Kurzgesagt – In a Nutshell
Sources – Middle of Scale
DISCLAIMER: We go with approximate numbers in this video and aim for the same order of magnitude in the relations between sizes, therefore the comparisons are not necessarily accurate to the last digit.
– A three story building is about 10 meters tall, six times bigger than you. In the opposite direction, six times smaller than you, you get things like a cute squirrel about 27 centimetres small. So the building is just as big relative to you as you are to a squirrel. It’s easy to understand. Let’s continue scaling up and down in small steps.
Throughout the video, we compare objects or structures of equal or nearly equal ‘scale difference’ to you. In this case, the ‘scale difference’ is six-fold, so we compare you to something six times larger and something six times smaller.
‘You’ in the script is an average human being. Average global height for men is 170 cm, for women it is 160 cm. So we split the difference used a value of 165 cm.
#Max Roser, Cameron Appel and Hannah Ritchie. Human Height. 2019
https://ourworldindata.org/human-height
Quote: “If we compare adult men born in 1996 versus those born a century earlier – men who had reached the age of 18 in 2014 versus 1914 – we see that the global mean height for men increased from 162 to 171 centimeters (cm). We see this in the chart. For women, this increased from 151 cm to 159 cm.”
A three story building is approximately 10 meters.
#Saad Iqbal. How tall are 1, 2, 3, 4, or 5 story buildings? Standard height. 2022
https://definecivil.com/standard-height-of-1-2-3-4-5-and-multi-storey-
A grey squirrel can reach 27 cm in length.
– An A320 is 37 meters long. The Rufous Hummingbird is around 7 centimetres. Both of these fliers are 23 times bigger or smaller than you, and both fly intercontinental distances - the tiny bird migrates between Alaska and Mexico! If the hummingbird were the same size as the jet, it would circle the Earth 85 times every year!
The A320neo variant has a range of 6400 km and a length of 37.57 m. (37 m/1.65 m is around 23.)
The Rufous Hummingbird ranges between 7 and 9 cm in length. 165 cm/7cm is around 23.
#Animal Spot. Retrieved Oct 2023.
The Rufous hummingbird can migrate as much as 4000 miles, which is about 6440 km.
#All About Birds. Retrieved Oct 2023.
https://www.allaboutbirds.org/guide/Rufous_Hummingbird/maps-range
Quote: “Long-distance migrant. Rufous Hummingbirds travel nearly 4,000 miles from breeding grounds in Alaska and northwest Canada to wintering sites in Mexico. They travel north up the Pacific Coast in spring and return by the Rocky Mountains in late summer and fall (see Cool Facts).”
To compare the flight distances for the plane and the bird, we use body-lengths travelled.
The hummingbird travels 6440 km/7cm = 92,000,000 body-lengths during its migration. If the A320neo travelled the same distance, it would cover 37 m x 92,000,000 = 3,404,000 km. That is 3,404,000 km/40,016 km = 85 times the Earth’s circumference.
The Earth's circumference is 24,855 miles or 40,016 km.
https://oceanservice.noaa.gov/education/tutorial_geodesy/geo02_hist.html
Quote: “If we plug these numbers into the above equation, we get: (360°÷ 7.12°) which equals 50; and 50 x 4,400 equals 220,000 stades, or about 25,000 miles. The accepted measurement of the Earth's circumference today is about 24,855 miles. Given the simple tools and technology that Eratosthenes had at his disposal over 2,000 years ago, his calculations were quite remarkable.”
– Dinoponera, the largest ant in the world, is about 55 times smaller than you. Their small colonies have around 100 individuals but no queens – instead they ruthlessly compete for status within the nest, which can reach 1.2 meters deep. If humans lived like Dinoponera, we’d be building towers of over 25 stories filled with offices and ruthlessly competing for status and... Wait…
Dinoponera can exceed 3 cm in length (which is 165 cm /3 cm =55 times smaller). They live in small colonies of a few individuals that can reach up to 1.2 m in depth, which is 120 cm / 3 cm = 40 times their size. A similar size ratio for us 1.65 m x 40 = 66 m, which roughly corresponds to a 25 storey building.
