[McQueen (OP)]

           Perhaps the greatest event in modern physics is the discovery of matter-energy equivalence. Certainly the equation E = mc²  is the most famous equation that  the world has seen or that had such far reaching implications.  Given the extreme renown that this equation has enjoyed and the practical benefits that have resulted from its implementation, it is amazing that relatively little is known about it. Traditionally we have been used to thinking of matter as one thing and of energy as another totally different thing. How was the leap made between thinking that solid objects that one could hold and touch were actually made up of such a transient and impalpable a concept as energy? The two were mutually exclusive, so that to learn that energy could be changed into matter and that matter could be changed into energy, was an epoch making event. How was the discovery made? What kind of thinking led to such a revolutionary change in the way we see the world around us? A little thought shows that there was an ordered sequence of events leading up to the climactic announcement of Einstein’s momentous equation  E = mc² and the phenomenon  of mass-energy equivalence.



           The newly announced discovery of radio-waves (electromagnetic radiation) made by Hertz in 1887, gave rise to many unanswered questions.  What were these radio waves? How were these radio waves able to convey energy, heat etc., Obviously, if anything can convey energy it must possess momentum, yet these radio waves had no mass! Hence the equation for momentum  p = mv could not apply. How was it possible for an object to convey energy without possessing mass?  In the same way the equation for potential energy p_e  = mg  was also ruled out since gravity cannot act on an object with zero mass. When Einstein came up with his equation for the energy of a photon E =fh, where f equals frequency of the photon, and h equals planck’s constant. it seemed to offer new avenues to explore in the search for a solution of defining what radio waves and electromagnetism actually were. Was it, for instance, a new kind of matter? As a completely new field, the problem of defining electromagnetic radiation,  attracted the attention of almost all of the leading physicists of the time.

   Therefore, the relationship between energy and mass was already being widely discussed by the time Einstein considered the matter. Henri Poincaré, one of the leading thinkers and mathematicians of the time, had stated that electromagnetic radiation had a momentum and thus effectively a mass. His approach closely approximated the solution that Einstein eventually came up with. Poincare’s idea was that a moving electron acquired mass. He eventually came up with the equation E₀ = 3/4 mc² in which he tries to indicate the increase in mass of a moving electron. Oliver Heaviside, the most gifted physicist and mathematician that England could boast of at the time, thought of the problem as a spherical electric field surrounding the electron. His solution was m = (4⁄3) E / c²  where E  is the energy of a spherical electric field. In Germany, physicist Max Abraham argued that a moving electron interacts with its own field, E₀, to acquire an apparent mass given by E₀ = 3/4 mc². Hasenohrl, also a German physicist whose name has often been (falsely?) implicated with anti-Semitism, approached the problem by asking whether a black body emitting radiation, experienced changes in mass when it is moving relative to the observer. He calculated that the motion adds a mass of 3/8c² times the radiant energy. The following year he corrected this to 3/4c². Hasenohrl’s approach was the closest to Einstein’s and allegations have even been made that his work predated Einstein in finding the correct solution. A claim that seems to have  been disproved by the work of two physicists, Boghn and Rothman, who have re-examined Hasenohrl’s papers.

      When considering the history or origin of the equation E = mc²  Einstein’s own recent history is often ignored. For instance on March 8th 1905 , he had submitted a paper entitled, "On a Heuristic Viewpoint Concerning the Production and Transformation of Light" to the prestigious German scientific journal Annalen der Physik.  This is in all probability one of the most remarkable scientific papers that was ever published.  In this single paper, Einstein not only validated Max Planck’s discovery that energy was discrete or made up of “quanta” by demonstrating why the photoelectric effect that was first discovered by  Heinrich Hertz worked in the way that it did but he also showed that light interacted with matter in ways similar to a particle. For instance, the amount of energy that each quanta of light delivered was fixed and for a given frequency of light, was always the same. Further, the solving of the photoelectric effect riddle which had occupied scientists for at least 15 years, paved the way for scientist’s like the Danish physicist Neils Bohr to investigate the working of the atom on a practical basis. It enabled the determination of the binding energies of atoms, and the energy with which electrons occupied different spaces ‘orbits’ in the atom.



            The whole point of bringing up Einstein’s paper on the photoelectric effect is to illustrate what a big part this paper must have played in his life: it also earned him, the lifelong friendship of both Max Planck and Neils Bohr.   His discovery that light did indeed come in discrete packets of energy or quanta, as stipulated by Max Planck, must have been very much on his mind. His paper on mass-energy equivalence entitled : “Does the Inertia of a Body Depend Upon Its Energy Content?” was published in the journal “Annalen der Physik” on November 21, 1905, just 6 months after the publication of the photoelectric effect. This gave him a huge advantage over his peers, since his paper on the photoelectric effect had not been fully absorbed or widely circulated. In his own mind, Einstein must have been very sure of the conclusion of his paper on the photoelectric effect ‘one photon emitted,one electron ejected ’. Einstein could not possibly have ignored the particle properties of these photon-electron interactions.  Instead of being caught up in thinking of light as a wave, he was able to, at least theoretically, treat light as a particle.  This approach enabled him to use the straight forward equation for energy of a moving object in his quest to determine the inertial mass of  light (electromagnetic radiation). It was already known from Bernoulli’s equations that  E  the energy of motion was  proportional; to the square of the velocity.  Thus it is perfectly possible that just using the equation for kinetic energy K.E = mc²/2 and eliminating the parts that were not relevant, yields an almost immediate answer.  Whether, Einstein actually used this method to formulate his theory or even to validate it, is not known, although Bernoulli’s equations themselves were widely taught. 

