# Essay:Rebuttal to Logical Flaws in E=mc²

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This is a rebuttal to the points in the Logical Flaws in E=mc² article.

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*The energy of a mass would change rapidly as the speed of light changes.*.- There is really no evidence that the speed of light changes "rapidly", or even perceptibly in the current epoch. Even the question of whether it has changed slightly over billions of years is controversial.
- Be that as it may, if the speed of light were to change in any perceptible way, we would notice it in malfunctions of the GPS system (whether you accept relativity or not!), and in telemetry from spacecraft. If it were to increase "rapidly", we could even be fried by the extra sunlight, now in transit from the Sun, piling up on our cosmic doorstep. Or we could be frozen if it slowed down.

*How is "m" defined?*- Many formulas are in terms of symbols and concepts that the reader is expected to be familiar with. This includes things like
- or
- It is simply not practical to put in an explanation for all the symbols. This is especially true for equations that are "eye-catching", which this one certainly is.
- Since this formula says something that is not straightforward in layman's terms, leading to silly things like saying that the formula says that "mass and energy are equivalent", it is worth being careful here.
- "m" is mass, obviously. Really. That's all. It's what you measure if you put something on a scale. There has historically been some extra complexity and confusion involving the terms "rest mass" and "relativistic mass", but those terms are obsolete. The old term "rest mass" is what we use in the present day, calling it just "mass". If you put a charged flashlight battery on a scale and weigh it, that's it's mass. If you put a spent battery on a scale and weight it, that's it's mass. They will differ by about a picogram, by the way, due to E=mc².
- "c" is the space-time calibration factor of the Lorentz transform and the Minkowski space. This calibration factor has a very deep meaning in relativity. It's everywhere. You need to understand it as the calibration factor. It is a speed, 3x10
^{8}meters per second. It happens that light travels at that speed.^{[1]}The work of James Clerk Maxwell explains why. Because of this, it is commonly called the "speed of light", but it doesn't actually involve light. "Speed of light" is just easier to say, and has a meaning that is more accessible to the layman, than "space-time calibration factor". But E=mc² is not about light. It's true even in the dark. - "E" is energy. It's not easy to give a good description of this from first principles. But it's really what you learned about in junior-high and high-school science classes. It's that thing that is conserved. It can be "potential" or "kinetic". It's the ability do work, for example, to make something move. A battery has energy (potential) because, if connected to a motor, it can make things move. A coiled spring does the same. A speeding bullet has kinetic energy, and moves whatever it hits.
- The fact that an equation has been presented without an explanation of the terms appearing in it does not constitute a "logical flaw" in the equation. It constitutes at best a "pedagogical flaw" in the book in which it was presented.

- Many formulas are in terms of symbols and concepts that the reader is expected to be familiar with. This includes things like
*The formula falsely implies that it is impossible for matter to increase its energy without increasing its mass in direct proportion*.- In fact it does imply exactly that, and it isn't false. If something's energy increases, its mass really does increase in direct proportion. The proportionality constant is which is about 10
^{−17}kilograms per joule. For normal things, that is way too small to measure. But a battery really does get heavier, by about 1 picogram, when it charges. If you had a scale that could weigh batteries at the picogram level, you could see E=mc² before your very eyes, and we wouldn't be having this debate.

- In fact it does imply exactly that, and it isn't false. If something's energy increases, its mass really does increase in direct proportion. The proportionality constant is which is about 10
*Why hasn't the formula led to anything of value?*- This issue has been discussed at length elsewhere, such as Counterexamples to Relativity and Essay:Rebuttal to Counterexamples to Relativity, item 33 or so. E=mc² is a much more narrow topic than the whole field of relativity, so we have to be careful about what makes an equation "valuable". Engineers and inventors actually use and in building useful things (airplanes and transformers, for example). The
*insights*from E=mc² are enormous, but the fact is, people don't take their nuclear reactor waste to the neighborhood waste dump and demand a lower disposal price on the grounds that it weighs slightly less than the original fuel. Nor would someone expect the "value" of paying a lower checked baggage fee on an airplane due to having discharged whatever batteries were in one's suitcase. - Mere equations should not be evaluated by their direct usefulness in making products. In particular,
*failure of an equation to provide actual things of value*does not constitute ain the equation. The logic of something transcends its immediate usefulness. An equation can be criticized for not leading to useful products, but that isn't a "logical flaw".**logical flaw**

- This issue has been discussed at length elsewhere, such as Counterexamples to Relativity and Essay:Rebuttal to Counterexamples to Relativity, item 33 or so. E=mc² is a much more narrow topic than the whole field of relativity, so we have to be careful about what makes an equation "valuable". Engineers and inventors actually use and in building useful things (airplanes and transformers, for example). The
*The formula implies existence of a unified theory of mass and light, when no such theory is possible.*- First, saying that "no such theory is possible", on any subject, is a rather slippery slope.
- Second, relativistic quantum electrodynamics is very much a "theory of mass and light". Physicists deal with this subject matter all the time. Perhaps the simplest example of the interaction of matter and light at the quantum-mechanical scale is Compton scattering.
- Finally, as noted above, the "c" in the equation is commonly called the "speed of light", but it is really just the calibration factor. The equation is not about light. Just mass and energy. The equation is true in the dark.

## References

- ↑ Actually, according to recent research involving "vacuum polarization", it has been determined that light travels at a speed which is very slightly less than c. This was determined by comparing arrival times of photons and neutrinos from an extremely distant supernova. Even though neutrinos have mass and therefore don't travel at speed "c", they traveled faster than the light did. The neutrinos didn't interact with the vacuum polarization.