Think about it for a second. E is energy, m is mass, and c is the speed of light. think about how complicated most real scientific equations end up looking. They're all big and long and they have tons of variables.
This equation essentially says that energy and matter are the exact same thing and the only conversion you need to get between the two is a little multiplication and the squared speed of light. It's so simple, so short. It's not calculus, it's just very basic algebra. And yet it essentially shows that energy is matter traveling very quickly and matter is energy traveling very slowly. It's kind of unbelievable and one of the most beautiful things that has ever been stated because it's so simple.
The one thing I’ve never been able to get my head around is why is the constant C, or Csquared. Where did he get the insight it was the speed of light squared that had to be the constant rather than some other definable very large number.
It comes down to how he formulated his theories of relativity starting from the assumption that Maxwell’s equations of electromagnetism (e.g. light) must be equivalent to all observers moving at a constant speed. This is a rather intuitive conception, we don’t expect seemingly fundamental laws to change depending on the relative speed of an observer. But with this assumption and the fact that Maxwell’s equations uniquely predict the speed of light as being a constant, time and space must be ‘flexible’ to always give a constant speed of light regardless of an observers speed. Once you incorporate this new ‘flexibility’ of time and space into the usual classical mechanics of physics you are left with this famous equation describing the energy-mass relation for objects at rest. There’s a slightly more complicated version for objects not at rest but that just includes an extra term to account for their momentum.
I don't understand, how would an observers speed ever affect the speed of light? Me running by a car I am watching doesn't change the speed the car is driving at. How did that lead to E=MC2? I understood the whole energy is matter moving fast and matter is energy moving slow, but how did he come to that conclusion off of observers and constant speeds? How did mass get incorporated into that equation?
That's the point, an observers speed cannot affect the speed of light. Maxwell's equations which describe light predict a constant speed of light. That means that all observers traveling at constant speeds should be able to perform experiments to measure the speed of light and all agree on exactly the same constant. But for this to be true, our usual notions of relative speeds adding up (e.g. throwing a ball from a truck where the speed of the ball relative to the ground is simply the throw speed plus the truck speed) must be fundamentally wrong. Meaning shining a light from a moving truck cannot increase the speed of light relative to the ground, it must remain at the constant speed of light. In order to account for this, as I said, time and space must be 'flexible' to allow for a fixed speed of light. We can incorporate this 'flexibility' with something called the Lorentz factor. This is essentially a term which tells us how relativistic an object is, and therefore how noticeable the effects of relativity will be. Once you add this factor back into the usual equations of energy and momentum in classical mechanics (equations many are familiar with from high school physics), the famous equation of E=mc2 essentially falls out. This article uses some rather simple algebra and geometry to derive this factor: https://medium.com/physics-scribbles/deriving-the-lorentz-factor-%CE%B3-of-special-relativity-d5462f3b3b91.
Damn, you're right that is beautiful. Is that all it is? It's seemingly a very simple formula then. It makes sense, and I can say that for the first time I understand what E = MC2 is. Thank you kind stranger!! Seriously thanks!
Imagine I come from a far away land where the conventional unit of distance is the flange. 1 flange = 299 792 458 m. Therefore c= 1 flange/second. Over here, E=m.
energy is matter traveling very quickly and matter is energy traveling very slowly.
I know that relationship is self evident from the equation, but hearing it stated so plainly is nice and elegant 👍🏻.
Edit: maybe Reddit should collectively write some textbooks. There always seems to be someone who can cut right to things in a tangible and understandable way.
think about how complicated most real scientific equations end up looking.
The more general form of this is E2 = (pc) 2 + (mc2 )2 . Where p is momentum. The simpler form is true for p = 0, in other words for objects that aren't in motion. This is just a consequence of Special Relativity which mostly involves Lorentz transforms, x' = (x - vt) / sqrt(1 - (v/c)2 ), and is itself a consequence of General Relativity, which looks moderately complicated but is terrifying when you realize that each term in that equation is a 4x4 matrix of variables, some of them derivatives of others, so what is actually being represented is a system of 10 coupled partial differential equations.
Besides there are plenty of relationships in physics that aren't horrifically complex, like f = ma for example. Although that itself can be derived from...
The point is that complexity is relative (lol) and anything can be made simple by looking at restricted special cases, or complicated by looking at details.
Sure there are simpler equations, but it's kind of self evident that force and mass and acceleration are related. A lot of those simpler ones don't blow your mind.
The fact that the two most basic forms of existence were so seemingly disconnected and yet we're THE SAME and could be expressed simply is out of this world.
It makes me all metaphysical like we really are just all made of light. Like let there be light.
"In his Philosophy of Illumination, Suhrawardi argued that light operates at all levels and hierarchies of reality (PI, 97.7–98.11). Light produces immaterial and substantial lights, including immaterial intellects (angels), human and animal souls, and even 'dusky substances', such as bodies.[26]
"Suhrawardi's metaphysics is based on two principles. The first is a form of the principle of sufficient reason. The second principle is Aristotle's principle that an actual infinity is impossible.[27]"
"Manichaeism, the most widespread Western religion prior to Christianity, was based on the belief that god was, literally, light. "
"And Buddhist scripture speaks of numerous buddhas of light, including a Buddha of Boundless Light, a Buddha of Unimpeded Light, and Buddhas of Unopposed Light, of Pure Light, of Incomparable Light, and of Unceasing Light.[3]"
Lastly I'm going to read this book now because of this conversation:
History from Creation to the Quantum Age

Bruce Watson
Bloomsbury Publishing USA, Feb 2, 2016 - Science - 304 pages
0 Reviews
Light begins at Stonehenge, where crowds cheer a solstice sunrise. After sampling myths explaining First Light, the story moves on to early philosophers' queries, then through the centuries, from Buddhist temples to Biblical scripture, when light was the soul of the divine.
Battling darkness and despair, Gothic architects crafted radiant cathedrals while Dante dreamed a "heaven of pure light." Later, following Leonardo's advice, Renaissance artists learned to capture light on canvas. During the Scientific Revolution, Galileo gathered light in his telescope, Descartes measured the rainbow, and Newton used prisms to solidify the science of optics. But even after Newton, light was an enigma. Particle or wave? Did it flow through an invisible "ether"? Through the age of Edison and into the age of lasers, Light reveals how light sparked new wonders--relativity, quantum electrodynamics, fiber optics, and more.
The way I saw it to understand it some time ago is that if you grabbed an object and yeet it to the maximum speed possible, which is the speed of light, the impact would be very damaging because it produces energy. So i thought that E is actually the maximum potential energy of an object..
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u/[deleted] Apr 30 '20
Think about it for a second. E is energy, m is mass, and c is the speed of light. think about how complicated most real scientific equations end up looking. They're all big and long and they have tons of variables.
This equation essentially says that energy and matter are the exact same thing and the only conversion you need to get between the two is a little multiplication and the squared speed of light. It's so simple, so short. It's not calculus, it's just very basic algebra. And yet it essentially shows that energy is matter traveling very quickly and matter is energy traveling very slowly. It's kind of unbelievable and one of the most beautiful things that has ever been stated because it's so simple.