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Einstein did not derive E =mc2 first

  1. May 30, 2004 #1
    Origin and escalation of mass-energy equation E=mc^2

    Ajay Sharma
    Community Science Centre. DOE. Post Box 107 Shimla 171001 HP INDIA
    Email physicsajay@lycos.co.uk , physicsajay@yahoo.com

    Einstein’s 27 Sep 1905 paper available at http://www.fourmilab.ch/etexts/einstein/E_mc2/www/


    E=mc^2existed before Einstein’s derivation in Sep. 1905. Isaac Newton, S. Tolver Preston, Poincaré , De Pretto and F. Hasenöhrl are the philosophers and physicists who have given idea of E=mc^2. Einstein derived existing E=mc^2starting with result of relativistic variation of light energy, but finally obtained L =mc^2 under applying classical conditions (v<<c). After Einstein, Max Plank also derived the same independently. Max Born has expressed surprise over non-inclusion of previous references by Einstein in the derivation of E=mc^2.

    1.0 Contributors of equation E =mc2

    Before Einstein, among other physicists, Isaac Newton [1], English S. T. Preston [2] in 1875, French Poincaré [3,4] in 1900, Italian De Pretto [5] in 1903, German F. Hasenöhrl [6,7] made significant contributions in speculations and derivations of E=mc^2. After Einstein Planck [8] has also derived E=mc^2 independently. J J Thomson in 1888 is also believed to have anticipated E=mc^2from Maxwell’s equations.
    (i) Issac Newton (1642-1727)
    The Great Sir Isaac Newton [1] has quoted "Gross bodies and light are convertible into one another...", 1704). In 1704 Newton wrote the book “Optiks”. Newton also put forth Corpuscular Theory of Light
    (ii) S. Tolver Preston
    S. Tolver Preston [2], who made predictions which are based essentially upon E=mc^2. Preston in his book Physics of the Ether proposed in 1875 that vast amount of energy can be produced from matter. Preston determined that one grain could lift a 100,000-ton object up to a height of 1.9 miles. This deduction yields the essence of equation E=mc^2.
    (iii) Jules Henri Poincaré (1854-1912)
    Poincaré in 1900 [3,4] put forth an expression for what he called the "momentum of radiation" M_R. It is M_R = S/c^2, where S represents the flux of radiation and c is the usual velocity of light. Poincaré applied the calculation in a recoil process and reached at the conclusion in the form mv = (E/c^2)c. From the viewpoint of unit analysis, E/c^2 takes on the role of a "mass" number associated with radiation. It yields E=mc^2.

    (vi) Olinto De Pretto
    An Italian Industrialist Olinto De Pretto [5] suggested E=mc^2, in concrete way. Firstly this article was published on June 16, 1903. Second time on February 27, 1904 the same was published in the Atti of the Reale Instituto Veneto di Scienze. Thus De Pretto published E=mc^2 about one and half year before. In 1921 De Pretto was shot dead by a woman over a business dispute. When De Pretto was killed he was trying to publish the complete book of his scientific ideas. This paper is in Italian; hence it remained away from accessibility of wider scientific community. However Einstein was affluent in Italian language also.
    (v) F. Hasenöhrl
    In 1904 F. Hasenöhrl [6,7 ], gave first derived expression for mass-energy conversion. He investigated a system composed of a hollow enclosure filled with "heat" radiations and wanted to determine the effect of pressure due to radiations. His calculations lead him to conclude that
    "to the mechanical mass of our system must be added an apparent mass which is given by
    m = (8/3)E/c^2"
    where E is the energy of the radiation. Further in later paper he maintained that improve result for mass exchanged is
    m = (4/3)E/ c^2"
    Ebenezer Cunningham [9] in 1914 in his book The Principles of Relativity showed that F. Hasenöhrl, has made a slight error in his calculations. F. Hasenöhrl, did not take characteristics of the shell properly. If errors are removed then
    m (mass exchanged) = E/c^2
    or E = (mass exchanged) c^2
    This is the same result as quoted by Einstein. It implies that E=mc^2 is contained in F. Hasenöhrl’s, analysis. Moreover Hasenöhrl’s work was published in the same journal in which Einstein’s method to derive E=mc^2 was published one year later.
    (vi) Albert Einstein
    In 1905, Einstein [10] derived L = mc^2, and then speculated from here E=mc^2, analogously without actual proof. Einstein derived already existing E=mc^2, strangely did not acknowledge his predecessors like de Pretto and Hasenöhrl. Both have suggested E=mc^2 just one and half year before Einstein’s derivation. However two years after i.e. 1907 when Max Plank [8] derived E=mc^2 independently, Planck acknowledged derivation of Einstein. Planck even pointed out the conceptual and mathematical limitations of Einstein’s method of derivation..
    (a) Although Einstein started to derive E=mc^2 using relativistic variation of light energy as in Eq.(2), yet he derived final results under classical condition. Einstein interpreted the results using Binomial Theorem which is applicable if v<<c.

