https://www.kalangfeld.com/blog daily 0.75 2026-01-04 https://www.kalangfeld.com/blog/kindred-of-old-an-origins-story monthly 0.5 2026-01-04 https://www.kalangfeld.com/blog/dimensions monthly 0.5 2022-02-20 https://images.squarespace-cdn.com/content/v1/612cc6fa771f533aa3836837/211781fb-fb9c-4eaf-b2e4-d4f196a587ab/cub_3d.png Blog - dimensions - I am not insisting. Giving our brains the peace and quiet to interpret the projection as a 3-dimensional object, we would use 3 coordinate axes (x,y,z) to handle what a cube is. https://images.squarespace-cdn.com/content/v1/612cc6fa771f533aa3836837/57afdd0f-5aa4-4f5f-b18b-988170e22406/4d_cube.jpeg Blog - dimensions - Tesseract …is not a mountain region on an alien planet, although it sounds like it; it is a 4-dimensional cube. It’s depicted in the adjacent picture (or a projection of the Tesseract into a 2-dimensional flat screen, to be precise). Note that each vertex has indeed 4 wire pieces attached. It is not entirely intuitive. It looks like a small cube inside a large cube with wires attached. https://images.squarespace-cdn.com/content/v1/612cc6fa771f533aa3836837/8280363d-8c56-4642-aa39-3d1e4d537dc3/dimensions.jpeg Blog - dimensions - How do we understand a high dimensional space? Our brain is particularly adapted to navigate 2 and 3-dimensional spaces: we might need a map to walk from the Institute of Contemporary Arts to the National Gallery in London, but the 3rd dimension - the height of the buildings - does not play a role in this: we navigate a 2-dimensional space: the surface of the Earth. https://images.squarespace-cdn.com/content/v1/612cc6fa771f533aa3836837/9f0a4e8b-30d6-4757-8424-28dee83a8de1/cub_2d.png Blog - dimensions - Let’s check that the rules work for a 2-dimensional space. We pick the x-axis and the direction “left-to-right” for the first stage. We thus move from (A) to (B). At (B), we need to pick another direction. There is only the y-direction. We have two choices to move: up or down (both work). In the adjacent picture, I have chosen “up” and proceeded to (C). https://images.squarespace-cdn.com/content/v1/612cc6fa771f533aa3836837/db6860e3-6770-4184-a26f-b7c558890ba5/2d_cube.png Blog - dimensions - What’s a cube? Let’s get started and look at a cube. Since from now on it is all Mathematics, it is helpful to be precise: If you look at the adjacent figure, you don’t see a cube. You see a cube projection on the 2-dimensional screen of your mobile, tablet or PC. https://images.squarespace-cdn.com/content/v1/612cc6fa771f533aa3836837/f37b3cde-99bc-4f69-b4bb-103f072a1e3a/cub_construct.png Blog - dimensions - Make it stand out Constructing a 3-dimensional cube. https://www.kalangfeld.com/blog/spacetime monthly 0.5 2022-01-22 https://images.squarespace-cdn.com/content/v1/612cc6fa771f533aa3836837/f15bb235-ffe2-4bc9-8c9c-010f016625a9/spacetime.jpeg Blog - spacetime - It all starts with coordinates. Time is different from space: we cannot see time but measure its passing with a clock. Still, time serves the same purpose as space - namely, to locate objects. If we want to communicate the location of things in a room, we first agree on an origin from which we will measure distances. We then choose three “axis” attached to it alongside as reference for the distances. https://images.squarespace-cdn.com/content/v1/612cc6fa771f533aa3836837/2d38111c-5431-4bd8-882f-9e975c9c061f/metric2.png Blog - spacetime - Make it stand out Finding my mobile. https://images.squarespace-cdn.com/content/v1/612cc6fa771f533aa3836837/bf22b82e-bfcc-4818-ab81-dab08b73d65e/minkowski_metric.png Blog - spacetime - What metric should we choose for spacetime? This is when physicists talk to mathematicians. Mathematicians say “everything is possible”, but physicists want to pick the option which describes the universe. The answer for the “distance” is shown in the figure. The distance squared is not