What is Relativistic energy: Definition and 61 Discussions

In physics, the energy–momentum relation, or relativistic dispersion relation, is the relativistic equation relating total energy (which is also called relativistic energy) to invariant mass (which is also called rest mass) and momentum. It is the extension of mass–energy equivalence for bodies or systems with non-zero momentum. It can be written as the following equation:

This equation holds for a body or system, such as one or more particles, with total energy E, invariant mass m0, and momentum of magnitude p; the constant c is the speed of light. It assumes the special relativity case of flat spacetime. Total energy is the sum of rest energy and kinetic energy, while invariant mass is mass measured in a center-of-momentum frame.
For bodies or systems with zero momentum, it simplifies to the mass–energy equation






{\displaystyle E=m_{0}c^{2}}
, where total energy in this case is equal to rest energy (also written as E0).
The Dirac sea model, which was used to predict the existence of antimatter, is closely related to the energy–momentum relation.

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  1. milkism

    Conservation of relativistic energy, collision of particles

    Question: With maximum do they mean that the speed of the pions is the same as the proton and an antiproton? Otherwise there will be two unknowns, and if I use both relativistic-energy and momentum conservation equations I get difficult equations.
  2. D

    Landau Energy Spectrum in the non-relativistic limit

    At non-relativistic limit, m>>p so let p=0 At non-relativistic limit m>>w, So factorise out m^2 from the square root to get: m*sqrt(1+2w(n+1/2)/m) Taylor expansion identity for sqrt(1+x) for small x gives: E=m+w(n+1/2) but it should equal E=p^2/2m +w(n+1/2), so how does m transform into p^2/2m?
  3. A

    I Relativistic Energy & Robert M. Wald's General Relativity

    In Robert M. Wald's General Relativity he writes on page ##61##: The energy of a particle as measured by an observer - present at the site of the particle - whose 4-velocity is ##v^a## is defined by $$E=-p_a v^a$$ Thus, in special relativity, energy is recognized to be the "time component" of...
  4. D

    Relativistic energy and momentum conservation

    Summary:: this is what I've done so far... i don't think it works since i believe the information given is not even enough. the formula I've used are 1. relativistic total energy = rest mass energy + kinetic energy (line 1, 3) 2. conservation of energy (line 4, 7, 8, 9) 3. conservation of...
  5. SEYED2001

    I Relativistic energy equation applied to a double-slit experiment

    My question: How do the values for the velocity, momentum and energy of an electron in a double-slit experiment are altered by the observation? Probably,energy is altered. Given that energy is a function of momentum and velocity, either or both of these must have been changed. However, I am...
  6. A

    I Relativistic Energy of Rotating Thin Ring: Quick Qs

    Quick question about the relativistic energy of a rotating thin ring, hoop or cylinder. Is there any reason why the relativistic energy would be anything different than ##E=\gamma_t m_0 c^2## where ##\gamma_t## depends on the tangential velocity ##v_t## observed by someone at rest with the...
  7. SamRoss

    B Relativistic Energy: Change of Consts. of Integration

    In this super short video of the derivation of the relativistic kinetic energy, , I'm just stuck on one thing. Around 1:00 minute in, the constants of integration change from 0 to pv when the integration changes from dx to dv. Where does the pv come from? Thanks!
  8. P

    I Relativistic Energy Dispersion Relation: Explained

    I'm in the process of learning special relativity (SR), and I'm a bit confused as to why the relativistic energy dispersion relation ##E^{2}=m^{2}c^{4}+p^{2}c^{2}## gives the energy for a free particle? I get that it is the sum of (relativistic) kinetic energy plus the rest mass term (a...
  9. Kara386

    I Relativistic Energy Equations: When to Use Each

    When would I use the equation ##E = \gamma mc^2## and when would I use ##E^2 = (mc^2)^2 + (pc)^2##? I'm a little confused because my textbook calls them both total energy equations. I know that for a particle at rest it has energy ##E=mc^2##. It can't be at rest for the equation ##E = \gamma...
  10. TheSodesa

    Escape Velocity of a Neutron Star: Relativistic Calculation

    Homework Statement Calculate the escape velocity on the surface of the neutron star in the previous problem (##m = \frac{2}{3} \cdot 2,1 \cdot M_{\odot}##; ##R = 15km##). Hint: Basic physics. Note, however, that the escape velocity is not going to be small when compared to the speed of light...
  11. K

