What is mass and energy: Definition and 60 Discussions

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




{\displaystyle E=mc^{2}}
. In a reference frame where the system is moving, its relativistic energy and relativistic mass (instead of rest mass) obey the same 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 300000 km/s or 186000 mi/s), the formula implies that a small amount of "rest mass", measured when the system is at rest, corresponds to an enormous amount of energy, which is independent of the composition of the matter.
Rest mass, also called invariant mass, is a fundamental physical property that is independent of momentum, even at extreme speeds approaching the speed of light. 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 (1854–1912). 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 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. WeirdUniverse

    I The answer for the total mass of the Universe?

    it requires less energy to impart acceleration to an object than to the entirety of the universe, This would break the principle of relativity since the amount of energy to move an object should be the same as the amount of energy to move the rest of the universe. This observation implies a...
  2. J

    B Does gravitational force act on system or its components?

    I want to emphasize that I am not familiar with general relativity. Consider a system of particles with masses ##m_i## in gravitational field of another body ##A##. Total gravitational force exerted on ##A## will not be $$\sum G \frac{m_i m_A}{r^2}$$ where ##r## is distance between system and...
  3. hongseok

    B Is Comparing Binding Energy and Mass to Kinetic and Potential Energy Valid?

    Can I understand the relationship between binding energy and mass by comparing it to the relationship between kinetic energy and potential energy? When an object falls, its gravitational potential, a scalar value, decreases, and its energy is converted into kinetic energy. Even when a nuclear...
  4. D

    I What can we scientifically measure directly?

    I am interested in finding out what we can objectively measure. How to define what we can measure directly, without (human) models getting involved, as in model-dependent realism as described by Hawking and Mlodinow? It seems as if everything we measure is either mass or energy (or spin?). Time...
  5. D

    A Mass density of radiation in Friedmann equation?

    \frac{1}{R}\frac{{{d^2}R}}{{d{t^2}}} = - \frac{{4\pi G}}{3}\left[ {{\rho _m} + {\rho _{rad}} + {\rho _\Lambda } + \frac{{3({P_m} + {P_{rad}} + {P_\Lambda })}}{{{c^2}}}} \right] In the Friedmann equation, ρ is the mass density. === https://en.wikipedia.org/wiki/Friedmann_equations They were...
  6. V

    Mass-energy conservation in nuclear reactions

    I found the total mass of the reactants and the products, found the change in mass, used E=mc^2 and changed my answer from Joules to eV, but my answer is wrong. I'm guessing I have to do something with the energy of the alpha-particle given in the question The answer is supposed to be: 6.58 MeV
  7. Tertius

    I Invariant Mass-Energy in FRW Spacetime

    GR has very limited situations in which a total mass-energy can be defined. The Komar mass, for example, requires the presence of a timelike killing vector field and an asymptotically flat spacetime. Basically, if the metric change with time or it's spacelike curvature does not flatten out...
  8. T

    B Mass of Space (B but approaching I)

    Since space is expanding, and that expansion moves things, then those moved things must be moved by something. If moved by space itself, then space must be providing the energy. And if gravity is a function of space and time interacting, then what is the energy or mass of a volume of space...
  9. R3ap3r42

    Invariant mass and energy balance

    a) Two particles have energies E1 and E2, and momenta p1 and p2. Write down an expression for the invariant mass of this two-particle system. Leave your answer in terms of E1 and E2, and p1 and p2. b) A typical photon (γ) in the Cosmic Microwave Background (CMB) has an energy of kBTCMB, where...
  10. Bix

    Hello - basic incline mass and energy question, thanks :)

    Hello. Be v grateful any assistance with this. Question is energy to haul 2000kg 4 metres up a 1 in 100 incline with 300 Newtons friction Answer is given as exactly 1.98 kJ. The only figures I can see that relate to anything here are 2000kg minus 10 = 1980, and 1:100 is 0.01 which times...
  11. F

    B Relationship between mass and energy

    Great. I will be moving into general relativity next. Before that, I will touch on one more topic: energy and mass, a topic of special relativity, and the formula ##E=m c^2##. There is rest mass ##m_0## (the amount of stuff an object is made off, an invariant) and the inertial mass...
  12. E

    B What would the universe be like with less mass and energy?

