What is E=mc2: Definition and 73 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. A

    I E Vector in E=mc2? Scalar Multiplication & Vectors

    If the energy is a vector, which as i understand for example, the potential energy , U=mgh, where g is the gravitational force, Then U is the product of scalars and vectors, so its a vector In that case being E a vector , can it be equal to mc2 (each are scalars). Like mulitplication of scalars...
  2. 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'...
  3. I

    I Derivation of E=pc & E=MC2: Which Came First?

    I have seen E=pc used to derive E=MC2. I have seen E=MC2 used to derive E=pc. This is circuitous. Which came first and how is E=pc derived?
  4. Ciaran H

    B Where does the increase in mass come from in fission?

    If energy is released during nuclear fission, why is the mass of the products (the two new nuclei and fission neutrons) greater than the mass of the original nuclei? In accordance to E=mc^2, shouldn't the release of energy result in the products having a lesser mass than the original nuclei?
  5. Zahidur

    I Subbing Planck length into length contraction equation?

    I was wondering if it is possible to work out the maximum amount of energy an object with mass can have using the length contraction equation (i.e. "actual" length divided by Lorentz factor). The way I thought of doing this was by rearranging e = mc^2 to get c^2 = e/m. Then, substitute e/m into...
  6. J

    B Derivation of E=Mc2? For the common man

    Ok this is perhaps the single most famous equation known to man. And I have basically zero idea how it came to be. I have a slight background in classical physics (a couple college classes) I know it states that energy is equal to mass multiplied by the speed of light squared. I have tried to...
  7. E=mc² is Incomplete

    E=mc² is Incomplete

    This is a video of one of our most frequently-asked question, and frequently misunderstood concept.
  8. Molar

    Confused by E=mc2, m & Photons: Help Needed!

    1. From E=mc2 , m= E/c2 "c" being huge, "m" should be small. 2. m= mo/√ [1-v2/c2] if v= c, then m should reach infinity. 3. Photons moving with speed of light are massless particles. All the above statements are confusing me. (1) doesn't match with (2), (2) doesn't match with (3). Please...
  9. T

    E=mc2 Pop Science for public waste of time?

    I'm posting this one in Relativity as a couple dozen of you gave excellent considerate answers in my other E=mc2 posts, so I'm hoping to get your personal opinion on Pop Science for curious kids and adults. From your posts I'd say most of you (probably all teachers) have been very patient...
  10. S

    The relationship between F=ma and E=mc2

    I'm wondering about the relationship between F=ma and E=mc2. Is it simply that, at relativistic speeds, E=mc2 replaces F=ma? (much like D = v x t is replaced by the Lorentz Contraction at relativistic speeds)
  11. E

    Bohr model and relativistic electron mass

    From the semi-classical Bohr model of the hydrogen atom the velocity of the electron in a certain orbit can be determined. With these velocities the electron's relativistic masses can be determined. With E=mc2 the energy levels are in agreement with those from the Bohr model. I know Bohr's model...
  12. Keermalec

    E=mc2: What is the Term for this Energy?

    Is E=mc2 the potential energy of a mass m? Is it the maximum energy such a mass can have? What is the correct term used to denote E in this context? For example, if an object is traveling at 10% of the speed of light, could one say it has a kinetic energy of 0.5 x m x 0.1² = 1/200th of its...
  13. E

    Converting Matter to Power: Calculating Mass for 3200W of Energy for 3 Days

    Homework Statement What mass of mater would be converted to energy to provide 3200W of Power for 3 days? Homework Equations P=E/t E=mc2 The Attempt at a Solution [/B] E=P*t Subbing mc2 for energy I get mc2=P*t m=P*t/c2 m=(3200W*3Days)/(9X1016m2/s2) m= 1.066X10-13kg This answer is...
  14. I

    Einsteins thoughts behind c2 in E=mc2

    I've seen a previous threads where it was a mathematical consistency based on four-dimensions, and a host of other reasons. I'm currently trying to reconcile my belief that it has to do with time dilation and the observer effect.
  15. L

    E=mc^2 vs energy in strong interaction

    Hi everyone, I have a simple and foolish question. I want to compare the energy of a given mass (obviously e=mc2); let's say the energy of a hydrogen atom, with the energy that binds together the fundamental particles of that atom (strong interaction). I know that e=mc2 holds always true, and...
  16. A

    E=MC^2 Explained: Photon Mass & Energy

    A photon has “zero” rest mass, but it does have Energy, But with zero Mass , E=MC^2 yields E=0 I am confused !
  17. A

    Uncovering the Constant C: Equal Mass Equals Equal Energy?

    Since C is constant, so all matter of equal rest mass have the same E ?! e.g. an equal rest mass of water and rest mass of Uranium have the same energy ?
  18. H

    Calculating Q-Value for given Beta- decay

    Hello, I've recently started studying Nuclear physics and would appreciate help from someone who could clarify my doubt. Given Problem: 19O -> 19F + e + v Calculate the Q-value in the given decay using following data: Atomic masses: 19O 19.003576u 19F 18.998403u The problem that I'm having...
  19. D.R.U

    What happens to electric charge in the destruction of mass by E=mc2?