#Lenhart P, Dash S, Mackay W (2013) A revision of the giant Amazonian ants of the genus Dinoponera (Hymenoptera, Formicidae).
https://jhr.pensoft.net/article/1626/
Quote: “Dinoponera Roger 1861 is a strictly South American genus in the subfamily Ponerinae, tribe Ponerini, commonly called tocandiras or giant Amazonian ants (Zahl 1959, Fourcassié and Oliviera 2002, Haddad et al. 2005). These ants are generally less well known than Paraponera clavata (Fabricius 1775), the bullet ant or hormiga bala (Haddad et al. 2005), yet Dinoponera workers may surpass 3 cm in total body length, making them the largest in the world.
[...]
Colonies vary in size depending upon species. Dinoponera australis colonies have an average of 14 workers (range 3–37) (Paiva and Brandão 1995, Monnin et al. 2003), Dinoponera gigantea average 41 workers (range~30–96) (Overal 1980, Fourcassié and Oliviera 2002, Monnin et al. 2003) and Dinoponera quadriceps has the largest colonies with an average of 80 workers (range 26–238) (Monnin and Peeters 1999, Monnin and Ratnieks 2001). Morgan (1993) excavated two Dinoponera longipes nests, a possible incipient colony with 7 workers and another mature colony of 120 workers.
The nest consists of large chambers and tunnels in the soil possibly with an earthen mound and can be 0.10–1.2m deep”
They are queenless ants.
#Thibaud Monnin, Francis L. W. Ratnieks & Carlos R. F. Brandão. Reproductive conflict in animal societies: hierarchy length increases with colony size in queenless ponerine ants. 2003.
https://link.springer.com/article/10.1007/s00265-003-0600-9
Quote: “In Dinoponera queenless ants, workers are totipotent females and can potentially reproduce, yet only the top-ranking worker actually reproduces. Individual workers ranked immediately below the dominant breeder worker (gamergate) are hopeful reproductives. Whether or not a worker benefits from joining the hierarchy of high-ranking workers depends on the trade-off between the probability of becoming dominant and reproducing directly, and the colony-level cost of an additional lazy high ranker.”
– The deadliest and most annoying insect in the world is the mosquito, 235 smaller than you, while on the other end the Empire state building is about that much larger than you. Kind of unimaginable how something this small creates so much devastation for something that big.
There are many species of mosquito but the one of the nastiest is the Asian Tiger mosquito that carries diseases like dengue, Zika and yellow fever. They can grow to 7 mm in length. (1650 mm / 7mm = 235.7)
#Sonja Swiger. Asian Tiger Mosquito. 2020.
https://extensionentomology.tamu.edu/insects/asian-tiger-mosquito/
Quote: “This aggressive, nuisance mosquito ranges from small to medium in size (4 to 7 millimeters).
[...]
They are vectors of dengue, Zika, chikungunya, and yellow fever in the tropics but less likely than Aedes aegypti.”
Mosquitoes are considered the deadliest animal by the CDC.
#CDC. Fighting the World’s Deadliest Animal. Retrieved October 2023.
https://www.cdc.gov/globalhealth/stories/2019/world-deadliest-animal.html
Quote: “The small, long-legged insect that annoys, bites, and leaves you with an itchy welt is not just a nuisance―the mosquito is the world’s deadliest animal. Spreading diseases like malaria, dengue, West Nile, yellow fever, Zika, chikungunya, and lymphatic filariasis, the mosquito kills more people than any other creature in the world. CDC is committed to providing scientific leadership in fighting these diseases, at home and around the world.”
The Empire State Building is 380m tall. (380 m / 1.65 m = 230)
#ESBNYC, Retrieved October 2023.
https://www.esbnyc.com/about/facts-figures
Quote: “At its top floor, the Empire State Building stands 1,250 feet (380 meters) tall. Counting the spire and antenna, the building clocks in at a mighty 1,454 feet (443 meters). It’s currently the 4th tallest building in New York City, the 6th tallest in the United States, and the 43rd tallest tower in the world.”
– Like coarse grains of sand about 3 millimeters, 550 times smaller than you. You can feel their shape and roughness between your fingers and if you focus, see them individually. We mix them into concrete that can hold up the tallest towers ever built, like the 828 meter tall Burj Khalifa that is 500 times larger than you. If you were that tall, people would be as small to you as grains of sand in your hand. Hey! Be gentle.