    So I have sort of a conceptual question about the big bang and gravity. Imagine yourself in a universe, in which existed about the number of particles/energy in a 3X3 metre room at any given moment. This universe has the same laws of physics, constants and is identical in every way to our...
  13. dRic2

    Mass and energy balance equations for a tank filled with H20

    Hi, this problem should be very simple: I have a tank containing water. (going in and out). I want to write the differential equations to see what happen to the temperature and the level of the vessel if the flow of water is not constant. the system should be: $$A \frac {dl} {dt} = F_{in} -...
  14. HethensEnd25

    Fin/Fan heat exchanger mass and energy balance

    I am currently working on a project which requires a mass and energy balance on a fin/ fan heat exchanger. The problem I am running into is finding how to apply the fin efficiency to find out the amount of hea tbeing dissipated through the fins. The hot fluid is water and the cooling fluid is...
  15. John M

    B Mass and energy from Earth's gravitational field

    Can someone please tell me how the energy field created by warped space (gravity) and centred at the Earth's core dissipates? Is it the pressure/compression of this force/energy that makes the core so volatile? Whilst time slows at altitude, do we become lighter, as we are further away from...
  16. Nicodemus Rex

    Kinetic Vehicle [flywheel powered] mass and energy

    1200lb total vehicle weight 800lb total flywheel mass [4x200ea] Diameter 18.75" Flywheel RPM 3500 [120v electric motor plugged into wall] Pulley to drive wheel at 1:1 [6"pulley] or to 12' pulley Please help write the end of this story before I start. This is a "rev up" car built for...
  17. A

    Relativity and Equivalence of Mass and Energy

    Homework Statement An electron is accelerated to a speed that is 99 percent the speed of light, and is moving through a 2-km-long tunnel. The rest mass of the electron is 9.11*10^-31 kg. What is the mass of the electron at this speed? c= speed of light Homework Equations t= (tsubscript(o))/...
  18. FallenApple

    I Exploring the Relationship Between Rest Mass and Energy in Objects

    So from what I've heard, the rest mass of a object increases when the object's internal energy increases. So a clock that is ticking has increased rest mass vs the same clock that is completely still. But doesn't the clock have moving parts that give kinetic and thermal energy? Then in what...
  19. CricK0es

    Calculating rest mass and energy (in an inertial frame)

    Homework Statement A particle is accelerated so it has a total energy of 10GeV measured in the accelerator’s rest frame. The particle's momentum is 8GeV/c in the same frame. Calculate... a.) Rest mass of the particle b.) Energy in an inertial frame in which its momentum is 6GeV/c c.) The speed...
  20. 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...
  21. Dadface

    The Equivalence of Mass and Energy

    Hello I've been trying to get confirmation, or otherwise, that the total mass of an atom can be considered to be equal to the sum of the masses of the individual atomic particles it contains plus the mass equivelent of the internal energy, (PE+KE), of the particles. I have also been trying to...
  22. K

    Conservation of matter, mass, rest mass and energy

    Homework Statement Could someone please let me know if this is correct? I'm unsure about matter always being conserved, does it change whether we're talking about Newtonian physics or special relativity? To me, matter is conserved regardless but maybe there is something I don't know...
  23. N

    Are Mass and Energy the same thing?

    Since E=mc2, that means that mass is energy and energy is mass right?
  24. B

    Is there a connection between the Higgs field and energy in Majorana framework?

    if the Higgs bosson field is responsible for giving particles mass. and mass and energy are interchangable e=mc^2. Then is there a field, like the higgs that is responsible for energy. maybe an exited state of the higgs?
  25. 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?
  26. atyy

    Is ADM Energy Equivalent to Komar Mass in All Spacetimes?

    Can I check whether these are right? Here let's define the ADM mass as length of the ADM energy-momentum vector. In the Schwarzschild spacetime ADM energy = Schwarzschild mass parameter In a spacetime in which the ADM energy and the Komar mass are both defined ADM energy = Komar mass
  27. N

    Conservation of mass and energy

    Hmm, I s matter always conserved? Is mass always conserved? Is rest-mass always conserved? Is energy always conserved? are there any exceptions?
  28. B

    Mass and Energy of Object that struck Earth and created moon

    Homework Statement This is third and last part of a question whose first part was solved on here earlier. Given the spin angular momentum of the Earth and the Orbital (around Earth) angular momentum of the moon calculate the mass of an object that if it hit the Earth at it's radius (glancing...
  29. L

    Can matter be defined strictly in terms of mass and energy?