guaranteed to be positive anymore. Such a space is called Minkowski space. https://images.squarespace-cdn.com/content/v1/612cc6fa771f533aa3836837/c1606328-7527-4379-9ee4-6854d82ac1be/pythagoras.png Blog - spacetime - There is something special about our space! The distance between two points in space is always positive, and if the distance is zero, it is the same point. Mathematically, everything is possible, meaning this is a feature of the space we are living in. In maths, we call this a “metric space”. https://www.kalangfeld.com/blog/bead-of-time monthly 0.5 2021-12-09 https://images.squarespace-cdn.com/content/v1/612cc6fa771f533aa3836837/d721d1e3-1e17-4d99-a057-17e1d8735e42/galaxy_sun.png Blog - Bead of time - Make it stand out Whatever it is, the way you tell your story online can make all the difference. https://images.squarespace-cdn.com/content/v1/612cc6fa771f533aa3836837/f75f90ef-993f-4f14-84fd-bc31240e2551/kindsstars.jpeg Blog - Bead of time - Make it stand out Whatever it is, the way you tell your story online can make all the difference. https://images.squarespace-cdn.com/content/v1/612cc6fa771f533aa3836837/763ff5fd-8c1c-4468-b2d8-6eef1fafbe7f/radiostelescope.jpeg Blog - Bead of time - Make it stand out The Big Silence https://www.kalangfeld.com/blog/break-of-dawn monthly 0.5 2023-04-09 https://images.squarespace-cdn.com/content/v1/612cc6fa771f533aa3836837/3a14c967-fa63-4dd2-8d75-55f7fc2e1687/desert2.jpeg Blog - Break of Dawn - Make it stand out Whatever it is, the way you tell your story online can make all the difference. https://www.kalangfeld.com/blog/interstellar-travel monthly 0.5 2021-10-31 https://images.squarespace-cdn.com/content/v1/612cc6fa771f533aa3836837/c4e378ba-d4e3-4e60-ab3d-34f3efaa582d/m35.jpeg Blog - interstellar travel - Journey to M35 - Cradle of Light Distance: 3,870 lightyears Max. speed: 99.9999874% speed of light Earth time: 3,872 years time onboard: 16 years https://images.squarespace-cdn.com/content/v1/612cc6fa771f533aa3836837/1635707379747-8B8T8ZHGI0LHM9VK9XY3/In_Andromeda.jpeg Blog - interstellar travel - On a planet in Andromeda And yet, it is entirely possible to set foot on a planet in the Andromeda galaxy within a human lifespan! How? https://images.squarespace-cdn.com/content/v1/612cc6fa771f533aa3836837/1635708744838-KRISA7UACZW7S42TI2VS/Jupiter.jpg Blog - interstellar travel - Journey to Jupiter Distance: 588 million kilometres (closest approach) Max. speed: 0.8% speed of light Earth time: 5.6 days time onboard: 5.6 days https://images.squarespace-cdn.com/content/v1/612cc6fa771f533aa3836837/1635711096534-L84STFO6LID17YK8SCNR/unsplash-image-Oze6U2m1oYU.jpg Blog - interstellar travel - Journey to Andromeda: Distance: 2.5 million lightyears Max. speed: 99.999999999972% speed of light Earth time: 2.6 million years time onboard: 28.7 years https://images.squarespace-cdn.com/content/v1/612cc6fa771f533aa3836837/1635094820474-2ZCF0NW50D73MZ1JRXJ4/alpha_centauri.jpeg Blog - interstellar travel - Journey to Alpha Centauri Distance: 4.3 lightyears Max. speed: 95% speed of light Earth time: 5.6 years time onboard: 3.6 years https://images.squarespace-cdn.com/content/v1/612cc6fa771f533aa3836837/1635711941218-263G77H21MJHQFA90028/giphy.gif Blog - interstellar travel - Flying through Andromeda We would reach Andromeda with a velocity of 99.99999999999305% speed of light. The flow of our time is much slower than that of the stars around us: 1 year around us would only last 11.8 seconds in the spacecraft. If stars are spaced on average by about ten lightyears (near the centre), we will pass a star every two minutes. Our instruments would show a picture similar to the adjacent BBC animation (by Giphy). https://www.kalangfeld.com/blog/faster-than-light monthly 0.5 2021-10-24 https://images.squarespace-cdn.com/content/v1/612cc6fa771f533aa3836837/50755bce-f6ab-47f8-9c15-2fef523e1791/vega_sm.jpg