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.

View More On Wikipedia.org
Recent contents Top users
  1. K

    Wondering e=mc^2 is derived from what equations

    i was just wondering e=mc^2 is derived from what equations and is linked to which other.
  2. Y

    Is E=mc^2 Fully Proven or Still Up for Debate?

    so this guy who says he's a computer science major said this. "E=MC^2 but for rigor you must prove and demonstrate M=E/C^2 as well of your proof to be complete.". and because of that he says E=mc^2 is not fully proven. inputs?. is he right or wrong?. thanks.
  3. M

    The Mystery of c^2 in Einstein's Famous Formula E=mc^2 Explained

    Why c^2 in "e=mc^2"? Ok, i'v got that e=mc^2 meens some mass at max possible speed will equal max possible energy. But max possible speed is c, not c^2. Nothing can have speed greater than speed of light, isn't it?
  4. A

    E=mc^2 and gravitational potential energy

    So, I've heard that if you lift a boulder into the air, it's mass increases slightly as per e=mc^2. Well, my question is, does gravity act on this new mass? If so then shouldn't it have slightly more gravitational potential energy, and thus slightly more mass etc. ad nauseum? Would the...
  5. F

    What does E=mc^2 mean? How can it be used in an example?

    I was trying to be more clear on how this equation works. I appreciate any help.
  6. N

    Clarification on 1st law of thermodynamics and e=mc^2

    I'm sure each of you is well-versed in the first law of thermodynamics: energy cannot be created or destroyed. Thus, there is the law conservation of energy. E=mc^2 states that energy and mass are functions of each other, basically one and the same less a conversion factor. I take mass to...
  7. R

    E=mc^2 can C^2 be described as a physical process?

    I have always had trouble appreciating E=mc^2 because I can't relate C^2 to a physical process, like velocity or acceleration. How should one imagine the dimensional characteristics of C^2? Along the same vein, is E=mc^2 a mathematical conversion only, or does C^2 describe an actual process by...
  8. Rasalhague

    Shady Crypt Observatory E=mc^2 derivation

    http://www.shadycrypt.com/ After equation (27) it says: "Keep in mind that we are not talking about the kinetic energy of the entire apparatus – only the kinetic energy of the mass associated with the pair of light rays that were measured. Since the moving observer measures higher radiated...
  9. E

    E=MC^2 and the creation of mass

    First of all, if anything in this post is incorrect I'm sorry. My physics is still developing and I hope to learn a lot here! So, E=MC^2 states that mass can be converted directly into energy, and a he'll of a lot of it, correct? However, energy cannot be created or destroyed, only...
  10. majormuss

    How Much Energy Is Released in Tritium Nucleus Formation?

    Homework Statement A tritium nucleus is formed by combining two neutrons and a proton. The mass of this nucleus is 9.106 × 10–3 universal mass unit less than the combined mass of the particles from which it is formed. Approximately how much energy is released when this nucleus is formed...
  11. T

    Is There a Basic Element That Connects All Matter and Energy in the Universe?

    So what exactly E=mc^2 says ?? ok all know E=mc2. but apart from that small matter is equi to huge amount of energy what other things can be derived. 1) how could matter directly relate to energy and not individual elements like Uranium, hyd etc. doesn't it mean that all elements and made...
  12. J

    Having trouble with Einstein's Derivation of E=mc^2

    Also posted this in the SR and GR forum, but wasn't sure which was more appropriate. Hi, I'm a non-physics student trying to use primarily Einstein's original 1905 essay to write a paper on the philosophical questions that E=mc^2 brings up. However, I've hit a snag which I can't seem to get...
  13. J

    Question about Einstein's Original E=mc^2 derivation

    Hi, I'm a non-physics student trying to use primarily Einstein's original 1905 essay to write a paper on the philosophical questions that E=mc^2 brings up. However, I've hit a snag which I can't seem to get past. Einstein essentially uses what he's proven about the Doppler shift to show that a...
  14. G

    Using e=mc^2 to calculate electrical properties

    from rearranging e=mc^2 i got time equivalent to (kg m^2/(A V) (kilogram meter squared per ampere volt))^(1/3) so if i have a material that is 1kg, 1m long, has 1amp, and 1volt, what does the time attribute mean? is that the amount of time it takes an electron to travel from one end of the...
  15. R

    Understanding the Equation E=mc^2: Any Thoughts?

    I'm new to the forum and I'm not being purposefully thick, but has anybody wondered how this equation works? I mean if c is the fastest anything can go, then what sense does it make to use a quantity like c^2? Thanks!
  16. J

    Is this explanation of E=mc^2 correct or incorrect and why?

    Hello, I came across the following explanation of E-mc^2 on pbs.org: "So why would you have to multiply the mass of that walnut by the speed of light to determine how much energy is bound up inside it? The reason is that whenever you convert part of a walnut or any other piece of matter...
  17. C

    Apparent paradox: e=mc^2 violates conservation of energy?