           Einstein’s explanation is based almost exclusively on relativistic ideas, in fact it could be said that the foundations of relativity can be found in this paper.  In his explanation Einstein conceives of an atom B with mass M that emits two bursts of light travelling in opposite directions along the z axis, therefore the energy emitted in any one direction equals E/2 and the total energy emitted is E .  These bursts of light are examined from two different inertial frames, F and F’. In one of the frames of reference F the atom B is stationary, while the second frame of reference is moving  along the x axis in the negative direction. An observer at rest in F judges that the light emitted by B travels up and down the page. For an observer at rest in F’ , the object B moves to the right with velocity v and the light is emitted toward the right making an angle θ with the x-axis. the atom B remains at rest in F frame . It follows directly from this that since B remains at rest in F, that the velocity of B does not change in F’ after the emission of light.
While the velocity of B does not change, the momentum of B does changes in both the F and F’ frames of reference  because the light it emits carries away momentum. If we assume the classical definition for the momentum of B as the product of its mass m and its velocity v, and v does not change, it follows that in order for the law of conservation of momentum to be satisfied, the mass (i.e., rest-mass) of B must change.

    Examining the light emission from the perspective of the inertial frame F’.  Relative to F’,B, moves (to the right) with velocity v. Because relative to F  the bursts of light are collinear (equal), the x-component of the velocity of the light as measured in F’ must be v. The velocity of the light also has a vertical component, i.e., a z-component.  The changes to the momentum along the z-direction are equal and opposite and cancel out. Therefore Using elementary trigonometry, for one of the bursts of light, the momentum along the x-direction is:



 the total momentum of the emitted photons, relative to F’, is:


 
Considering that B does not change in either F or F’ it is possible to use the equation for classical momentum:



or



This means that the total momentum lost by B due to emission of light equals:



                 In Einstein’s own words:“If a body gives off the energy L in the form of radiation, its mass diminishes by L/c² . The fact that the energy withdrawn from the body becomes energy of radiation evidently makes no difference, so that we are led to the more general conclusion that The mass of a body is a measure of its energy-content; if the energy changes by L, the mass changes in the same sense by L/9 × 10²⁰, the energy being measured in ergs, and the mass in grammes.”

     From the wording of this paper on mass-energy equivalence two very important aspects emerge. The first is that using the concept of an aether it is possible to arrive at the expression E = mc² using classical physics. Instead, in this paper, Einstein laid the foundations for relativity by abandoning the ether and making the speed of light invariant. What does become clear from a reading of the paper is that although Einstein begins by using a relativistic framework he ends up by approximating away all of the relativistic parts, until what is  left  is a classical calculation. It is clear that even at this early stage Einstein already had a clear intention of introducing a radically new physics, namely relativity, to the world.

        Einstein is often castigated for never citing prior works or giving due credit to fellow physicists who had made contributions to the field. The reason for this probably lies in his work at the Swiss patent office. He must have quickly learned that any admissions of using prior material could quickly lead to landing up in court. So his discretion in not mentioning contemporary  research into the subject might have been the better part of valour.

         It is interesting to explore what his motivation might have been in taking such a radical approach, instead of trying more conventional methods. That his work was indeed radical there can be little doubt; even fifty years after he had first published his research on mass-energy equivalence and  special relativity and long after any Nazi intimidation was possible,  the Nobel prize committee refused to acknowledge these two topics. There must surely have been valid grounds for them to do so. As to Einstein’s own motivation, the prospect of introducing a radical new physics to the world must have been captivating, even though he, like many other scientists of the time, must have been disillusioned at the horrendous use to which science was put in the name of nationalism.

         There would be no point in relating the events that led up to Einstein’s E = mc² equation if one did not follow up on the events that ensued.  For almost thirty-five years after the publication of the mass-equivalence paper, it remained an oddity on which much speculation was spent. Then due to the efforts of a truly extraordinary person, the theory was finally proved.  Lisa Meitner was an Austrian born Jewish physicist, who was one of the first women scientists to gain fame, renown and recognition for her work. She received her doctorate in –physics from the University of Vienna in 1905 at a time when most women did not know what a University was. She moved to Berlin in 1907 in high hopes that she would be able to work with Max Planck.  She was in for a rude shock, women at the time were not allowed to gain official recognition in German Universities.  She was shunned by almost everyone that she met. Fortunately one of the Professors, Otto Hahn a chemist, had read her work and arranged for collaboration. Despite being a colleague of Hahn’s , Lisa was not recognised by the University, a disused unheated carpenter’s shed was allotted to them for their research. Neither of them received remuneration for their research from the University.  Nevertheless, the partnership made great progress and five years later, Hahn and Meitner moved to the Kaiser Wilhelm Institute where Meitner and Hahn both were appointed as professors.