Blog - Faster than Light - Vega - 25 lightyears Vega is the brightest star in the northern hemisphere. It has about twice the sun's mass, has about a tenth of the sun's age, and has almost twice the surface temperature of our sun. Vega predominantly emits light in the blue spectrum. Vega is surrounded by a disk of debris (as is our sun - the Kuiper belt). It might have a hot Neptune orbiting Vega in close proximity. It is doubtful that conditions around Vega are suitable to sustain life as we know it. (Artist impression BelleDeesse) https://images.squarespace-cdn.com/content/v1/612cc6fa771f533aa3836837/c4e378ba-d4e3-4e60-ab3d-34f3efaa582d/m35.jpeg Blog - Faster than Light - M35 cluster - 3870 lightyears M35 is a cluster of about 300 - 400 stars relatively close to our sun compared to the diameter of our galaxy of 100,000 lightyears. Its core has a diameter of about 11.4 lightyears with 1600-3200 solar masses. An alien life-form inhabiting a stellar system inside the cluster must have a spectacular night sky. If those aliens looked to Earth now (with a hypothetical super telescope), they would see humankind at about 1900 BC. They would see the end of the early Helladic culture in Greece and the rule of the 12th dynasty in Egypt. Still, 1849 years to go to watch the birth of Christianity. https://images.squarespace-cdn.com/content/v1/612cc6fa771f533aa3836837/b932aad8-61f9-44c7-9b01-11cf55195b04/spacetime.png Blog - Faster than Light - Make it stand out Whatever it is, the way you tell your story online can make all the difference. https://images.squarespace-cdn.com/content/v1/612cc6fa771f533aa3836837/004fc0e7-f39c-44db-b6b5-96f456713b45/alpha_centauri.jpeg Blog - Faster than Light - Alpha Centauri - 4.4 lightyears Our immediate cosmic neighbourhood hosts a double star system - Alpha Centauri AB. The brighter one of the two stars is more extensive than our sun but emits light in the same spectrum. The other star is a cooler K-type star producing an orange type light, which might be even more suited to host a habitable planet and life than our sun (see here). https://www.kalangfeld.com/blog/light-barrier monthly 0.5 2021-10-17 https://images.squarespace-cdn.com/content/v1/612cc6fa771f533aa3836837/1634501896329-CHY3I4DFMA5GZ409U8P9/newton_speeds.png Blog - Light barrier - Approaching the barrier of light Things pan out differently when we move with a speed comparable to the speed of light. We keep quadrupling the spacecraft's energy; the speed increases, but with smaller and smaller amounts. We would need an infinite amount of energy to approach the light barrier, let alone surpass it. https://images.squarespace-cdn.com/content/v1/612cc6fa771f533aa3836837/1634493456270-UQ5BXPI2UXLB0CHSVI3J/water_barrier.jpeg Blog - Light barrier - barriers The answer is: no! We are very much used to barrier-free velocities: we could cycle with 10 mph or 20 mph. And yet, the vacuum speed of light is a hard limit: no object can travel speedier, and not even information can spread faster. The universe is like a bubble, and we are like fish in the sea that cannot break through the ocean's surface. https://images.squarespace-cdn.com/content/v1/612cc6fa771f533aa3836837/1634494047846-XEA8JIKR0VDXFF12BYSC/unsplash-image-AReKs141iaI.jpg Blog - Light barrier - Sir Issac Newton (1643-1727) Newton is the founder of Classical Mechanics, which excellently describes all our physics affairs in everyday life. There is, of course, a connection between (kinetic) energy and the speed of a car, and true: the higher the energy of the vehicle, the higher its speed. In fact, according to Newtonian mechanics, if we quadruple the (kinetic) energy of a car, we double its speed. Assume a space rocket flies through space with 1% of the speed of light, that is with 3,000 km per second. If we quadruple its energy seven times, we will travel faster than the speed