What Is a Tensor, Really? A Physicist's Honest Answer The Transformation Trap If you ask a mathematician what ...
What Is a Tensor, Really? A Physicist's Honest Answer The Transformation Trap If you ask a mathematician what is a tensor in physics, they will tell you it is a multilinear map from a product of vector spaces and their duals to the real numbers. If you ask a physicist, they will likely tell you that a tensor is an object that transforms like a tensor. This physicist definition is notoriously infuriating. It is entirely circular, offering absolutely no conceptual foothold for an undergraduate trying to survive a ge…
You have probably been told that Earth has five billion years before the Sun dies and swallows our planet. That comforting cosmic timeline is a flat-out lie. Our planet has less than one billion years of habitability left before a lethal solar eviction notice cancels life as we know it. Long before the Sun expands into a red giant, an insidious stellar transformation will boil our oceans and bake the surface to a crisp. The culprit is not carbon emissions or asteroid impacts, but the fundamental physics powering our nearest star. Right now…
Why General Relativity Exists In 1859, the French astronomer Urbain Le Verrier announced a disturbing glitch in the solar system. For decades, celestial mechanics had stood as the ultimate triumph of Newtonian physics, tracking the motions of planets with pinpoint precision. Yet, when Le Verrier applied Isaac Newton's universal law of gravitation to the orbit of Mercury, the numbers refused to clean up. After accounting for the gravitational pulls of every other known planet, there remained a stubborn, unexplained drift in the planet…
Right now, a sphere of electromagnetic radiation is expanding outward from Earth at the speed of light. It has been growing since the first powerful radio transmissions of the early 1900s. Today that bubble is roughly 240 light-years across and it contains every piece of music, every TV broadcast, every radar ping, and every deliberate message we have ever sent into the cosmos. To any civilisation with a sufficiently sensitive receiver sitting within that bubble, we have already announced ourselves. The numbers are simultane…
Voyager 1 is currently so far away that a radio signal traveling at the universal speed limit the speed of light takes over 23.6 hours to reach it. If you sent a "ping" to the spacecraft right now, you would not get a reply until the day after tomorrow. Despite being launched nearly half a century ago, these twin explorers are still screaming through the dark, and we have the fresh data to prove exactly where they are two tiny machines adrift beyond the edge of our solar system entirely. What are the Voyager probes and…
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A Physicist's Guide to GR
10 posts from tensors to black holes. Start at Post 01.
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