    Take two uncharged particles (e.g., neutrons) at rest with respect to one another in empty space. Now apply 1 Joule of energy to accelerating them apart. They will eventually come again to rest with 1 Joule of gravitational potential and accelerate back together due to gravity. Their kinetic...
  18. Q

    Explaining E=mc^2: What Does It Mean Physically?

    Could someone explain to me, what does E=mc^2 mean? I've got a feeling that this famous relation is just a definition of m. First, if we use an old version E=mc^2\:\:(1) where E is total energy and m is relativistic mass, then is there a way to measure m and E independently so that this...
  19. S

    Why is c squared in Einstein's equations?

    Now i know it will be impossible to explain to me in depth on a forum the full explanation of the equation. But maybe you guys could give me some pointers as to why in so many of einsteins equations the speed of light is squared. Is it because of the fact that if u had a flashlight traveling at...
  20. F

    Does the Higgs violate E=mc^2?

    The Higgs boson couples to all particles with mass. But even a photon has, through E=mc^2, an equivalent mass. Therefore, the Higgs should also couple to the photon. But every text says that it does not, because it is uncharged. How can this paradox be solved? François
  21. P

    Matter @ speed of light and e=mc^2

    I seem to have read that matter can't be accellerated to the speed of a photon because it would take an infinite amount of energy. But it seems that mc^2 = E means that matter can be transformed to E (and doesn't E move at the speed of light?)
  22. A

    E=mc^2 and is it possible E/c^2=m

    can anyone explain in simple terms Einstein's equation E=mc^2 and is it possible E/c^2=m, because it is said mass can neither be created nor destroyed!
  23. B

    Derivation of E=mc^2 in Wikipedia

    http://en.wikipedia.org/wiki/Kinetic_energy#Relativistic_kinetic_energy_of_rigid_bodies" derives the kinetic energy of a rigid body at relativistic speed to be E_k = m\gamma c^2 - m c^2 The continue to say: Can anybody explain this reasoning? Just because the zero value of the kinetic...
  24. M

    Energy is neother created nor lost? How about E=mc^2

    Hi, I know that energy is neither created nor lost based on everyday observation but how about E=mc^2 when mass converts to energy. Do physicist consider that as energy created because mass is loss while it creates a huge amount of energy.
  25. M

    Solving E=mc^2: Exploring the Error in Results

    I was doing the equation of E=mc^2 So its like this: If M = 1kg and C=300 million m/s, Then E= 1 x 300 million x 300 million = 90 000 million joules/90 billion joules But the qs is, If I convert c to 0.3 billion m/s, then E = 1 x 0.3 billion x 0.3 billion = 0.09 billion joules...
  26. T

    Math Proof for E=mc^2 | Find It Here

    Is there a mathematical proof or derivation for E = mc2, and if so, where can I find it?
  27. timallard

    Electron mass/energy do not conform to e=mc^2

    Using E=mc^2, if you use the standard Coloumb charge for an electron and the typical value in textbooks for its mass, the difference is 10^5 off, it's way too heavy, 9.11x10^-31 vs 1.78x10-36 kg. What does this difference represent, shouldn't the mass conform to the equation for that energy...
  28. C

    How does the theory of relativity explain changes in mass and energy?

    So, by the theory of relativity: m=\frac{m_{0}}{\sqrt{1-\frac{v^2}{c^2}}} But then, we have E=mc^2. So if you have (relative to YOU) a very fast moving body, when it radiates, the radiation is actually of higher energy than it would be if the body was static?
  29. F

    Understanding E=mc^2: Exploring Total Energy of Objects and Particles

    If we want to know the totality of the energy of an object/particle do we only have to look at the mass, since mass changes with speed, or do we have to also add the classical kinetic energy of the object to the changed mass energy? I think it is is former but it is not obvious to me right...
  30. N

    E=mc^2 in 1,2,3,5,6 dimentions?

    maybe the universe works in a 4-D environment because a 3-D(two space axis, one time axis) environment will not allow sufficient energy exchange, and movement in 5-D needs too much energy? just some speculations... anyone more knowledgeable on this subject who can help me?
  31. X

    What Is the Momentum of a Particle with Energy Four Times Its Rest Mass?

    What is the momentum of a particle whose total energy is four times its rest energy? Give your answer as a multiple of mc. Well the rest energy of an object is E=mc^2 so the total energy for this particle would be E= 4(mc^2) in order to achieve this Energy value the Lorentz factor would...
  32. P

    Relationship between E=mc^2 and gravity

    As I understand it, a way to look at E=mc^2 is to think of it as the energy required to accelerate a given amount of mass. I also understand that mass warps space-time creating an acceleration (gravity) in objects near that mass. Is there a direct correlation between the energy required to...
  33. N

    Is E=mc^2 a Relativistic Concept? Exploring the Origins of the Famous Equation

    While searching the net I've come across numerous derivations for the equation of E=mc^2, the most understandable of which I found to be the photon-in-the-box momentum derivation. However, this derivation and other ones don't necessarily seem to be based on Special Relativity. So my question is...
  34. L

    Understanding E=mc^2: Explained in Plain English | Junior's Dilemma

    I have read the wikipedia article on this but my mind just can't seem to comprehend the meaning of this equation. I maybe unconsciously thinking too hard...but I'm still junior... Someone please explain the meaning to me in plain English. :) PS: BTW, did this equation lead to the discovery of...
  35. A

    How to apply e=mc^2 to a photon?

