fe47202
Quote: “Dyson Swarms collect considerable amounts of energy from the stars they contain. If some of that energy can be stored, then directed towards a target in a different planetary system, considerable damage can result. In practice, the outermost elements of the swarm, or the outer surface of a dynamically supported Dyson Shell, become a phased array emitter. This allows a powerful beam to be focused on a distant target in another planetary system. This concept was first suggested by James Nicoll in the Information Age, and is known as a Nicoll-Dyson Beam for this reason.”
Nonetheless, we can estimate its performance. All laser beams are subject to diffraction over long distances - an effect that makes them beam spread out. Diffraction depends on the wavelength of the laser and the diameter of the mirror, lens or other aperture used to focus it. This equation tells us how wide the beam becomes (spot size) after travelling a certain distance:
Spot size = 4/π x Wavelength x Distance / Aperture Diameter
All the units are in meters.
Diffraction and its equation are explained here:
#Limits of Resolution: The Rayleigh Criterion, DOUGLAS COLLEGE PHYSICS 1207 (2018)
Quote: “The accepted criterion for determining the diffraction limit to resolution based on this angle was developed by Lord Rayleigh in the 19th century. The Rayleigh criterion for the diffraction limit to resolution states that two images are just resolvable when the centre of the diffraction pattern of one is directly over the first minimum of the diffraction pattern of the other. See Figure 2(b). The first minimum is at an angle of θ = 1.22λ/ D, so that two point objects are just resolvable if they are separated by the angle θ = 1.22λ/ D”
A visible laser, like a green laser, has a wavelength of half a micron, or 5 x 10^-7 meters. A laser built on Earth today would have an Aperture Diameter of around 1 meter or less. If it had to travel 42 lightyears from the HD40307 system to reach us (a distance of 3.97 x 10^17 meters), this regular laser’s beam would spread out to become 2.5 x 10^11 meters wide, or 19,620 times larger than the Earth! A beam that large would have its energy spread out so much that it wouldn’t be able deal any damage, so it wouldn’t be a great interstellar weapon.
A phased array made out of a Dyson Swarm would have an Aperture Diameter of a million kilometers. That lets it focus a laser beam a billion times better than the 1 m wide mirror of a regular laser. If you set the spot size as equal to the Earth’s diameter (12,742,000 m), the wavelength as 5 x 10^-7 meters and the Aperture Diameter as 10^9 meters, then you can solve for Distance. You should find a result of 2 x 10^22 meters, equivalent to 2.11 million lightyears.
That is over 10 times more than the diameter of the Milky Way.
#M. López-Corredoira et al., Disk stars in the Milky Way detected beyond 25 kpc from its center (2018), Astronomy & Astrophysics Volume 612
https://www.aanda.org/articles/aa/full_html/2018/04/aa32880-18/aa32880-18.html
Quote: “Our analysis reveals the presence of disk stars at R > 26 kpc (99.7% C.L.) and even at R > 31 kpc (95.4% C.L.).”
– Ok. Let us shoot it. Countless tiny beams combine into a single huge beam – Laser beams are normally invisible in space, but the Star-Laser is so powerful that light scattering off bits of dust and gas in its path makes it clearly visible in the sky. A gigantic column of green light.
Lasers are made up of photons travelling in one single direction. They do not stray to the sides so they don’t normally reach your eyes, making the beam invisible. However, if there is something in their path, the photons can be scattered in all directions, allowing some light to reach your eyes and rendering the beam visible.
You can see this effect with a laser pointer. In a clean room, you will only see the spot it produces on the wall. In a room with some dust in the air, you will see a sparkling line between the pointer and the wall.
The vacuum of space is generally considered too empty to produce this effect. An enormously powerful source of light changes that. The Sun, for example, scatters enough light off the dust in our Solar System to produce zodiacal light. That is the diffuse glow in the night sky we can see even without any other source of light (Sun or Moon).
#Zodiacal Light, Encyclopedia Britannica (retrieved 2023)
https://www.britannica.com/science/zodiacal-light
Quote: “zodiacal light, band of light in the night sky, thought to be sunlight reflected from cometary dust concentrated in the plane of the zodiac, or ecliptic. The light is seen in the west after twilight and in the east before dawn, being easily visible in the tropics where the ecliptic is approximately vertical.”
Laser light can scatter off dust, even microscopic particles, in a similar way. The Dyson Swarm’s laser becomes visible for this reason. Interstellar dust can keep it visible over long distances too.