of light according to Newton - in fact, the rocket's speed would be 1.28 times that of light. If you have followed my previous blogs, you might suspect that this is not what happens - the flow of time changes, and the story is different from what we are used to in everyday life. https://www.kalangfeld.com/blog/time-and-gravity monthly 0.5 2021-10-13 https://images.squarespace-cdn.com/content/v1/612cc6fa771f533aa3836837/1633895751543-YQPT07NBBVRLLJAOH1UF/unsplash-image-CPxL6Thi5XE.jpg Blog - time and gravity - Twin Paradox From my previous blogs, you can convince yourself that the constancy of the vacuum speed of light implies that the flow of time is personal: time itself slows down if you move with speed compared with the time of an observer at rest. Let us think this through a bit more, and we will discover that things might not add up. We seem to encounter an inconsistency that puzzled the greatest minds of our time for decades - the twin paradox. https://images.squarespace-cdn.com/content/v1/612cc6fa771f533aa3836837/1633901343904-Z7X1K5SH0Z7YYEAZP3PU/unsplash-image-R8Hco_-WcxQ.jpg Blog - time and gravity - Sat Nav Is this all relevant for our lives on Earth? Yes - you might use these effects every day. A hand-held Sat Nav (e.g., GPS) receives time signals from as many as 24 satellites. It then calculates your position with an accuracy of 5-10 metres. Note, however, that time flows slower for you on Earth. This effect is partially compensated by the high speed of the satellites, which makes their clock going slower. The net result is that the time flows faster for the satellites by about 0.000,000,038 seconds per day. This is slow enough not to mess with our everyday life experience, namely, a universal flow of time. But to achieve position accuracy, the time measurements must be very precise. The details are (see the Ohio State website) that your Sat Nav would be wrong by about 10 kilometres at the end of a day if it would not correct for the differences in the flow of time. https://images.squarespace-cdn.com/content/v1/612cc6fa771f533aa3836837/1633897098093-7QK6U6P2DO1KEJOLZEUZ/unsplash-image-8_9Rix4OvrM.jpg Blog - time and gravity - Acceleration Before we resolve this conundrum, a quick word about force and acceleration. Acceleration quantifies how much the velocity changes per second. If it does not change, the acceleration is zero. Mechanics tells us that acceleration is related to force: if a car accelerates, we feel a force pushing us into the seat. The gravitational acceleration on Earth is about 9.81 m/s/s, and the force coming with it keeps our feet on the surface of the Earth. https://www.kalangfeld.com/blog/speed-of-light monthly 0.5 2021-10-10 https://images.squarespace-cdn.com/content/v1/612cc6fa771f533aa3836837/1633185248654-D15KU07I4CF7DVZT7SIZ/Advanced_Test_Reactor.jpg Blog - Speed of Light - Cherenkov Radiation: The speed of light propagating through a medium such as water is smaller than the vacuum speed of light. I just wanted to mention it to avoid confusion when you find different claims. This decrease of speed has some beautiful consequences: in a reactor, the electrons can move with velocities lower than the vacuum speed of light but faster than its speed in the medium. This mechanism creates a bluish light (Cherenkov radiation), the analogue of a sonic boom with light rather than sound waves. https://images.squarespace-cdn.com/content/v1/612cc6fa771f533aa3836837/1633213147365-84N9QYUMQNADT8LXFUIO/sunset.jpg Blog - Speed of Light - Sun - bringer of life Light is weird. Every other wave has a medium to propagate: water waves use water - like ripples on a pond. Sound is slight pressure variations in the air. Light does not need a medium to propagate. If this weren't true, the universe would look so different. The space between the sun and Earth is largely empty if we disregard the odd