    Hey can sum1 please tell me if we can apply e=mc^2 to a photon? Also if the energy of a photon is relative and speed of light isn't relative and e=mc^2*lorentz factor then how is energy of a photon relative in the above Case?
  36. D

    Is this a valid derivation of E=mc^2?

    I'm just a high school student and thus not particularly knowledgeble about special relativity. However, I've always wanted to find a derivation of the famous equation E=MC^2. I could never find one in textbooks or on the web that didnt rely on oversimplifications or unexplained steps, so I...
  37. L

    Does velocity dammage e=mc^2?

    Does velocity "dammage" e=mc^2?? hi there, this is my first post in this forum, so i can begin to introduce myself: i'm 17 years old and i really enjoy logic, as physics has matematics(that is logic) and make me think(use the brains, you know) i love it more than any other subject:-p , I'm from...
  38. R

    How Do Quark Matrix Masses Relate to Einstein's E=mc^2?

    Recently I have managed to understand some basics of the Standard Model and even have written some note about it (see http://arxiv.org/abs/math.DG/0605709" ). The quark masses there are matrix quantities. Two tripples of quarks (the upper row - one from each generation and the lower row - one...
  39. P

    Unraveling the Mystery of E=mc^2: The Surprising Truth About Light's Energy

    "I believe E=mc^2 works." But! Photon (Packet of energy as described by Einstein in 1905, "Photoelectric effect") is mass less particle. So, the relation suggests that light should not have energy, though it has. Is this wrong, if yes why?
  40. DaveC426913

    E=mc^2 in Natural Units: Understanding the Meaning of c^2

    Somewhere a month or two ago, there was a discussion about E=mc^2 and the question of what the c^2 represents. The answer was that c^2 was simply a conversion unit, to put it in more common units of kg, m and s. That, if the formula were considered in more natural distance units of light...
  41. M

    Do we lose weight through exercise according to E=mc^2?

    Do we lose weight through exercise according to that equation? I mean fat is turned to heat during exercise right?
  42. H

    Energy-mass equivalence - E=mc^2

    We all know that if we break up an atom, we get a lot of energy in return. I'm having trouble visualizing what this equation actually means. Does it mean that a large amount of energy is required to bring matter together? Does it mean a large amount of energy can be converted mass? Isn't energy...
  43. D

    Can Black Holes Be Used as a Source of Antimatter?

    Just curious about the energy/mass relationship and how it factors in when making nuclear weapons. (or hopefully a more peaceful use for such a reaction in the future.) I know manhattan era nukes used plutonium and polonium/ beryllium for fission reaction. Einstein's famous equation would have...
  44. U

    E=MC^2: Exploring the Connection Between Matter and Energy

    I have read a bit on E=MC^2, and would I be correct in saying that matter and energy are essentially the same thing? I was wondering about this because I asked my Physics teacher and she said that matter and energy are two separate entities. but can't matter be converted into energy? It would...
  45. M

    Discover the Method to Derive E=mc^2 - A Comprehensive Guide

    Hi, I am very eager to know how to derive e=mc^2. I am sure that you all would be knowing how to derive the world famous equation E=mc^2.i know the basics but still it is a tough job to explain that. But I am hoping that you would send me a reply as soon as possible. Thank you
  46. D

    The Significance of C in Einstein's Famous Equation E=MC^2

    Why "C" in E=MC^2 What special property of the speed of light imposes itself on the amount of energy in a mass? Why should that energy be an exact multiple of the speed of light squared? Why not a multiple of some other constant like the Bohr radius, the Boltsmann constant, or the free...
  47. ZapperZ

    Confirmed: E=mc^2 Validated Once Again, Despite Skepticism | PhysLink

    Was there ever any doubt? The more they test it, the more convincing it becomes. But I don't think the quacks will be satisfied with this. http://www.physlink.com/News/051229Emc2Einstein.cfm Zz.
  48. P

    D - E=mc^2 for ordinary matter

    I saw in a TV show about E=mc^2 by NOVA that a physicst said that it was possible to convert the mass of for example, an ordinary pen into lots of energy through E=mc^2 I know how energy can be unlocked from Uranium atom but how could one unlock the energy from an ordinary pen? Would it take...
  49. C

    E=mc^2 in gravitational fields

    hi, i have recently been studdying relativity and the whole e=mc^2, mass energy exchange stuff... and i have a major question (in my mind) that i can't get answered, sincei don't have a teacher, i thought this would be the best palce to come... What happens when you start accelerating an...
  50. B

    Experiment evidence for E=MC^2

    I have a question that asks for experimental evidence for Einsteins famous E=MC^2 equation that isn't from an astrophysics, but the only evidence I can think of is nuclear fission, but I'm sure this occurs in stars in some way. Would this count as evidence that isn't from astrophysics or would...
Back
Top