#Laser Scattering – A brief Introduction, Dr. Günther Crolly, Fritsch GmbH (retrieved 2023)
Quote: “For particle diameters on the order of the wavelength of light and below, Mie theory then comes into play. The Mie theory is the complete solution of Maxwell's equations for the scattering of electromagnetic waves by spherical particles. Now what does this mean? Well, you can imagine that the electromagnetic light wave couples to the atoms and molecules in a particle, so to speak, and causes them to oscillate. These oscillations then in turn generate electromagnetic light waves of the same wavelength (we are talking only about elastic scattering here), which are radiated in all possible directions. Superposition of the individual
waves from the different areas of the particle then leads to the formation of a characteristic intensity distribution, which, unlike in Fraunhofer diffraction, can be observed not only in the forward direction but also at scattering angles greater than ninety degrees.”
Lasers are not all equally visible. Our eyes do not respond well to red light so a red laser seems invisible in clean air. We are much more sensitive to green light. The light scattering off air molecules in a green laser beam will be visible to us when a red beam would not.
#RP-Photonics, Beams Of Laser Pointers: Visible In Air? (2010)
https://www.rp-photonics.com/spotlight_2010_01_11.html
Quote: “The human eye is much more sensitive to the green light (around 530 nm) than for the red light (670 nm). Interestingly, the difference in sensitivity depends strongly on the overall brightness of the scene. Under normal daylight conditions, one has to use the photopic sensitivity curve, which tells us that the sensitivity at 530 nm is roughly 20 times higher than at 670 nm. With the eye adapted to the dark night, however, that difference becomes much stronger. The reason for this is that the eye uses different sensors. Under normal daylight conditions, it uses three types of cones for color vision, whereas in the dark it uses the rods. The latter are more sensitive for green light, but have a very poor response at 670 nm.
In combination, one should expect that the visible brightness of the scattered light from the green laser is much larger than for red light. And this perfectly fits to the experimental experience!”
The Star-Laser will be visible when it fires. It has about 1% of the total power of the HD 40307 star, but its green colour will make it more visible, so our expert Luke Campbell estimates it will seem 10% as bright as midday sunlight on the Smorpian home world. The beam thins down from 1 million km wide to Earth-sized by the time it reaches our Solar System, so it will be even more intensely visible.
– The laser travels at the speed of light – which oddly enough is still pretty slow on a galactic level. It takes a whole day until the laser has left the Smorpian system. Shooting into the emptiness between stars. It will travel for decades, occasionally melting the odd bit of interstellar dust or asteroid.
The speed of light is fast: about 300,000 kilometers per second.
#Speed of Light, Encyclopedia Britannica (retrieved 2023)
https://www.britannica.com/science/speed-of-light
Quote: “speed of light, speed at which light waves propagate through different materials. In particular, the value for the speed of light in a vacuum is now defined as exactly 299,792,458 metres per second.”
But the distances in space are greater. From here to the heliopause, which we can call the edge of the Solar System, is 18 billion km wide. It takes light 16.7 hours to cross that distance. After 1 day, light would only be 0.065% of its way to the nearest star.
#Heliopause, Encyclopedia Britannica (retrieved 2023)
https://www.britannica.com/science/heliopause
Quote: “The heliopause is about 123 astronomical units (AU; 18 billion km [11 billion miles]) from the Sun.”
– 42 years after being fired, it arrives without warning. Humans only notice a weird green glow in the sky and then they are gone. 1% of the energy of a star, concentrated into a beam the diameter of earth, travelling 42 light years – burns the exposed half of the planet with the intensity of 3 million Suns. The seas boil and evaporate, fires scour the land and within minutes earth's crust begins to melt into a sea of lava. As the planet rotates it turns into a red hot hell, with no trace of life. After a day it is all over and the laser dies down.
Since information travels at the speed of light, we’ll notice the arrival of the laser beam at the same time it starts dealing damage.
We assume the beam is sized to cover the entire Earth on arrival. That’s 10^24 Watts spread over an exposed area of 2.55 x 10^14 m^2. The average intensity of the laser light is 3,921,568,627 W/m^2. Normally we only experience the 1361 W/m^2 of light that reaches us from the Sun. So this laser beam has an intensity 2,881,387 greater than sunlight, or about 3 million suns.
#Solar Irradiance, NASA (2018)
https://sunclimate.gsfc.nasa.gov/article/solar-irradiance
Quote: “Since the strength of solar radiation reaching Earth is not evenly distributed across the electromagnetic spectrum, in addition to the total solar irradiance (TSI), measurement of the spectral solar irradiance (SSI) is also essential, especially as it interacts with different materials and processes on the Earth’s surface and atmosphere in different ways.”
Quote: “Satellite TSI measurements have enabled significant convergence in scientific consensus on the TSI value, which observations from the currently operational NASA Solar Radiation and Climate Experiment (SORCE) have determined to be 1,361 watts per square meter (W/m2).”
We can use the blackbody radiation equation (also called the Stefan-Boltzmann Law) to estimate how hot things get. At equilibrium temperature, the energy being received matches the energy being radiated back out.