    Relativistic Energy and Lorentz factor

    Homework Statement [/B] Two particles of rest mass m0 approach each other with equal and opposite velocity v, in a laboratory frame. What is the total energy of one particle as measured in the rest frame of the other? But the question gives a clue which reads "if (v/c)^2 = .5, then E =...
  12. P

    Relativistic Energy and Velocity

    Homework Statement A proton has a mass of 938 MeV/c2. Calculate the speed, momentum, and total energy of a 1760 MeV proton. Homework Equations E= mc^2 (Rest Energy) E= Ɣmc^2 (Total Energy) p= Ɣmv (momentum) KE= mc^2(Ɣ-1) (Kinetic Energy)The Attempt at a Solution I'm not sure how the last...
  13. C

    Relativistic Energy Derivation

    Whilst reading following a derivation of the Relativistic Energy equation I came across the following: d/dt[mu/(1-u2/c2)1/2] = [m/(1-u2/c2)3/2] du/dt. I was wondering how that step was done.
  14. PsychonautQQ

    What is the total kinetic energy of two protons in different reference frames?

    Homework Statement In the reference frame S', two protons, each moving at .5c, approach each other head on. Calculate the total kinetic energy of the two protons in frame S', and calculate the total kinetic energy of the two protons as seen in reference frame S which is moving with one of the...
  15. N

    Inconsistency in formulas for relativistic energy

    I'm very noob at this and am a bit confused: Formula 1: E_T = \gamma \cdot m c^2 Formula 2: p = \gamma m v Formula 3: E_T^2 = (pc)^2 + (mc^2)^2 Formula 3 says a particle of negligible mass can have energy, but isn't this in contradiction to formula 1? Unless maybe the velocity of the...
  16. K

    Exploring Relativistic Energy: Solving λmu and d(λmu) Equations"

    Homework Statement I am trying to grasp this stuff, but it is getting late and my mind is noodeling. Can I have some help on this? show that d(λmu) = m(1-(u^2/c^2)^(-3/2) du thanks! Homework Equations λ = 1/√(1-(u^2/c^2)) The Attempt at a Solution I have attacked this through...
  17. J

    Relativistic Energy question

    Hi, I`ve been dabbling in some basic special relativity and when your deriving the famous equation E = mc^2 you get to this equation just before it. KE = mc^2/sqrt1-v^2/c^2 - mc^2 ie KE = Etotal - Erest but when I try assign a mass and velocity of one i get a kinetic energy of...
  18. M

    Relativistic Energy Derivation math problem

    Hey, In a derivation of relativistic energy (in Physics for Scientists and Engineers, 5th edition, Serway and Beichner) they use a method of integration by substitution: Given that F=\frac{dp}{dt} and relativistic momentum is given by p=\frac{mv}{\sqrt(1-(v^2/c^2))} W=∫F...
  19. D

    What is a joule, when you calculate relativistic energy?

    Energy is E=γmc^2, but when I calculate this, will my result be in joules? I am unsure what the units are when I calculate it, and I keep hearing people saying joules. Also, what is PJ and MJ?
  20. T

    Conservation of Relativistic energy and momentum

    I was reading through this article http://en.wikipedia.org/wiki/Four-momentum#Conservation_of_four-momentum It says "The conservation of the four-momentum yields two conservation laws for "classical" quantities: The total energy E = P0c is conserved. The classical three-momentum p is...
  21. ElijahRockers

    How long will the sun shine for? (relativistic energy)

    Homework Statement The sun radiates about 4.0E26 J/s. a) How much mass is released as radiation each second? b) If the mass of the sun is 2.0E30 kg, how long can the sun survive if the energy release continues at its present rate? Homework Equations Not sure, but I think I'm...
  22. P

    How Is the Kinetic Energy of a Proton Calculated in an Electric Field?

