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. 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...
  2. 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 !
  3. B

    Can Energy Equal Mass if c=1 in Particle Physics?

    Since in particle physics c can be take to equal 1, does this mean that Energy can equal mass if we use electronvolts ?
  4. R

    E=mc^2 Proof: Is it OK? - Adam Aulton

    http://www.adamauton.com/warp/emc2.html
  5. R

    How does one get time dilation, length contraction, and E=mc^2 from spacetime metric?

    How does one get time dilation, length contraction, and E=mc^2 from the spacetime metric? Suppose all that you are given is x12 + x22 + x32 - c2t2 = s2 How do you derive time dilation, length contraction, and E=mc^2 from this? What is the most direct way to do this?
  6. svenskaTom

    Using E=mc^2 does thermal energy add to an object's mass?

    Hi everybody, I hope this is the appropriate place to post this question: A middle school physics book here in Sweden poses this question after giving a brief explanation of E = mc2: For you Swedish speakers here is the original text: So my answer is "Yes" to both since the additional...
  7. O

    Deriving E=mc^2: Special Relativity Explained

    Reading into some special relativity, I have seen E=mc^2 proposed from the assumption of four momentum conservation and the fact that the 'mass' component varies with velocity with the gamma factor, like a kinetic energy. This seems a bit of a leap of faith to me so I was wondering if there...
  8. B

    Calculating Sun Mass Loss Over Time Using E=mc^2

    I am working on a question: Doing this, the Sun produces it luminosity, the 3.8 × 10^26 Joules of energy it emits each second. Use this information to determine the percentage decrease of the Sun’s mass over its total lifetime of 10 billion years. It's a multiple choice question and each...
  9. R

    Playing with E=MC^2: Exploring Energy Conversions

    Hi all, I've been teaching myself about energy unit conversions (because I never paid attention at school) and just wondered if someone could check my math please? It's not a homework question - I've not been to school for 10 years! Just a curiosity on my part... I was trying to work out...
  10. A

    E=mc^2 in a gravitational field

    Let us say that we have small object of mass ##m## at some location far away from the Earth (with zero velocity compared to the earth). The energy of this object is according to relativity ##E=mc^2##. Now we drop this object and it starts falling towards the earth, transforming potential...
  11. J

    E=mc^2 states mass and energy are interchangeable but ?

    e=mc^2 states mass and energy are interchangeable but ?? But daltons law of constabt mass is voilated as states that while a reaction the mass of product = mass of reactant any explanations?
  12. J

    How does E=MC^2 convert to Joules?

    How does E=MC^2 convert to Joules? How can the speed of light measured in m/s and mass measured in grams convert to joules?
  13. J

    Meaning of E=mc^2: Are Mass and Energy the Same?

    I recently came across an article from Stanford Encyclopedia of Philosophy titling "The Equivalence of Mass and Energy" (link: http://plato.stanford.edu/entries/equivME/#2.2 ) which has really confused me about the nature of mass an energy. The article contains many interpretations of...
  14. F

    What is the status of E=mc^2 in QM/QFT

    I mean is the formula taken as a postulate or can we derive it from QFT at least?
  15. F

    Does E=mc^2 apply to the proton

    Most of the proton REST mass is energy anyway. So how does that work?
  16. B

    Visualizing Mass Acceleration to Speed of Light: Is E=mc^2?

    A long time ago I visualized mass accelerated to the speed of light(or theoretical maximum to this speed) as an upside-down parabola touching the y=0 line. Now, today I thought of the following: if you would represent a certain parabola(equation according to ^2 of the mass/energy ratio...
  17. Z

    Explaining E=mc²: Simplified for 12-Year-Olds

    explain it like I am 12 years old.
  18. K

    How Do Planck's Constant and E=mc² Interrelate in Physics?

    1.how to derive the Planck's constant ? how does he found that?how can it be correct? 2.derivation of E=mc^2.
  19. M

    Calculating e=mc^2 using foot-pounds of force

    I have seen the on-line calculators, but would like to see how the formula works in full detail. I have seen the kilograms / meters / second example already. The second part of the question is, what is the actual formula for converting foot pounds of force to Newton meters? Again, the...
  20. J

    What is the relationship between mass and energy according to E=MC^2?

    Quick question... does that equation refer to any type of matter, like a point particle? Or does it refer to atoms that have nuclei that are attached by the strong force? Lemme put it another way. Take a point particle, an electron... now if you found a way to convert that single electron into...
  21. S

    E=MC^2 Mass and Energy, synonymous?

