There is not and never was a physical formula that changed the face of humanity like that. From the moment Einstein discovered that mass could be converted into energy, it was impossible to stop the destructive consequences
Prof. Hanoch Gutfreund, "Odyssea"
Many of the laws of nature are formulated as mathematical equations, which connect symbols representing physical quantities. Mathematical methods are used in the processes that lead from simple assumptions to these equations, and mathematical, analytical and numerical calculations make it possible to deduce from these equations phenomena that can be measured through observations or experiments in the laboratory.
When faced with the challenge of formulating the theory of general relativity, in which the laws of nature do not depend on the frames of reference in which they occur, Albert Einstein needed sophisticated mathematical methods, which were developed by mathematicians to treat geometry in curved spaces.
At the same time, he wrote to his friend, the physicist Arnold Sommerfeld: "I acquired an enormous respect for mathematics, whose refined parts, out of ignorance, I treated as a luxury." From Newton's time, a number of apparently simple equations appeared on the stage of physics, which changed worldviews and became the pillars of modern physics.
Among them are Newton's equation of gravity, Maxwell's equations, which unite electricity, magnetism, optics and radio waves into one framework, the Schroedinger equation, which describes the wave nature of a material particle in quantum theory, and others.
Among all these, the most famous equation in the world of science is a simple equation containing only five symbols - E=mc2. This equation, which connects quantities that are seemingly completely different from each other: energy (E), mass (m) and the speed of light (c), has become a cultural symbol nowadays.
It appears on pieces of clothing, in advertisements for commercial products, on bills and coins, and I don't know if there is a single country that has not issued a stamp with E=mc^2 on it in various and creative designs.
The energy content of a material body
At the end of 1905, Einstein published an article called "On the Electrodynamics of Moving Bodies", in which he formulated his special theory of relativity. The Torah is based on two assumptions: a) The speed of light does not depend on the speed of the source or the speed of the observer. b) In two reference systems that move at a constant speed relative to each other, the same laws of nature apply.
To explain the second assumption, Einstein sometimes used the metaphor of a train traveling at a constant speed, its windows closed and its wheels well oiled. There is no experiment that an observer on such a train could perform to learn anything about its state of motion relative to the platform.
These are two apparently simple assumptions, and yet, no one except Einstein was able to propose them until his time. From these assumptions it is possible to draw a series of conclusions about the effect of the observer's speed on the measurement of lengths, the measurement of times and the measurement of electric and magnetic forces.
After publishing the article, Einstein noticed that there is another conclusion, fundamental and surprising, that stems from the assumptions of the special theory of relativity, and then published another short article, in which only three pages, under the title "Does the persistence of a body depend on its energy content?" (Here persistence is synonymous with mass).
In this article, Einstein showed that "if a body emits energy L, then its mass is less by L/V^2... The mass of a body is a measure of its energy content... If the theory fits the facts, then radiation transfers mass between the emitting body and the absorbing body". (In those days, physicists used to mark energy with L, and Einstein here marks the speed of light with V).
This is the first formulation of E=mc^2, though not in this notation. Einstein showed in this article the equivalence between mass and electromagnetic radiation energy, but claimed that this result is general and independent of the mechanism by which a body emits energy.
All forms of energy have mass. When Einstein came to this conclusion, he wrote to his friend Conrad Habicht:
"The mass is a direct measure of the energy contained in the body... The argument is amusing and tempting, but as far as I know, God may be laughing at it and leading me by the nose."
Does the equivalence between mass and energy mean that it is really possible to convert mass into energy? Einstein thought that it would be possible to notice this phenomenon in radioactive decay: "It is not impossible to test this theory with the help of bodies in which the change in energy is large (such as radium salts)". This prediction came true about thirty years later.
The beginning of the nuclear age
The conversion of mass to energy occurred in a controlled laboratory experiment for the first time in 1932. Physicists John Cockroft and Ernst Walton from Cambridge University in England succeeded in accelerating hydrogen nuclei (protons), which hit the nuclei of the element lithium (consisting of three protons and four neutrons).