#NYSDEC Environmental Education. Soil Studies: Soil Particle Sizes. Retrieved October 2023.
https://www.dec.ny.gov/docs/administration_pdf/lpsoilstudies.pdf
Quote: “Soil particles vary greatly in size, and soil scientists classify soil particles into sand, silt, and clay. Starting with the finest, clay particles are smaller than 0.002 mm in diameter. Some clay particles are so small that ordinary microscopes do not show them. Silt particles are from 0.002 to 0.05 mm in diameter. Sand ranges from 0.05 to 2.0 mm. Particles larger than 2.0 mm are called gravel or stones. Most soils contain a mixture of sand, silt and clay in different Proportions.”
#Emily Lakdawalla. "Sand" means something different to me than it does to you, probably.
2013
https://www.planetary.org/articles/01241000-sand-means-something
The Burj Khalifa is 828 m tall, which is 828 m / 1.65 m = 501, ~500 times taller than you.
#Burj Khalifa Fact and Figures. Retrieved October 2023.
https://www.burjkhalifa.ae/en/the-tower/facts-figures/
Quote: “At over 828 metres (2,716.5 feet) and more than 160 stories, Burj Khalifa holds the following records:
Tallest building in the world
Tallest free-standing structure in the world
Highest number of stories in the world
Highest occupied floor in the world
Highest outdoor observation deck in the world
Elevator with the longest travel distance in the world
Tallest service elevator in the world”
– A medium sized city like Lisbon is about 6000 times larger than yourself and permeated by a network of highways, roads and alleys. On the other end, about 6000 times smaller than you, are your small arteries permeating your whole body. Actually you are in the middle between your network of blood vessels and the network of a city like Lisbon. If you think of a city as a living being, you find more and more parallels. A small alley is as small to the city as an arteriole 0.1 millimeters wide is to you. Your tiniest capillaries are to you, what the pipes bringing water to homes are to Lisbon.
We use the North-South extent of Lisbon from the coast to the edge of the city limits as its size. We found a rough figure of 10 km. (10km/1.65m =6060)
Pipes supplying buildings with water come in several standard sizes. We take the DN 50 (50 mm) pipe as an example.
#The Engineering Toolbox. NPS - 'Nominal Pipe Size' and DN - 'Diametre Nominal'. Retrieved October 2023.
https://www.engineeringtoolbox.com/nps-nominal-pipe-sizes-d_45.html
Quote: “ISO 6708 defines the nominal size - DN - as an alphanumeric designation of size for reference purposes. It comprises the letters DN followed by a dimensionless whole number which is indirectly related to the physical size in millimetres of the bore (ID) or outside diameter (OD) of the end connections.”
A 50 mm water pipe has the same diameter relative to Lisbon as an 8 micrometer capillary to your body. A small alley of about 0.66 m wide would be as small to the city as an arteriole 0.1 millimeters wide to you.
#Tse-Yi Tu and Paul C.-P. Chao. Continuous blood pressure measurement based on a neural network scheme applied with a cuffless sensor. 2018.
– Going further, 100,000 times smaller than you, we reach a typical skin cell about 30 micrometers in diameter, a neutrophil is half as big and one of your red blood cells is merely 7 micrometers. They are as small to you, as you are to the entire Tokyo Metropolitan Area, the largest urban area in the world spanning over 160 km.
Skin cell is about 30 microns in diameter.
#Jennifer McAlpine. How Big is a Micron? 2020.
https://www.bench.com/setting-the-benchmark/how-big-is-a-micron
Quote: “Moving to more familiar territory, our own bodies, our cells are on a similar scale to the placement precision required in microelectronics. A human skin cell is 20-40 microns across, and a white blood cell is approximately 30 microns. Red blood cells get closer to microelectronics tolerances with an average width of 6-8 microns.”
Neutrophils are 12-15 micrometers in diameter. We use 15 micrometers for our comparison.
#Tigner A, Ibrahim SA, Murray IV. Histology, White Blood Cell. [Updated 2022 Nov 14].
https://www.ncbi.nlm.nih.gov/books/NBK563148/
Quote: “Neutrophils are 12 to 15 µm in diameter, have multi-lobed nuclei typically consisting of 3 to 5 segments joined by thin strands, or isthmuses.”
