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Does the Inertia of a Body Depend upon its Energy-Content? (1905) [pdf] (fourmilab.ch)
51 points by utkarshs12 6 days ago | hide | past | web | 17 comments | favorite

An interesting point to note is that Einstein derived m = E / c^2 rather than E = mc^2. Even though both formulae are obviously equivalent, the interpretations may vary.

For instance, for nuclear fission we use E = mc^2. Uranium breaks into smaller atoms, but some mass has disappeared: it's because it has been radiated in the form of immaterial energy, hence nuclear plants and A-bombs.

On the other hand, m = E/c^2 gives an interesting interpretation to what inertial mass is. According to this equation, mass is actually "energy at rest". If you want to move your object, you have to give it some energy, so that the resulting energy of the body will result into the desired motion. It's kind of similar to how hot air (the energy you give) and cold air (system at rest) mix to form "medium-hot" air (system in motion).

And just because I like writing, note that we have no idea whether inertial mass (the m in m = E / c^2 and Newton's Third Law, F = ma) is equivalent to gravitational mass (the m in F_gravitation = G * m_earth * m / d^2), but experiments dismiss any difference bigger than 1 in 10^12. The principle of equivalency between these two masses is the fundamental postulate of general relativity.

In a nutshell, m = E/c^2 defines the inertial mass, and general relativity assumes it's equal to the gravitational mass.

I'm not really seeing the difference between m = E / c^2 rather than E = mc^2. Isn't c just a proportionality constant that we can set to 1 by choosing different units?[1] Then you are saying that E = m suggests something different than m = E.

[1] https://en.wikipedia.org/wiki/Natural_units

You can think of it as a dual approach. We can consider "E is defined as mc^2, so basically we can extract energy from mass". Alternatively, we can consider "m is E/c^2, so inertial mass is actually energy at rest".

Both explanations are valid, which doesn't mean they are contradictory.

It's kind of like one person in the train sees the person on the ground moving, even though from the person on the ground's point of view, it's the person on the train who is moving. Who's moving? Well, the interpretation depends on the referential you choose. So here, you can say there is a referential "mass" and a referential "energy". They will give seemingly different interpretations, but which are actually equivalent.

(On a side note, there are indeed no differences between E=mc^2 and m=E/c^2, it's just that it's easier to conceptualize inertial mass as being energy at rest with the latter.)

   It is not impossible that with bodies whose energy-content 
   is variable to a high degree (e.g. with radium salts) the 
   theory may be successfully put to the test.
One of the more understated assertions in history, there.

Here's my favourite understated claim in a paper:

"It has not escaped our notice that the specific pairing we have postulated immediately suggests a possible copying mechanism for the genetic material".

Watson & Crick, "Molecular Structure of Nucleic Acids: A Structure for Deoxyribose Nucleic Acid" (DNA), having almost certainly discovered the mechanism of heredity in complex life forms: one of the most significant discoveries in the history of biology. Very dry.

Is this a translation from German, or was it originally published in English? I ask, because this is so awkwardly worded as to be nearly unparseable:

> The laws by which the states of physical systems alter are independent of the alternative, to which of two systems of coordinates, in uniform motion of parallel translation relatively to each other, these alterations of state are referred (principle of relativity)

The last page says, "This edition of Einstein’s 'Does the Inertia of a Body Depend upon its Energy-Content' is based on the English translation of his original 1905 German language paper."

That line got me mind-boggled too. But I realized the English people spoke and specially wrote back in the day was quite verbose and the sentence construction was obviously quite elaborate.

To help you out, I think that line equates to - "Considering two coordinate systems that are moving in uniform motion of parallel translation relative to each other ("which we now conveniently call an Inertial Reference Frame"), the laws governing the movement of a physical body is independent of which of the 2 systems you choose."

Which also equates to - "The laws of physics are the same for all observers in uniform motion relative to one another "

This 1920's translation by Perrett and Jeffery is so bad you might as well read the original (search 'Ist die Trägheit eines Körpers von seinem Energieinhalt abhängig?')

It makes a lot more sense in German, even though I'm not that fluent in it. I searched but didn't find a better translation. It's been over a hundred years now, surely someone made the effort...

Thanks, the full stop at the end of that URL was causing trouble.

For those who read comments before reading the article, and to riff off of the recent HN discussion of Classic Papers: Articles That Have Stood The Test of Time

It doesn't get much more "classic" (or maybe that should say "relativistic") than A. Einstein demonstrating E = mc²

See the "About the Document" at the end for the details.

>Neglecting magnitudes of fourth and higher orders...

What if we don't?

You get essentially the same answer.

Einstein discovered a counterexample to Betteridge's law?

Many academic articles are titled with yes/no questions. That how the whole "hypothesis" thing often works.

I should really write an article titled "Is Betteridge's law true?"

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