What is E=mc^2: Definition and 175 Discussions

In physics, mass–energy equivalence is the relationship between mass and energy in a system's rest frame, where the two values differ only by a constant and the units of measurement. The principle is described by the physicist Albert Einstein's famous formula:

The formula defines the energy E of a particle in its rest frame as the product of mass (m) with the speed of light squared (c2). Because the speed of light is a large number in everyday units (approximately 3×108 meters per second), the formula implies that a small amount of rest mass corresponds to an enormous amount of energy, which is independent of the composition of the matter. Rest mass, also called invariant mass, is the mass that is measured when the system is at rest. It is a fundamental physical property that is independent of momentum, even at extreme speeds approaching the speed of light (i.e., its value is the same in all inertial frames of reference). Massless particles such as photons have zero invariant mass, but massless free particles have both momentum and energy. The equivalence principle implies that when energy is lost in chemical reactions, nuclear reactions, and other energy transformations, the system will also lose a corresponding amount of mass. The energy, and mass, can be released to the environment as radiant energy, such as light, or as thermal energy. The principle is fundamental to many fields of physics, including nuclear and particle physics.
Mass–energy equivalence arose from special relativity as a paradox described by the French polymath Henri Poincaré. Einstein was the first to propose the equivalence of mass and energy as a general principle and a consequence of the symmetries of space and time. The principle first appeared in "Does the inertia of a body depend upon its energy-content?", one of his Annus Mirabilis (Miraculous Year) papers, published on 21 November 1905. The formula and its relationship to momentum, as described by the energy–momentum relation, were later developed by other physicists.

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  1. Bobski

    I Discover the Relationship Between Mass and Energy in Electromagnetic Fields

    When E=mc^2 is rearranged using the substitution c=1/√ε0μ0 , and making mass the subject we get m=Eε0μ0 This equation basically says that mass is directly proportional to the energy contained in an electromagnetic field. Does it not? Does this equation tell us that mass particles are made up of...
  2. Slimy0233

    B What is m in Kinetic Energy? Relativistic mass or Rest mass?

    note: m = relativistic mass ##m_o## = rest mass v = velocity of the objectQuestion 1: If a particle is moving at relativistic speeds what would it's kinetic energy be? I think it's ##K.E. = \frac{1}{2} m_o v^2## and my friend thinks it's ##K.E. = \frac{1}{2} \frac{m_o...
  3. Dave Gungan

    B How many nuclear weapons are needed to make a wormhole?

    Hi guys! After many years of lurking quietly I finally have a question that I'd like to know, please. I'd like to know how much energy is needed to make a wormhole in terms of our current nuclear weapons, or how much mass is needed to turn into pure energy, maybe via antimatter annihilation...
  4. ohwilleke

    I Scope of General Relativity: Assumptions & Implications

    Assumptions 1. General Relativity is the modern and most complete widely accepted theory of gravitation, formulated in a background independent, geometric way. 2. General Relativity is formulated in a manner consistent with Special Relativity and I could imagine that it might be possible to...
  5. George Keeling

    I Uncovering a Decent Proof of E=mc^2

    Sean Carroll says that in SR the time component of the 4-momentum of a particle is its energy. It is of course also ##mc^2dt/d\tau##. He uses that to prove that ##E=mc^2##. Which begs the question why does ##E=p^0##? Misner, Thorne, Wheeler do roughly the same thing. I find these 'proofs'...
  6. S

    B Is E=mc^2 a Bidirectional Equation in Physics?

    Hello All Does the most famous and elegant equation in physics imply bidirectionality in the way it describes the relationship between energy and mass? There are many examples of matter being converted into energy (stars, bombs, reactors, etc), but can energy be converted into matter? At the...
  7. MagneticNeutron

    Semi-Empirical Mass and E=mc^2 close, but both off? Binding Energy calc

    Hi, I am calculating the binding energy of 11- Na- 18 Stats: Table of nuclides has BE/A = 6.202276 ± 0.006249 MeV m used = 18.026878252 amu E= mc^2 answer = 5.894327537620224 MeV Semi Empirical Answer = 5.919667778950925 MeV Including excess mass in E = mc^2 method 1 - Calculate...
  8. snoopies622

    B Does E=mc^2 apply to gravitational potential energy?