            In 1932 after Chadwick had discovered the neutron, Meitner and Hahn tried to bring about the transmutation of Uranium into a heavier element by bombarding the Uranium nucleus with neutrons.  In 1938, when the work was just beginning to bear fruit, Meitner was stripped of her position and her privileges. She received numerous requests from foreign Universities to attend conferences and seminars, but all such requests were turned down by the fascist Nazi party.  In 1939 Lisa Meitner managed to flee to Sweden, where she continued her work. Remarkably she was still allowed to communicate with Hahn through letters. She instructed Hahn on what experiments to conduct to maximise results. These experiments were performed in Germany in Otto Hahn’s laboratory. He wrote back to  Meitner  that strange things could be seen in the Uranium sample used for bombardment by neutrons. Instead of seeing a heavier element, what Hahn found were traces of  Barium,  which was a much lighter element than Uranium. Thinking about this result Lisa Meitner realized that the weight difference between a barium atom and a uranium atom amount to about 200,000,000 eV. Lisa Meitner realized that the splitting of atoms to form new elements resulted in the release of enormous amounts of energy, she called this new process nuclear fission.   Einstein’s equation E = mc² came to mind and when it was checked was found to agree phenomenally well with the result. Lisa Meitner had discovered nuclear fission. Unfortunately, Otto Hahn her one time partner, failed to recognize her contribution and in 1944 was awarded the Nobel prize as the sole discoverer of fission. Lisa Meitner’s contribution was not mentioned, she did, however, receive many other awards, she was nominated for the Nobel prize no less than 23 times between 1922 and 1944.

             A wonderful turning point in the history of the human race. However, doubts remain. In the excitement of all these discoveries did Einstein quietly remove our version of the Universe and just as quietly replace it with his own version of the Universe?

   

[Eternal Student]

Hi.

That seems well written.
I haven't had time to check all the facts.
I can't see any obvious questions you want answered, so it seems you want a discussion.

Some things could be disputed.  For example,  E=mc^2  isn't  what Einstein is or should be most famous for, it's just a small equation that is frequently associated with him by the media and general public.
Einstein did seem to change the modern understanding of time and space as you suggested in the last paragraph.  Did he do it quietly?   Maybe.   Was it forced upon us?  Probably not, it just seems to be a good working theory and so it has become accepted.

[Colin2B]

This isn’t really a science question, more a monologue.
However, Einstein didn’t quietly replace our version of the universe and replace it with his own; what he did was to extend our understanding of that universe. It’s a little like when Leyden discovered you can store electricity in a battery, Einstein discovered a relationship that describes the amount of energy that is stored in mass.
Like most great discoveries they are always built on the work of colleagues and predecessors, but it sometimes take a leap of genius and imagination to make the final breakthrough. Isaac Newton famously summed it up by saying "If I have seen further, it is by standing upon the shoulders of giants"

[criggsb33]

Traditionally we have been used to thinking of matter as one thing and of energy as another totally different thing. How was the leap made between thinking that solid objects that one could hold and touch were actually made up of such a transient and impalpable a concept as energy? The two were mutually exclusive, so that to learn that energy could be changed into matter and that matter could be changed into energy, was an epoch making event.

[criggsb33]

Thank you for your well written article.  Brian Cox and Jeff Forshaw wrote a book titled “Why does E=MC2?”  I bought and read the book, but I'm still left with the question “What does it mean?”  Your article was helpful, but something is still missing.

I believe that from this equation it is reasonable to conclude that when mass changes to energy, the energy is distributed over a 2d plane, and that the equation is trying to tell us that the natural state of the universe is 2d.  What does energy look like?  No one knows!  Something that is 2d can not be seen.   Mass and energy are equivalent, but also different.  If we say that energy is the 2d state of mass it begins to make more sense.   By not considering E = mc2 in the context of a 2d, geometrical representation, we may be missing a very important point. It seems very likely that there exists a 2d part to our universe that we are literally, and figuratively, not seeing.

[Origin]

I believe that from this equation it is reasonable to conclude that when mass changes to energy, the energy is distributed over a 2d plane

There is nothing in the equation nor in any of physics that would lead to that conclusion.

If we say that energy is the 2d state of mass it begins to make more sense.

That certainly does not make sense to me.  The idea that there is a mass-energy equivalency in this 4 dimensional space time continuum makes much more sense.  When mass is converted to energy in the form of fission products, the energy from those fission products is imparted to materials in 3 dimensions spatially and over the course of time, so that sounds like normal space time, not 2D.