5 ms·

Does the Inertia of a Body Depend upon its Energy-Content? (1905) [pdf]

51 points by utkarshs12 9y ago

ahh 9y ago
Einstein discovered a counterexample to Betteridge's law?
- JshWright 9y ago
  Many academic articles are titled with yes/no questions. That how the whole "hypothesis" thing often works.
- adtac 9y ago
  I should really write an article titled "Is Betteridge's law true?"
CamperBob2 9y ago
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.
- robotresearcher 9y ago
  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.
PhantomGremlin 9y ago
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.
monochromatic 9y ago
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)
- kcanini 9y ago
  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."
- Luc 9y ago
  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...
  - detaro 9y ago
    working link: https://de.wikibooks.org/wiki/A._Einstein,_Ist_die_Tr%C3%A4gheit_eines_K%C3%B6rpers_von_seinem_Energieinhalt_abh%C3%A4ngig%3F_-_Kommentiert_und_erl%C3%A4utert%2E https://de.wikibooks.org/wiki/A._Einstein,_Ist_die_Tr%C3%A4g...
    - Luc 9y ago
      Thanks, the full stop at the end of that URL was causing trouble.
- utkarshs12 9y ago
  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 "
aisofteng 9y ago
>Neglecting magnitudes of fourth and higher orders... What if we don't?
- idlewords 9y ago
  You get essentially the same answer.
plopilop 9y ago
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.
- nonbel 9y ago
  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 https://en.wikipedia.org/wiki/Natural_units
  - plopilop 9y ago
    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.)

51 points by utkarshs12 9y ago

ahh 9y ago

Einstein discovered a counterexample to Betteridge's law?

JshWright 9y ago
Many academic articles are titled with yes/no questions. That how the whole "hypothesis" thing often works.
adtac 9y ago
I should really write an article titled "Is Betteridge's law true?"

CamperBob2 9y ago

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.

robotresearcher 9y ago
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.

PhantomGremlin 9y ago

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.

monochromatic 9y ago

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)

kcanini 9y ago
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."
Luc 9y ago
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...
- detaro 9y ago
  working link: https://de.wikibooks.org/wiki/A._Einstein,_Ist_die_Tr%C3%A4gheit_eines_K%C3%B6rpers_von_seinem_Energieinhalt_abh%C3%A4ngig%3F_-_Kommentiert_und_erl%C3%A4utert%2E https://de.wikibooks.org/wiki/A._Einstein,_Ist_die_Tr%C3%A4g...
  - Luc 9y ago
    Thanks, the full stop at the end of that URL was causing trouble.
utkarshs12 9y ago
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 "

aisofteng 9y ago

>Neglecting magnitudes of fourth and higher orders... What if we don't?

idlewords 9y ago
You get essentially the same answer.

plopilop 9y ago

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.

nonbel 9y ago
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 https://en.wikipedia.org/wiki/Natural_units
- plopilop 9y ago
  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.)