    I'm reading Schutz's A First Course In General Relativity and in chapter 5 he discusses an idealized experiment in which an object is dropped from a tower, then turned into a photon and sent back up to its original height. In classical mechanics we would say that as the object falls it loses...
  9. Demystifier

    I History of E=mc^2 Before Einstein

    A short historical paper gives evidence that Einstein was not the first who discovered ##E=mc^2##. https://arxiv.org/abs/physics/0608289
  10. A

    I E=mc^2 Mass: Rest Mass m0 vs Relativistic Mass γm0

    Is the mass that appears in E=mc2 the rest mass m0, or the relativistic mass γm0?
  11. T

    B Why is E=MC2 Squared and not Cubed?

    Problem Statement: Trying to understand the principles for the equation e=mc2. Relevant Equations: E=mc2 So just started at a physics A level and so far loving it. I understand this question has indeed been asked before, however for different reasons. I understand the purpose of e=mc2 and I...
  12. DaveC426913

    B Where did the 1/2 go in E=mc^2?

    In explaining to a curious member on a another forum what E=mc^2 means, I finally came to understand it better myself. The member wanted to know why c is squared. What sense does it make to square a velocity? I stated comparing it to the kinetic energy formula K=1/2mv^2 A 1 ton car moving at...
  13. P

    B What is the meaning of the famous equation E=mc^2?

    E=mc^2 Can someone explain this equation to me? Does this mean that energy has mass in the sense that energy will create gravity? For instance, if I have a massless ball and I somehow place (3*10^8)^2 Joules or c^2 joules of electromagnetic energy inside the ball, would that ball now have a...
  14. sush

    I Why E=mc^2 is different from E=1/2 mv^2?

    Why kinetic energy is ½ m v2? Why it is different from Einstein’s equation for Energy E= m c2?
  15. B

    I Fact Check: Is E=mc^2 Accurate?

    I am doing an article that includes a brief explanation of Einstein's basic equation, and want to check my work. As I understand it, the equation is e(energy in Joules)=m(in grams)×speed of light in meters/second squared(9×10 to the 16th). Is this reasonably correct? Thanks.
  16. F

    I Real life example of the energy contained at E=γmc^2

    We've just begun studying about relativity, and I find it amazing that bodies have the energy of E=γmc^2. Even at rest they have E=mc^2. But where exactly is this energy present in real life? For example the keyboard I am currently typing this post with has a huge amount of energy, according to...
  17. G

    I Need a practical example of E=mc^2 with real numbers

    Need a practical example of E=MC2 with real numbers Ok, so I understand that Energy = Mass of an Object * Speed of light square, if we must convert this to numbers, how can this be presented for let’s say 1,000 hydrogen atoms? Energy = 1.008 (Hydrogen mass) * 1,000 (hydrogen atoms) * speed of...
  18. snoopies622

    I Can one get E=mc^2 using classical EM theory?

    I'm wondering if one can arrive at E=mc^2 using only the physics of the late 19th century, in the following way: As light waves pass over an electrically charged particle, they push it in the direction of the wave motion, transferring both (kinetic) energy and momentum to the particle. Let's...
  19. bhobba

    I Was Einstein's Proof of E=MC^2 Flawed?

    Hi All I am reading the following interesting book: https://www.amazon.com/dp/0393337685/?tag=pfamazon01-20 In it he makes the claim Einsteins proof of E=MC^2 had errors. They were fixed (not by Einstein - but by Von-Lau in 1911 using Minkowski's tensor formalism) - but, he claims, even now...
  20. G

    A Usage of kinetic energy in proof for E=mc^2

    http://bildr.no/view/aWc4dW95 Above is a question that I posted on a school help site. This is the answer I got: https://www.scribd.com/document/352723366/problem-about-usage-of-E-mc-2-for-v-much-smaller-then-c-ans Can you use this answer to show that the type of calculation that I tried in...
  21. snate

    I Assumption that the rest mass energy is mc^2

    In all the derivations of E2=p2c2+m2c4 ,that I've stumbled on, it's assumed that the rest mass energy is m*c2 just because kinetic energy is mc2λ-mc2. Was it originally assumed? If so, can someone explain me why is it a logical assumption? Are there any derivations without such assumptions?
  22. D

    Can Matter-Antimatter Annihilation Yield High Energy Output per Gram?