    Hi, A proton initially at rest finds itself in a region of uniform electric field of magnitude 5.0 x 106 Vm-1. The electric field accelerates the proton for a distance of 1 km. Find the kinetic energy of the proton. So, what I did was the following: KE = q * E * s I then...
  23. D

    Show that the total relativistic energy of a proton

    Homework Statement The mass of a proton when at rest is m. According to an observer using the detector frame, the speed of the anticlockwise moving bunch, A, is such that va^2/c^2=24/25 Show that the total relativistic energy of a proton in bunch A, as observed in the detector frame, is...
  24. X

    Deriving power from the relativistic energy equation

    Homework Statement I recently finished a test that asks you to derive Power = \frac{dE}{dt} = F \times v from the energy equation: E^2 = E_{0}^2 + (pc)^2 Homework Equations Power = \frac{dE}{dt} = F \times v E^2 = E_{0}^2 + (pc)^2 p = \gamma m v The Attempt at a Solution I got...
  25. G

    Relativistic Energy in an Inverse Square Field: The Impact of Velocity

    for an inverse square field the force is proportional to 1/r^2 obviously we integrate over distance to get energy ≡ 1/r (where energy = 0 at infinity) but what happens when velocity becomes relativistic? is relativistic energy proportional to 1/r?if its any easier what I am really looking for...
  26. jaketodd

    Relativistic Momentum: Is It a Vector in Relativistic Energy?

    Relativistic momentum is a vector, just as non-relativistic momentum is a vector, right? Part of the relativistic energy equation includes relativistic momentum. See here please: http://hyperphysics.phy-astr.gsu.edu/hbase/relativ/releng.html" Could the relativistic momentum energy part of...
  27. R

    Relativistic energy and momentum 2

    Homework Statement proton hits a stationary proton which then produces a pion with the following reaction p + p = p + p +pion if the initial proton has just enough energy to produce the pion what are the speeds of the final protons and pion in the laboratory frame? m(pion)=0.144m(proton)...
  28. R

    Relativistic energy and momentum

    Homework Statement protons and electrons react in the following way to make an alpha particle 4p + 2e = He + 6gamma rays + 2neutrinos the energy created by this is taken up as kinetic energy of the alpha particle, gamma rays and neutrinos. the energy of the alpha particle and gamma rays...
  29. S

    Conservation of relativistic energy

    A particle of rest mass m_0 disintegrates into two particles of rest masses m_1 and m_2. Use conservation of relativistic energy and relativistic 3-momentum to find the energies E1 and E2 of the particles in the rest fram of the original particle. Relevant equations: E0 = E1 + E2 p0 = p1+...
  30. M

    Small Conceptual Relativistic Energy Question

    Hi, I have an assignment due in the morning, and it is complete, there is just one tiny thing I am unsure of: In a rest frame, a mass m moves west at speed v, and another mass also m moves east at speed v. Now consider the setup as viewed by an observer going west at speed u. I had to find the...
  31. S

    Relativistic energy and momentum in particle collisions

    Homework Statement Two particle P and Q each of restmass m0 and moving in collision course at 2/3c in the laboratory frame of reference. In the same collision but in particle P's frame of reference, P is at rest. Homework Equations As the total energy of the particles depends on the frame...
  32. S

    Relativistic energy and momentum in particle collisions

    Homework Statement Two particle P and Q each of restmass m0 and moving in collision course at 2/3c in the laboratory frame of reference. In the same collision but in particle P's frame of reference, P is at rest. Homework Equations As the total energy of the particles depends on the frame...
  33. jaketodd

    Understanding Relativistic Energy Equations: Are They Linear?

    Are Einstein's energy equations for relativistic speeds linear? For example, if you had something going at relativistic speed and then slowed it, but still had it at relativistic speed, would the decrease in energy be directly proportional to the amount you slowed the thing down? Thanks, Jake
  34. A

    Relativistic Energy of a Ball: Understanding the Equivalence of Mass and Energy

    according to mass-energy equivalent theorem, Regardless of whether the object is at rest or moving, the object of mass m having energy E=mc2. suppose a ball of mass m is placed on ground, then how much energy this ball have? Is it equal to E=mc2 ?? now if we place this ball above the...
  35. E

    Max Energy Transfer Relativistic Collision: Electron & Photon

    Homework Statement "A photon of energy E collides with an electron at rest. Calculate the maximum amount of Energy Ek that may be transferred to the electron. Make a graph of Ek versus E, labeling the scale in electronvolts. Homework Equations Transfer = Ek = E - mc^2*E/(mc^2 + 2E)...
  36. D

    Relativistic energy and momentum question

    [b]1. A lambda particle decays into a proton and pion and it is observed that the proton is left at rest. a. what is the energy of the pion? b. what is the energy of the original lambda? m of lambda = 1116MeV/c^2, m of proton = 938 MeV/c^2, and m of pion = 140 MeV/c^2 Homework...
  37. T

    How Do You Calculate Work Done by a Spaceship's Engine in Relativistic Terms?