    (b) Einstein never considered the any Relativistic Increase in Mass of body.
    ThE equation of Relativistic Increase In Mass was first justified by Kaufman [11] in 1900.
    Further Einstein speculated E=mc^2 for all energies from E=mc^2 without justifying that eq.(2) i.e. holds good for sound, heat, chemical , electrical energy etc. If eq.(2) holds good for sound and heat energies, then E=mc^2 will be analogously transformed as
    Sound energy = E=mc^2 (3)
    or Every type of energy = E=mc^2 (4)

    (vii) Max Planck
    In 1907, Planck [8] made an in-depth investigation of the energy "confined" within a body, but he did not use Einstein approach at all. Plank presented his findings in
    Planck derived an expression
    m-M= E/c2
    and interpreted that
    ” The inertia mass of body is altered by absorption or emission of heat energy. The increments of mass of body are equal to heat energy divided by square of speed of light”
    Then in a footnote at page 566 Planck writes, "Einstein has already drawn essentially the same conclusions”. Planck maintained Einstein derivation as approximation.
    (ix) Recent developments.
    In 1907 Planck [8] even pointed out the conceptual and mathematical limitations of Einstein’s derivation. In 1952, H E Ives [12] stressed that Einstein’s derivation of the formula E=mc^2 is fatally flawed because Einstein set out to prove what he assumed.
    Sharma [13] in 2003 extended E=mc^2 to E =Ac^2m, where A is conversion co-efficient and can be equal, less or more than one, depending upon inherent characteristics of conversions process in nature. The value of A is consistent with concept of proportionality factor existing since centuries. Energy emitted in celestial events Gamma Ray Bursts (most energetic events after Big Bang) is 10^ 45 Joule/s. It can be explained with value of A equal to 2.57x10^18. Similar is the case of Quasars. Like wise kinetic energy of the fission Fragments of U^235 or Pu^239 is found 20-60 MeV less than Q-value ( 200MeV), Bakhoum [14] The similar deviations in experimental results are also quoted by Hambsch [15], Thiereus [16] etc. It can be explained with value of A less than one. Till date E=mc^2 is not confirmed in chemical reaction due to technical reasons, but regarded as true.
    Also a particle Ds (2317) discovered at SLAC [17] has been found to have mass lower than current estimates based upon E=mc^2. Incidentally, there are proposals for both theoretical and experimental variations (increase or decrease) in value of c [18-19]; as fine structure constant is reported to be increasing over cosmological timescales, implying slowing down of speed of light, c. The proposals for variations of speed of light definitely affect status of E =mc2, indirectly.
    2.0 Einstein and priority of E=mc^2
    Einstein did not mention Hasenöhrl’s work (who gave first derived expression for mass-energy equation) in any of his paper on this subject from 1900 - 1909. However Hasenöhrl has published in 1904 the paper in the same very journal in which Einstein later published his derivation of E=mc^2 in 1905.
    Einstein [20] applied his E=mc^2 derivation in 1906. In this paper he gave reference of Poincaré' s work [3, 4]. Einstein gave credit to Poincaré for mass energy equivalence at least for electromagnetic radiations.
    But, even with Planck's complete derivation and this Poincaré acknowledgement, Einstein later refused to accept any other priority for this notion. Stark [21] stated that Planck gave first derivation of E=mc^2, in fact Planck and Stark were convinced that Einstein derivation of E=mc^2 is inconsistent. Then Einstein [22] wrote Stark on 17 Feb 1908, “I was rather disturbed that you do not acknowledge my priority with regard to the connection between inertial mass and energy.” Max Born [23], co-originator of Quantum Mechanics stated, "The striking point is that it contains not a single reference to previous literature”.
    Einstein [24] in 1907 spelled out his views on plagiarism: "It appears to me that it is the nature of the business that what follows has already been partly solved by other authors. Despite that fact, since the issues of concern are here addressed from a new point of view, I am entitled to leave out a thoroughly pedantic survey of the literature..."
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  3. May 30, 2004 #2


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    [tex]E=mc^2[/tex] can actually be derived from Maxwell equations (of course,if you're skillful in manipulating them).Believe it or not,SR is not a must for reaching the formula.But,the derivation from SR principles is shorter and more elegant one.
  4. May 30, 2004 #3
    Its a variable and "manipulatable" theory, anyway...
  5. May 31, 2004 #4
    Energy Absolution...

