C O N T E N T S:

- In HW 4a, multiplicity of an Einstein solid of N oscillators and energy qA was found to be: a) Starting from this formula, obtain an expression for entropy S and show why the square root term can be ignored for large values of N and qA. b) Use above result to calculate temperature T of the solid as a function of energy U qAE, where ? is a constant.(More…)

- In the famous relativity equation, E m c 2, the speed of light ( c ) serves as a constant of proportionality linking the formerly disparate concepts of mass ( m ) and energy ( E ).(More…)

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**KEY TOPICS**

** In HW 4a, multiplicity of an Einstein solid of N oscillators and energy qA was found to be: a) Starting from this formula, obtain an expression for entropy S and show why the square root term can be ignored for large values of N and qA. b) Use above result to calculate temperature T of the solid as a function of energy U qAE, where ? is a constant.** [1] ?with the mass-increase effect is Einstein?s famous formula E m c 2 : mass and energy are no longer conserved but can be interconverted. [2] A relation is discovered between the mass and binding energy of space objects, corresponding to the Einstein formula (equivalence of mass and energy); discreteness of stellar parameters and quantization of parameters of cosmic systems are revealed; stellar Planck, Dirac, Boltzmann and other stellar constants are determined; combined SP? symmetry with respect to similarity of physical processes at different scale levels of matter is introduced. [3] Figure 3 – Albert Einstein took Max Planck?s formula for the quantization of energy in black bodies and extended it to describe light. [4]

The formula basically states that energy (E) equals mass (m) times the speed of light (c) squared (2). [5] This yields approximate formulas for the ground-state energy and for the first excited-state energy. [6]

Einstein showed that light quanta, as he called the particles of energy, could help to explain phenomena being studied by experimental physicists. [5] Einstein said that light is made up of individual ‘particles’ of energy, which he called quanta. [7]

Einstein is probably familiar to most people for his mathematical equation about the nature of energy, E MC2. [5] In HW 4a, multiplicity of an Einstein solid of N oscillators and energy qA was found to be: a). [1] While there was a well-known kinetic energy theory that explained heat as an effect of the ceaseless motion of atoms, it was Einstein who proposed a way to put the theory to a new and crucial experimental test. [5]

Here the first equality follows from the first part of Einstein’s theory, the third equality follows from the definition of Boltzmann’s constant as k B R / N, and the fourth equality follows from Stokes’s formula for the mobility. [8] The formula EMC2 is probably the most famous calculation from Einstein’s special theory of relativity. [5] An identical expression to Einstein’s formula for the diffusion coefficient was also found by Walther Nernst in 1888 in which he expressed the diffusion coefficient as the ratio of the osmotic pressure to the ratio of the frictional force and the velocity to which it gives rise. [8] Introducing the ideal gas law per unit volume for the osmotic pressure, the formula becomes identical to that of Einstein’s. [8]

In 1905 Albert Einstein, with the advent of special relativity, derived the standard configuration formula ( V in the x -direction ) for the addition of relativistic velocities. [9]

In 1905 Albert Einstein had his miracle year, publishing 5 papers, including the Special Theory of Relativity, the Mathematical Description of Brownian Motion, and the Emc 2 formula. [4] Albert Einstein received the 1921 Nobel Prize in Physics and is well known for his mass-energy formula. [10] M ost everyone knows the name, the face (the hair) of Albert Einstein, even if most everyone doesn?t know what he?s famous for except, perhaps, emc 2, the formula that catapulted the species into the atomic era. [11]

Einstein’s formula of theory of relativity on a chalkboard. [12] I must therefore inevitably take my cue from Kornberg and ask the following question: What equation would you regard as the most important one in science? For most people the answer to this question would be easy: Einstein’s famous mass-energy formula, Emc 2. [13] Einstein’s formula on a chalkboard with an apple, a book and some chalks. [12]

The thing with light is, the shorter wavelength the more energy it has, and this was already well-known, from Max Planck?s formula E h f but what was worth a Nobel prize, was the idea that the light hits one electron at a time. [4] For the first time a mathematically precise derivation of the Newton formula of emergence of the gravitation force is provided based on the concept of gravitons; the energy density and penetrability of gravitons in the substance are found. [3]

Einstein called this particle a quantum of light, meaning that it is a discrete exchange of energy. [4]

