The Equivalence of Mass and Energy (Stanford Encyclopedia of Philosophy)
E = mc2Proof of Albert Einstein's special-relativity equation E = mc2. The mass- energy relation, moreover, implies that, if energy is released from the body as a. Einstein deriving special relativity, for an audience, in It's so much more than mass-energy equivalence; it's the key to unlocking the . The full and general relationship, then, for any moving object, isn't just E = mc². Einstein therefore concluded that mass and energy are really different results to indicate the true nature of the relationship between mass and energy.
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.
E=mc^2 - Deriving the Equation - Easy
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.
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.Why E=mc² is wrong
In their famous paper, Cockcroft and Walton noted that the sum of the rest-masses of the proton and the Lithium nucleus i. This means, for example, that it takes far more than twice the energy to travel at twice any particular speed. We can see this by working through the equation for two values of v, where: This equation is fine at "low" speeds, i.
However, we know that mass appears to increase as the speed increases and so the Newtonian equation for kinetic energy must start to become inaccurate at speeds comparable to the speed of light. So, how do we compensate for the observed mass increase? Advertisement Relativistic Kinetic Energy and Mass Increase In order to compensate for the apparent mass increase due to very high speeds we have to build it into our equations. We know that the mass increase can be accounted for by using the equation: From this equation we know that mass m and the speed of light c are related in some way.
What happens if we set the speed v to be very low? Using this term we now have an equation that takes into account both the kinetic energy and the mass increase due to motion, at least for low speeds: This equation seems to solve the problem.
What's more, we can rearrange the equation to show that: This result is fine for low speeds, but what about speeds closer to the speed of light? We know that mass increases at high speeds, but according to the Newtonian part of the equation that isn't the case. How can we do this? We have now removed the Newtonian part of the equation. The reason for this will become apparent in a moment.
Rearranging the result shows that: It can now be seen that relativistic energy consists of two parts. The first part is kinetic and depends on the speed of the moving body, while the second part is due to the mass increase and does not depend on the speed of the body.
However, both parts must be a form of energy, but what form? We can simplify the equation by setting the speed i.
Mass and Energy: Description and Interchangeable Relationship
We now have the famous equation in the form it's most often seen in, but what does it mean? We have seen that a moving body apparently increases in mass and has energy by virtue of its speed the kinetic energy. Looking at the problem another way we can say that as the speed of a body gets lower there will be less and less kinetic energy until at rest the body will have no kinetic energy at all.
In relativity, all the energy that moves with an object that is, all the energy present in the object's rest frame contributes to the total mass of the body, which measures how much it resists acceleration.
Each bit of potential and kinetic energy makes a proportional contribution to the mass. As noted above, even if a box of ideal mirrors "contains" light, then the individually massless photons still contribute to the total mass of the box, by the amount of their energy divided by c2.
In a nuclear reaction, the mass of the atoms that come out is less than the mass of the atoms that go in, and the difference in mass shows up as heat and light with the same relativistic mass as the difference and also the same invariant mass in the center of mass frame of the system.
In this case, the E in the formula is the energy released and removed, and the mass m is how much the mass decreases. In the same way, when any sort of energy is added to an isolated system, the increase in the mass is equal to the added energy divided by c2. An object moves with different speed in different frames, depending on the motion of the observer, so the kinetic energy in both Newtonian mechanics and relativity is frame dependent.
This means that the amount of relativistic energy, and therefore the amount of relativistic mass, that an object is measured to have depends on the observer. The rest mass is defined as the mass that an object has when it is not moving or when an inertial frame is chosen such that it is not moving.
Einstein’s mass-energy relation
The term also applies to the invariant mass of systems when the system as a whole is not "moving" has no net momentum. The rest and invariant masses are the smallest possible value of the mass of the object or system. They also are conserved quantities, so long as the system is isolated. Because of the way they are calculated, the effects of moving observers are subtracted, so these quantities do not change with the motion of the observer.
The rest mass is almost never additive: The rest mass of an object is the total energy of all the parts, including kinetic energy, as measured by an observer that sees the center of the mass of the object to be standing still. The rest mass adds up only if the parts are standing still and do not attract or repel, so that they do not have any extra kinetic or potential energy.
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. 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.