In the collision, two nuclei of helium (α particles, containing two protons and two neutrons) were formed, which moved at high speed in opposite directions. The sum of the masses of the proton and the lithium nucleus is greater than the mass of two α particles. The mass that was lost in this process became the kinetic energy (energy of motion) of two α particles.
This experiment confirmed the phenomenon of turning mass into energy and showed that the quantitative balance between the two is determined by the formula E=mc^2. It turned out that God did not laugh and did not lead Einstein by the nose.
This discovery received sensational coverage in the "New York Times": "In recent scientific experiments, it has been shown that the innermost fortress of matter, the atomic nucleus, can be cracked, creating enormous amounts of energy, and most likely also new sources of gold, radium and other precious minerals".
Lord Ernest Rutherford, considered the father of nuclear physics, was less enthusiastic. He writes in 1933:
"These atomic transformations are of great interest to scientists, but we cannot control atomic energy to the extent that the matter will be of economic value, and I believe we will never be able to do so in the future... Our interest in the subject is purely scientific, and these experiments contribute to a better understanding of the structure of matter ".
In the same year, he spoke on the subject at a scientific conference in London: "Whoever talks about atomic energy is talking nonsense." This statement indicates how dangerous it is to predict the future and the impact of scientific discoveries.
Twelve years later, the same atomic energy, which one of the greatest physicists of the time regarded as nonsense, was responsible for the destruction of two large cities in Japan.
"Einstein Breaks the Universe"
On July 1946, 2, the weekly magazine "Time" published on the cover page the picture of Einstein against the background of a swirling mushroom of smoke with the equation E=mc^XNUMX. Under the picture appeared the inscription: "Einstein from the universe."
The equation E=mc^2 is not a diagram for building an atomic bomb. It represents the physical principle of converting mass into energy, which explains why such a phenomenon is possible. It explains the process of producing energy in nuclear reactors, just as it explains the source of the sun's energy and of all the stars in the universe.
Between this principle and the construction of an atomic bomb there is a long way of scientific research and technological development. Einstein was not involved in this process in any way and at any stage, yet his name was associated with the atomic bomb. This thing haunted and troubled him until the end of his days.
Near his death in 1955, Einstein wrote to his friend Max von Laue, who was the only German physicist with whom he corresponded after World War II:
"My activity in connection with the atomic bomb was only my signature on the letter to Roosevelt. Because of the danger that Hitler might be the first to have the bomb, I signed the letter drafted by Szilard. If I had known that the fear was not justified, I, like Szilard, would not have opened this Pandora's box, because my lack of trust in governments was not only aimed at the German government."
During the Cold War, the equation E=mc2 was associated in the consciousness of humanity with nuclear weapons. It symbolizes a combination between the understanding of complex and mysterious physical principles, which arouses astonishment in the general public, and an apocalyptic message about the end of the human race.
However, this simple equation guided generations of scientists in research in various fields of physics such as astrophysics and cosmic radiation, in the development of a new field - elementary particle physics, and in the construction of powerful particle accelerators.
In the fission of a uranium atom, only a small part of the mass is converted into energy. In contrast, when an electron collides with a particle known as a positron, both disappear and their mass becomes all electromagnetic radiation energy.
The positron is the antiparticle of the electron - identical to it in all properties except that it has an opposite electric charge. Converting mass into energy by meeting matter and antimatter on a macroscopic scale could provide enormous amounts of energy to build a new industrial world, or create destructive power beyond anything we've known so far. Meanwhile, such a possibility exists only in science fiction stories.
Hanoch Gutfreund is a professor emeritus of physics and a center on behalf of the Hebrew University for activities related to Albert Einstein around the world.
The full article was published in issue No. 8 of the "Odyssia" magazine.
17 תגובות
Ehud, thank you!
Where is Tali when you need her? Because she has expertise in what is discussed in the article and in the responses to it, I look forward to reading her words here.
deer,
Just a side note. I agree with you that it is not necessary to know relativity to get nuclear energy, but on the other hand it is not necessary to know quanta either. It is true that the energy originates from the nucleus whose structure is given through quantum models: the drop model (less quantum) or the shell model. Nowadays, by the way, there are slightly more complex nuclear models, but as far as I know, there is no model that describes nuclear fission well, which is an extremely complex process.
