# Energy and mass relationship

### The Equivalence of Mass and Energy (Stanford Encyclopedia of Philosophy)

Nov 26, Albert Einstein's most famous equation says that energy and matter are two sides And finally, Although energy and mass are related through special . Frozen light is the inverse analogy in the relationship and equally valid. Sep 12, Einstein correctly described the equivalence of mass and energy as “the most The relationship between mass-energy equivalence and. He included the second term on the right to make sure that for small velocities the energy would be the same.

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.

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 Equivalence of Mass and Energy

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. 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.

Relation to gravity[ edit ] In physics, there are two distinct concepts of mass: The gravitational mass is the quantity that determines the strength of the gravitational field generated by an object, as well as the gravitational force acting on the object when it is immersed in a gravitational field produced by other bodies.

The inertial mass, on the other hand, quantifies how much an object accelerates if a given force is applied to it. The mass—energy equivalence in special relativity refers to the inertial mass.

Thus Lange uses Lorentz invariance as a necessary condition for the reality of a physical quantity. However, in several other places, for example when Lange argues for the reality of the Minkowski interval p. However, if Lange adopts Lorentz-invariance as both a necessary and sufficient condition for the reality of a physical quantity, then he is committed to the view that rest-energy is real for the very same reasons he is committed to the view that rest-mass is real.

Thus, Lange's original suggestion that there can be no physical process of conversion between mass and energy because they have different ontological status seems challenged.

### Einstein’s mass-energy relation | physics | nickchinlund.info

As it happens, Lange's overall position is not seriously challenged by the ontological status of rest-energy. Lange could easily grant that rest-energy is a real property of physical systems and still argue i that there is no such thing as a physical process of conversion between mass and energy and ii that purported conversions result from shifting levels of analysis when we examine a physical system. It is his observations concerning ii that force us to face once again the question of why the energy of the constituents of a physical system manifests itself as the mass of the system.

Lange's interpretation, unfortunately, does not get us any closer to answering that question, though as we shall suggest below, no interpretation of mass-energy equivalence can do that see Section 3. One of the main examples that Lange uses to present his interpretation of mass-energy equivalence is the heating of an ideal gas, which we have already considered above see Section 1. He also considers examples involving reactions among sub-atomic particles that, for our purposes, are very similar in the relevant respects to the example we have discussed concerning the bombardment and subsequent decomposition of a 7Li nucleus.

In both cases, Lange essentially adopts the minimal interpretation we have discussed above. In the case of the ideal gas, as we have seen, when the gas sample is heated and its inertial mass concurrently increases, this increase in rest-mass is not a result of the gas somehow being suddenly or gradually composed of molecules that are themselves more massive.

It is also not a result of the gas suddenly or gradually containing more molecules. Lange summarizes this feature of the increase in the gas sample's inertial mass by saying: Of course, it is unlikely that Lange means this.

Surely, Lange would agree that even if no human beings are around to analyze a gas sample, the gas sample will respond in any physical interaction differently as a whole after it has absorbed some energy precisely because its inertial mass will have increased.

First, as we have suggested implicitly, some of the interpretations of mass-energy equivalence seem to assume certain features of matter. Second, some philosophers and physicists, notably Einstein and Infeld and Zaharhave argued that mass-energy equivalence has consequences concerning the nature of matter. We discuss the second relationship in the next section Section 2. To explain how some interpretations of mass-energy equivalence rest on assumptions concerning the nature of matter, we need first to recognize, as several authors have pointed out, e.

However, one could argue that although the same-property interpretation makes this assumption, it is not an unjustified assumption. Currently, physicists do not have any evidence that there exists matter for which q is not equal to zero. Such interpretations can simply leave the value of q to be determined empirically, for as we have seen such interpretations argue for treating mass and energy as distinct properties on different grounds.

Nevertheless, the Bondi-Spurgin interpretation does seem to adopt implicitly a hypothesis concerning the nature of matter. According to Bondi and Spurgin, all purported conversions of mass and energy are cases where one type of energy is transformed into another kind of energy.

This in turn assumes that we can, in all cases, understand a reaction by examining the constituents of physical systems. If we focus on reactions involving sub-atomic particles, for example, Bondi and Spurgin seem to assume that we can always explain such reactions by examining the internal structure of sub-atomic particles. However, if we ever find good evidence to support the view that some particles have no internal structure, as it now seems to be the case with electrons for example, then we either have to give up the Bondi-Spurgin interpretation or use the interpretation itself to argue that such seemingly structureless particles actually do contain an internal structure.