    I am just curious on this one, if you could efficiently turn matter into energy (the whole e=mc2 thing) how much energy could you get per gram?
  23. J

    I Question about deriving E=mc^2

    I have a question about the velocity of a mass that is being accelerated from its resting position, for deriving its energy according to ##E=mc^2## The energy needed for accelerating a mass is: ##E = F \cdot s = m \cdot a \cdot s##. Where s is the distance over which the mass is moved. Now, I...
  24. gabi123

    B Can you reverse Einstein's famous E=mc^2 equation?

    E=mc^2 states that when you speed up matter to the speed of light, it becomes pure energy, of mc^2 joules. Now, if that is true, can you reverse the equation? Wouldn't energy speed up to the negative speed of light(-c^2), turn into matter? Or is that the wrong balance?
  25. Algr

    B Did I Just Create 2.5 Kilograms of Energy?

    Okay, I know I have no business playing around with relativity, but things got heated and I grabbed this: And turned it into: Give it to me straight. Did I blow up the Earth?
  26. S

    B Exploring the Mystery of E=mc2: Why is c Squared and Not Another Value?

    Hi everyone, I'm not a physicist, so please excuse my ignorance. In E=mc2, why is c squared? And why is the value exactly to the power of 2? Why not 2.1, or 2.438? I looked at a few other threads on this forum about this equation, but couldn't find anything addressing this aspect of it. Thanks...
  27. S

    B Cox & Forshaw: "Why E=mc^2" - A Newbie's Question

    Hi All My first post here and I'm sure it's going to be one of the easiest for you to answer. I've just read Einstein's book on the theory of relativity and now I'm currently reading 'Why does e=mc2 (and why should we care)' by Brian Cox and Jeff Forshaw. My Math isn't up to much but I have a...
  28. A

    B How can we derive the value of energy in rest mass and the relationship to c^2?

    I have read different version/interpretations of Einstein derivation of the formula, no one is logically satisfying. But my question is more general: the value of energy in rest mass is a scalar, which is not related to anything, how can we use logic or math to derive such a value? Stretching...
  29. E

    I Cox & Forshaw: Explaining E=mc^2's "Negative" Option

    Great book. Reading it for the second time. There are several "jumps" that are made in their lines of reasoning that certainly make the explanations easier to follow, but also left me wondering "Why or where did that assumption or statement come from?" On page 77 (in my 2009 Da Capo Press...
  30. A

    Finding relativistic mass and energy of an electron

    Homework Statement A resting electron was sped up to 0.5 of the speed of light. Find: A. relativistic mass of the electron, B. total energy of the electron, C. kinetic energy of the electron. Homework Equations K = mv^2/2 E=mc^2 The Attempt at a Solution Let’s first find the kinetic energy...
  31. G

    B From dE=dm*c^2 to E=m*c^2: Integration constant?

    Hi, I've read some high school "derivations" of ##E=m\cdot c^2## that all considered single photons with momentum ##p=E/c## that are absorbed or emitted from some massive object, changing its mass. So they actually only showed the incremental $$\Delta E=\Delta m\cdot c^2 .$$ Most of those...
  32. Zarich12

    B How to simply solve for E=MC^2?

    I was wondering how to simply solve for E=MC^2. I have basic idea but I just want to check it. You take the mass times the speed of light (in miles per second?) and square that. Over one second that is equal to the number of watts the object could produce. Is that right. If there are any...
  33. D

    Is kinetic energy included in the equation E = hν for a photon?

    For a photon the energy is given by $$E = h\nu$$ Does this includes both kinetic energy and energy due to mass? If so then de Broglie gave the equation λ = h/p by equating hν with mc2 but since E = mc2 just gives the energy due to relativistic mass at that speed it would not include kinetic...
  34. Kris Lemkens

    B E=mc^2 & Universe Expansion - Answers Wanted!

    Hello everybody! I've just joined this forum looking for answers to my possibly newby questions. I read somewhere (don't recall the source) that the universe is expanding at a rate that is faster than the speed of light, and is slowing down. Is there any kind of relation of this expansion and...
  35. F

    I Einstein's E=mc^2 equation -- question....

    Let's say we have a particle traveling at the speed of light, energy would be E=mc^2, momentum would be then p=mc, let's manipulate, m=E/c^2, momentum would then be p=E/c, but what energy does that equal, the particle only has kinetic energy correct? Then it would be p=1/2mc. Where is the other...
  36. S

    I Can Anyone Help Understand Einstein's 1905 Derivation of E=mc^2?