In phy. sics, mass-energy equivalence is a concept formulated by Albert Einstein that explains the relationship between mass and energy. [14] It expresses the law of equivalence of energy and mass using the formula E mc2 where E is the energy of a physical system, m is the mass of the system, and c is the speed of light in a vacuum (about 3×108 m/s). [14] Because the speed of light is a very large number in everyday units, the formula implies that any small amount of matter contains a very large amount of energy. [14]

Planck guessed, therefore, that he should try to combine these two expressions in the simplest way possible, and to transform the result into a formula relating the energy of the radiation to its frequency. [15] Planck had to assume that the oscillators comprising the blackbody and re-emitting the radiant energy incident upon them could not absorb this energy continuously but only in discrete amounts, in quanta of energy; only by statistically distributing these quanta, each containing an amount of energy h? proportional to its frequency ?, over all of the oscillators present in the blackbody, could Planck derive the formula he had hit upon two months earlier. [15] For those interested, the kinetic energy formula according to special relativity would be the series mc + mv/2 + 3/8mv^4/c+ where v equals the velocity of the particle considered. [16] Therefore, the relativistic kinetic energy reduces to the classical KEmv formula. [16]

Kids E mc2 T-Shirt Albert Einstein Formula Equation Tee Shirt 8. [14]

**POSSIBLY USEFUL**

** In the famous relativity equation, E m c 2, the speed of light ( c ) serves as a constant of proportionality linking the formerly disparate concepts of mass ( m ) and energy ( E ).** [2] ?expressed as energy by using Albert Einstein?s relativity equation in the form E (? m ) c 2. [2] ?his special theory of relativity; E m c 2 expresses the association of mass with every form of energy. [2]

Each body of rest mass m possesses m c 2 of “rest energy,” which potentially is available for conversion to other forms of energy. [2] The mass-energy relation, moreover, implies that, if energy is released from the body as a result of such a conversion, then the rest mass of the body will decrease. [2] In special relativity, however, the energy of a body at rest is determined to be m c 2. [2] The energy of a body at rest could be assigned an arbitrary value. [2]

The explosive power of the atomic and hydrogen bombs derives from the conversion of mass to energy. [2] In physical theories prior to that of special relativity, mass and energy were viewed as distinct entities. [2] In the equation, the increased relativistic mass ( m ) of a body times the speed of light squared ( c 2 ) is equal to the kinetic energy ( E ) of that body. [2] The quantity of energy calculated in this way is called the nuclear binding energy ( E B ). [2] Such a conversion of rest energy to other forms of energy occurs in ordinary chemical reactions, but much larger conversions occur in nuclear reactions. [2] This is particularly true in the case of nuclear fusion reactions that transform hydrogen to helium, in which 0.7 percent of the original rest energy of the hydrogen is converted to other forms of energy. [2]

Stars like the Sun shine from the energy released from the rest energy of hydrogen atoms that are fused to form helium. [2]

We may likely achieve God-like status in the distant future when we figure out how to manipulate between matter and energy bidirectionally without much wastage or risk, and where we may be able to convert any form of energy to any form of mass at the pinnacle of that much dreamt about futuristic super-technology? Kaiser T, MD. [17] This equation means “The energy of a particle, measured in Planck units of energy, equals the mass of the particle, measured in Planck units of mass.” [18] The equation says that mass (m) can be converted to energy (E). [7] There is no gamma factor in that derivation since there’s no gamma factor when E mc^2 relates the mass and energy of EM radiation. [19] A little mass can make a lot of energy, because mass is multiplied by c 2 where c is the speed of light, a very large number. [7] Since the speed of light squared is an enormous number, a small amount of mass can be converted to a phenomenal amount of energy. [5]

Or if there’s a lot of energy available, some energy can be converted to mass and a new particle can be created. [5] The increase in mass is equal to the energy provided by the electric current divided by c squared. [17] They only refer to the basic structure of the laws of physics: c and G are part of the structure of spacetime in general relativity, and ? captures the relationship between energy and frequency which is at the foundation of quantum mechanics. [18]

You convert energy to mass every time you make a cup of tea. [17] Nuclear reactors, for instance, work because nuclear reactions convert small amounts of mass into large amounts of energy. [5] Photons colliding with nucleons can give nucleons more energy which they can convert to mass with ultratransient mass gain, or just energy gain which if in excess, will be emitted out as photons to maintain the nuclear mass tightly. [17] Yes nuclear fission and nuclear fusion are examples of mass converted into energy,also the binding energy of nuclei is mass converted into energy,etc. [17] Conversion of mass in atomic nuclei to energy is the principle behind nuclear weapons and is the sun’s source of energy. [7] One more unit is needed to construct a usable system of units that includes energy and mass. [18] You’re thinking of the one where he deduced the equivalence of mass and energy of electromagnetic radiation. [19] Yes of course. 99% of proton?s (and neutron?s) mass is energy of quarks converted into binding mass. [17]