particles flying around now and then. How would the sun send its warmth to Earth if light needs a medium? Planets would be deeply frozen, lightless worlds, and life as we know it would not exist. If we look at a sunset, we see the light that has left the sun's surface about nine minutes ago. It has traversed the emptiness between the sun and Earth just to be seen by our eyes. https://images.squarespace-cdn.com/content/v1/612cc6fa771f533aa3836837/1633196058032-YNU3GPG1WVYVT31NXC7I/einstein_maxwell+_sm2.png Blog - Speed of Light - Make it stand out From Maxwell’s equation to the theory of special relativity. https://www.kalangfeld.com/blog/flow-of-time monthly 0.5 2021-10-10 https://images.squarespace-cdn.com/content/v1/612cc6fa771f533aa3836837/1632595860249-Z3J18MO59A3XAYHGZVD4/clocks.png Blog - Flow of Time - A rather strange clock consists of two parallel mirrors with some distance d, say 1 metre, apart. We emit a light pulse from the top mirror. It gets reflected by the bottom mirror, and when it is back at the mirror on the top, we say 1 time unit has passed. It would be a rather precise clock since 1 time unit is about 7 nanoseconds. Time dilation explained https://images.squarespace-cdn.com/content/v1/612cc6fa771f533aa3836837/1632577177491-37KG0A47W3F9OOKQ9HZZ/speeds2.png Blog - Flow of Time - The first thing to notice is, the vacuum speed of light is enormous for everyday living standards. A cyclist can cycle about 8 metres in a second, and we write for their speed 8 m/s. The figure above shows that light is about 300,000 times faster than we can possibly move on Earth. 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https://www.kalangfeld.com/home daily 1.0 2026-01-09 https://images.squarespace-cdn.com/content/v1/612cc6fa771f533aa3836837/1630702056523-SW8H61ALY1P41WNK8QXX/guillermo-ferla-lLExhYl-cXQ-unsplash.jpg Home - Frozen in time. Millenia pass and the star constellations still look the same. —— Thumee in First Light Rising “Even the closest stars created their light decades ago. It travelled through all space for the vanity moment of being seen by my eyes. I am staring back at the oldest of the stars near the centre of the galaxy, and I know that I am peering 30,000 years into the past.” https://images.squarespace-cdn.com/content/v1/612cc6fa771f533aa3836837/1630446869266-44T25CEHJPDAOQAJIMHM/ahmet_sm.jpg Home - Quo vadis, homines? —— Tom Wright in First Light Leading Dinosaurs reigned Earth for 120 million years. Humans started settling 10,000 years ago, began scratching symbols into clay 5,000 years ago, invented the steam engine 309 years ago, discovered radio communication 125 years ago, travelled into outer space and set foot on the moon 52 years ago. https://www.kalangfeld.com/about daily 0.75 2026-01-09 https://images.squarespace-cdn.com/content/v1/612cc6fa771f533aa3836837/1633273406998-TN28D0IUW4ALO8V2J6TN/Kurti_600.jpg About - Make it stand out K A Langfeld (drawing by Carolin Marek) Revised 9 January 2026 https://www.kalangfeld.com/books daily 0.75 2026-01-09 https://images.squarespace-cdn.com/content/v1/612cc6fa771f533aa3836837/1630792737905-FE8Z9WLFSPJT27KXG9DJ/6776252.png Books - Make it stand out Whatever it is, the way you tell your story online can make all the difference. https://images.squarespace-cdn.com/content/v1/612cc6fa771f533aa3836837/1767524550315-GS8L9TOL9KY60RON8Y3E/92f6257b-ff30-4a37-8388-eb51ef803b6b.png https://images.squarespace-cdn.com/content/v1/612cc6fa771f533aa3836837/1636754726401-CKNM33WJ3U2NP8Y2J1NU/desert2.jpeg https://images.squarespace-cdn.com/content/v1/612cc6fa771f533aa3836837/f37b3cbc-da0d-46a3-acbd-30551b09b50f/Kurt_Ever_After_Twitter_Thumbnail_1600_x_900px_RGB_SM_V5.png https://images.squarespace-cdn.com/content/v1/612cc6fa771f533aa3836837/da1e4f57-eedc-4318-99eb-64ff51e67751/tablet_langfeld.png Books https://www.kalangfeld.com/contact-us daily 0.75 2025-10-28