# Relationship b mass and energy

### Relationship between mass, energy, and a force? - Physics Stack Exchange

So I don't think equivalence relation is possible b/w them. . In classical physics, there is an intimate relation between mass and energy (for example, kinetic. History of Derivations of Mass-Energy Equivalence We can display the relationships between the various masses and energies we have. There is so much detail one could go into, but I will try to point out the most important aspects: The concept of force is closely related to energy: force can be seen.

The other possibility is that they have a positive kinetic energy and a negative potential energy that exactly cancels.

Binding energy and the "mass defect"[ edit ] This section needs additional citations for verification. July Learn how and when to remove this template message Whenever any type of energy is removed from a system, the mass associated with the energy is also removed, and the system therefore loses mass. However, use of this formula in such circumstances has led to the false idea that mass has been "converted" to energy.

Mass? Energy? What's The Difference?!

This may be particularly the case when the energy and mass removed from the system is associated with the binding energy of the system. In such cases, the binding energy is observed as a "mass defect" or deficit in the new system.

The fact that the released energy is not easily weighed in many such cases, may cause its mass to be neglected as though it no longer existed. This circumstance has encouraged the false idea of conversion of mass to energy, rather than the correct idea that the binding energy of such systems is relatively large, and exhibits a measurable mass, which is removed when the binding energy is removed. The difference between the rest mass of a bound system and of the unbound parts is the binding energy of the system, if this energy has been removed after binding.

For example, a water molecule weighs a little less than two free hydrogen atoms and an oxygen atom. The minuscule mass difference is the energy needed to split the molecule into three individual atoms divided by c2which was given off as heat when the molecule formed this heat had mass.

Likewise, a stick of dynamite in theory weighs a little bit more than the fragments after the explosion, but this is true only so long as the fragments are cooled and the heat removed. Such a change in mass may only happen when the system is open, and the energy and mass escapes.

Thus, if a stick of dynamite is blown up in a hermetically sealed chamber, the mass of the chamber and fragments, the heat, sound, and light would still be equal to the original mass of the chamber and dynamite. If sitting on a scale, the weight and mass would not change.

This would in theory also happen even with a nuclear bomb, if it could be kept in an ideal box of infinite strength, which did not rupture or pass radiation. If then, however, a transparent window passing only electromagnetic radiation were opened in such an ideal box after the explosion, and a beam of X-rays and other lower-energy light allowed to escape the box, it would eventually be found to weigh one gram less than it had before the explosion.

This weight loss and mass loss would happen as the box was cooled by this process, to room temperature. However, any surrounding mass that absorbed the X-rays and other "heat" would gain this gram of mass from the resulting heating, so the mass "loss" would represent merely its relocation.

Thus, no mass or, in the case of a nuclear bomb, no matter would be "converted" to energy in such a process. Mass and energy, as always, would both be separately conserved.

Massless particles[ edit ] Massless particles have zero rest mass. This frequency and thus the relativistic energy are frame-dependent. If an observer runs away from a photon in the direction the photon travels from a source, and it catches up with the observer—when the photon catches up, the observer sees it as having less energy than it had at the source. The faster the observer is traveling with regard to the source when the photon catches up, the less energy the photon has.

As an observer approaches the speed of light with regard to the source, the photon looks redder and redder, by relativistic Doppler effect the Doppler shift is the relativistic formulaand the energy of a very long-wavelength photon approaches zero.

## Mass–energy equivalence

This is because the photon is massless—the rest mass of a photon is zero. Massless particles contribute rest mass and invariant mass to systems[ edit ] Two photons moving in different directions cannot both be made to have arbitrarily small total energy by changing frames, or by moving toward or away from them.

The reason is that in a two-photon system, the energy of one photon is decreased by chasing after it, but the energy of the other increases with the same shift in observer motion. Two photons not moving in the same direction comprise an inertial frame where the combined energy is smallest, but not zero.

This is called the center of mass frame or the center of momentum frame; these terms are almost synonyms the center of mass frame is the special case of a center of momentum frame where the center of mass is put at the origin. The most that chasing a pair of photons can accomplish to decrease their energy is to put the observer in a frame where the photons have equal energy and are moving directly away from each other. In this frame, the observer is now moving in the same direction and speed as the center of mass of the two photons.

The total momentum of the photons is now zero, since their momenta are equal and opposite. In this frame the two photons, as a system, have a mass equal to their total energy divided by c2. This mass is called the invariant mass of the pair of photons together.

It is the smallest mass and energy the system may be seen to have, by any observer. It is only the invariant mass of a two-photon system that can be used to make a single particle with the same rest mass. If the photons are formed by the collision of a particle and an antiparticle, the invariant mass is the same as the total energy of the particle and antiparticle their rest energy plus the kinetic energyin the center of mass frame, where they automatically move in equal and opposite directions since they have equal momentum in this frame.

If the photons are formed by the disintegration of a single particle with a well-defined rest mass, like the neutral pionthe invariant mass of the photons is equal to rest mass of the pion. In this case, the center of mass frame for the pion is just the frame where the pion is at rest, and the center of mass does not change after it disintegrates into two photons. After the two photons are formed, their center of mass is still moving the same way the pion did, and their total energy in this frame adds up to the mass energy of the pion.

Thus, by calculating the invariant mass of pairs of photons in a particle detector, pairs can be identified that were probably produced by pion disintegration. A similar calculation illustrates that the invariant mass of systems is conserved, even when massive particles particles with rest mass within the system are converted to massless particles such as photons.

In such cases, the photons contribute invariant mass to the system, even though they individually have no invariant mass or rest mass.

Thus, an electron and positron each of which has rest mass may undergo annihilation with each other to produce two photons, each of which is massless has no rest mass. However, in such circumstances, no system mass is lost.

### The Relationship between Energy and Mass

Instead, the system of both photons moving away from each other has an invariant mass, which acts like a rest mass for any system in which the photons are trapped, or that can be weighed.

Thus, not only the quantity of relativistic mass, but also the quantity of invariant mass does not change in transformations between "matter" electrons and positrons and energy photons. The waves are called seismic seiches, a term first used in when lake levels in England and Norway oscillated from side to side as a result of the Assam earthquake of in Tibet. They were first described in the Proceedings of the Royal Society in when they were seen in English harbors and ponds after a large earthquake in Lisbon, Portugal.

Seismic seiches were also observed in many places in North America after the Alaska earthquake of March 28, Those occurring in western reservoirs lasted for two hours or longer, and amplitudes reached as high as nearly 6 ft along the Gulf Coast. The height of seiches is approximately proportional to the thickness of surface sediments; a deeper channel will produce a higher seiche.

Consequently, a standing wave cannot exist under these conditions. Unfortunately, his explanation also contains one major feature that we know to be incorrect: The Heisenberg Uncertainty Principle Because a wave is a disturbance that travels in space, it has no fixed position.

One might therefore expect that it would also be hard to specify the exact position of a particle that exhibits wavelike behavior. This situation was described mathematically by the German physicist Werner Heisenberg —; Nobel Prize in Physics,who related the position of a particle to its momentum.