Radiation Intensity = 5.67 x 10^-8 x Temperature^4
Radiation intensity is in W/m^2. 5.67 x 10^-8 is the Stefan–Boltzmann constant, in W/m^2/T^4. Temperature is in Kelvin.
If we input the radiation intensity of 3,921,568,627 W/m^2 from the laser, we get a temperature of 16,217 Kelvin. That’s about three times hotter than the surface of the Sun!
#Stefan-Boltzmann Law, Warwick University (retrieved 2023)
https://warwick.ac.uk/fac/sci/physics/intranet/pendulum/stefan/
– What if instead of converting the energy of their dyson swarm into a laser, the Smorpians used it to shoot a super bullet? A relativistic missile, going as close to the speed of light as possible.
A relativistic missile is a projectile accelerated to a large fraction of the speed of light, shot over interstellar distances to destroy the surface of entire planets. It is a concept with a scientific basis; it essentially combines the very real kinetic missiles with the technically possible relativistic rocket.
#Daniel C. Sproull, Kinetic Energy Weapons The Beginning of an Interagency Challenge
(2017), InterAgency Journal Vol. 8, Issue 2
https://thesimonscenter.org/wp-content/uploads/2017/05/IAJ-8-2-2017-pg62-68.pdf
Quote: “A KEW [Kinetic Energy Weapon] travels at hypersonic velocities and converts part or all of its mass into energy on impact. The kinetic effect of objects impacting at hypersonic speeds is easy to demonstrate in nature.
Hundreds of craters, the result of impacting asteroids—some small, others extraordinarily large—can be found all over the earth. The U.S. has contemplated artificially creating this phenomenon ever since the RAND Corporation first proposed placing tungsten rods on intercontinental ballistic missiles (ICBMs) in the 1950s. In 2002, the RAND Corporation issued a report detailing what a possible rodbased KEW weapon system would look like.”
#Philip Gibbs, The Relativistic Rocket (2004),The Physics and Relativity FAQ
https://math.ucr.edu/home/baez/physics/Relativity/SR/Rocket/rocket.html
Quote: “The theory of relativity sets a severe limit to our ability to explore the galaxy in space ships. As an object approaches the speed of light, more and more energy is needed to maintain its acceleration, with the result that to reach the speed of light, an infinite amount of energy would be required. It seems that the speed of light is an absolute barrier which cannot be reached or surpassed by massive objects[...] Another way to get around the problem may be to use the relativistic effects of time dilation and length contraction to cover large distances within a reasonable time span for those aboard a space ship. When a rocket accelerates at 1g (9.81 m/s^2), its crew experiences the equivalent of a gravitational field with the same strength as that on Earth. If this acceleration could be maintained for long enough, the crew would eventually reap the benefits of the relativistic effects that increase the effective rate of travel.”
However, it has not been studied much and remains a feature of mostly science fiction.
Read about it here:
#Relativistic Weapons, Atomic Rockets (retrieved 2023)
https://www.projectrho.com/public_html/rocket/spacegunexotic.php#id--Relativistic_Weapons
Quote: “Relativistic weapons are kinetic-kill weapons where the projectile moves faster than 14% the speed of light (42,000 kilometers per second or so) although the real fun doesn't start until about 90% the speed of light. [...] Such weapons do incredible amounts of damage, but by the same token they require absurd amounts of energy (refer to second equation below). They are very likely to remain science-fictional for centuries to come.”
– This sort of weapon is at the limits of what the Smorpians technology can handle, as it requires loads of a highly dangerous material: antimatter, the evil twin of regular matter. Humans have only managed to produce a few nanograms of antimatter. With their unlimited energy, Smorpians can manufacture it at an industrial scale to build antimatter rockets!
Antimatter has an energy potential of 9 x 10^16 Joules per kg, far surpassing chemical, fissile or fusion fuels. However it is very difficult to produce.
#Antimatter Propulsion, Dr. Mike LaPointe, NASA (2020)
https://ntrs.nasa.gov/api/citations/20200001904/downloads/20200001904.pdf
We have only managed to produce a few nanograms of it; the weight of a single cell, at an efficiency of 0.0000001%. It takes 1 Gigajoule of energy input to produce 1 Joule worth of antimatter output.
#Making antimatter, CERN (2011)
https://angelsanddemons.web.cern.ch/antimatter/making-antimatter.html
Quote: “The total amount of antimatter produced in CERN’s history is less than 10 nanograms - containing only enough energy to power a 60 W light bulb for 4 hours.”
Quote: “The efficiency of antimatter production and storage is very low. About 1 billion times more energy is required to make antimatter than is finally contained in its mass. Using E = mc^2, we find that 1 gram of antimatter contains:
0.001 kg x (300,000,000 m/s)^2 = 90,000 GJ = 25 million kWh
Taking into account the low production efficiency, it would need 25 million billion kWh to make one single gram! Even at a discount price for electric power, this would cost more than a million billion Euros!”
