What is Mass-energy equivalence: Definition and 24 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. Stephen Bulking

    I The Tritium Puzzle: Unravelling Mass-Energy Equivalence

    I was finding the energy required to separate tritium into it's component parts, the binding energy when it hit me that how could 1amu= 931.2 MeV and 1.66e-27 kg at the same time?
  2. P

    I Time Dilation, Mass-Energy Equivalence: Implications for Time Passage

    I'm an amateur physics enthusiast, and there is a question that's been in the back of my mind for some time that I haven't been able to answer on my own, and haven't gotten a satisfactory answer elsewhere. First, I want to define a couple of terms and make sure my understanding isn't breaking...
  3. F

    I The new definition of kg and the mass-energy equivalence

    Hi, today I stumbled upon a 2016 article in Scientific American about the (then) possibility of re-defining the kilogram through Planck's constant. The article is really a very quick review of the topic. At some point the author states the following "So for years, physicists have chased an...
  4. Robin04

    I Transition between energy and mass

    How well is the transition between energy and mass understood? Energy can turn into matter and matter can turn into energy but what is actually happening between the two states? Imagining that matter just simply appears and disappears under an infinitesimal amount of time feels weird to me.
  5. A

    B Mass-Energy Equivalence: Matter as Potential Energy?

    I think mass as a form of potential energy and am always told that this is wrong. According to wiki: "In physics, potential energy is the energy possessed by an object because of its position relative to other objects, stresses within itself, its electric charge, or other factors." Why do this...
  6. arupel

    I Exploring Mass-Energy Equivalence: What Causes Different States?

    I am not sure exactly what E = mc^2 means. 1. Does it simply means if we were able to convert mass into energy this is the amount of energy. 2. That mass and energy are different states of the same thing. An example would be water which can either be a solid (ice), a liquid (water) or a...
  7. Comeback City

    Mathematical Proof that Photons have No Rest Mass

    Using these equations I am about to prove that photons have a rest mass of zero (mathematically) ________________________________________________________________________________________ E=hc/λ Photon Energy Equation E2=(pc+mc2)2 Mass-Energy Equivalence with Momentum Equation p=h/λ Momentum...
  8. S

    What is the correct value for the mass-energy equivalence of an alpha particle?

    Homework Statement Calculate the energy equivalent of the mass of an alpha particle. alpha particle (amu) = 4.00150618 u 1 amu = 1.660566*10-27 kg 1 amu = 931.5020 MeV alpha particle (kg) = 6.64465675 * 10-27 kg Homework Equations e = mc2 The Attempt at a Solution 931.5020 MeV *...
  9. E

    Understand Mass-Energy Equivalence: Einstein's Thought Exp.

    In the Wikipedia entry on mass-energy equivalence*, there is a reference to an elementary derivation of mass-energy equivalence in an article by Rohrlich (AJP 1990), which apparently expands on the original thought experiment by Einstein (ie observer in middle of moving train, light pulses...
  10. L

    Entery level Mass-energy equivalence questions

    Homework Statement The diagram shows a proton moving with Ek of (0.178)(10-12)J towards a stationary nucleus X. The proton hits X and is absorbed. The resulting nucleus splits into two alpha particles, which move off in the directions shown with equal Ek of (1.481)(10-12)J 1. Calculate the...
  11. C

    Help Me Find Mass-Energy Equivalence Formula!

    Simple algebra to find the strict mass–energy equivalence formula, and I can't do it! find ((m^2)*(c^4)=(E^2)-(p^2*c^2)) from (E=m*c^2*y) (p=m*y*v) (y=1/(1-(v^2/c^2))^(1/2)) Yeh i can find the m^2c^4 parts and the E^2 obvioulsy. but then i am stuck with E^2(v^2/c^2) when instead i want...
  12. J

    The Full Equation for Mass-energy Equivalence

    Hi. I've seen a video by MinutePhysics that talked about the mass-energy equivalence equation, usually known as E=mc^2. It said that there is an extra part to it, and I didn't really understand what it meant. (E^2)=((mc^2)^2)+((pc)^2) seems to be the full one (p being momentum) So...
  13. H

    Mass-Energy Equivalence and Storng Nuclear Force

    This really isn't a homework question per se, but I really don't want to post in the big boys' fora. I am learning about basic modern physics at school, as the title suggests, but I am very confused on one matter. Take the tritium nucleus as an example. If tritium nucleons are separate...
  14. S

    About Relativistic Mass-Energy Equivalence

    While I was looking up E=mc^{2}, I have learned such formula only applies to stationary objects and for kinetic object, the formula is this: E_{r}=\sqrt{(m_{0}c^{2})^{2}+(pc)^{2}} Where E_{r} is relativistic energy and m_{0} is rest mass In the formula, what is p and what is (pc)^{2}...
  15. J

    Implications of the Mass-energy equivalence

    Hello All, Let m be a mass, equivalent to energy E such, that E=mc^{2}. Does it follow that c is the cosmic speed limit? ====================================== To say the above with more words: 1) m is a mass 2) in some process, it is established that through...
  16. J

    Question on Mass-energy equivalence

    Hello All, is the following in principle, correct: Scenario A:------------ 1A) A box with mass M contains mass m, their weight is g(m+M) 2A) the mass m is (somehow) converted to energy E=mc^{2} 3A) at this moment, the box still has weight g(m+M) Scenario B: ---------- 1B) A box...
  17. S

    Mass-energy equivalence and how it relates to the content of the universe

    I've always been interested in Physics so have finally decided to do a Physics degree. I've been reading various things to help prepare myself and have just been reading about the laws of thermodynamics and mass-energy equivalence. As I'm reading through different articles about these subjects...
  18. K

    Can more than one photon participate in pair-production?

    Pair-production is the event when a particle and anti-particle is created from a single photon. We don't see 2 or more photons participating in a single pair-production event. Further, it seems in all the events of energy-mass conversion, photons act independently. Two or more photons can...
  19. V

    Unraveling the Mystery of Mass-Energy Equivalence in Nuclear Reactions

    I was reading WikiPedia's entry on this, and there was one paragraph that surprised me: E = mc2 has sometimes been used as an explanation for the origin of energy in nuclear processes, but mass–energy equivalence does not explain the origin of such energies. Instead, this relationship merely...
  20. S

    Can someone explain the concept of Mass-Energy Equivalence in simple terms?

    Homework Statement My textbook is only confusing me further and I need to understand this for a presentation in front of the class! The chapter is entitled Mass-Energy Equivalence, with sub titles Relativistic Momentum and Relativistic Energy. I don't understand relativity, I'm reading the...
  21. A

    Can Energy be Converted into Mass?

    So, there are tons of examples of mass being converted to energy, but can energy be converted to mass? Thanks
  22. S

    Einstein's box in media and mass-energy equivalence

    Einstein proposed a very simple derivation to E=mc^2 in 1940s which is well-known as Einstein’s box and a brief introduction is in http://galileo.phys.virginia.edu/classes/252/mass_and_energy.html . If this event occurs in media instead of vacuum, the light speed should be u=c/n rather than c...
  23. H

    Mass-energy equivalence where's the arbitrary constant?

    I'm curious about the famous formula, e=mc^2 . Since mass can be measured in any of several unit systems, shouldn't the formula read e\propto mc^2 ? Thanks!
  24. quasar987

    Exploring Mass-Energy Equivalence and Nucleons

    I was thinking just a moment ago and fragments of random knowledge and ideas gathered to make this question... If I remember my college physics class correctly, an evidence of the mass-energy equivalence is that in an atom, the sum of the rest masses of the nucleons is greater than the rest...