He argued that light can act as though it consists of discrete, independent particles of energy similar to particles of a gas. [5] Bundles of light (he called them quanta) with the correct amount of energy can eject electrons from metals. [7] The energy each ‘particle’ of light carries is proportional to the frequency of the light waves. [7]

• discovered the hugely important and iconic equation E mc 2, which shows that energy and matter can be converted into one another. [7] A few years before, Max Planck’s work had contained the first suggestion of discrete particles in energy. [5] Angels & Demons – The science behind the story describes how the energy of particles in an accelerator creates new particles on impact. [17] The unit of energy is called the Hartree energy in the Hartree system and the Rydberg energy in the Rydberg system. [18] Using the Hartree convention, in the Bohr model of the hydrogen atom, an electron in the ground state has orbital velocity 1, orbital radius 1, angular momentum 1, ionization energy 1 / 2, etc. [18] The energy difference between the two wells is 2 ?, the tunneling occurs with amplitude J, the on-site interaction between the atoms in the same well is U, and the interwell interaction is V. [6]

Solid line shows the exact solution, dashed line is the approximated energy of Eq. ( 26 ), horizontal dotted line is N ?. [6] It is important also to note that the kinetic energies of the molecular Brownian motions, together with those of molecular rotations and vibrations sum up to the caloric component of a fluid?s internal energy. [8]

All those wonderful particles created in accelerators are formed by turning kinetic energy into particles with mass. [17] In particle accelerators kinetic energy of colliding particles gets converted to heavier particles. [17]

Einstein showed that light can behave as a particle as well as a wave. [7] Einstein wrote a paper based on the new understanding of the structure of light. [5] Einstein published his general theory of relativity paper in 1915, showing, for example, how gravity distorts space and time. [7] Smoluchowski’s theory of Brownian motion starts from the same premise as that of Einstein and derives the same probability distribution ?( x, t ) for the displacement of a Brownian particle along the x in time t. [8] From this expression Einstein argued that the displacement of a Brownian particle is not proportional to the elapsed time, but rather to its square root. [8] Einstein was led to consider the collective motion of Brownian particles. [8] With the motion demonstrated in detail, Einstein had reinforced the kinetic theory and created a powerful new tool for studying the movement of atoms. [5] In essence, Einstein showed that the motion can be predicted directly from the kinetic model of thermal equilibrium. [8]

In laymans terms, why is Einsteins famous equation ” E mc ^2″ and not ” E mc ” or ” E mc ^3″? In other words, what does the fact that the sp. [17] In this way Einstein was able to determine the size of atoms, and how many atoms there are in a mole, or the molecular weight in grams, of a gas. [8] While studying at the Polytechnic, Einstein learned about one of the biggest problems of the day that was baffling physicists. [7] They found that it was! Just as Einstein had said, space truly is curved. [7] Every experiment ever done to test special relativity has confirmed what Einstein said. [7] This is primarily a mathematical work, but the first four chapters discuss the history of the topic, in the era from Brown to Einstein. [8] Atoms and molecules had long been theorized as the constituents of matter, and Albert Einstein published a paper in 1905 that explained in precise detail how the motion that Brown had observed was a result of the pollen being moved by individual water molecules, making one of his first big contributions to science. [8] Albert Einstein (in one of his 1905 papers ) and Marian Smoluchowski (1906) brought the solution of the problem to the attention of physicists, and presented it as a way to indirectly confirm the existence of atoms and molecules. [8]

Legendary scientist Albert Einstein (1879 – 1955) first gained worldwide prominence in 1919 after British astronomers verified predictions of Einstein’s general theory of relativity through measurements taken during a total eclipse. [5] The special theory of relativity, formulated in 1905 by Albert Einstein, implies that addition of velocities does not behave in accordance with simple vector addition. [9]

Albert Einstein was awarded the Nobel Prize in Physics in 1921. [7]

The second part of Einstein’s theory relates the diffusion constant to physically measurable quantities, such as the mean squared displacement of a particle in a given time interval. [8] The confirmation of Einstein’s theory constituted empirical progress for the kinetic theory of heat. [8]

Einstein’s equation E mc 2 can be rewritten in Planck units as E m. [18] The first part of Einstein’s argument was to determine how far a Brownian particle travels in a given time interval. [8] Although scientists today are comfortable with Einstein’s ideas, in his time, they were completely revolutionary. [7]