    If m mass is complete ly distroy by e=mc2...then what happen about electric charge and magnetic energy?
  20. S

    Can We Harness Energy from Light to Power Space Travel?

    Hey guys, my mind has been racking for the past week or so, and I'm just wanting to make sure I have all the right info. At first, I was like, "How long would it take to get to Gleise 581 g if I accelerated at 1 g for a year and coasted". That was pretty cool to think of and get the math and...
  21. A

    Questions about e=mc2 and probably other equations

    Hello, So, I was wondering something about the units used with other units in a equation like e=mc2 For example; m = 1.67x10^24 grams c = 292.792.458 m/s that makes e about 1.437x10^-8 but what is the unit used to represent e in this context? and what if I used kg in m and km/s in c, what...
  22. K

    E=mc2 is more complicated that I originally thought

    I've been reading up on radiation and it appears to me that if you add up all of the protons, neutrons, and electrons in the universe, the number would never change (except for temporary positron borrowing). I guess this is no surprise considering conservation of matter. On the other hand...
  23. G

    Unraveling the Mystery of e=mc2: How Much Mater is Needed?

    e=energy m=mater c=speed of light Squared. i am not one of you. I am a simple joe. so. energy =mater times the speed of light. Times the speed of light. ? or energy=mater times (ℂ time ℂ) ? (aprox 36 trillion)Next question. If we know the formula, what are the measurements? are we talking...
  24. L

    Rohrlich's derivation of E=mc2 wrong?

    http://en.wikipedia.org/wiki/Mass%E2%80%93energy_equivalence#Alternative_versionAccording to Wikipedia, "The velocity is small, so the right-moving light is blueshifted by ... Doppler shift factor 1-\frac{v}{c} But 1-\frac{v}{c} should not be applied under relativistic conditions. The...
  25. N

    E=mc2: Understanding the Squaring of Light Speed

    E=mc2. I am an avid reader of physics and science in general and a question popped into my head concerning the squaring of the speed of light in the equation E=mc2. It is my understanding that the speed of light is constant it does not accelerate. What rule or mechanism or whatever allows for...
  26. K

    Exploring the E in E=mc2: Wave Motion & Energy

    i'm really a beginner in this topic. So, I'm really confused even about this simple thing an object has so many types of energies like energy due to mass in it, kinetic energy, pot. energy etc. So does the 'E' in E=mc2 give sum of all these energies or only the energy due to mass? also...
  27. K

    Where Can We Find Anti-Particles for E=mc2 Energy Release?

    I have been doing research in e=mc2, and to release the energy , you have to get an anti-particle to collide with the particle equivalent to a specific value of energy. Now i want to know where do you get this anti-particle, or is it just theoretically described?
  28. J

    Just some basic question on e=mc2

    I know that any time energy is generated, you can use the equation in the form of E = mc^2. Also, that energy becoming matter can be described as m = E/(c^2). But, going as those are, is it also assumable that you could say c^2 = m/E? In other words, would the speed of light in a perfect...
  29. D

    Question about rearranging formula in Brian Cox's Why Does E=MC2

    This has been driving me insane. I don't get how he went from s/c to t/y. If someone could explain step by step how you do it I would greatly appreciate it.
  30. narrator

    History Exploring the History of E=mc2: How Did Einstein Discover His Famous Equation?

    I've been Googling to find out how Einstein worked out his famous equation. Some texts (that may or may not be factual) suggest it was an educated guess and not even expressed as the equation initially. Wiki http://en.wikipedia.org/wiki/E%3Dmc2#Einstein:_mass.E2.80.93energy_equivalence" that...
  31. A

    Unraveling the Mystery of E=mc2: Speed of Light

    i know this might be a dumb question but it was in my head and i would love to hear an answer, so the famous E=mc2..e obviously energy, m mass, c is the speed of light, but what speed of light? we all know that c is constant at vacuum but it changes when it goes through another medium like...
  32. F

    Answer to light speed travel is E=mc2 itself?

    First off, I'm new here so if this is in the wrong section I apologize. Now to the question: As dumb as this may sound to people that know more about physics then me (I'm a med student but I find myself reading about physics time to time) it makes perfect sense in my head (due to lack of...
  33. Z

    E=mc2 How did Einstein get to this equation?

    How did Einstein get to this equation?...I mean the math behind it and why E=mc2? why not F=mc2? we can get so much force from m*c2 right? but why did Einstein write E=mc2? :smile:
  34. C

    Can Lasers Produce Matter Through 'Collisions'?

    We all know about particles colliding and producing various other particles plus energy i.e. EM radiation, but is the reverse possible? Is it be possible for laser beams to 'collide' and produce matter? Has this been done experimentally or is there a theoretical reason that it cannot happen?
  35. bcrowell

    Interpretation of Einstein's E=mc2 paper

    In "Does the inertia of a body depend upon its energy content?," http://fourmilab.ch/etexts/einstein/E_mc2/www/ , Einstein says: My interpretation of this is that these energies contain both potential and kinetic terms. A potential energy U is only defined up to an additive constant. If, for...
  36. S

    E=mc2 involve mass and energy as relative values?