    [tex]E = Aymc^2[/tex] :biggrin:
  6. May 31, 2004 #5


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    Meaning what? SR is a deduction from the two postulates, and has only the one parameter, c. Where is the manipulability?
  7. May 31, 2004 #6


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    ajay, you raised an interesting question on the genesis of probably the most famous formula of all time.But,why on earth in "Stellar astrophysics" subforum(is it becouse you mentioned Quasars)?This thread should be removed to SR@GR subforum.
    Firstly,as concerns Poincare's and Planck's contribution to the discovery ,as well as of the unlucky De Pretto's one,it was real.I have heard of that already.
    Secondly,as concerns J.J.Thomson's "anticipation" of the formula from the Maxwell's set ,it was possible to do that in 1888.IMO,I think it is just believed by some people (who usually like to dispute Einstein's role ) and incorrect rumour that well-known discoverer of electron had the formula.I have got Thomson's collected works.He was a great experimental physicist,but my impression he wasn't that strong in pure math and theoretical models to derive the formula.Even less to interprete it's meaning (like Einstein did).
    Lastly, Newton, the great one.Eh..,surely he must have knew of the formula in 1700. ,only with one "little" difference:multiplying factor 1/2 always on the right side of the equation..
    P.S.Orion,how about multiplying *factors* on the left side of the famous formula.
    Like this: [tex]Einstein=mc^2[/tex] ?
  8. May 31, 2004 #7


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    Why is so many people obsessed with this? even to the point of writing things like this:

    Did this guy actually read Einstein's paper? It certainly does not seem like it, since the 1905 paper clearly states:

    The use of a different letter (L instead of E) does not affect the interpretation.
  9. May 31, 2004 #8

    Light is.
    The speed of light IS NOT a constant (and NEVER has been).
  10. Jun 1, 2004 #9


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    Then how do you explain:
    a. That all experiments that measure it directly or indirectly (starting from the Michaelson-Morley interferometer and including communication with space probes and GPS satelites) give the same result, and
    b. That all consequences of SR (in whic c is assumed to be a constant) have been confirmed by experiment?
  11. Jun 1, 2004 #10


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    Agree. But did you derive that conclusion yourself? :wink:
    --moving topic--
  12. Jun 1, 2004 #11


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    And the French think Poincare discovered Relativity nearly 10 years before Einstein. Amazingly, though, it was Einstein alone who explained it to the rest of the physics community AND took the heat over his revolutionary theories. AFTER they were generally accepted, some others claimed credit. Hmmm.

    Anyway, who really thinks Einstein developed those areas without being aware of the state of the art in physics? All scientists depend on the work of predecessors.
  13. Jun 1, 2004 #12


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    Well no...It was extreeemly difficult to reach that conclusion alone ...without meeting and consultation with experts.. :smile:

    DrChinese,fair enough said.Nothing before Maxwell's times could suggest SR.
    Hence,suggestion that Newton had something to do with mass-energy equivalence formula got me in stitches.
  14. Jun 1, 2004 #13
    I'm not starting a fight here, nor am I trying to bolster or assault anyone, but here are a few thoughts:

    1) c is variable under general relativity.

    2) All measurements of c have been made under relatively low-speed and limited local conditions.

    3) c is, of course, not constant in any medium other than a vaccuum.

    4) I'm quite murky on this, but I am also quite sure that some recent measurements of distant stars have shown that either c or alpha has probably been different in the past.

    I am not poking at SR here. I am just pointing out some cases in which the statement The speed of light IS NOT a constant (and NEVER has been). can be said to be true.

    Though this may not be what "Nommos Prime (Dogon)" means...

    Anyway... I'm butting out now.
  15. Jun 1, 2004 #14
    Sorry to inform you but such observations on the origin on E = mc2 have been mentioned before. Most notably by Herbert Ives in 1953 and more recently in

    Did Einstein really discover "E = mc2", W.L. Fadner, Am. J. Phys. 56(2) Feb 1988

    Also by me at


    See On the concept of mass in relativity in that page
  16. Jun 1, 2004 #15


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    I agree. A few days ago, someone on the forum suggested Newton had invented the Big Bang too. Newton's accomplishments are large enough that he doesn't need any "exaggerated extras" to bolster his reputation.

    Ditto Einstein, regardless of the specifics of how much he was aware of the work of others.

    Every Nobel winner stands on the backs of many other scientists. That is one of the difficulties of such prizes, trying to draw a line as to who did what. There aren't enough prizes to go around for all the great contributions made by so many dedicated people.
  17. Jun 1, 2004 #16
    Hmmm ...
  18. Jun 2, 2004 #17
    fathomed factoring...

    [tex]E = Aymc^2[/tex]

    It is certainly plausible:

    [tex]\frac{E}{A} \sqrt{1 - \left( \frac{v}{c} \right)^2} = mc^2[/tex]
  19. Jun 2, 2004 #18


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    "Inevitable"[tex]A[/tex] would be now the prime suspect for further criticism ,but never mind :biggrin:
  20. Jun 2, 2004 #19


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    Only knowledge is finite, ignorance is infinite.
  21. Jun 2, 2004 #20


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    Only in the same way that you can vary c by measuring it with a watch that ticks too fast.

    What do you mean? c isn't "low-speed". And what about measurements of the speed of light involving particle accelerators? (I imagine there are cosmological measurements too)

    Only because you're measuring a different kind of speed.

    It's certainly a popular theory, but I haven't heard anything that has shown it to be true.
    Last edited: Jun 2, 2004
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