Einstein’s theories expanded upon universal laws formulated by physicist Isaac Newton in the late seventeenth century. [5] As people read Einstein’s papers and argued about their significance, his work gradually gained acceptance, and his reputation as a powerful new intellect in the world of physics grew. [7] I heard of something called Einstein’s box which could yield the equivalence without working with the gamma factor. [19]

The aberration of light, of which the easiest explanation is the relativistic velocity addition formula, together with Fizeau’s result, triggered the development of theories like Lorentz aether theory of electromagnetism in 1892. [9] The speed of light in a medium uniformly moving with speed V in the positive x -direction as measured in the lab frame is given directly by the velocity addition formulas. [9]

In relativistic physics, a velocity-addition formula is a three-dimensional equation that relates the velocities of objects in different reference frames. [9] Such formulas apply to successive Lorentz transformations, so they also relate different frames. [9]

This is mostly harmless, since if either one particle type is stationary or the relative motion is collinear, then the right result is obtained from the incorrect formulas. [9] If the emitter is not firing bullets in empty space, but emitting waves in a medium, then the formula still applies, but now, it may be necessary to first calculate s ? from the velocity of the emitter relative to the medium. [9]

Relative error for the approximated formula ( 17 ) vs c for different values of ? 0.01, 0.5, 1, for (a) N 100 and (b) N 1000. (c) Relative error for the approximated formula ( 18 ) vs U / J for marked values of ? / J, and for V 0 and N 100. [6] Relative error ? for all the approximation formulas of the paper, for different N ?. [6] The relative error ? for all the approximate formulas in this paper versus the dimensionless interaction c. [6]

Standard applications of velocity-addition formulas include the Doppler shift, Doppler navigation, the aberration of light, and the dragging of light in moving water observed in the 1851 Fizeau experiment. [9] Some classical applications of velocity-addition formulas, to the Doppler shift, to the aberration of light, and to the dragging of light in moving water, yielding relativistically valid expressions for these phenomena are detailed below. [9]

It is also possible to use the velocity addition formula, assuming conservation of momentum (by appeal to ordinary rotational invariance), the correct form of the 3 -vector part of the momentum four-vector, without resort to electromagnetism, or a priori not known to be valid, relativistic versions of the Lagrangian formalism. [9] Reverse formula found by using standard procedure of swapping v for -v and u for u?. [9] The formulas for boosts in the standard configuration follow most straightforwardly from taking differentials of the inverse Lorentz boost in standard configuration. [9] The ordering of operands in the definition is chosen to coincide with that of the standard configuration from which the formula is derived. [9]

Background with blackboard, with relativity and string theory equations, formulas and hand drawings. [12] These formulas are based only on the field equations, unlike formulas of polytropic model originating from the estimated equation of state in polytropic process. [3] One result of the concept of the general field is the model of gravitational equilibrium, which allows estimating the parameters of cosmic bodies using simple formulas. [3]

In order to avoid this embarrassing result, Einstein reluctantly conjured up a new term, the “cosmological constant,” and applied it to the field equations of his theory in order to keep the cosmos static. [11] To account for the Universe?s apparent stability, Einstein included a constant in his equations, a constant that would neutralize the inexorable pull of gravity. [20] The equations lie at the boundary of physics and chemistry, and both of them are derived from a science whose basic truths are so permanently carved in stone that Einstein thought they would never, ever need to be modified. [13] Before Hubble?s revolutionary discovery, based on the dissonance in various astronomical observations and his equations, Einstein was prodded by several of the most brilliant astrophysicists of his generation to modify his current model. [20]

What about accelerating or decelerating non-uniform motion, the way that most things go from point A to point B? Einstein labored 10 more intense years until publishing, in 1915, his Theory of General Relativity, a radical new understanding of gravity (gravity was not a force, he said, but the curvature of space itself) that, if not upending Newton?s work, greatly limited its application. [11] Einstein also talks about what we can learn from Darwin’s theory. [13]

Einstein argued that measurements of space and time are not absolute but are determined by many factors, including the relative position of the observer. [10] He famously alerted Einstein to the implications of fission – at this point in time (July 1939) Szilard and his fellow Hungarian expatriates were probably the only scientists who clearly saw the danger – and helped Einstein draft the now iconic letter to President Roosevelt. [13]

