What is Four momentum: Definition and 24 Discussions

In special relativity, four-momentum is the generalization of the classical three-dimensional momentum to four-dimensional spacetime. Momentum is a vector in three dimensions; similarly four-momentum is a four-vector in spacetime. The contravariant four-momentum of a particle with relativistic energy E and three-momentum p = (px, py, pz) = γmv, where v is the particle's three-velocity and γ the Lorentz factor, is

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{\displaystyle p=\left(p^{0},p^{1},p^{2},p^{3}\right)=\left({E \over c},p_{x},p_{y},p_{z}\right).}
The quantity mv of above is ordinary non-relativistic momentum of the particle and m its rest mass. The four-momentum is useful in relativistic calculations because it is a Lorentz covariant vector. This means that it is easy to keep track of how it transforms under Lorentz transformations.
The above definition applies under the coordinate convention that x0 = ct. Some authors use the convention x0 = t, which yields a modified definition with p0 = E/c2. It is also possible to define covariant four-momentum pμ where the sign of the energy (or the sign of the three-momentum, depending of the chosen metric signature) is reversed.

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1. I Why "time part" represents energy in Four-momentum?

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2. De-excitation of a moving atom with photon emission

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3. Gamma factor when doing four momentum problems

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4. Question on four momentum squared

So i have taken a beginner course on relativity, first year physics student. I am confused as to why four momentum squared simply gives m2* c2*ϒ2 -(three vector multiplied and added with corresponding parts) *ϒ2 so as the three vector part which is being subtracted, is the same as - (P...
5. 4 momentum mass non-conservation, special relativity

Homework Statement A particle with mass M and speed v along the positive x-axis hits a stationary mass m. Two particles, each with mass µ, emerge from the collision, at angles with respect to the x-axis. (a) Write the equation for conservation of the 4-momenta, for arbitrary angles θ_1, θ_2 of...
6. B 4 four momentum energy component direction

I have been reading about four momentum. There are four component vectors, three spatial, momentum, components and a time, energy, component. They each have a direction. I understand direction for the momentum components, being in the direction of the respective spatial components of the...
7. I De Broglie relation using four momentum in particle physics

In particle phyisics four-momentum is used and De Broglie relation is used to understand what lenghts can be "seen" in an experiment. Here (page 6) https://people.phys.ethz.ch/~pheno/PPP/PPP2.pdf it is claimed Where ##Q^2## is not actually "momentum" but its the square of the four momentum...
8. Conservation of Four Momentum Problem

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11. Four momentum proton-proton scattering question

Homework Statement In a fixed target experiment a particle of mass M and kinetic energy T strikes a stationary particle of mass M. By evaluating s, t and u in the laboratory frame and using the above relation, or otherwise, show that the kinetic energy T' of the particle scattered elastically...
12. Four Momentum in General Relativity

Alright, I'm rather new to General Relativity, and I'm getting confused with four momentum. Back in SR, p^α=mU^α, but, this relationship doesn't hold in curved space, does it? Because, now I'm seeing that four momentum is somehow a covector in GR, and p_0=-E, so the time component of the...
13. Solving Relativistic Collision using Four Momentum Vector

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14. Conservation of Four-Momentum in Inertial Frames

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15. Conservation of four momentum question

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16. Four momentum of fused particles

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17. Understanding the Four Momentum of a Photon in General Relativity

Hi, I'm trying to reconcile some general relativity stuff and I'm getting confused on a few topics. Would someone be able to explain the properties of the four momentum of a photon? The way I understand it is that you take the four wave-vector of the photon and multiply it by \hbar. The four...
18. Conservation of Four-Momentum in Neutrino-Electron Collision

Hi physics people, This is a past (3rd year university level) exam question, so I hope it's ok that I didn't post this in the homework section even if it's set out like a homework question. The Question: Suppose we are observing the collision Anti-electron-neutrino + electron ---> W-minus...
19. How can I express the force in Special Relativity using four momentum?

Homework Statement To write the expression of force in STR \ F=\frac{dp}{dt}=\ m\gamma\ a +\ m\gamma\frac{\ u .\ a}{\ c^2 -\ u^2}\ u Here a is acceleration Homework Equations I used the equation \ p=\gamma\ m\ u I interpreted F as four force,p as four momentum, a as four-acceleration, u...
20. Four momentum vector from energy-momentum-tensor

Hi, for a real scalar field one has the energy momentum tensor from Noethers theorem T^{\mu\nu} = \frac{\partial \mathcal{L}}{\partial \partial_\mu \phi} \partial^\nu \phi - \eta^{\mu\nu} \mathcal{L} and the conserved quantities P^\nu = \int d^3 x \ T^{0\nu} Now, how can one show that P...
21. Four momentum of Photon in Center of Mass frame?

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22. Understanding the Four Momentum of a Relativistic Field

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23. Relativistic Energy and four momentum

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24. Why Is the Fourth Component Necessary in Relativistic Momentum?

I've been trying to see how relativity shows that the quantity gamma*m*c^2 (total energy) is conserved. I assumed that this would proceed from the conservation of momentum. So I researched momentum in relativity, and noticed that it has a time-component: gamma*m*c (which is E/c). So this...