# Mass energy relationship pdf converter

According to Einstein's famous equation E = mc2, the energy E of a .. of physical systems and that we convert mass into energy when we shift. The concept of conversion between mass and energy is discussed in .. I also will submit a novel wave-particle relation to explain the charged. In physics, mass–energy equivalence states that anything having mass has an equivalent The mass–energy formula also serves to convert units of mass to units of energy (and vice versa), no matter what system of measurement units is used. contribute rest mass and invariant mass to systems; Relation to gravity.

These explanations have the merit of emphasizing that in many cases the mysteries of mass-energy equivalence do not concern one physical property magically being transfigured into another. However, the Bondi-Spurgin interpretation of mass-energy equivalence has the demerit that it fails to address reactions such as the electron-positron annihilation reaction 6. In such reactions, not only is the number of particles not conserved, but all of the particles involved are, by hypothesis, indivisible wholes.

Thus, the energy liberated in such reactions cannot be explained as resulting from a transformation of the energy that was originally possessed by the constituents of the reacting particles. Of course, Bondi and Spurgin may simply be hoping that physics will reveal that particles such as electrons and positrons are not indivisible wholes after all.

Indeed, they may even use annihilation reactions combined with their interpretation of mass-energy equivalence to argue that it cannot be the case that such particles are indivisible. Thus, we witness here explicitly just how closely related interpretations concerning mass-energy equivalence can be to views concerning the nature of matter. The second demerit of the Bondi-Spurgin interpretation, which it shares with all other interpretations of mass-energy equivalence that hold that mass and energy are different properties, is that it remains silent about a central feature of physical systems it uses in explaining apparent conversions of mass and energy.

Thus, for example, in the bombardment and subsequent decomposition of 7Li, i. 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.

- Mass is energy
- Mass-Energy

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. 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.

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

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.

### Mass–energy equivalence - Wikipedia

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.

## Mass–energy equivalence

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 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.

## The Equivalence of Mass and Energy

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. 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.

However, already in the context of Newton gravity, the Weak Equivalence Principle is postulated: Thus, the mass—energy equivalence, combined with the Weak Equivalence Principle, results in the prediction that all forms of energy contribute to the gravitational field generated by an object. This observation is one of the pillars of the general theory of relativity.

The above prediction, that all forms of energy interact gravitationally, has been subject to experimental tests. The first observation testing this prediction was made in The effect is due to the gravitational attraction of light by the Sun. The observation confirmed that the energy carried by light indeed is equivalent to a gravitational mass.

Another seminal experiment, the Pound—Rebka experimentwas performed in The frequency of the light detected was higher than the light emitted.

This result confirms that the energy of photons increases when they fall in the gravitational field of the Earth. The energy, and therefore the gravitational mass, of photons is proportional to their frequency as stated by the Planck's relation.

Application to nuclear physics[ edit ] Task Force One, the world's first nuclear-powered task force. Max Planck pointed out that the mass—energy equivalence formula implied that bound systems would have a mass less than the sum of their constituents, once the binding energy had been allowed to escape.

However, Planck was thinking about chemical reactions, where the binding energy is too small to measure. Einstein suggested that radioactive materials such as radium would provide a test of the theory, but even though a large amount of energy is released per atom in radium, due to the half-life of the substance yearsonly a small fraction of radium atoms decay over an experimentally measurable period of time.

Once the nucleus was discovered, experimenters realized that the very high binding energies of the atomic nuclei should allow calculation of their binding energies, simply from mass differences. But it was not until the discovery of the neutron inand the measurement of the neutron mass, that this calculation could actually be performed see nuclear binding energy for example calculation.

InRainville et al. By measuring the mass of different atomic nuclei and subtracting from that number the total mass of the protons and neutrons as they would weigh separately, one gets the exact binding energy available in an atomic nucleus. This is used to calculate the energy released in any nuclear reactionas the difference in the total mass of the nuclei that enter and exit the reaction.