Unable to find a teaching job after completing his PhD, most likely because Einstein was such a smart aleck that he ticked off his professors, the 26-year-old clerk in a Swiss patent office nevertheless published in 1905 four physics papers, any one alone enough to have established his credentials. [11] There is no doubt that both Einstein and Newton are supremely important for understanding the universe, but they both suffer from the limitations of reductionist science that preclude the direct application of the principles of physics to the everyday workings of life and matter. [13] Figure 1.A -Max Planck presents Einstein with the 1929 Planck Medal for extraordinary achievements in theoretical physics. [4]

Except in certain special cases, Einstein therefore does not figure in chemical or biological processes. [13] In 1931, Einstein retracted his “cosmological constant,” reputedly calling it his “biggest blunder” because the universe was, in fact, expanding. [11] Along with Einstein, von Neumann thus became one of the first scientists to leave Europe in the early 30s. [13] It’s pretty obvious that this list pales in comparison with an equivalent list of European physicists which would include names like Einstein, Dirac, Rutherford, Bohr, Pauli and Heisenberg; and this is just if we include twentieth-century physicists. [13] That America is truly a land of immigrants; it’s only by including foreign-born physicists like Fermi, Bethe, Einstein, Chandrasekhar, Wigner, Yang and Ulam can the list of American physicists start to compete with the European list. [13]

Einstein Proposes the Theory of Relativity In 1905 and 1916, the German-born physicist Albert Einstein introduced his theories of relativity. [10] The answer to that question tends to usually settle on Isaac Newton or Albert Einstein; in fact few American physicists if any would show up on the top ten list of greatest physicists ever. [13] As a graduate student in Berlin – where he hobnobbed with the likes of Einstein and von Laue – Szilard came up with a novel way to consolidate the two microscopic and macroscopic aspects of the science of heat, now called statistical mechanics and thermodynamics. [13] The man who contributed the most to their conception, Josiah Willard Gibbs, was called “the greatest mind in American science” by Einstein. [13]

As nuclear technology spread, Einstein advocated for international controls and limitations. [10]

Einstein?s most famous equation, the one people most immediately associate with him, E MC, showed that mass and energy are interchangeable, that they are different forms of the same entity. [20] These equations are derived in a covariant form, which also allows us to determine the metric inside the viscous substance and its energy. [3] Thirdly, based on the field equations a theorem is proved that relates the energy fluxes of various kinds in the space volume with the laws of conservation of momentum, energy and angular momentum. [3] The relationship between the energy of fundamental fields and the corresponding body mass (as well as the gravitational mass) is described in the article. [3] For the total energy of the massive body and its mass the expression is derived, which includes only the energy of fundamental fields and the energy of strong gravitation. [3] The 4/3 problem, according to which the field mass found through the field energy is not equal to the field mass determined through the field momentum, is solved in article and more precisely in the article. [3] Such a possibility is admitted in an article, which examines the relationship between mass and energy in a variety of cases, including heating of bodies, fusion of atomic nuclei, as well as analyzes the findings of the general theory of relativity and covariant theory of gravitation. [3] The analysis of thermodynamics using the theory of relativity is done, the effective reaction force in the principle of Le Chatelier – Brown is determined, a new fourth energy definition of entropy is presented. [3] He also wrote a paper connecting entropy and energy to information, predating Claude Shannon’s seminal creation of information theory by three decades. [13] Later during the 1930s, after he was done campaigning on behalf of expelled Jewish scientists and saw visions of neutrons branching out and releasing prodigious amounts of energy, Szilard helped perform some of the earliest experiments in the United States investigating fission, publishing key papers with Enrico Fermi and Walter Zinn in 1939. [13]

What was heuristic was that he described light as “energy quanta” (photons) for the first time but what was worth a Nobel Prize, was that he was correct. [4] This implied that light delivered its energy in bundles of Ehf. [4] That?s right, blue light ACTUALLY DOES have more energy than red and green light. [4] Light travels as photons, and the shorter the wavelength of light, the more energy per photon. [4] Figure 5 – The energy of blue light can cause electron conduction in a small neon bulb. [4] Stepping off the curb at a traffic light across from the British Museum in London in 1933, Leo Szilard saw the true nature and the consequences of the chain reaction six years before reality breathed heft and energy into its abstract soul. [13]

For a fixed and a moving body in the form of a sphere the total energy and momentum of all the four fields inside of the body are equal to zero. [3] Adding the 4-potentials of gravitational and electromagnetic fields and tensor invariants of these fields to the Lagrangian allows us to find the Hamiltonian, i.e. the relativistic energy of the system of multitude of particles and fields. [3] Each particular field is relatively independent of the other fields in equilibrium state, when the process of energy exchange between the fields and particles is completed. [3] Interpretation of the cosmological constant is given as the energy density of the particles at rest at infinity located at a distance from each other. [3]