    I was reading some articles and discussions on the topic and got confused when I read that conventionally photons and all other massless particles aren't considered a form of matter. The Wiki article on matter begins with the statement that the term itself is poorly defined. I was thinking...
  30. R

    Mass and energy analysis of control Volumes (thermodynamics)

    Homework Statement 1) A cylinder with an initial volume of 1.5 m3 initially contains water 1 MPa and 200 ° C (condition 1). Container is cooled at constant temperature until the volume is 42% of the initial volume (state 2). The constant temperature process is followed by a constant volume...
  31. 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...
  32. C

    Mass and Energy Differentiation

    Hello friends: My Question: A massive object cannot move at the speed of light. Photons can move at the speed of light because they are massless. However, since energy and mass are equivalent, due to Einstein's famous equation E^2=(m(c^2))^2+(pc)^2, mass is energy by a conversion...
  33. D

    Mass and energy when traveling at near the speed of light

    I was reading about the speed of light and it says that no object can travel at the speed of light because the mass of the object increases as it moves faster. How is that possible? Also if light travels at such a speed because it has no mass, then why does light get affected by gravity near...
  34. C

    Interesting Coincidence with Classical/Modern View of Mass and Energy

    Has anyone ever noticed that, even in classical physics, energy is shown as a scalar multiple of mass? For example, consider the joule; 1 J = 1 kg*(m/s)^2 If you consider the units of motion (m/s) to be a vector quantity, then squaring such a vector would be interpreted as a dot product...
  35. M

    Rotational Mass and Energy Required

    Thinking about rotating mass (for example a bike tire) and the disadvantages / advantages that come with differing weights/masses. Most everybody you speak to are programmed to think that a lighter tire will require less energy, thus, everyone tries to find the lightest tire possible...
  36. E

    Does a Photon Traveling at Light Speed Imply Infinite Mass and Energy?

    If a photon is traveling at the speed of light, wouldn't infinite mass and energy be a condition?
  37. B

    Thermodynamics mass and energy analysis Problem

    Im doing a balloon problem. The problem states that the volume increases linearly with pressure in the solution manual they that P2/P1=V2/V1 i think that is related linearly but i can't figure how. Can some explain?
  38. Mordred

    Total gravity of all mass and energy in Universe.

    I would like to endeaver to calculate what the force of gravity would be on a mass encompassing the total mass and energy. Some articles refer to a "god particle" I personally prefer to simply call it the orginal mass/energy particle. assuming that at the very beginning before this particle...
  39. 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...
  40. K

    Why are mass and energy related by the speed of light?

    Im a 3rd year physics major. I understand the equation E=mc^{2}. But i don't understand why mass and energy are related by the number c. How are mass, energy, and the speed of light so inextricably related that we can describe their relationship with one simple equation?
  41. J

    What is the difference between mass and energy?

    since the equation, E=MC2, indicates that mass and energy are equivalent, what exactly is the difference between them? ie, how do you explain that energy can travel at C, but not matter? or is there some significant difference between matter and an object which has mass? also, if mass and...
  42. O

    Why Do Objects Gain Mass at High Speeds and Seek Minimum Energy?

    Do you know what should I read to understand why everything wants to have the smallest energy and why every object which is approaching light speed puts on mass?
  43. Jonnyb42

    Mass & Energy: What's the Name?

    Mass and Energy "Stuff" Since mass and energy are both different forms of the same "thing," is there a name for that "thing?"
  44. K

    Mass-Energy Conversion: Solving Energy Crises with MegaW

    If your entire mass were to be converted to pure energy, how long could you provide a MegaW (10^6 W) of energy to help in solving our energy crises?
  45. N

    Recoil velocity of atom interms of mass and energy

    Homework Statement I have a question to answer but am struggling to even start it. The question is basically an atom absorbs a photon (energy E), rest mass of atom is m, find recoil velocity in terms of E and m after absorbtion. Homework Equations i think i need th emomentum of the...
  46. Rasalhague

    Equivalence of mass and energy

    Some naive questions about the meaning of this expression. In what follows, I'll use the word mass for "rest mass", the magnitude of the energy-momentum 4-vector. (Answers in terms of "relativistic mass" are fine, just let me know what definitions you're using. Taylor & Wheeler in Spacetime...
  47. F

    Relativity: Conversion of Mass and Energy

    Homework Statement A lambda particle decays into a proton and a pion, and it is observed that the proton is at left at rest. A. What is the energy of the pion? B. What was the energy of the original lambda? (The masses involved are m_{}\lambda = 1116, m_{}p = 938, and m_{}\pi = 140, all in...
  48. R

    Relativistic Mass and Energy Convservation

    Does relativistic energy contribute to gravitational 'pull'? If so, then does the acceleration of a body being 'pulled' by gravity cause it to increase in mass, thus weighing more and accelerating even faster? Does an object have greater mass because it's original mass pulled it toward...
  49. T

    Relationship between Mass and Energy

    Can someone explain in detail the relationship between mass and energy? Apparently there's not much of a difference...
  50. S

    Do Mass and Energy Share Vibrational Properties?

    does it make sense to say that the reason mass is energy is because they are both vibrations, which are distinguished because they occur on different spatial and temporal scales? and can position-momentum uncertainty be conceptualized as a frequency-amplitude uncertainty?