    Hello everyone, I just want to throw out a perhaps rehashed idea just to see people's opinions on the matter. Given Einstein's equation; E=MC^2 If matter could travel at the speed of light it would posses maximum kinetic energy; maximum energy or pure energy is a photon. Theoretically...
  22. M

    Is the Einstein equation E=Mc^2 correct?

    I wonder if Einstein equation E=mc^2 was used when the A bombes were designed and tested. How was the output estimated? Was all the matter thransformed into energy, as the equation indicates? Were there any restrictions to how this equation ( or nny other) was used? Thanks, Michael
  23. A

    What is the meaning of E=mc^2?

    Can someone explain to me this formula?
  24. E

    E=mc^2: What is Mass & Matter?

    Mass or Matter in E=mc^2 ?? I understand that m stands for mass but I thought matter was transformed into energy. Is matter what mass is made of? I just don't get it.
  25. D

    Questions about E=mc^2 - Understanding the Complexity

    Hi. I have some questions that I'm not sure about to do with this equation. I may just be missing something obvious but would be nice to get an answer nonetheless.. First is to do with the LHC. My understanding is that they are colliding particles at such force that they break down into...
  26. G

    Exploring the Relationship Between F=ma and e=mc^2: A Scientific Analysis

    Could this two equations be used together, since they have a common variable "m"? For example, you could deduce that the speed of light = sqrt(a*m), and since the speed of light is a constant, if acceleration goes up, then mass must go down. Is this true?
  27. Q

    What is the relationship between mass and energy according to E=mc^2?

    so... just learned about mass energy equivilance. 10kg object. e=mc^2 e=9*10^17which is insane. my mind is blown. wiki says this: I guess this implies some stoichiometry. Could someone give me an example of mass being conserved in a reaction like this?
  28. A

    Energy, Mass, & Volume: Exploring the Equivalence of E=mc^2

    1. Energy is proportional to mass. 2. Mass (of nucleus) is proportional to volume. 3. Volume can be determined from cross-sectional area. If this is the case, then is E=mc^2 equivalent to kE=(pi)r^2 where r is the radius of the nucleus and k is some constant?
  29. S

    Why Does E=mc^2 Imply Creation of Particles?

    Many references of quantum field theory begin with an explanation of the necessity of a field theory as opposed to a single particle theory. Sometimes they use the argument that E=mc^2 implies particle creation. For example, in Peskin "the Einstein relation E=mc^2 allows for the creation of...
  30. A

    E=mc^2, wikipedia says mass can't be turned into energy?

    Hi all, Recently, I was surprised to find that Wikipedia asserts that “rest mass” cannot be turned into energy via E=mc^2 (webpage link at bottom). If Wikipedia is correct, A) why don’t people conserve “rest mass” in high-energy reactions? B) How do I know when I have mass that can’t...
  31. N

    Can someone describe E=mc^2 to me in laymans terms

    Please do your best to describe E=Mc^2 to me in the most plain English you know and as basic as possible without leaving out details. Any links you think would help would be great. Thank you
  32. L

    Is the energy required for fission equal to that for fusion?

    Hi, this is my second year studying physics and few weeks ago we went into nuclear physics very briefly because we are learning it next year. I'm not sure if the energy required to fission is equal to the energy required to fusion. For example is energy required to fission hydrogen atom...
  33. J

    So what units should i use with E=mc^2?

    I guess this is a question about what units to use in any equation. Which ones pair together. If you use 300,000,000 m/s and 1 gram in e=mc^2, you will get 300,000,000, but what unit? Joules? How do you know which to use and which ones pair together?
  34. B

    Does Gravity Influence the Speed of Light in Space?

    Hi, Energy is mass times lightspeed squared. Outside our Earth spere there is zero gravity. Why wouldn't gravity determine lightspeed to be between 1 and 2 squared "c"?Is there a single variable for distance between the planets? This is induction, not sure what it means and what not. Is it...
  35. J

    Understanding the Equation E=mc^2 and Its Applications

    Homework Statement see attached question Homework Equations The Attempt at a Solution I chose A but this is wrong :S - why? The answer is C but I cannot see why B/D are wrong. I literally guess A as this was the only time I had used the fomula
  36. A

    Solving E=mc^2: What Units to Use?

    When solving with E=mc^2 what units should I use in the answer?? For example: (if I have an object with a mass of 43kg) E=mc^2 E=(43kg)(299792458m/s)^2 E=3.86464727 × 10^18 Now here's my problem, do I include units of J/kg (joules per kilogram) or eV (electron volts)?? If someone could...
  37. A

    Can quantum mechanics explain the relationship between mass and energy?

