# Essay:Rebuttal to Attempts to prove E=mc²

This is a rebuttal to the points in the Attempts to prove E=mc² article.

Unlike most essay pages, anyone is welcome to contribute. We ask that you abide by the usual guidelines—do not remove non-vandal, non-parody, non-libelous material without discussing it first on the talk page, or explaining after-the-fact for serious problems.

Since the "Attempts to prove E=mc²" article is not a list of bullet points with a rebuttal for each, this article will just repeat the contents of "Attempts to prove E=mc²" with commentary inserted where needed.

Briefly, the equation "E=mc²" is one of the most carefully established equations in all of science—established both by numerous mathematical proofs and numerous experiments.

## Contents

## The article

**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*.

- Reply: Saying "there is no mass-energy equivalence" is meaningless. People often assert that the equation says that there is such an equivalence, but that is a meaningless statement, often made by people who are interested in snappy quotes but don't actually understand the topic very well. The equation says that potential energy has mass. It doesn't imply any "equivalence" in a way that is meaningfully described by saying simply that the equation asserts an equivalence.
- Inferring from this that attempts to prove the equation are futile is not logically supported. Proofs exist in great numbers, as will be described below.
- The equation, both in its proofs and in its experimental validation, is accepted by virtually the entire wold-wide science community. Some of them are liberals, and some are people who avoid the Bible. That has nothing to do with the correctness of the equation.
- Scientific facts do not require Nobel Prizes to be true.

### Flaws in "Proofs"

Many of these "proofs" are either circular in logic, or assume unproven (and often implausible) premises.

- That's not so. The logic is not circular, and the premises are usually stated, and supported, quite clearly. See below.

The typical defect in these proofs is an unstated premise that the Theory of Relativity must be consistent with the conservation of energy. The "proofs" implicitly redefine mass as a function of energy (and the speed of light) so that energy is then conserved under Relativity.

- Yes, relativity is consistent with precise conservation of both energy and momentum, at all times, and in all reference frames. In fact, the equation E=mc² was derived from the need to have this be so.
- Modern treatments of relativity do not redefine mass to be a function of energy. The mass of an object is what you would get when you measured it (on a scale, or, more properly, in an inertia experiment) in its own reference frame. Always. Everyone, in every reference frame, agrees with that value. Always.

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.

- The proofs given in the references state their assumptions very clearly and succinctly:

- Galilean and Newtonian mechanics.
- Galilean relativity, that is, the notion that there is no absolute frame of reference.
- Conservation of energy.
- Conservation of momentum. (So far this is just classical physics.)
- The universality of the speed of light. (That is, special relativity.)

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.

- We do not know what is meant by "bootstrapping". We do not know what "energy of a resting mass" means. If an object is at rest, its kinetic energy is zero.

### 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.

- Yes, the potential energy does manifest itself as an increase in the mass beyond what the rest mass would be without the potential energy. The conclusion sought is that the mass increases by [potential energy]/c². The equation shows that that is in fact what happens.
- 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.

### False experimental claims

- These experimental claims are in fact true and accepted by essentially the entire scientific community.

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.

- Yes, 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^{1}H into one atom of^{4}He 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. - These experimental results are accepted by virtually all scientists, atheist and theist alike. Relativity is not in any way inconsistent with any religious sensibilities that we know of.

- Yes, 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

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.

- Yes, broken clocks are correct twice a day. E=mc² is correct all the time. It has been verified in an extremely wide range of experiments, as detailed below.

### 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.

- 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.
^{[1]}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.

- 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.

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.

### 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.^{[2]}

## See also

- E=mc²
- Logical Flaws in E=mc²
- Essay:Rebuttal to Logical Flaws in E=mc²
- Attempts to prove E=mc²
- Quantitative Analysis of Alpha Decay