# Relationship between mass and energy

### The Relationship between Energy and Mass Einstein used E = mc^2 to prove that mass and energy are relative to each other. This lesson describes how energy can be converted into mass. 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. Einstein's photons of light were individual packets of energy having many of the characteristics of particles. Recall that the collision of an electron (a particle) with .

However, the Bondi-Spurgin interpretation offers no explanation concerning why the energy of the constituents of a physical system, be it potential energy or kinetic energy, manifest itself as part of the inertial mass of the system as a whole. Rindler for example, inagrees that there are many purported conversions that are best understood as mere transformations of one kind of energy into a different kind of energy. Thus, Rindler too adopts the minimal interpretation of mass-energy equivalence of, for example, the bombardment and subsequent decomposition of 7Li.

However, for Rindler, there is nothing within special relativity itself that rules out the possibility that there exists fundamental, structureless particles i.

Thus, Rindler seems to be suggesting that we should confine our interpretation of mass-energy equivalence to what we can deduce from special relativity. The merit of Rindler's interpretation is that it confines the interpretation of Einstein's equation to what we can validly infer from the postulates of special relativity. Unlike the interpretation proposed by Bondi and Spurgin, Rindler's interpretation makes no assumptions about the constitution of matter.

Lange begins his interpretation by arguing that rest-mass is the only real property of physical systems. Lange then goes on to argue that a careful analysis of purported conversions of mass-energy equivalence reveals that there is no physical process by which mass is ever converted into energy.

Instead, Lange argues, the apparent conversion of mass into energy or vice versa is an illusion that arises when we shift our level of analysis in examining a physical system. 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.

As it happens, Lange's overall position is not seriously challenged by the ontological status of rest-energy.

• The Equivalence of Mass and Energy
• Mass is 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.

## Einstein’s mass-energy relation

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. 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.

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

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.

## Mass–energy equivalence

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.

Thus the vibrational energy of the string is quantized, and only certain wavelengths and frequencies are possible. Notice in Figure 6. The amplitude of the wave at a node is zero. Quantized vibrations and overtones containing nodes are not restricted to one-dimensional systems, such as strings. A two-dimensional surface, such as a drumhead, also has quantized vibrations. Similarly, when the ends of a string are joined to form a circle, the only allowed vibrations are those with wavelength Equation 6. The standing wave could exist only if the circumference of the circle was an integral multiple of the wavelength such that the propagated waves were all in phase, thereby increasing the net amplitudes and causing constructive interference.

Otherwise, the propagated waves would be out of phase, resulting in a net decrease in amplitude and causing destructive interference. Higher energy levels would have successively higher values of n with a corresponding number of nodes. Standing waves are often observed on rivers, reservoirs, ponds, and lakes when seismic waves from an earthquake travel through the area.