    Link: https://www.fourmilab.ch/etexts/einstein/E_mc2/www/ The only part I'm having trouble with is how he gets the plus sign in that 1+(v/c)cos(φ) numerator for the "other" light ray (emitted in the opposite direction of the first). My understanding is that the φ he uses in his general Doppler...
  37. C

    I How can MeV be equal to MeV/c^2

    How can 1 u be eaual to 931,5 MeV, and at the same time be equal to 931,5 MeV/c^2? (1) 1 u = 931,5 MeV (2) 1 u = 931,5 MeV/c^2 Becuase then 931,5 MeV would equal to 931,5 MeV/c^2? 1 u = 1 u (1) = (2) 931,5 MeV = 931,5 MeV/c^2I understand that you can derive both separately or say...
  38. B

    Deriving E=mc^2 from relativistic doppler effect

    How is E=mc^2 derived from relativistic doppler effect? I looked up on wikipedia but it seems to have some errors. https://en.wikipedia.org/wiki/Mass%E2%80%93energy_equivalence#Alternative_version
  39. Isaac0427

    How did E=mc^2 contribute to the atomic bomb?

    Before I got into physics, I thought that ##e=mc^2## was the atomic bomb equation. I now know that the equation itself has nothing to do with the atomic bomb. So, I'm wondering, how did ##e=mc^2## contribute to the development of nuclear/atomic weaponry/power? Edit: I do not know if this is in...
  40. T

    E=mc^2 how you picture it in nature?

    When you close your eyes and visualize E=mc2 in nature without math, what images do you see? I always saw the Hiroshima mushroom cloud, but after reading your posts, I agree bombs are not the right image when introducing concept to kids. 1. I now see star core nuclear fusion of hydrogen into...
  41. T

    E=MC^2 - easy explanation for kids

    Been lurking on these threads looking for easy explanations of E=mc2 as it relates to nuclear fission weapons. Shame, SHAME, to yall advanced physicists who dismiss and disrespect and flame amateurs on other threads asking for easy examples for kids. I'm a humanities teacher teaching...
  42. B

    Kinetic Energy & E=mc^2: A Physics Query

    The kinetic energy equ. is 1/2m*v^2 but why just 1/2m and why v^2? I understand why m*v but the rest of it not make sense for me. There is the well known E=mc^2 where c is v.light but the mass is not half here. Why?
  43. P

    Does E in E=mc^2 Include Gravity?

    Does the E in E=MC^2 include the gravitons?
  44. L

    E=mc^2 Conversion to eV=u: What Happens to the Distance Units?

    Hi, I'm new to the site and not sure if I'm posting in the right place as this is not exactly a homework problem, but just a problem in general. I'm looking at E=mc2 and how the units can be broken down into eV=u (I think?). I don't know what happens to the distance units, though, if we keep...
  45. S

    Why is E=MC^2 such a neat and simple formula?

    OK.. my question I've pondered in the past.. why is E=MC2 such a nice and clean formula.. with no corrections or " x .00003845" etc. Was metric based on the universe (physics) or is the universe somehow based on metric?
  46. H

    Binding energy per nucleon and fission/fusion

    Homework Statement Ok so i know that the binding energy per nucleon inceases after fission and fusion and the difference in the binding energy is given out as energy. But if the binding enrgy increases shouldn't there be energy taken in(rather than given out)? Also why is the net loss in my =...
  47. Deepak K Kapur

    Discover the Relationship Between E=mc2 and Time with m=1kg and d=1m

    If i put c=d/t in E=mc2, then E=m×d2/t2 Now take m=1kg and d=1m Does this mean that E is inversely proportional to time?
  48. N

    Mass problem or something of a sort (E=mc^2)

    Hi guys! My question is kinda stupid and I'm new here so: At the border between the quantum and classics worlds how E=mc^2 works? Like in which states you'll have quantum tunnelling, in which just the classic classical way of not passing the barrier (I do not mean classic/quantum world) and when...
  49. akashpandey

    About light, photon mass and E=mc^2

    Light is form of energy. Accordingto einstine theory if we concentrate the energy of light we have to get mass of light. But their is no mass of light. Acc.to E⇒mc2.
  50. paulo84

    Solving the Mystery of e=mc^2: Understanding the Power of Squared in Physics

    Hi, Sorry to bring this up again but I have a new question. I understand the e=mc part, you've only got to look at a nuclear explosion, but I don't really get the 'squared'. Given that a nuclear explosion is literally a 3 dimensional shape (let's leave exploring possible hidden dimensions for...