To compare with the human scale, we use a cell size of 15 micrometers. So we get a scale difference of 1.65 m /0.000015 = 110,000.
If we scaled up a human 110,000 times we get a length of 181.5 km.
This is similar to the width of the area represented with the line crossing the Tokyo metropolitan area on this map:
#Tokyo-Yokohama Metropolitan Area. 2023.
https://www.britannica.com/place/Tokyo-Yokohama-Metropolitan-Area
– Germany is around 875 km from North to South and the 4th biggest agricultural exporter in the world. Rhizobia is a nitrogen-fixing bacteria up to 3 micrometers long and without it, that sort of agricultural production is impossible. So we have a country and a bacterium depending on each other, and you are in the middle, both being 550,000 times larger or smaller than you.
Germany is the world’s fourth largest agricultural exporter.
#Nils-Gerrit Wunsch. Statista. Leading global exporters of agricultural products in 2020, by country. Retrieved October 2023.
Its North-South length can be measured to be around 825 km.
#Facts about Germany. Retrieved October 2023.
https://www.tatsachen-ueber-deutschland.de/en/germany-glance/land-diversity
Quote: “From its northernmost to its southernmost point, Germany measures 876 km, and 640km from the most easterly to the most westerly point.”
Rhizobial bacteria take nitrogen from the air and turn it into nutrients in the soil for plants to grow on. Their size ranges between 1 and 3 micrometers. We use 3 micrometers for our comparison.
#Artis Micropia. Retrieved October 2023.
https://www.micropia.nl/en/discover/microbiology/rhizobium/
Quote: “Rhizobium is a genus of bacteria associated with the formation of root nodules on plants. These bacteria live in symbiosis with legumes. They take in nitrogen from the atmosphere and pass it on to the plant, allowing it to grow in soil low in nitrogen.”
– What about the whole Earth? It’s about 12,700 km in diameter; about 7.7 million times larger than you. On the other side of the scale is Corynebacterium, as little as 0.3 micrometers across, living on your skin and eyes along with 100 billion other bacteria. More than ten times more than there are humans on earth.
Earth has a diameter of 12,756 km (radius 6378 km).
#NASA. Earth Fact Sheet. Retrieved October 2023.
https://nssdc.gsfc.nasa.gov/planetary/factsheet/earthfact.html
#G. Betts. Chapter 23 - Other spoilage bacteria. Food Spoilage Microorganisms. 2006
https://www.sciencedirect.com/topics/agricultural-and-biological-sciences/corynebacterium
Quote: “Corynebacterium are Gram-positive, slender, non-spore-forming rods. Some species may be slightly curved or have club ends. Cell dimension can be from 0.3 to 0.8 μm in diameter and 1.5 to 8.0 μm in length. Corynebacterium are facultatively anaerobic and catalase positive (Table 23.3).”
There are 100 billion bacteria on the skin.
#Sender R, Fuchs S, Milo R. Revised Estimates for the Number of Human and Bacteria Cells in the Body. PLoS Biol. 2016.
– 4 times wider than Earth is Neptune, a cold blue gas giant 49,500 km wide. The largest planet though is Jupiter, 140,000 km in diameter. A titanic abyss shrouded in terrible winds. You could drop Earth whole into its depths and it would simply vanish.
#Neptune Fact Sheet. Retrieved October 2023.
https://nssdc.gsfc.nasa.gov/planetary/factsheet/neptunefact.html
Jupiter has a diameter of 142,984 km (radius 71,492 km), which is 11.2 times wider than the Earth.
#Jupiter Fact Sheet. Retrieved October 2023.
https://nssdc.gsfc.nasa.gov/planetary/factsheet/jupiterfact.html
– On the opposite scale we find the deadly West Nile virus, 50 nanometers in diameter. Or one step down, the spike proteins on a coronavirus, that open up cells for its RNA payload – they are as small to you as you are to the planet Jupiter. You are in the middle between gigantic planets and the world of viruses. These tiny things. So deadly.
