Einstein Accidentally Discovered the Most Dangerous Equation in History

Today's lecture is the untold story behind Einstein's E= MC² discovery. You have block of solid iron. It sits perfectly still on very precise scale. You read the number. You take blowtorrch and heat that iron until it glows blindingly white. You put it back on the scale. It weighs more. Not because it expanded, not because it picked up dust. The actual amount of stuff, the inertia, the sheer resistance to being pushed increased simply because it got hot. The heat itself has mass up. Albert Einstein figured this out in the fall of 1905. He did not do it by measuring hot iron. He did it by sitting in patent office in Burn, Switzerland, staring at the ceiling and imagining box emitting two bursts of light. want to walk you through exactly what he did. We are going to trace the logic step by step. We have to strip away the myth of the lone genius pulling formulas out of thin air. Real physics is gritty. It is confusing. People stumble around in the dark for years. Einstein was obsessed with very specific mundane problem involving magnets and coils of wire. That frustration led him to light which led him to space and time which eventually forced him to conclude that mass and energy are the exact same physical property. We need to understand what mass actually is before we can talk about changing it into energy. Isaac Newton gave us the rules back in 1687. You walk up to shopping cart. It is empty. You push it. It accelerates easily. You fill that same cart with 60 lb of bricks, but you push it again with the exact same force. It barely moves. It resists your push. That resistance is inertia. Newton said inertia is fundamental property of matter. brick has certain amount of inertia. bowling ball has more. It never changes. You can move the brick. You can paint the brick. You can drop the brick from roof. Its mass remains constant. The universe according to classical mechanics is giant ledger book. In one column you have mass, in the other column you have energy. You never mix the columns. Energy was just description of what mass was doing, right? moving brick has kinetic energy. brick sitting on high shelf has potential energy. Heat is just that the microscopic jiggling of the atoms inside the bricky. The energy changes forms, but the brick is always just brick. That's so this made perfect sense. we are. It matched every experiment anyone ever did for 200 years. No. Then James Clerk Maxwell ruined everything. In the 1860s, Maxwell wrote down set of equations describing electricity and magnetism. look at those equations almost every day. They are beautiful. They show that changing electric field creates magnetic field and changing magnetic field creates an electric field. They feed off each other. They leapfrog through empty space. Maxwell calculated the speed of this leaprogging wave. The number came out to 186,000 m/s. That happened to be the exact speed of light. Maxwell realized light is an electromagnetic wave. This created massive logical headache. The speed has to be measured relative to something. If you drive car at 60 mph, you're moving 60 mph relative to the asphalt. If another car drives next to you at 60 mph, you look out the window and the other driver seems to be sitting perfectly still. Maxwell's equations did not specify what light was moving relative to. The speed was baked into the laws of electricity and magnetism. It sat there naked number indifferent to the observer. Think about what that implies. You stand on the ground. shine flashlight at you. The light hits you at 186,000 per second. Now you jump in rocket ship and fly toward me at half the speed of light. shine the flashlight again. Common sense tells us the light should hit you faster. The speeds should add up. Nature completely ignores common sense. The light hits you at 186,000 m/s. Exactly. If you fly away from me at half the speed of light, the beam still hits you at 186,000 m/s. Einstein was 26 years old. He realized that if the speed of light is always identical for everyone, the rest of the universe has to bend to accommodate it. Distance and time cannot be rigid. want you to picture train. You stand on the platform. The train rushes past you at near the speed of light. am inside the train. stand in the exact middle of the dining car. flip switch. light bulb above my head flashes. Inside the train, see the light hit the front door and the back door at the exact same instant. Well, the distances are equal. The speed of light is constant or simultaneous. You watch this from the platform. The train is moving. While the light travels from the bulb outward, the back door of the train is rushing forward to meet the light. The front door is running away from the light. Because the speed of light is the same for you as it is for me. You see the light, hit the back door first. say the events are simultaneous. You say the back door was hit before the front door. Who is right? Both of us. Time itself passes differently depending on your state of motion. Your second is not my second. Your inch is not my inch. Einstein published this in June 1905. He called it on the electronamics of moving bodies. We call it special relativity. It dismantled the Newtonian clockwork universe. Space and time became rubbery flexible stage. Einstein went back to his desk at the patent office and he kept thinking about the consequences of his new rules. He realized he missed