Double Slit

The Origins: Maupertuis and the "Least Action" Principle. In the 1740s, Pierre-Louis Moreau de Maupertuis, a French polymath and president of the Berlin Academy of Sciences, proposed a bold philosophical idea: “Nature is economical. It does nothing in vain. It chooses the path that requires the least effort.” He formulated this as the Principle of Least Action, suggesting that physical systems evolve in such a way that a certain quantity—action—is minimized. But Maupertuis was vague. He claimed this principle explained everything from optics to planetary motion but provided no real mathematics. Some even accused him of cloaking philosophy in scientific language to gain prestige. --- -------------------------------------------------------------------- Enter Euler: Turning Philosophy into Mathematics Maupertuis’s vague principle reached Leonhard Euler, already one of the greatest mathematicians of his time and also working at the Berlin Academy. Unlike Maupertuis, Euler wanted ...

  For over a thousand years, mathematicians struggled to calculate the digits of π (pi) , the mysterious number that relates a circle's circumference to its diameter. The ancient Greek genius Archimedes had started it all around 250 BC by drawing polygons inside and outside a circle, calculating their perimeters to trap π between two values. This method was ingenious but painfully slow. For centuries, this "polygon method" was the best humanity had — with later minds like Ludolph van Ceulen calculating π to 35 digits using thousands of polygon sides. He dedicated his entire life to this — so much that his digits were engraved on his tombstone . Then along came a man named Isaac Newton .   The Calculus Revolution Newton didn’t need thousands of polygon sides. He had something far more powerful: calculus — and a brilliant idea. He thought: Why not express the geometry of the circle in a completely different language? Not with shapes, but with algebra and infinit...

Prelude: The Mathematical Abyss In the early 1500s, Europe was climbing out of the mathematical shadows of the Middle Ages. Algebra had been reborn through translations of Arabic and Greek works. Yet, one ancient problem still haunted every serious mathematician: S olve the general cubic equation. Specifically, the form of the equation we now call the "depressed cubic":        x³ + ax = b This was not just a technical curiosity — it was a badge of honor. Solving it meant ascending into the pantheon of mathematical greats. Act I: Scipione del Ferro — The Keeper of the Secret In the city of Bologna, a quiet, brilliant man named Scipione del Ferro held the position of mathematics professor at the University of Bologna. Around 1515, del Ferro made a breakthrough — he discovered how to solve the depressed cubic. Del Ferro, cautious and soft-spoken, chose not to publish his discovery. He feared scrutiny, misappropriation, and possibly religious controversy. Instead, he passed the m...

... and that's how Rømer calculated Speed of Light  Rømer found differences in Jupiter's Eclipses of Io. The confusion here is, the total time of a eclipse will always be same regardless the earth's position around the sun so how did he get the time difference. Jupiter is so large that eclipses occur at regular intervals. Every time Io completes a revolution around Jupiter, the appearing time and disappearing (behind Jupiter) time can be observed by a telescope. Rømer predicted all of Jupiter's eclipses for the next year. But as the Earth was moving away from Jupiter, there was the time difference between predicted starting time of eclipse and actual starting time of Eclipse. The maximum difference was 22 minutes. Rømer concluded that Io 's Orbital Period cannot be changed. The only possibility is Speed of Light is not infinite. He noticed that when Earth moved away from Jupiter, the observed eclipses of Io were delayed by up to 22 minutes compared to when Earth w...

  1. The future visibility limit is 62 billion light-years. This does NOT mean that objects at this distance emit photons toward us now, and that those photons will reach us sometime in the future. 2. Any object farther than 16.5 billion light-years emits photons toward us now, but those photons will never reach us, even if we wait for an infinite amount of time. 3. So what is 62 billion light-years? Well, it is the radius of a sphere from HERE NOW. Those objects within this sphere, whose photons we have not yet received, emitted light in the past when they were within 16.5 billion light-years of us. These photons are still on their way, and when they reach us in the future, we will be able to see those objects. 4. We will only be able to see objects in the future that are currently within the 62 billion light-years radius, and whose photons have already entered the 16.5 billion light-years radius. 5. We will never receive photons from these objects that haven't yet...

Wheeler's delayed choice experiment is a thought experiment in quantum physics that was proposed by physicist John Archibald Wheeler in 1978. The experiment is designed to explore the nature of wave-particle duality and the role of observation in quantum measurements. Case : A The experiment involves a setup where a beam of photons is directed towards a beam splitter at lower left corner. There is 50-50 probability that the photons will be transmitted (pass through straight direction to the bottom right mirror) or reflected (sent to the top left mirror).  At beam splitter, if photon is transmitted, it is sent to the mirror which is placed at the lower right corner. It will reflect the photon to the top of the apparatus where screen - A is placed At beam splitter, if photon is reflected to the top left mirror, it will reflect the photon to the top right where screen - B is placed.  In both cases we will find the path of the photon. Either it follows clockwise route or anti cl...

 In Young's Double Slit experiment, Interference pattern depends on the position of the detector. Here are the experiment data results, A single photon is sent at a time and next is sent when previous photon hits the screen. 1. If a detector is placed just after the source then observer will not be able to find the slit in which electron is going to pass so the interference pattern will appear on the screen. Interference pattern (Fringes) appears because electron acts as a wave and passes through both the slits. 2. If a detector is placed just before the slits then observer will be able to find the 'which way' path of the electron and interference pattern will not appear on the screen. We will see the two fringe pattern on the screen.   3. If a detector is placed just after the slits then observer will be able to find the 'which way' path of the electron and interference pattern will not appear on the screen. You must think, if interference pattern will not a...