There have been some studies on how to improve that efficiency, possibly up to 0.01% or even 0.025% and scale up the production of antimatter to more interesting amounts.
#R. L. Forward, Antiproton Annihilation (1985), Air Force Rocket Propulsion Laboratory
https://apps.dtic.mil/sti/pdfs/ADA160734.pdf
Quote: “Section 3 is a detailed discussion of the limitations of the present antiproton production techniques and methods for improving the antiproton production efficiencies. If the improvements were to be made, the antiproton production efficiency in terms of number of antiprotons captured per incident protons hitting the target could be raised from the
present p/p=4x 10^-7 at CERN and 3x10^-5 at Fermilab to a production ratio of p/p=5x10^-2. Then, if the proton accelerator were optimized for energy efficiency, the overall energy efficiency could be raised to 2.5x10^-4. Although an energy efficiency of 0.025% does not seem very efficient, it is adequate to allow the production of antimatter at a cost of
10M$/mg, at which point antimatter becomes cost effective for space propulsion.”
We assumed Smorpian technology lets them manufacture it at an industrial scale with an efficiency of 0.001%. That means their 10^24 Watt Dyson Swarm can manage to generate 10^19 Watts’ worth of antimatter. That is equivalent to 111.1 kg of antimatter per second, or 3.5 million tons per year.
– When antimatter and matter are mixed, they annihilate, which in more practical terms means: there is a big, big boom releasing gamma rays and plasma. The physics is complicated, but basically, if you have a really strong magnetic field, you can deflect the plasma through a nozzle, just like in the chemical rockets humans use. But it would be much, much faster. The fastest rocket possible basically.
Antimatter used for rocket propulsion is a well-discussed concept. There are many variants, but the one with the most promising performance is the Proton-Antiproton Beam Core Engine. A stream of antimatter in the form of antiprotons meets regular matter (hydrogen) and annihilates, producing multiple forms of radiation: gamma rays, neutrinos, pions and more. Only the pions have an electric charge. That means they can be manipulated by magnetic fields. We could build a magnetic nozzle to funnel those pions out the back of a spaceship to produce thrust. It is all described here:
#Antimatter Propulsion, Dr. Mike LaPointe, NASA (2020)
https://ntrs.nasa.gov/api/citations/20200001904/downloads/20200001904.pdf
Another study finds that the exhaust velocity of such a rocket can be 69% of the speed of light (or 0.69 C):
#Ronan L. Keane and Wei-Ming Zhang, Beamed Core antimatter propulsion: Engine design and optimization (2012), JBIS
https://arxiv.org/ftp/arxiv/papers/1205/1205.2281.pdf
Quote: “The main finding is that effective exhaust speeds Ve ~ 0.69c (where c is the speed of light) are feasible for charged pions in beamed core propulsion, a major improvement over the Ve ~ 0.33c estimate based on prior simulations.”
The combination of power from antimatter annihilation, great thrust and extraordinary exhaust velocity makes this the ultimate rocket.
– Our relativistic missile is much bigger than a skyscraper. At the bottom is the bell-shaped magnetic nozzle 100 meters wide. On top of it are 250 floors filled with antimatter and matter ready to annihilate each other. At the top floor is a 300 kg projectile looking quite small, about the size of a person. To stop them getting damaged on the way, the missiles have dozens of sacrificial layers that form a whipple shield. To make sure they do their job, the Smorpians build 1000 missiles.
All rockets are subject to the Tsiolkovsy rocket equation. If they want to accelerate to a certain velocity (the DeltaV) they need to expend a certain fraction of their mass (the propellant) at a certain rate, which makes their Mass Fraction and Exhaust Velocity the most important qualities.
DeltaV = Exhaust Velocity x ln(Mass Ratio)
DeltaV in m/s is how fast a spaceship can get. Exhaust velocity, also in m/s, is how fast the exhaust exits the nozzle. For a relativistic rocket, it is more practical to use fractions of the speed of light ‘C’ instead of m/s. Mass Ratio is then the ratio between fully loaded mass and mass after all propellant has been exhausted.
#Ideal Rocket Equation, NASA (2021)
What makes things more complicated is that we are calculating the performance of a relativistic rocket. Things become stranger when we start approaching the speed of light. A rocket that accelerates for one week to get to 0.5C won’t get to 1C after accelerating for another week. It’ll only reach 0.76C. If it spends another week accelerating, it only speeds up a little more to 0.9C. A fourth week, and it expects to be travelling at 2C, but only reaches 0.964C.
That relativistic effect means a rocket needs a DeltaV of several times the speed of light to reach those high 0.999C+ velocities. It can be calculated using the tanh(x) function.
