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.

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.

False experimental claims

It is common for atheists to claim that E=mc² is proven by what are, in fact, ordinary chemical reactions that emit energy. Nuclear-fusion reactions, such as the transformation of hydrogen to helium, do not demonstrate any connection between the rest energy of a mass and the speed of light, as E=mc² asserts.

Broken clocks are correct twice a day, and some isolated experiments have asserted verification of E=mc² in certain carefully framed scenarios. But no experiment has demonstrated E=mc² with any reasonable degree of generality.

Experimental verification

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.

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.

A proof

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.

See also

• Logical Flaws in E=mc²
• Essay:Rebuttal to Logical Flaws in E=mc²
• Quantitative Analysis of Alpha Decay