#Martín-Acebes MA, Saiz JC. West Nile virus: A re-emerging pathogen revisited. 2012
https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3782267/
Quote: “West Nile virus (WNV) is a small enveloped virus about 50 nm in diameter. The genomic RNA is enclosed within a nucleocapsid formed by the capsid (C) protein that constitutes the core of the virion and is enveloped by a lipid bilayer derived from the host cell.”
#Taha BA, Al-Jubouri Q, Al Mashhadany Y, Hafiz Mokhtar MH, Bin Zan MSD, Bakar AAA, Arsad N. Density estimation of SARS-CoV2 spike proteins using super pixels segmentation technique. 2023
https://www.ncbi.nlm.nih.gov/pmc/articles/PMC10019041
Quote: “In terms of diameter, the mean and standard deviation for each of the three preparations is 911, 949, and 928 nm, respectively [17]. Many studies described the length of the viral spike protein, which was around (9–12) nm in length and gave virions the appearance of a solar corona.“
– Let that sink in – a tiny virus is taking over and killing lung cells up to 500 times larger than itself, with the help of a tiny protein weapon. That is like you trying to kill a giant the size of the Burj Khalifa with a screwdriver.
Epithelial cells in lung tissue are 50-100 micrometers in diameter. 500 times smaller makes 0.1 to 0.2 microns. Coronavirus diameter falls in the same range.
#Katsumiti, A., Ruenraroengsak, P., Cajaraville, M.P. et al. Immortalisation of primary human alveolar epithelial lung cells using a non-viral vector to study respiratory bioreactivity in vitro. 2020.
https://doi.org/10.1038/s41598-020-77191-y
Quote: “The respiratory alveolar epithelium is composed of alveolar type 1 (AT1) and type 2 (AT2) cells. AT1 are flattened cells (~ 0.2 µm deep, 40–80 µm across) which cover 95% of the alveolar surface, providing a large surface area for gas exchange1. They are involved in protein transport and translocation via transcytosis2 and regulate fluid fluxes and ion transport1, and emerging evidence suggests they are involved in alveolar maturation and modulation of immune functions.”
https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7224694/
– But the real boss of the Solar System is the Sun. Ten times bigger than Jupiter, a billion times larger than you, controlling all the planets and source of all energy that drives life. A billion times smaller than you, clearly the boss of our body is a DNA strand, containing all the information making your life possible. You’re right in the middle between the most important factors keeping everything alive.
Our Sun is 1.4 million kilometers in diameter.
#NASA. The Sun: Facts. Retrieved October 2023.
https://science.nasa.gov/sun/facts/
Quote: “The Sun is about 100 times wider than Earth and about 10 times wider than Jupiter, the biggest planet.
[...]
Our Sun is a medium-sized star with a radius of about 435,000 miles (700,000 kilometers).”
A DNA strand is around 2 nanometers in diameter.
#Simpson B, Tupper C, Al Aboud NM. Genetics, DNA Packaging. [Updated 2023 May 29].
https://www.ncbi.nlm.nih.gov/books/NBK534207/
Quote: “Although the DNA helical diameter is only 2 nm, the entire DNA strand in a single cell will stretch roughly 2 meters when completely unwound”
– The supermassive black hole at the center of our galaxy, Sagittarius A*, is 14.5 billion times bigger than you. A hydrogen atom is 15.5 billion times smaller than you.
If we use the event horizon as the size of the Sagittarius A* black hole, then it has a diameter of roughly 24 million km.
#Britannica. Sagittarius A*. Retrieved October 2023.
https://www.britannica.com/place/Sagittarius-A-astronomy
Quote: “Sagittarius A* is a strong source of radio waves and is embedded in the larger Sagittarius A complex. Most of the radio radiation is from a synchrotron mechanism, indicating the presence of free electrons and magnetic fields. Sagittarius A* (pronounced “Sagittarius a star”) is a compact, extremely bright point source. X-ray, infrared, spectroscopic, and radio interferometric investigations have indicated the very small dimensions of this region; the event horizon of the black hole has a radius of 12 million km (7 million miles). “
A hydrogen atom has a diameter of 106 picometers.
#Atomic Radius of the elements. Retrieved October 2023.
https://periodictable.com/Properties/A/AtomicRadius.v.html
Quote: “Hydrogen 53 pm”
– The solar system is 22 trillion times larger than you – On the other end of the scale is the wavelength of low energy neutrinos released from fusion reactions in our Sun – about a hundred trillion of them are passing through you every single second, like ghosts a trillion times smaller than you, basically never hitting any of the particles inside you. If you moved through the solar system in a straight line you probably would also not hit anything.