#TANH function, MedCalc (2023)
https://www.medcalc.org/manual/tanh-function.php
We find that for tanh(10), we get a result of 0.999999996. In other words, a deltaV of 10 times the speed of light gets you to 0.999999996C.
Now we can use the Tsiolkovsy equation. The engine has an exhaust velocity of 0.69C. We want to find the necessary mass fraction.
10C = 0.69C x ln(Mass Ratio)
Mass Ratio = e^(10/0.69) = 1,968,443
The result says that for every 1 kg of missile, we must load up with 1,968,443 kg of propellant. Half of that is normal matter, the other half is antimatter. So that can be 984,221 kg of frozen hydrogen and 984,221 kg of frozen anti-hydrogen.
We chose for the missile to be 300 kg. That means it is loaded with about 590,500 tons of antimatter-matter mix as propellant. Frozen hydrogen has a density of 86 kg/m^3.
#Properties of Hydrogen, Isoflex (retrieved 2023)
Quote: “Density of solid 0.086 g/cm^3”
The propellant mix will have a total volume of 6.87 million m^3. We can shape it into a cylinder with a base of 99.6 meters width and a height of 882.2 meters. That’s enough for 250 ‘floors’ of 3.5m height each.
1000 missiles of that size would have to be loaded with 984,221,000 kg of antimatter in total. At the Smorpian production rate of 111.1 kg/s, that only takes 102.5 days to manufacture.
– Let’s fire them! Launching all the relativistic missiles is a spectacular event. For a moment, the antimatter engines lighting up outshine their star. Their exhaust is a long trail of brilliant white, and as they accelerate away, they appear redder and redder until they turn invisible.
The missiles experience redshift as they accelerate away. The light the missiles produce is stretched into longer wavelengths. Blue light becomes green, green light becomes red, and red becomes invisible infrared. This process becomes extreme at relativistic velocities, until all the light leaving the missiles has become very long, invisible wavelengths.
#Redshift, Las Cumbres Observatory (retrieved 2023)
https://lco.global/spacebook/light/redshift/
Quote: “Redshift is an example of the Doppler Effect. As an object moves away from us, the sound or light waves emitted by the object are stretched out, which makes them have a lower pitch and moves them towards the red end of the electromagnetic spectrum, where light has a longer wavelength.
In the case of light waves, this is called redshift. As an object moves towards us, sound and light waves are bunched up, so the pitch of the sound is higher, and light waves are moved towards the blue end of the electromagnetic spectrum, where light has a shorter wavelength. In the case of light waves, this is called blueshift.”
– They arrive shortly after you can see them. The light from their launch will take 42 years to reach earth. So human astronomers might see the flash of the missile's launch. And then a few days later they will hit – not enough time to prepare.
The relativistic missiles travel at 0.999999996 C. Light, and the information it carries, travels at 1 C. So the information about a missile attack travels just 0.000000004C ahead of the missiles themselves. 42 years of relativistic travel only gives a ‘heads up’ of 5.3 seconds.
However, the missiles do not instantly go relativistic. There is a period where they are accelerating with their antimatter rockets. Light is produced during that period, travelling away at 1C, while the missiles are still climbing from 0.1C to 0.2C to 0.3C and so on. That first light is the only warning humanity gets. Its length depends on how hard the missiles accelerate, but it can be reduced to only a few days.
– Each relativistic missile packs the kinetic energy of a dinosaur-killer asteroid – so only one needs to hit. They never reach the ground – disintegrating instead at the edge of Earth’s atmosphere. Intense blue flashes light everything on fire. Then continent-sized fireballs slam down on the surface to smash everything into dust. Repeatedly. Until nothing is left but rubble and smoke.
300 kg at 0.999999996C has a relativistic kinetic energy of 3 x 10^23 Joules.
#Relativistic Energy, HyperPhysics (retrieved 2023)
http://hyperphysics.phy-astr.gsu.edu/hbase/Relativ/releng.html
That is in the range of estimates for the impact energy that produced the Chicxulub crater.
#Joanna V. Morgan et al., The Chicxulub impact and its environmental consequences (2022), Nature Reviews Earth & Environment volume 3, pages 338–354
Volume 68, Issues 7–8
https://www.nature.com/articles/s43017-022-00283-y
Quote: “The Chicxulub crater’s asymmetric shape and size suggest an oblique impact and an impact energy of about 10^23 joules, information that is important for quantifying the climatic effects of the impact.”
The relativistic missiles act mostly like cosmic rays. They are absorbed at the top of the Earth’s atmosphere. However, that doesn’t make their energy disappear!