As a consequence, the content of the principle of mass and energy equivalence is specified. [3] It is the conversion of mass into energy inside the Sun?s core that fuels its copious radiation. [20]

This allows us to uniquely express the energy and momentum of the system, and to ultimately simplify the equation for the metric. [3] Szilard’s day in the sun came when he circulated a petition directed toward the president and signed by 70 scientists advocating a demonstration of the bomb to the Japanese and an attempt at cooperation in the field of atomic energy with the Soviets. [13] The energy definition is given in the tensor form and the meaning of entropy is established. [3] Yet Strauss remained one of von Neumann’s most steadfast supporters and genuine admirers, nominating him to the Atomic Energy Commission and making sure he got special treatment during his last days when he was struck down too early by cancer. [13] One is the enthalpy, usually denoted by the symbol H, and roughly representing the quantity of energy and the strength of interactions and bonds between different atoms and molecules. [13]

In case of a weak field it is proved that the invariant energy of a massive body is not just the sum of non-gravitational and gravitational energies of the body according to the general theory of relativity, but also is equal to the difference between the substance energy, as the sum of masses of individual baryons of this substance, and the sum of other energies, including the energy of fields and the internal kinetic energy of the substance. [3] In order to describe the dissipation of the kinetic energy of substance fluxes in a viscous medium, the 4-potential of the dissipation field, dissipation field tensor and dissipation stress-energy tensor are considered in the field theory. [3]

Another result is clarification of the virial theorem — in the model under consideration the energy, associated with the forces acting on the particles, is approximately 5/3 times greater than the kinetic energy of the particles, whereas in the classical approach this ratio is equal to 2. [3] Introduction of nuons allows explaining the redshift and background radiation effects, solving the problem of invisible dark matter and dark energy, and understanding the effect of attenuation of radiation from distant supernovae as a result of photons? scattering on the nuons. [3] If cosmologists are correct about dark matter and dark energy, it would mean that we know so much less about the created world than we had imagined. [11]

Currently, dark energy is believed to be the personification of Einstein?s cosmological constant, which is why he was wrong, albeit not entirely. [20] What about dark energy? Its work on space or vacuum implies that space harbors an enormous amount of energy, even when it’s devoid of all matter or radiation. [20]

Some of these issues must have been on Einstein’s mind as he first emphasized what he had already learnt from his own bitter Gymnasium experience, the erosion of individuality in the face of a system of mass education, similar to what was happening to the erosion of individuality in the face of authoritarian ideas. [13] What about the teachers themselves? What kinds of characters need to populate the kind of school which imparts a liberal and charitable education? Certainly not the benevolent dictators that filled up German schools in Einstein’s time or which still hold court in many schools across the world which emphasize personal authority over actual teaching. [13] The icing on this cake really is Einstein’s views on the emphasis on general ability rather than specialized knowledge, a distinction which is more important than ever in our age of narrow specialization. [13]

B – Albert Einstein c1905 at the patent office desk where he worked as a third-class clerk, and occasionally worked on his “miracle” papers. [4]

Blackboard with physical equations and formulas. 2d illustration. [12]

**RANKED SELECTED SOURCES**(20 source documents arranged by frequency of occurrence in the above report)

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2. (21) The Curious Wavefunction

3. (15) E = mc^2 | Equation, Explanation, & Proof | Britannica.com

4. (15) Albert Einstein – Biography, Facts and Pictures

5. (15) Brownian motion – Wikipedia

6. (14) The Life and Achievements of Albert Einstein

7. (14) Velocity-addition formula – Wikipedia

8. (11) Demonstration of The Photoelectric Effect! – Labs, Activities, and Other CoolStuff

10. (6) Adventist Review Online | Oy Vey

11. (6) Natural units – Wikipedia

12. (6) Why Is The Universe Expanding? Science ABC

14. (4) Scientific Discoveries

16. (4) Slash Prices on Albert Einstein

17. (3) The formula E = mc^2 never have been proved? – Page 2 – Physics Help Forum

18. (2) Solved: 3. In HW 4a, Multiplicity Of An Einstein Solid Of . | Chegg.com

19. (2) Zur Theorie des Gesetzes der Energieverteilung im Normalspectrum | Max PLANCK | First edition

20. (2) Miracles and Einstein, Part 1 | A Well-Designed Faith