If we count the radius of the solar system as the distance between the Sun and the heliopause, then it is 123 AU or 18 billion km. That makes the whole solar system 36 billion km in diameter.
#Britannica. Heliopause. Retrieved October 2023.
https://www.britannica.com/science/heliopause
Quote: “Heliopause, boundary of the heliosphere, the spherical region around the Sun that is filled with solar magnetic fields and the outward-moving solar wind consisting of protons and electrons. Nearer the Sun than the heliopause lies the heliosheath, a region of transition where the solar wind slows to subsonic speeds—that is, slower than the speed with which disturbances travel through the interstellar medium. The heliopause is about 123 astronomical units (AU; 18 billion km [11 billion miles]) from the Sun.”
Neutrinos are ‘point-like’ particles like electrons - they have no physical size if you manage to make them sit still.
#Physics Questions People Ask Fermilab. 2014
https://www.fnal.gov/pub/science/inquiring/questions/jim.html
Quote: “First, about the "spin" of particles. This is not really like the spin of large objects like the Earth or a top, because a particle like an electron or neutrino has no known finite size, it seems to be like a point to all scales we can probe. However, like the Earth, electrons behave like magnets with a North and South pole. If you have them in a magnetic field they can align themselves with their magnetic axis either parallel or antiparallel to the field.”
But, neutrinos are usually moving. That gives them momentum. Using that momentum in the de Broglie equation tells us a wavelength, which neutrino particles can have due to the particle-wave duality concept in quantum mechanics.
#R.S. Panvini. Matter waves
https://labman.phys.utk.edu/phys222core/modules/m10/matter_waves.html
Quote: “The relationship between momentum and wavelength for matter waves is given by p = h/λ, and the relationship energy and frequency is E = hf. The wavelength λ = h/p is called the de Broglie wavelength, and the relations λ = h/p and f = E/h are called the de Broglie relations. These are the same relations we have for the photon, but for non-relativistic particles E = ½mv2 = p2/(2m), so E = ћ2k2/(2m), λ = h/√(2mE).”
Particles do not have sizes. But theorists use a conversion trick, which we also utilized here, and use modified Planck constant (hbar) and speed of light (c) to change between energies and lengths. Modified Planck constant is Planck constant divided by 2pi and a convention to convert the angular momentum.
A solar neutrino is produced by fusion reactions in the star’s core. They have an energy of around 0.1 megaelectronvolts (100,000 eV). Using the de Broglie equation tells us they have a wavelength of 2 picometers.
Therefore, the wavelength of a neutrino, i.e. ‘its size’, can be calculated from its energy value:
Wavelength = (Planck’s constant x Speed of light) / Neutrino Energy.
If we plug a typical energy value of about 100,000 eV,
Wavelength = hbarc / 100,000 eV = 2.00E-12 m
where hbarc ~ 2E-7 eV m
#Ann Finkbeiner. Looking for Neutrinos, Nature’s Ghost Particles. 2010
Quote: “We’re awash in neutrinos. They’re among the lightest of the two dozen or so known subatomic particles and they come from all directions: from the Big Bang that began the universe, from exploding stars and, most of all, from the sun. They come straight through the earth at nearly the speed of light, all the time, day and night, in enormous numbers. About 100 trillion neutrinos pass through our bodies every second.
The problem for physicists is that neutrinos are impossible to see and difficult to detect. Any instrument designed to do so may feel solid to the touch, but to neutrinos, even stainless steel is mostly empty space, as wide open as a solar system is to a comet. What’s more, neutrinos, unlike most subatomic particles, have no electric charge—they’re neutral, hence the name—so scientists can’t use electric or magnetic forces to capture them. Physicists call them “ghost particles.””
– A single proton at the heart of the hydrogen atom is almost exactly 1 quadrillion times smaller than you. If you were the size of this proton, you’d find the surrounding hydrogen atoms taller than twelve Mt. Everests. On the other end, we meet something that just breaks human brains: the incredible vastness of space, we just have no reference to these distances at all. The distance to the closest star to earth, Alpha Centauri, is not 1 quadrillion times in the other direction from the tiny proton – but 24 quadrillion.