# J.J. Beatty et al., Cosmic Rays (2017), Particle Data Group, Lawrence Berkeley National Laboratory
https://pdg.lbl.gov/2017/reviews/rpp2017-rev-cosmic-rays.pdf
Quote: “Except for protons and electrons near the top of the atmosphere, all particles are
produced in interactions of the primary cosmic rays in the air. Muons and neutrinos are
products of the decay chain of charged mesons, while electrons and photons originate in
decays of neutral mesons”
Extremely large nuclear weapons detonated at high altitude were considered an option during the Cold War. The flash from their detonation would be enough to set entire countries on fire, instantly. In the document below, a gigaton-yield weapon is discussed. That’s an energy of 4.2 x 10^18 Joules. The relativistic missiles release over 71,000 times that energy, each.
#Jack C. Rogers and T. Miller, Survey of the Thermal Threat of Nuclear Weapons (1964), US Department of Defense
https://apps.dtic.mil/sti/tr/pdf/ADA383988.pdf
Quote: “Recent analyses of high altitude and above-the-atmosphere bursts are summarized in Figure 5. Note that the radius at which 10 cal/cm^2 (in one second) is received from a 10,000-mt burst at 45 miles altitude can vary from 80 to 325 miles, depending on weather conditions. Note also that only bursts larger than 10,000 mt would be a threat at orbital altitudes. The relationship of these thermal radii to the radii at which materials will burn is summarized in Rogers (1963).”
– Humans do funny things to their food to rid it of bacteria and make it safe to eat – like shooting electron beams at strawberries. Small particle accelerators send electrons into the food with an energy similar to the radiation from nuclear reactions. Not enough to burn the food but deadly to bacteria. Smorpians had the same idea but bigger.
#How does E-Beam Sterilization work?, EBeamServices (retrieved 2023)
https://ebeamservices.com/e-beam-sterilization/
Quote: “The e-beam inactivates microorganisms either by causing microbial death as a direct effect of the destruction of a vital molecule or by an indirect chemical reaction. Advanced electronics precisely control the use of electrons in the sterilization of medical devices and pharmaceuticals. The process involves accelerating a beam of electrons to near light speed where it passes through a scan chamber and then transitions into a curtain of electrons. Materials moving through the chamber on a conveyor system are showered with”
Electron beam sterilization uses electrons with energies ranging from a few tens of kiloelectronvolts to tens of megaelectronvolts, putting them at the same energy level as radiation from fission reactions of radioactive decay.
#Use of Mathematical Modelling in Electron Beam Processing: A Guidebook, IAEA (2010)
Quote: “Electron accelerators provide electron beams with the desired energy and beam current. Electron beam currents are usually in the order of 1 mA to several 100 mA, depending on the desired application and the acceleration principle. The electron energy used in industrial irradiation may range from 80 keV for curing films to as high as 25 MeV for the radiation treatment of gemstones.”
– The main challenge with an electron beam is range. Electrons are negatively charged particles, so they don’t want to stay near each other. A regular electron beam will quickly spread out, making it harmless. Smorpians need it to cover distances of dozens of light years. So they used the rules of the universe to trick the electrons, by building an Ultra Relativistic Electron Beam, or UREB.
Particle beam weapons have been built and tested. They deal penetrating radiation damage that is difficult to protect against. However, they spread out relatively quickly into harmless beams and it is more difficult to get them to focus than a laser (which can just use a bigger mirror for focusing). Different particles at different energy levels were tested to get around this problem.
Electrons perform the worst. They are lightweight charged particles. Electrostatic repulsion pushes apart an electron beam quickly as a result. Heavier particles, like protons, fare better. Neutral beams, made of ions with the charges removed or balanced in some way, spread the least and have the most range. Neutral particle beams have therefore received the most attention as weapons.
One has even been launched into space.
#P. G. O'Shea at al., A linear accelerator in space - The Beam Experiment Aboard Rocket (BEAR) (1990), Los Alamos National Laboratory.
https://accelconf.web.cern.ch/l90/papers/th454.pdf
Quote: “On July 13, 1989 the BEAM experiment Aboard Rocket (BEAR) linear accelerator was successfully launched and operated in space. The flight demonstrated that a neutral hydrogen beam could be successfully propagated in an exoatmospheric environment. The accelerator, which was the result of an extensive collaboration between Los Alamos National
Laboratory and industrial partners, was designed to produce a 10 mA (equivalent), 1 MeV neutral hydrogen beam in 50 us pulses at 5 Hz.”
However, electrons are the easiest to accelerate to higher energies. At a certain energy level, exceeding the gigaelectronvolts (equivalent to 1.6 x 10^-10 joules per particle), relativistic effects start to take effect and limit their rate of spread. From their internal perspective, electrons feel electrostatic repulsion and spread out as normal. From an external perspective, the electrons spread very slowly because of time dilation effects.