something. In September, he published tiny addendum, three pages. The title translated to, "Does the inertia of body depend upon its energy content?" He set up thought experiment. It is brutally simple. Imagine block of material floating in empty space. It is completely stationary. It has specific mass. Let's call it The block suddenly emits two pulses of light. One shoots straight to the left. The other shoots straight to the right. Light carries energy. Each pulse carries exactly half of the total energy emitted. Because the pulses shoot in opposite directions with equal energy, the block does not move. It feels recoil from the left pulse and an identical recoil from the right pulse. They cancel out. The block just sits there slightly less energetic than before. Now we look at the exact same event from moving perspective. You fly past the block in spaceship at steady velocity You look out your window. From your perspective, you are sitting still and the block is drifting backward away from you at velocity The block fires its two light pulses. Here is where the physics trap snap shut. We have to apply the rules of relativity. This you see the block moving. That means the light pulse shooting forward in the same direction the block is drifting looks slightly different to you than the light pulse shooting backward. The energy of light depends on its frequency. Its color. This is the Doppler effect. When police siren drives toward you, the pitch shifts up. When it drives away, the pitch drops. The light pulse shooting in the direction of the block's motion gets blueshifted. It carries little more energy from your perspective. The pulse shooting in the opposite direction gets redshifted. It carries little less energy. Einstein calculated the total energy of the two light pulses from your moving perspective. He compared it to the energy of the pulses from the stationary perspective. The total energy you measure is slightly higher. Where did that extra energy come from? It has to come from the block's motion. The kinetic energy of the block. Kinetic energy is determined by two things. velocity and mass. Did the velocity of the block change when it emitted the light? No. The pulses were symmetrical. They canceled each other's push. The block kept drifting past your window at the exact same velocity. V5. If the kinetic energy changed, but the velocity stayed exactly the same. There's only one mathematical possibility left. The mass changed or the block itself has less inertia than it did before it flashed. Einstein wrote out the algebra. will describe the shape of the math. The kinetic energy difference involved term that looked like the total emitted energy divided by the speed of light 2 c^ 2 multiplied by the velocity squared over 2. Classical kinetic energy is mass time velocity squar / 2. Einstein matched the terms. The chunk of mass that vanished was exactly equal to / C². Move the variables around. E= MC². He did not use those exact letters in the 1905 paper. He used for energy and for the speed of light. The equation read minus sub0= over V^2. The symbols shifted over the years, but the physical reality remained rigidly fixed. Energy possesses inertia. If body gives off energy, its mass diminishes. If body absorbs energy, its mass increases. Let me pause here. The implications of this are so severe that people often misunderstand what Einstein actually proved. He did not prove that you can convert matter into energy. He proved that mass and energy are two different ways of measuring the exact same underlying stuff. Mass is bounded energy. Energy is liberated mass in itself. Think back to the hot iron block on the scale. When you heat the block, you agitate the iron atom. They vibrate violently. You are pumping thermal energy into the system. That thermal energy has inertia. The total mass of the block increases. The change is incredibly small because you have to divide the added energy by the speed of light squared. The speed of light is an enormous number. When you square it, you get phenomenally massive number. Dividing normal amount of heat energy by 90 quintilion yields tiny fraction of gram. The scale won't register it unless it is sensitive to the billionth of decimal place. But but the mass is there. wound up pocket watch weighs slightly more than watch with dead spring. The potential energy stored in the tension of the coiled metal possesses mass. The flashlight shines beam until the battery dies. The flashlight weighs less at the end of the electromagnetic radiation carried away fraction of the battery's inertia. For decades, physicists treated this as mathematical curiosity. The amount of mass change in chemical reactions or thermal heating was so impossibly small that nobody could measure it. stick of dynamite explodes. It shatters rock and creates massive shock wave. The energy released is terrifying. If you gathered every single gas molecule, every speck of ash in every fragment of debris and put them on scale, you would find they weigh about 1 billionth of gram less than the original stick of dynamite. The missing mass became the explosion. Chemical bonds involve the electrons orbiting the outer edges of atoms. The energy changes are tiny. The true brutality of E= MC squared hid deep inside the atom, the nucleus. In 1932, John Cockraftoft and Ernest Walton built particle accelerator in room at the Caendish Laboratory in Cambridge. They built it out of glass cylinders, vacuum