To get nuclear energy all you need to know is classical or semi-classical physics. Nuclear energy is obtained in a chain reaction so all you need to know is to describe the neutron population in time and space and for that the transport equation is sufficient. The only input to the neutron transport equation from a nucleus are the nuclear cross sections, but these are often obtained from measurements and not from basic theory. So although E=MC^2 determines the amount of energy that will be released in fission (a calculation first made by Lisa Meitner), but beyond that there is no need for relationships to obtain nuclear energy from both neutron cross sections for various reactions (fission, scattering, (n,2n) and more). .) have their physical origin in quantum but there is no need to know about quantum theory in order to build and operate a reactor.
By the way, in the neutron transport equation (Boltzmann equation), the neutrons are described as point particles (as mentioned, this is a semi-classical equation).
Zvi and Ehud:
I agree with what you said, but I would like to point out a phenomenon that I think you did not address.
The fact that they manage to find a catchy name for the theory is no accident.
It may help to spread it, but the basis for this is an inner beauty that exists in the theory from the beginning.
As I wrote in my article about beauty https://www.hayadan.org.il/meta-beuty-2911082/ Absorption is one of the obvious, natural and even justified (instrumentally) characteristics of the beauty of a theory.
A short and catchy expression that encapsulates the ideas of the theory in a compact way is likely to be found in any theory that we judge as "beautiful".
This expression does not have to be literal - the general theory of relativity has a "pictorial expression" that "caught" very well (this is the drawing that illustrates the curvature of space by a sphere placed on a rubber sheet as well as its derivative that demonstrates the black hole as a curvature that actually becomes a hole).
In my opinion, one of the most catchy phrases ever proposed in science is the phrase "the selfish gene".
As soon as I read it for the first time - I immediately knew all the important things that Dawkins wrote in the book in which he coined the term.
sympathetic,
It is clear to me that you do not underestimate science - you know too much... (:
As a sociological question it is indeed interesting, I agree with most of the reasons you gave but I think I can offer a few more:
- Unlike the special theory of relativity, which had many partners, 10 years later Einstein created the general theory of relativity from the ground up - a mighty theory with almost no introductions from other physicists. With the verification of the general theory of relativity in 1919, Einstein gained a special status as the one who challenged Newton's theory - this status may have been justified but the field equation of the general theory of relativity could not become a kind of logo since it is too complicated - therefore, E = mc ^2 You are her place. The Schrödinger equation you mentioned therefore suffers from a low status for two reasons - on the one hand it is complicated and on the other hand, quantum theory does not have one father.
- E=mc^2 is seen as the theoretical explanation for nuclear energy, this is not quite true of course (developing a nuclear bomb requires more quanta than relativity), but nevertheless the fission of the nucleus is the first event in which a change in mass accompanied by the release of energy was actually predicted. After the Second World War, nuclear energy is seen as a very significant matter and the majority of the public does not concern itself with the true nature of nuclear energy and is satisfied with the simple claim that mass turns into energy. In any case, this is not an explanation of why Einstein is so famous (because he was famous before) but only why E=mc^2 is famous.
- It seems to me that Einstein became a sort of American hero and as such, received extraordinary publicity even in relation to other great scientists. In a culture that loves cults of personality, it's no wonder that great scientists, and certainly colorful types like Einstein, become heroes (and let it not be understood that my words diminish their value, but only the value of the cult of personality).
Zvi, thank you!
I was just wondering when the famous equation was formulated in its popular form. There is an interesting sociological question here and it is when does a scientific theory gain public recognition and be commemorated as an icon? Schrödinger's equation is also an equation of great importance and of course also Maxwell's equations, but I think that the simple formulation of equivalence between mass and energy containing only 5 symbols is what made the equation so popular. The simplicity of the symbols is also important in the recognition the equation has received. The equation contains only equating and squaring operations known to the general public (it does not contain derivatives or integrals for example...) and the physical concepts are also intuitively understood: mass, energy, speed and light. We must of course add to the fame of the formula Einstein's personal charisma, a rare trait in scientists that can perhaps be found in Feynman or Landau.