The mechanisms of particle accelerators, the effects of beam spread and the logic behind the Ultra Relativistic Electron Beam are described here:
#Particle Accelerators, Galactic Library (2023)
The time dilation factor can easily be calculated by dividing the electron’s energy by its rest mass energy (511,000 eV). An electron with an energy of 10^20 electronvolts as an example experiences a time dilation factor of 195 trillion. Whatever effects cause the beam to spread, are reduced by a factor 195 trillion, making them negligible.
– What it does is accelerate the electrons to 99.999999999999999999999999998% of the speed of light, faster than even the most powerful cosmic rays.
The fraction of lightspeed achieved by a relativistic particle can be calculated with a rearranged Lorentz factor equation.
B = (1 - 1/(y^2))^2
B is the fraction of lightspeed. y is the relativistic gamma, which we obtained earlier by dividing the particle energy by its rest mass energy.
#E. Daw, Lecture 1 - Introduction, then Beta (β) and Gamma (γ) (2012), University of Sheffield
https://www.hep.shef.ac.uk/edaw/PHY206/Site/2012_course_files/phy206rlec1.pdf
You can use this calculator:
#Lorentz Factor Calculator, Calctool
https://www.calctool.org/relativity/lorentz-factor
However, we are dealing with very large numbers that most calculators struggle to handle. Use this Full Precision Calculator if necessary:
#Full Precision Calculator, MathsisFun
https://www.mathsisfun.com/calculator-precision.html
In this case, the electron has an energy of 10^20 electronvolts, and its relativistic gamma y is 1.95 x 10^14. We get B = 0.99999999999999999999999999998. That’s 28 nines and one 8.
For comparison, the most powerful particle ever detected is the Oh-My-God particle, with an energy of 3.2 x 10^20 electronvolts. Assuming it was a proton, which is 1836 times heavier than an electron (rest mass 938 MeV) and therefore only reaches a speed of 0.999999999999999999999995 C. That’s 22 nines and one 8.
#Jonathan O'Callaghan,The Oh-My-God particle (2023), New Scientist Volume 258, Issue 3441,
https://www.sciencedirect.com/science/article/abs/pii/S0262407923010102
Quote: “On the night of 15 October 1991, Fly's Eye spotted the flash of a cosmic ray with a whopping 320 EeV of energy.”
– The closer something travels to the speed of light, the slower time moves for it, relative to the rest of the universe. And since these electrons are moving so incredibly fast, for every second of spreading they experience, over 5 million years pass in real time. A physics trick that lets the beam cross interstellar distances while remaining tightly focused on its target.
A 10^20 electronvolt electron experiences a time dilation factor of 158 trillion. That means for every second that passes from its internal perspective, 158 trillion seconds pass in the outside world, which corresponds to 5 million years.
– The biggest particle accelerator on Earth is 27 km long, The Smorpians needs one that is over 100,000 km long - a megastructure eight times longer than earth is wide. It’s mostly a tube of magnets holding the beam together until the exit. Like a long trumpet of doom surrounded by an aura of deadly radiation. When it is fired, it produces a ruler-straight lightning bolt pointed at Earth.
We are referring to CERN’s Large Hadron Collider. It is a 27 km circumference ring accelerating particles up to energies of 1.36 x 10^13 electronvolts.
#ATLAS Experiment records “first physics” at new high-energy frontier, CERN (2022)
https://atlas.cern/Updates/Press-Statement/Run3-first-collisions
Quote: “The LHC is colliding proton beams at a world-record-breaking energy of 13.6 tera electron volts (TeV).”
The next generation of particle accelerators use powerful laser pulses to accelerate particles using the Laser Plasma Wakefield Accelerator (LPWA) scheme. We are already breaking records with this new technology. The energy level of the Large Hadron Collider could be achieved by a chain of LPWAs just 136 meters long.
#Stuart Mangles, Introduction to plasma wakefield acceleration (2015), The John Adams Institute for Accelerator Science
#Physicists Just Smashed an Insane Record of Particle Acceleration in a Plasma Channel, ScienceAlert (2019)
Quote: “In a breathtaking achievement, physicists have shattered the world record for particle acceleration. In just 20 centimetres (8 inches), they have increased the acceleration of electron beams from 0 to a whopping 7.8 billion electron volts (GeV).”
We assume the Smorpians develop this technology further, enough to match the performance of the LHC with a tube just 13.6 meters long. Reaching an electron energy level of 10^20 electronvolts would need an accelerator 100,000 km long. Too big to fit on their planet. All the better for it, as it would produce deadly radiation.
– Its effects on arrival are less visible than the other weapons. No flashes of light, no massive firestorms, no explosions. It doesn’t destroy rocks, it destroys DNA. People get dizzy, then fall sick as their cells are pierced by radiation. You might think that a deep bunker could save a few humans, but no. The UREB is so penetrating that its effects accumulate to lethal doses even underground, over days or weeks. In the end, just like our strawberries, earth becomes sterile.