pumps, and car batteries. They fired protons at piece of lithium foil. Lithium has three protons. When they hit it with high-speed proton, the two fused together briefly. Poor proton. An unstable burillium nucleus. It violently ripped itself apart into two helium atoms. Cochroft and Walton measured the kinetic energy of the helium atoms flying away. They moved incredibly fast. The energy was massive. Then they looked at the masses of the ingredients. They knew the precise mass of lithium atom. They knew the precise mass of proton. They added them together. They knew the mass of helium atom. They multiplied it by two. The two numbers did not match. The incoming lithium and proton weighed significantly more than the outgoing helium fragments. About quarter of percent of the mass had completely vanished. They took that missing mass. They multiplied it by the speed of light squared. The number they got matched the kinetic energy of the fleeing helium atoms with perfect precision. It was the first direct physical confirmation of Einstein's equation for the nucleus of an atom is very crowded place. Protons have positive electric charge. Positive charges repel each other violently. And if you put two protons next to each other, the electrostatic force tries to shove them apart. Inside uranium nucleus, you have 92 protons packed into an infinite decimally small volume. The electrical repulsion is staggering. The only reason the nucleus does not instantly detonate is different force. The strong nuclear force, it acts like Velcro. It only works at incredibly short ranges, but it is vastly stronger than the electrical repulsion. It binds protons and neutrons together. This binding energy is enormous. If you take completely isolated proton and put it on scale, you get specific mass. You do the same with neutron. You had the masses. If you let the strong force snap them together to form dutyium nucleus and you put that nucleus on scale, it weighs less than the sum of its parts. The missing mass radiated away as energy when the strong force snapped them together. This is called the mass defect. It is the secret to everything. It it is why we are alive. The sun is giant sphere of hydrogen gas. The gravity of all that gas pulls inward creating immense pressure and heat at the core. The protons are moving so fast and are packed so tightly that they overcome their electrical repulsion and smash into each other. The strong force grabs them. They fuse into heavier elements. Every time they fuse, tiny fraction of their mass converts into energy. The sun loses about 4 million tons of mass every single second. 4 million tons of physical matter vanish, transforming into radiation that shoots out across the solar system, hits the Earth, warms the oceans, and drives the weather. If E= MC² were slightly different equation, if the squared multiplier was smaller, the sun would barely glow. You life would never have started. But you can also run the process backward. Fishing uranium 235 is fragile. It has 92 protons and 143 neutron. It is wobbling. The strong force is barely holding it together against the electrical repulsion of all those positive charges. If you flick single stray neutron into uranium 235 nucleus, it becomes uranium 236. It starts to vibrate. The shape elongates like water droplet. The distance between the ends gets just large enough that the strong force weakens. The electrical repulsion takes over. The nucleus violently rips itself in half. It produces two lighter atoms like barium and krypton. It also spits out two or three loose neutrons. If you weigh the original uranium and the incoming neutron, and then you weigh the barerium, krypton, and outgoing neutrons, you find missing mass. The fragments weigh less. The missing mass becomes the kinetic energy of the fragments. They fly apart at fraction of the speed of light. They smash into neighboring atoms creating immense heat. Those two or three loose neutrons fly outward and hit other uranium atoms. They split so they release more heat and more neutrons. Two become four. Four become eight. Eight become 16 in chunk of pure uranium. 235 you get 80 generations of splitting in microscond. was at Los Alamos during the war. was junior physicist. My job was calculating the efficiency of the boom. We were trying to figure out exactly how much energy would be released before the physical structure of the metal blew itself apart and stopped the reaction. We use mechanical calculators, merchant machines, room full of people punching numbers, simulating the flight of neutrons through sphere of plutonium. You look at the math on chalkboard, you write E= MC², you multiply the missing mass by 9 * 10 to the 16 squar/s squared. There's just an abstract number on piece of paper. Then came July 1945. Alamogordo. The Trinity tests. sat in truck about 20 miles away. They handed out dark glasses like welding goggles. did not want to use them. figured the only thing that could really hurt my eyes was ultraviolet light. So got behind the windshield of this truck. Glass blocks ultraviolet. The countdown hit zero. The world turned white. cannot emphasize the sheer scale of the light. It was not flash. It was sustained, silent, blinding white dome expanding in the desert. It illuminated the mountains in the distance brighter than noon. About minute and half later, the sound hit, sharp, loud crack, followed by low rumble that echoed off the mountains for what felt like an eternity. remember