As a side note, many times in science it is important to find a catchy presentation or a successful name for the theory, so that the theory will gain resonance. Examples of this are the catchy names: the Big Bang or black holes.
I would like to point out that I do not underestimate science or think that a catchy name is enough for a theory to catch on, but the interesting question is which of the innovative theories are the ones that gain recognition in the general public?
Ehud and Koshan
Koshan - You must differentiate between a complete and well-founded scientific theory like the one presented by Einstein and people who claimed without sufficient substantiation that it seems that such an equivalence would be possible. Before Einstein, there was not enough understanding to make such a claim and therefore the claims that existed were speculative and unfounded - to say that they developed the equation first is tantamount to claiming that Democritus was the one who discovered the atomic model.
In any case, since you did not explain on what basis you say these things, I suggest you read the link below. According to this link at the end of the 19th century it was claimed (Nikolai Imov) that E=kmc^2 when k is between 0.5 and 1 (such equivalence is a hypothesis that can be raised from considerations of units with a lower barrier which is kinetic energy multiplied by natural speed c - also in the system Planck units Planck energy is Planck mass multiplied by c^2)
Ehud - Please note that action has different units than energy (units of TNA), so it is unlikely that Einstein was wrong about this.
In the link below it is claimed that the original formulation was dm=L/c^2
In physics, the claim was that the body emitting radiation with a total energy L (I think this notation for energy originally came from the Lagrangian notation), would lose mass at this rate - that is, the problem was that Einstein treated it as a change in the mass of a body that still exists and not as the ability to convert all the mass into energy (a process that could only be realized given antimatter).
In the link it is also indicated that the correction was made by Planck, but it is not clear from the link that he was the first to write the equation as E=mc^2 really.
In any case, I think that, as is the way of scientific discoveries, the theory of relativity also has early legs and there are half things that were discovered earlier - the examples of this should not be included in anecdotes like those presented here because it has a hold on much more significant things, for example the Lorentz transformations were developed by Henrik Lorentz even before Einstein as well as Poincaré's work led to a good understanding of some of the results without the mathematical formalism.
In this context, I suggest reading Yoram Kirsch's book "The Universe According to Modern Physics" where the author emphasizes that despite the work that was done before - a coherent and complete fundamental work was performed for the first time by Einstein and therefore, the respect given to him is justified.
http://en.wikipedia.org/wiki/Mass%E2%80%93energy_equivalence#Einstein:_Mass.E2.80.93energy_equivalence
As written in the article, Einstein did not write the formula for equating mass and energy in his groundbreaking article on special relativity in 1905, the idea did appear in a later article (as noted in the article) but not in the famous formulation. I remember that the famous formula appears in Einstein's writings (it even appears on the cover of the book showing the page from Einstein's notebook) but I am not sure exactly where and in what year the formula was published in its popular form. By the way, if I remember correctly, the formula appears in Einstein's notebook with an error. He thought at first that the equality was between the mass and the action L and then deleted the L and wrote E. I would love to hear if anyone knows when and where the equation appeared in its famous form.
Kushan:
A simple check shows that even Wikipedia didn't know about your simple check.
What exactly is the simple test you did?
A simple check will reveal to you that Einstein did not formulate the equation in question in the article.
antimatter bomb. I wonder if the US has such a thing.
The last paragraph should have been expanded on.
I am a proud Jew, but street
Yoav: Let's count:
E - 1
= - 2
M-3
C-4
2-5 (in uppercase script - Yaani Riwa)
And let me guess, you didn't count the =, perhaps the most important symbol in this series of signs that gives it meaning as an equation.
To Yoav, they count the 'equal'.
e=mc^2, five symbols? (puzzled face), do you count the square chopstick as a symbol?
Very beautiful writing