    E=mc^2 , defines mass energy "Equivalence", but after some surfing, I don't guess that Mass can be straight converted into pure energy. Is there any place which defines mass in terms of energy?
  38. C

    Derive E=mc^2 - Doubts at Red Place

    Hi Is this derivation of E = mc^2 correct? ... I have some doubt at the red place ... \large{ F = \frac{dp}{dt} = \frac{d}{dt}(mv) } \large{ F = v\frac{dm}{dt} + m\frac{dv}{dt} } Let this force cause a displacement dx \large{ dW = F \cdot dx } Assuming body was initially at...
  39. AakashPandita

    E=MC^2 Here,say we want to find the energy of a single

    E=MC^2 Here, say we want to find the energy of a single photon. that means, mass of photon x speed of light squared = energy of photon but a photon is mass less. isn't it? but how can a photon have no energy?
  40. C

    E=mc^2, but nothing can travel faster than light?

    I tried to find an answer to this here, but may have missed it. There must be a flaw in my understanding here, since it seems to be contradictory. Mass times the speed of light squared = Energy, and yet (according to Einstein), nothing can travel faster than the speed of light? I'm just...
  41. L

    What is the energy of a photon in relation to E=MC^2?

    E=MC^2 question about the "M" So, energy equals mass times the speed of light squared. Energy can determine speed, because the energy is transferred into the 3 spatial dimensions. My question is with E=MC^2 itself, Energy of light would equal zero mass times the speed of light squared...
  42. T

    Understanding Einstein's E=mc^2 Theory

    How does E=mc^2 ?? Hey, After looking on the internet I am having trouble finding some explanation of how E=mc^2. I know what it means and how to use it but how did Einstein arrive at this conclusion? Don't worry if the answer is a bit complex I can handle some meaty maths :-) Thanks! :-)
  43. B

    Why is energy released during nuclear fission?

    When a massive nucleus splits, it forms two smaller fragments. For Uranium, we have A=235, and the typical fragments are A=140 and A=95. Looking at the binding energy curve, these two fragments have greater binding energy per nucleon than the original uranium nucleus. Hence, if the uranium...
  44. SamRoss

    E=mc^2 proof. Why use Newtonian kinetic energy?

    E=mc^2 proof. Why use Newtonian kinetic energy? In "Does the Inertia of a Body Depend Upon its Energy-Content?" Einstein says that the difference in kinetic energy of a body before and after it releases some energy is... K(0)-K(1)=E(gamma-1) In his previous paper, he worked out the...
  45. J

    What is the kinetic energy of an object traveling at the speed of light?

    When an object is traveling at the speed of light, c, what is its kinetic energy? Is it the objects mass multiplied by the speed of light squared, according to Einsteins special relativity? Or is it the objects mass multiplied by its velocity (speed of light) squared, divided by 2, according...
  46. P

    Why are E=MC^2 and E=1/2MV^2 equivalent equations?

    Today in my physics class we learned the equation for kinetic energy; E = 1/2MV^2 I found the equation strikingly similar to Einsteins famous equation E=MC^2 The only real difference is the 1/2 coefficient (Since C is just a constant for V) So i figured there should be a constant for V...
  47. M

    Calculating Energy Released When Hydrogen & Anti-Hydrogen Collide

    So theirs this question Particle accelerators can be used to accelerate particles up to 95% the speed of light. Determine the energy released when 1 hydrogen atom collides with an anti-hydrogen atom. E=mc^2 = (1.00794)(2.998x10^8 x 0.95)^2 = 1.00794 x 8.1225 x 10^ 16 = 8.1869 x 10^16...
  48. G

    E=mc^2 Explained: Momentum and c

    In this proof of E = mc^2: http://www.youtube.com/watch?v=g1_Z7UZWmVQ At around 5:40, he says that E = Pc. I understand that this means that energy is equal to the momentum of the system (in this case 2mv) multiplied by c. However, this doesn't make sense to me. If energy is force times...
  49. W

    Small problem with getting to E=mc^2

    First of all, I'm not sure where to post this. Now, I am reading some lectures about relativity, I came quite far and understand the concept. The steps in the following I just can't follow. "Kinetic Energy and Mass for Particles of Arbitrary Speed For a particle of rest mass m0...
  50. S

    Is the presence of 'c' in E=mc^2 coincidence?

    Hi With special relativity I understand that if for example you have one gram of matter and it is converted to pure energy you will get E=0.001*299,792,458^2 joules of energy. However what I ‘am unsure of is; is it merely a coincidence that the value of the speed of light relates to...
Back
Top