Proton radius is 0.833 femtometers so its diameter is 1.67 femtometers.
#Bezginov et al., A measurement of the atomic hydrogen Lamb shift and the proton charge radius. 2019.
https://www.science.org/doi/10.1126/science.aau7807
Quote: “Our measurement determines the proton radius to be rp = 0.833 femtometers, with an uncertainty of ±0.010 femtometers.”
A hydrogen atom of 106 picometers or 106,000 femtometers. That makes it 63,473 times wider than a proton. If the proton was the size of a human, the hydrogen atom would appear to be 63,473 x 1.65 = 104,730 meters wide. That’s about 104,730 / 8848 = 11.8 ~12 times
#Britannica. Mount Everest. October 2023
https://www.britannica.com/place/Mount-Everest
Quote: “There is disagreement over the exact elevation of Mount Everest because of variations in snow level, gravity deviation, and light refraction, among other factors. However, in 2020 China and Nepal jointly declared Mount Everest's elevation to be 29,031.69 feet (8,848.86 metres), which was subsequently widely accepted.”
Alpha Centauri is 4.2 lightyears from Earth. That’s equal to 3.974 x 10^16 meters, or 24.08 quadrillion times the average human’s height.
#Britannica. Alpha Centauri. Retrieved October 2023
https://www.britannica.com/place/Alpha-Centauri
Quote: “Alpha Centauri, also called Rigil Kentaurus, triple star system, the faintest component of which, Proxima Centauri, is the closest star to the Sun, about 4.2 light-years distant.”
– A quintillion times smaller than you is the strange world of the quarks. The proton is not actually like a tiny ball but kind of just a ripple on the surface of the ocean of quarks. Every moment, countless quarks pop into existence, along with their anti-particle enemies, before doing furious battle and annihilating each other in an instant. How many? Impossible to say, because the harder you look for them the more quarks seem to appear. We’re simplifying so much it’s like a lie anyway. However we choose to illustrate this, it is wrong. What actually is a quark, what does it look like to human minds? Nobody knows.
There are multiple types of quark with different sizes. Their size is defined by their energy, like the neutrinos. It is around 1 attometer.
Despite their incredibly tiny size, quarks live a very active life.
#Decades-Long Quest Reveals Details of the Proton’s Inner Antimatter. 2021.
Quote: “In reality, the proton’s interior swirls with a fluctuating number of six kinds of quarks, their oppositely charged antimatter counterparts (antiquarks), and “gluon” particles that bind the others together, morph into them and readily multiply. Somehow, the roiling maelstrom winds up perfectly stable and superficially simple — mimicking, in certain respects, a trio of quarks. “How it all works out, that’s quite frankly something of a miracle,” said Donald Geesaman, a nuclear physicist at Argonne National Laboratory in Illinois.”
– As you sit here, confused, let’s look up again. The ocean of quarks in a proton, inside a single atom of a single cell of your body is as small to you, as you are compared to a sphere around 174 light years across, containing about 16 thousand stars.
A scale 10^18 times greater than a human is 174.4 lightyears. An 87.2 lightyear radius sphere has a volume of roughly 87.2^3 x 4/3 x 3.142 = 2,777,757 cubic lightyears.
Average stellar density near the Sun is just under 0.2 stars per cubic parsec, which is roughly 0.006 stars per cubic lightyear.
#Barbara Ryden. The Center Of Our Galaxy. 2003.
https://www.astronomy.ohio-state.edu/ryden.1/ast162_7/notes31.html
Quote: “Infrared light is useful for studying stars near the galactic center. Infrared light of about 2000 nanometers is emitted copiously by cool stars (K and M stars), but is not strongly scattered or absorbed by dust. Within a parsec of the galactic center, the estimated number density of stars is about 10 million stars per cubic parsec. By contrast, the number density of stars in the Sun's neighborhood is a puny 0.2 star per cubic parsec.”
We can therefore expect 2,777,757 x 0.006 = 16,000 stars in a sphere 174.4 lightyears wide centered on the Sun.