sitting there staring at the purple glow of the ionized air. knew exactly what had just happened. sphere of plutonium the size of grapefruit had been crushed by high explosives. chain reaction ripped through it. About one gram of actual mass, the weight of paperclip, had been removed from the universe. One paperclip of missing mass created that entire blinding inferno. lot of the guys cheered. Bob Wilson sat there looking miserable. He said, "It's terrible thing that we made." Later, was back in New York. sat in restaurant. looked out the window at the buildings as long. mentally calculated the blast radius. knew the damage boom like that does. saw people building bridge or making new road and thought they don't understand why are they building things. It it's completely useless that we know how to destroy it all now. it took me long time to get over that feeling. The math became physically real to me in way never wanted. Let me bring us back to the physics because we are not done with mass. We established that mass is just confined energy. But if you look closely at proton, the situation gets even stranger. teach quantum electronamics at Clarine. have spent my whole life calculating how light interacts with matter. understand the math deeply. But if you ask me what an electron actually is or what photon fundamentally is, have to admit do not know. only know how they behave. We look inside proton. For long time, we thought proton was solid sphere of positive charge. It is not. It is made of smaller particles called quarks with two up quarks and one down quark. You know, you would logically assume that if you add up the mass of the two up quarks and the one down quark, you get the mass of the proton. You try the addition. The quarks account for about 1% of the proton's total mass. Where is the other 99%. The quarks are moving around inside the proton at near the speed of light. They are held together by particles called gluons. Gluons carry the strong force. Gluons have zero mass. They are completely massless particles. The quarks are ripping back and forth transferring momentum via the massless gluons. The sheer kinetic energy of the moving quarks and the potential energy of the strong force field is enormous. You apply E= MC². You take all that roaring chaotic energy inside the tiny volume of the proton and you divide it by the speed of light squared. It equals 99% of the mass of the proton. Your body is made of atoms. Atoms are mostly protons and neutron. That means 99% of your physical weight, your inertia, the reason you hit the ground when you jump is not due to solid matter. It is due to the frenzied movement of massless gluons and incredibly light quarks trapped inside subatomic prisons. Your mass is mostly just motion. The universe is fundamentally an energy construct. Einstein saw the edge of this in 1905 and he did not know about quark and he did not know about gluons. He barely believed in atoms at the time. He actually helped prove their existence earlier that same year with his paper on Brownian motion. He was working purely from the macroscopic rules of thermodynamics and the geometry of spacetime. want to revisit his thought experiment. The box emitting light. There is subtle genius in how he framed it. He didn't build machine in his mind. He didn't worry about how the light was produced. light bulb, burning piece of coal, radioactive isotope. The mechanism did not matter. Only the conservation laws matter. The laws of physics must be identical for all observers in uniform motion. That is the core postulate of relativity. If the stationary observer sees energy conserved, the moving observer must also see energy conserved. The only way the algebra balances for both people is if inertia is not constant. People ask if E= MC² means we can turn lead block into pure energy like battery. Yes and no. You can't just flip switch and erase block of lead. The universe has rules. Conservation of barrier number, conservation of electric charge. Yet you can't destroy proton without an anti-roton. Antimatter is the only way to get 100% conversion rate. An electron has negative charge. You die. posetron is its antimatter twin. Sedata. Exact same mass but positive charge. And if you bring an electron and posetron together, the charges cancel out to zero. The mass completely annihilates. The entire combined mass of both particles transforms into two high energy photon. Gamma rays shooting off in opposite directions. No mass remains. Only pure propagating electromagnetic energy. Does it? You measure the energy of those gamma rays and go. You divide by squared. You get the exact mass of the electron and the positron. But we do this in hospitals every single day. PET scan, posetron emission tomography. You drink slightly radioactive sugar solution. The sugar goes to the active parts of your brain. The radioactive atoms decay, spitting out posetron. The posetrons hit electrons in your brain tissue. They annihilate. The gamma rays shoot out of your skull and hit ring of detectors. We use Einstein's 1905 derivation to map the inside of living human body. The sheer predictive power of man thinking about trains and light bulbs is terrifying. Let's look at the math one more time. skipped over something important earlier. The actual derivation uses mathematical trick, tailor expansion. When you calculate the relativistic energy of moving object, the exact formula is E= MC^ 2 / the of 1 - ^ 2 / C^ 2. That square root in the denominator is the Lorren factor. It dictates how time slows down and length contracts as you approach the speed of light. Einstein looked at that fraction for normal objects, space balls, trains, planets, the velocity va is microscopic compared to the speed of light. So, so v^2 over c^ 2 is fraction so close to zero it is practically invisible. When you have an equation with tiny fraction like that, you can use binomial expansion to stretch it into an infinite series of terms. The first term is just one. The second term is ^ 2 / 2 ^ 2. There are more terms, but they get smaller and smaller, so you just chop them off. If you multiply the top by the expanded bottom, you get two main pieces. The first piece is mc^ squ. The second piece is 1/2 mv². Look at that second piece. 