Thus, according to both interpretations, mass and energy are the same properties of physical systems. For both Einstein and Infeld and Zahar, matter and fields in classical physics are distinguished by the properties they bear.

### How are Energy and Matter the Same? - Universe Today

Matter has both mass and energy, whereas fields only have energy. However, since the equivalence of mass and energy entails that mass and energy are really the same physical property after all, say Einstein and Infeld and Zahar, one can no longer distinguish between matter and fields, as both now have both mass and energy. Although both Einstein and Infeld and Zahar use the same basic argument, they reach slightly different conclusions.

Einstein and Infeld, on the other hand, in places seem to argue that we can infer that the fundamental stuff of physics is fields. In other places, however, Einstein and Infeld seem a bit more cautious and suggest only that one can construct a physics with only fields in its ontology. As we have discussed above see Section 2.

However, the inference from mass-energy equivalence to the fundamental ontology of modern physics seems far more subtle than either Enstein and Infeld or Zahar suggest. This derivation, along with others that followed soon after e. However, as Einstein later observedmass-energy equivalence is a result that should be independent of any theory that describes a specific physical interaction. Einstein begins with the following thought-experiment: In this analysis, Einstein uses Maxwell's theory of electromagnetism to calculate the physical properties of the light pulses such as their intensity in the second inertial frame.

A similar derivation using the same thought experiment but appealing to the Doppler effect was given by Langevin see the discussion of the inertia of energy in Foxp. Some philosophers and historians of science claim that Einstein's first derivation is fallacious. For example, in The Concept of Mass, Jammer says: According to Jammer, Einstein implicitly assumes what he is trying to prove, viz.

Jammer also accuses Einstein of assuming the expression for the relativistic kinetic energy of a body. If Einstein made these assumptions, he would be guilty of begging the question.

Recently, however, Stachel and Torretti have shown convincingly that Einstein's b argument is sound. However, Einstein nowhere uses this expression in the b derivation of mass-energy equivalence. As Torretti and other philosophers and physicists have observed, Einstein's b argument allows for the possibility that once a body's energy store has been entirely used up and subtracted from the mass using the mass-energy equivalence relation the remainder is not zero.

One of the first papers to appear following this approach is Perrin's Einstein himself gave a purely dynamical derivation Einstein,though he nowhere mentions either Langevin or Perrin.

The most comprehensive derivation of this sort was given by Ehlers, Rindler and Penrose More recently, a purely dynamical version of Einstein's original b thought experiment, where the particles that are emitted are not photons, has been given by Mermin and Feigenbaum Derivations in this group are distinctive because they demonstrate that mass-energy equivalence is a consequence of the changes to the structure of spacetime brought about by special relativity.

The relationship between mass and energy is independent of Maxwell's theory or any other theory that describes a specific physical interaction. In Einstein's own purely dynamical derivationmore than half of the paper is devoted to finding the mathematical expressions that define prel and Trel. This much work is required to arrive at these expressions for two reasons.

First, the changes to the structure of spacetime must be incorporated into the definitions of the relativistic quantities. Second, prel and Trel must be defined so that they reduce to their Newtonian counterparts in the appropriate limit.

This last requirement ensures, in effect, that special relativity will inherit the empirical success of Newtonian physics. Once the definitions of prel and Trel are obtained, the derivation of mass-energy equivalence is straight-forward.

For a more detailed discussion of Einstein'ssee Flores, Finally, we can now appreciate why no interpretation of mass-energy equivalence can explain why the rest-mass of the constituents of a physical system contributes to that system's rest-energy, or why the energy of the constituents contributes to the rest-mass of the system.

Given the changes to the structure of spacetime imposed by special relativity, and given the definitions of dynamical quantities one adopts for well-motivated reasonsone can certainly derive mass-energy equivalence from special relativity. Such a derivation, however, can only show that mass is equivalent to energy in the sense we have struggled to elaborate above. For further discussion of this point, see Flores Experimental Verification of Mass-Energy Equivalence Cockcroft and Walton are routinely credited with the first experimental verification of mass-energy equivalence.

Cockcroft and Walton examined a variety of reactions where different atomic nulcei are bombarded by protons. They focussed their attention primarily on the bombardment of 7Li by protons i. In their famous paper, Cockcroft and Walton noted that the sum of the rest-masses of the proton and the Lithium nucleus i.

Thus, it seems as if an amount of mass of 0.