Attempts to prove E=mc²
See also E=mc².
Attempts to prove E=mc² are futile because there is no mass-energy equivalence. But that has not stopped people, including liberals who avoid the Bible, from insisting that they have cleverly developed a "proof" of E=mc², and thereby established a mass-energy equivalence which, in fact, does not exist. No Nobel Prize has ever been awarded for any experimental verification of this implausible equation, because no such verification exists.
Flaws in "Proofs"
Many of these "proofs" are either circular in logic, or assume unproven (and often implausible) premises.
The typical defect in these proofs is an unstated premise that the Theory of Relativity must be consistent with the conservation of energy. The "proof" implicitly redefine mass as a function of energy (and the speed of light) so that energy is then conserved under Relativity.
Proponents of the formula rarely state their assumptions clearly. In fact, they assume what they purport to prove: that Relativity can make sense only if energy is somehow directly related to mass based on the speed of light. By assuming that Relativity is true and that energy is conserved, the formula itself is thereby also assumed.
Many of the "proofs" use contrived thought experiments to try to bootstrap the kinetic energy of a moving particle into an assertion about the energy of a resting mass. Aside from changes in potential energy, there is no direct connection between the kinetic energy of a moving mass and its rest energy.
Example of circularity in "proofs"
The argument in some "proofs" is that although overall energy, kinetic plus potential, is conserved, the potential energy can manifest itself as an increase in the resting mass—an assumption that implicitly redefines mass to comport with the conclusion sought.
Redefining mass to comport with the conclusion sought
Concepts and terms have undergone minor changes, to match new or more accurate observations, throughout the history of science. For example, the circular planetary orbits in Copernicus' heliocentric model became ellipses in Kepler's model, to match observations. Similarly, the long-held notion that atoms are indivisible and immutable was overthrown around 1900. Neither of these changes, nor the change in the definition of mass to be consistent with relativity and observation, involved circular reasoning.
Choosing a theory, or the parameters used in a theory, to match observation and thereby make the theory describe reality correctly, is a time-honored tradition in science. As an example of "tweaking" of parameters to comport with the conclusion sought, Kepler set all the orbital parameters of the planets to be what they had to be in order to match the observed behavior. The parameters of motion of the PSR B1913+16 pulsar pair were of course set by Hulse and Taylor to match observation. Interestingly, nothing about General relativity had to be "tweaked" to predict the precession of the perihelion of Mercury.
Scientists commonly claim that E=mc² is true for what are, in fact, ordinary chemical reactions that emit energy, even though the mass change implied by such reactions is far too small to measure. This is because the formula can be proven (see below) for all interactions. So no one claims that chemical reactions prove or verify E=mc², just that it logically must be true. Nuclear reactions are another matter. The formula is verified constantly, and, in fact, its consequences can be seen in the atomic weights in periodic table charts hanging in science classrooms all around the world. Nuclear-fusion reactions, such as the transformation of hydrogen to helium, also demonstrate the validity of the formula E=mc². The transformation of 4 atoms of 1H into one atom of 4He occurs constantly in the Sun, and has a mass defect of .02916 amu, which works out to 27.162 MeV. Several interactions are involved in the total transformation, and their energies have been observed in the laboratory. Alpha decay energies have been measured for many isotopes, and agree with the mass change. See Quantitative Analysis of Alpha Decay.
This equation is somewhat obscure in everyday life—scenarios that effectively demonstrate it need to be carefully framed. But it has been accurately verified in every scenario for which a verification or refutation could occur.
In addition to the purely logical or mathematical derivations of this formula, it has been verified in many experiments and with great accuracy. A mathematical derivation may be found in the references at the end of this article. These derivations show that the equation is true not only for nuclear reactions (for which the equation can be verified experimentally) but for ordinary chemical reactions as well. So, while the equation is not proven by ordinary chemical reactions, there are extremely strong logical reasons to believe it applies.
Nuclear fission and fusion experiments, such as the transformation of hydrogen to helium, clearly demonstrate the connection between mass and energy, with the square of the speed of light as the proportionality constant. For example, the mechanism of the Sun's energy creation is quite well understood in terms of the atomic weights of the isotopes involved.
Perhaps the most general and all-encompassing demonstration of this equation can be found in the examination of atomic weights and alpha particle energies in alpha-radioactive elements. See Quantitative Analysis of Alpha Decay. These experiments are not isolated or conducted in "carefully framed scenarios".
Motivation for E=mc²
The insistence on E=mc² is partly motivated by a quest for a "grand unified theory," which has never been found despite the waste of billions of dollars and roughly a century looking for it. If mass and energy were equivalent as E=mc² asserts, then there should be a theory that unifies gravitation and electromagnetic forces. There isn't, and the Bible correctly predicts that there isn't.
- Actually, the idea of a "grand unified theory" didn't arise until about the 1950's, give or take a couple of decades. Einstein's formula was published in 1905. The formula has nothing to do with gravity, and the canard of "mass-energy equivalence" is really a meaningless notion. The equation simply says that potential energy has mass; nothing more.
Another motivation of E=mc² is to try to make the Theory of Relativity consistent with the principle of the conservation of energy, by pretending that mass gains or loses energy to make up for the energy discrepancy in Relativity.
- That is quite true, and is in fact how the equation arises. It arises because of the need for these principles:
- Conservation of energy is precisely obeyed, for all phenomena, in all frames of reference.
- Conservation of momentum is precisely obeyed, for all phenomena, in all frames of reference.
- These two principles, along with the required relativistic definitions of energy and momentum, directly lead to the need for potential energy to have mass. It's that simple.
Proofs of the formula E=mc² abound in the scientific literature, in print and on the internet, though many of them are more complicated than they need to be, because they are proving it in a more wide-ranging and less focused context. A good example may be found on pages 121-138 of Spacetime Physics by Edwin Taylor and John Wheeler (W. H. Freeman, 1966, ISBN 0-7167-0336-X). An exposition on the internet may be found at Wikiversity.
- Logical Flaws in E=mc²
- Essay:Rebuttal to Logical Flaws in E=mc²
- Quantitative Analysis of Alpha Decay