    Hi- I have a question regarding relativistic kinetic energy. If a spaceship is moving at a velocity relative to the Earth and then accelerates, to compute the work done by the engine/KE, should I use the given final velocity(the problem isn't entirely clear what this speed is in reference to)...
  38. H

    Deriving Relativistic Energy Problem

    Homework Statement Taking into account the electrons momentum and relativistic energy prove that W=(m(sub0)^2c^4+p^2c^2)^(1/2) Homework Equations p=(gamma)m(sub0)v; W=(gamma)m(sub0)c^2. The Attempt at a Solution I have tried expanding the relativistic factor...
  39. D

    Speed of Proton at 750keV Kinetic Energy

    Homework Statement What is the speed of a proton after being accelerated to a kinetic energy of 750keV? Homework Equations E=K+E0 E0=mc^2 K=(gamma-1)mc^2 gamma=1/(sqroot(1-v^2/c^2)) The Attempt at a Solution Alright, so to find the speed, I used the equation: K=(gamma-1)mc^2...
  40. S

    Relativistic Energy: Matter & Photon

    Homework Statement Energy of a particle may be of the form: E = \gamma mc^{2} E = \sqrt{p^{2}c^{2} + m^{2}c^{4}} Are both valid for every particle? matter and photon? Can they be equated?
  41. B

    Finding velocity using relativistic energy equations

    Hello all, I was wondering how you take the relativistic kinetic energy equation: Total Energy=(gamma)mc^2 and solve it for a certain velocity. In our homework we have to take a high amount of energy that is put on an object with mass initially at rest, and find out what velocity it will...
  42. W

    Relativistic energy of particle of mass

    Homework Statement A particle of mass M decays into two identical particles each of mass m, where m = 0.3M. Prior to the decay, the particle of mass M has a total energy of 5Mc2 in the laboratory reference frame. The velocities of the decay product are along the direction of motion M. Find...
  43. F

    Relativistic energy and momenta

    Homework Statement An electron with a kinetic energy of 1MeV collides with a stationary positron. The two particles annihilate each other and produce 2 photons, of equal energy traveling at angle theta to the direction of the electron. Find, a. The momenta of the electron b.the energy of the...
  44. B

    Relativistic Energy of Antimatter

    Hi. I was wondering, as I never really knew for certain, does antimatter have positive or negative relativistic energy?
  45. A

    Relativistic Energy: Calculate Decay Product Kinetic Energy

    Homework Statement A radium isotope decays to a radon isotope by emitting an α particle (a helium nucleus) according to the decay scheme 226Ra --> 222Rn + 4He. The masses of the atoms are 226.0254 u (226Ra), 222.0176 u (222Rn), and 4.0026 u (4He). What is the total kinetic energy of the decay...
  46. M

    Relativistic energy and time dilation

    hi there! I`m stuck on the following two questions and I hope you could help me :) I´m given the kinetic energy of a particle. How am I supposed to calculate its velocity? there´s no mass of rest, no total energy, just the kinetic energy. 2. While trying to calculate the time...
  47. M

    Do I use Relativistic Energy here?

    Homework Statement What is the speed of a proton when its kinetic energy is equal to its rest energy? Homework Equations K = mc^2(\gamma - 1) E_0 = mc^2 \gamma = \frac{1}{\sqrt{1 - \frac{v^2}{c^2}}} The Attempt at a Solution K = E_0 mc^2(\gamma - 1) = mc^2 \gamma = 2...
  48. F

    Threshold Energy Calculation for Proton-Proton Collision

    Homework Statement When a beam of high-energy protons collides with protons at rest in the laboratory (e.g., in a container of water or liquid hydrogen, neutral pions are produced by the reaction p+p --> p+p+(pion). Compute the threshold energy of the protons in the beam for this reaction...
  49. L

    Relativistic Energy of Omega- particle

    Homework Statement An Omega- particle has rest energy 1672 MeV and mean lifetime 8.2X10-11 s. It is created and decays in a particle track detector and leaves a track 24mm long. What is the total energy of the Omega- particle? Homework Equations E=E0/Sqrt(1-v^2/c^2) E0=1672 MeV...