High energy radiation at high intensity can cause death via Acute Radiation Syndrome. DNA is damaged, organs destroyed and no recovery possible above certain doses.
#Radiation Effects on Humans, AtomicArchive (retrieved 2023)
https://www.atomicarchive.com/science/effects/radiation-effects-human.html
Quote: “Certain body parts are specifically affected by exposure to different types of radiation sources. [...] The most important factor is the amount of the dose - the amount of energy actually deposited in your body. The more energy absorbed by cells, the greater the biological damage. Health physicists refer to the amount of energy absorbed by the body as the radiation dose. The absorbed dose, the amount of energy absorbed per gram of body tissue, is usually measured in units called rads. Another unit of radation is the rem, or roentgen equivalent in man.”
#Acute Radiation Syndrome: A Fact Sheet for Clinicians, CDC (2018)
https://www.cdc.gov/nceh/radiation/emergencies/arsphysicianfactsheet.htm
Quote: “Acute Radiation Syndrome (ARS) (sometimes known as radiation toxicity or radiation sickness) is an acute illness caused by irradiation of the entire body (or most of the body) by a high dose of penetrating radiation in a very short period of time (usually a matter of minutes). The major cause of this syndrome is depletion of immature parenchymal stem cells in specific tissues. Examples of people who suffered from ARS are the survivors of the Hiroshima and Nagasaki atomic bombs, the firefighters that first responded after the Chernobyl Nuclear Power Plant event in 1986, and some unintentional exposures to sterilization irradiators.”
The levels of radiation that cause these effects are generally associated with nuclear weapons. A particle beam weapon can deliver those doses without the overt destruction of a bomb.
#Joseph Rotblat, Acute Radiation Mortality in a Nuclear War (1996), National Academy of Sciences
https://www.ncbi.nlm.nih.gov/books/NBK219167/
Quote: “At very high doses death may occur within hours, but with decreasing dose, the time of death is extended to weeks. Down to a dose of the order of 1,000 rads mortality is 100 percent.”
UREB: Ultra Relativistic Electron Beam
An Ultra Relativistic Electron Beam’s radiation is also very penetrating. It can deliver lethal doses despite concrete barriers, steel shields or hundreds of meters of rock in its path. We know this is possible by looking at the behaviour of actual cosmic rays and the radiation showers they produce after hitting the Earth’s atmosphere.
Some particles from cosmic rays were detected underneath 2400m of rock.
#Guo, Zi-yi at al., Muon flux measurement at China Jinping Underground Laboratory (2021), Chinese Physics C, High Energy Physics and Nuclear Physics, Volume: 45; Issue: 2;
https://www.osti.gov/pages/servlets/purl/1768763
Quote: “We assumed Jinping mountain’s average rock density to be 2.8 g/cm3 from Ref. [10], so the water equivalent depth was 6720 m for 2400 m rock.”
If the particles are too powerful, they’ll generate radiation that passes through the ground without stopping anywhere. It’ll make its way through any humans hiding underground without dealing much damage. If the radiation is too weak, it’ll be blocked by the top layers of rock and not reach the lower layers at all. It is a problem encountered in radiation therapy. If the radiation is too strong, it’ll pass right through the patient’s body. If it is too weak, it’ll burn the skin without affecting the tumor underneath. The Bragg peak effect is used to get around this problem.
A particle beam’s energy can be adjusted to penetrate the skin and upper layers of tissues without harming them and still deposit a tumor-destroying dose at a specific depth, if the right energy level is used.
A particle beam weapon can exploit the same effect to penetrate multiple layers of rock without losing too much energy, before unleashing its deadly dose at a specific depth.
#Bragg Curves and Peaks, Brookhaven National Laboratory
https://www.bnl.gov/nsrl/userguide/bragg-curves-and-peaks.php
Quote: “Charged particles, such as protons and heavy ions, lose energy when passing through material primarily through ionization. The Bethe-Bloch equation describes that energy loss. The Bragg Curve is a graph of the energy loss rate, or Linear Energy Transfer (LET) as a function of the distance through a stopping medium. The energy loss is characterized primarily by the square of the nuclear charge, Z, and the inverse square of the projectile velocity, β. This gives the Bragg Curve its familiar shape, peaking at very low energies, just before the projectile stops. It is this Bragg Peak that makes ion therapy advantageous over X-ray treatment for cancer. The Bragg Curve falls with increasing energy until a minimum is reached near a velocity of β = 0.9, about 2.2 GeV for protons. LET increases slowly, rising logarithmically for energies above the minimum.”
Of course, the Smorpians don’t know what the correct energy levels are, nor can they adjust the beam with 42 years of light delay, so they’ll just try all energy levels on a slider and hope they catch everyone that way.