1/2 mass time velocity squared. That is Newton's exact formula for kinetic energy. The classical formula you learn in high school. It pops right out of relativity at low speeds. But what is that first piece? The MC². It has no velocity variable in it. It exists even when is zero. It is the energy an object has just by existing. It's rest energy. Before 1905, physicists only cared about changes in energy. The baseline did not matter. If ball rolls down hill, you measure the difference in potential energy from the top to the bottom. You define the bottom of the hill as zero energy. It was completely arbitrary baseline. Einstein proved the baseline is not arbitrary. The absolute zero of energy is an object with zero mass. If you have mass, you have staggering reservoir of intrinsic energy. We missed it for centuries because we never saw the reservoir drain. It was closed vault. We only noticed the loose change rattling around on top, the kinetic energy, the chemical heat. think about the patent office lot. Einstein was third class examiner and he evaluated electromechanical devices and the synchronization of clocks and telegraph signal relays. He spent 8 hours day looking at physical mechanisms designed to transmit information and coordinate time across distances. He was drowning in the practical problems of timekeeping. The Swiss rail network was expanding. Clocks in different cities had to be synchronized perfectly so trains would not crash. They synchronized them using electrical pulses traveling through copper wires at near the speed of light. Einstein was looking at patents for these exact system. He saw the physical limitation of the synchronization process. The signal is not instantaneous. He took gritty engineering problem. How do you know what time it is in Zurich if you're standing in bar? And he stripped away the gears and wires. He reduced it to pure thought experiment involving beams of light. He realized that if the signal speed is absolute, the clocks will never agree if they are moving relative to each other. Once he accepted that time is local, everything else fell apart. mass was the final casualty. It took the physics community long time to absorb this. Max plank read the paper. Plank was the older established giant of German physics left. He immediately realized Einstein was right. He championed the paper. But many experimentalists were furious. They wanted to disprove it. Walter Kaufman did an experiment in 1906. He measured the mass of high-speed electrons emitted by radioactive source. He applied electric and magnetic fields to bend the path of the electron. If their mass increased as they move faster, they would be harder to bend. The curve would be flatter. Kaufman analyzed his photographic plates. He published paper saying his results definitively contradicted Einstein's theory. Einstein didn't blink. He essentially said, "The data must be wrong because my theory is too logically beautiful to be incorrect." Kaufman's experimental setup had tiny vacuum leak. The data was flawed. Einstein's confidence was utterly terrifying. He trusted the internal consistency of the mathematics over preliminary lab results. This is dangerous way to do physics. Usually, the experiment is the supreme judge. If your theory disagrees with the experiment, the theory is wrong. Period. But Einstein saw deeper truth. He knew the principles of relativity were inescapable. Let's think about the sheer density of energy and mass. Take single drop of water. It weighs about 12th of gram. If you could convert that entire drop of water into pure energy, how much do you get? You do the multiplication. It comes out to about a,000 megawatt hours. single drop of water contains enough dormant energy to power small city for month. We walk around surrounded by an ocean of frozen concentrated energy. The wood in the desk, the glass in the windows, the oxygen we breathe. Every speck of dust is vault of trapped cosmological power. We only interact with the superficial layer. We break chemical bond here. We burn carbon atom there, extracting billionth of percent of the available energy and we call it an industrial revolution. The true fire is locked inside the nucleus. want to return to the process of discovery. We often tell the story of science backward. We start with the pristine finished equation and we work backward to the confused human. When Einstein wrote the E= MC² paper, he was exhausted. He had published four revolutionary papers in one year. The photoelectric effect, Browning in motion, special relativity, mass energy equivalent. He wrote to his friend Conrad Habik. He described the mass energy idea as immune.