– And this is just a tiny speck of dust to our galaxy. The Milky Way is close to one sextillion times larger than you. At the opposite end, we have particles a sextillion times smaller than yourself; like the wavelength of high energy neutrinos released when cosmic rays hit our atmosphere.
The Milky Way’s disk diameter is 200,000 lightyears as best we know.
#Elizabeth Howell. How Long Would It Take to Cross the Milky Way at Light Speed? 2018
https://www.livescience.com/62977-how-big-is-milky-way.html
Quote: “The new study estimates the size of the Milky Way's disk at 200,000 light-years across. Past studies have suggested the Milky Way is between 100,000 light-years and 160,000 light-years across. (One light-year is the distance light travels in a year, about 6 trillion miles or 10 trillion kilometers.)”
Cosmic ray neutrinos have an energy a hundred million times greater than the solar neutrino we described previously. This makes their wavelength a hundred million times smaller.
#The Detection of Neutrinos in IceCube
https://masterclass.icecube.wisc.edu/en/learn/detecting-neutrinos
“Picking an energy value of around 1E13 eV, towards the upper limit for an atmospheric neutrino from the chart in the source, we calculated a wavelength of : hbarc / 1E13 eV = 2.00E-20 m, where hbarc = 1.97E-7 eV m.”
– The Observable Universe is 93 billion lightyears in diameter. Close to a billion billion billion human lengths. But it’s still finite. It’s ‘only’ 465,000 Milky Way side by side. If you were the size of our galaxy, the observable Universe would only be a day’s drive across.
The Observable Universe diameter is 93 billion lightyears. That is 465,000 times the diameter of the Milky Way, which we take as 200,000 lightyears.
#Britannica. Observable Universe. Retrieved October 2023.
https://www.britannica.com/topic/observable-universe
Quote: “The observable universe is approximately 93 billion light-years in diameter. ”
If the Milky Way was the size of a 1.65m human, it would exist in an Observable Universe that appears to be 465,000 x 1.65 = 767,250 meters wide.
That’s 767.25 km, a distance a car could drive in 7.6 hours at highway speeds.
– On the other end of that scale, we have the tiniest particle ever detected, a proton travelling so close to the speed of light it got squished into a pancake. As small compared to you as the whole Observable Universe is big to you.
We are referring to the Oh My God particle with an energy of 3.2 x 10^20 electronvolts.
#Bird et al, Detection of a Cosmic Ray with Measured Energy Well Beyond the Expected Spectral Cutoff due to Cosmic Microwave Radiation. 1994.
#Steve Nerlich, Universe Today. Oh-My-God Particles. 2011.
https://phys.org/news/2011-06-oh-my-god-particles.html
Quote: “The Oh-My-God particle detected over Utah in 1991 was probably a proton traveling at 0.999 (and add another 20 x 9s after that) of the speed of light and it allegedly carried the same kinetic energy as a baseball traveling at 90 kilometers an hour.”
It is likely to have been a proton. Using the Lorentz factor, one can calculate the change in the properties like length, mass, time in a moving object.
The energy of the OMG particle is reported to be about 3.2E20 eV, and the rest-mass energy of a proton is about 938 MeV, giving a 3.2E20 eV / 938 E6 eV ~3.4E11 Lorentz factor. In the direction of motion, it is contracted by
Diameter of proton/ Lorentz factor = 1.6E-15 m /3.4E11 = 4.7E-27 m
Do note the ~30% uncertainty in the energy, which corresponds to a ~30% uncertainty in the final answer.
– We are at the border of things that we have evidence for – are you truly in the middle of everything? The theoretical smallest physical distance is the Planck length, a hundred million times smaller than even the pancake proton.
The Planck length of 1.6 x 10^-35 meters is considered to be the smallest real distance in quantum mechanics.
#FermiLab Today. Planck length, minimal length? Retrieved October 2023.
https://www.fnal.gov/pub/today/archive/archive_2013/today13-11-01_NutshellReadMore.html
Quote: “A modern treatment of Planck's work begins with the speed of light c, gravitational constant G, reduced Planck constant ħ, Coulomb constant k and Boltzmann constant kB.* By taking different combinations of these variables, one can find Planck units, which are truly universal. For instance, by taking √ ħG/c3 , one gets a length. This length is the Planck length, and it is 1.6 x 10-35 meters.”