    Homework Statement Einstein's E=mc2 Homework Equations E=mc2, mass dilation, relativistic energy. The Attempt at a Solution Does Einstein's E=mc2 involve mass and energy as relative values? or does the equation mc2=moc2+Ek ie: the same eqn just with mass dilation and...
  37. M

    Ed: The Significance of C in E=mc2 Explained

    Basic Question: Of the infinite number of other values which could have been the multiplier in E=mc2, it surely cannot be a coincidence that the value of the speed of light squared was the number. So why c? Ted
  38. O

    E=mc2 | If something has near zero mass, can it move?

    Ok, I'm still only in high school (UK) and we haven't covered Quantum Physics yet, but I know a thing or two; however, don't get mad if I get something wrong. So here's my question: Am I correct by saying that if something has let's say theoretically 0 or near 0 mass it would not be able...
  39. G

    E=MC2 vs. m² = E² - p²: Motion vs Rest

    Okay, so I know that E=MC2, is an equation in regards to an object at rest. But I recently came across another formula: m² = E² - p²; in the description, it stated, that it was basically E=MC2, in regards to an object in motion. Is this information valid?
  40. K

    How did Einstein Use Minkowski Spacetime to Derive E=mc2?

    There are many derivations of E=mc2 out there, but did Einstein actually used Minkowski space time for his original derivation of E=mc2? How did he do it?
  41. P

    Understanding Einstein's Theory of Relativity

    I'm not really a physics genius or professor so forgive my lack of knowledge. I was thinking about Einstein's theory of relativity earlier,then it just popped into my head doesn't that contradict The Law of Conservation of Charge?Ex:111grams of hydrogen = 10,000,000,000,000,000 Joules.but in...
  42. T

    Solving E=MC2: What Does C2 Imply?

    So, I understand the implications (basically, anyway) of solving the equation E=MC2 for E, and solving for M. But, what is the implied outcome of solving for C2? Just curious because the concept of C2 would imply faster-than-light velocity of something in my mind. Of course, my flawed thinking...
  43. H

    E=mc2 and Postulates to prove it

    As we know very famous equation E= mc2 While deriving this equation there are two postulates Postulate I: The laws of physics are the same in same in all inertial frames. Postulate II: The speed of light (in a vacuum) has the same constant value c in all inertial frames. If we...
  44. A

    Exploring the Intriguing History of E=mc2: A Review of David Bodani's Book

    I'm 3/4 of the way through David Bodani's, E=mc2: A Biography of the World's Most Famous Equation book and I'm really enjoying it. Thanks to this book, I finally understand that "e=m" and also understand why "C^2", but I still can't understand why Einstein used the speed of light to connect the...
  45. B

    What is the relationship between the strong force and E=mc2?

    I have read that the strength of the strong interaction between two quarks is roughly the same as the weight of a 10 tonne truck (i.e. 105 N). There is a relationship between Force and distance and work and energy and mass (and I am aware of the extent to which Newtonian mechanics is...
  46. F

    How to Get E=mc2: Exploring Einstein's Equations

    Hi Somewhat usual question for you guys I guess. How do we get the formula E=mc2? I saw in a video where it said Einstein combined these equations Mv=E/c t=L/c x=vt Mx=mL and got EL/c2=mL => E/c2=m But I don't quite follow. What is Mv? What is Mx? And what time does L/c...
  47. I_am_learning

    Derivation of E=mc2: Examining Einstein's Theory

    I have looked at the Einsteins Derivation of the Relation E=mc2. http://www.adamauton.com/warp/emc2.html But I don't if this shorthand derivation is O.k. or not. like the derivation, I use maxwells law and say the momentum p is given by p = E / c ---> 1 Now from Newtonian mechanics, we...
  48. H

    Solving the Mystery of E=mc2: Exploring c2 and Potential Energy

    Okay, I started thinking about relativity earlier, and got stuck on how to square speed. I went with some basics to try and figure it out, this is some of what i came up with; Main Question: Does (10mph)^2 equal? A. 10 m^2 per h^2 B. 100 m^2 per h^2 C. 100 mph Logically "B." makes...
  49. V

    Understood this equation e=mc2

    I think i have understood this equation ( don`t be to hard on me, only 15 and have just started to read physics ). As i understand it says the following : Energy can be turned into mass, and mass can be turned into energy. It also says how much energy you get if you turn mass into energy...
  50. T

    Understanding the Relationship Between Matter, Energy, and the Speed of Light

    I'm a layman, not a mathmetician or physicsist so go easy on me ok? Can somone explain in reasonably easy to understand terms, why does the energy content of some given quantity of matter depend on the speed of light? or the square of the speed of light. Why does the speed of light have...