The Derivation of the Energy–Momentum Relation in Relativistic Classical Mechanics
The Difference Between Momentum And Kinetic Energy. In physics you often hear the words "momentum" and "kinetic energy". It might be tempting to think that. The energy–momentum relation is a relativistic equation that relates an object's rest mass, its total energy and momentum. Holds for systems such as a particle. which is the ordinary definition of momentum with the mass replaced by the to make use of the Einstein relationship to relate mass and momentum to energy.
All three equations hold true simultaneously.
Special cases of the relation 1 include: For photonsthis is the relation, discovered in 19th century classical electromagnetismbetween radiant momentum causing radiation pressure and radiant energy. A more general form of relation 1 holds for general relativity. The invariant mass or rest mass is an invariant for all frames of reference hence the namenot just in inertial frames in flat spacetime, but also accelerated frames traveling through curved spacetime see below.
- Energy–momentum relation
- Energy momentum Formula
- The Difference Between Momentum And Kinetic Energy
The relation allows one to sidestep Lorentz transformations when determining only the magnitudes of the energy and momenta by equating the relations in the different frames. E and p as determined by particle physicists in a lab, and not moving with the particles.Relation between relativistic momentum and energy - IAS 2013
In relativistic quantum mechanicsit is the basis for constructing relativistic wave equationssince if the relativistic wave equation describing the particle is consistent with this equation — it is consistent with relativistic mechanics, and is Lorentz invariant. In relativistic quantum field theoryit is applicable to all particles and fields. Origins of the equation The equation can be derived in a number of ways, two of the simplest include: This is completely general for all particles, and is easy to extend to multi-particle systems see below.
The relativistic energy E and momentum p include the Lorentz factor defined by: Therefore, the object weighing 0.
In fact, the kinetic energy of the 0. The kinetic energy of an object is directly proportional to how much damage it will inflict when it strikes something. But interestingly enough, it's the object weighing less that will do more damage, for a given momentum. And it is the square of the velocity in the kinetic energy equation which makes this effect possible.
You can generalize this result to say that the ratio of kinetic energy of two objects having the same momentum is the inverse ratio of their masses. This principle readily applies to firearms.
When a bullet leaves a gun it has the same momentum as the gun which recoilsdue to conservation of momentum. But the bullet has much more kinetic energy than the gun.
Looking at this more deeply you realize that much more of the gunpowder energy was transferred to the bullet than the gun, in the form of kinetic energy. As an analogy to the gun and bullet consider the figure below showing two blocks with a spring held between them. This spring represents the gunpowder which stores the energy pushing the bullet and gun apart, represented by the smaller block and larger block, respectively.
Energy and Momentum in Lorentz Transformations
Initially, the spring is compressed between the blocks. The spring is then released and pushes the two blocks apart. In this system momentum is conserved, and as shown previously, the kinetic energy of the smaller block of mass M2 is larger than the kinetic energy of the larger and heavier block of mass M1.