Statistical Entropy of Radiation: Different Approaches

... According to the memoirs C. Shannon, when discussing the ideas that formed the basis of his famous work [1], John von Neumann told him: "You should call it entropy, for two reasons ... In the second place, and more important, nobody knows what entropy really is". Now a number of problems in quantum ...

... According to the memoirs C. Shannon, when discussing the ideas that formed the basis of his famous work [1], John von Neumann told him: "You should call it entropy, for two reasons ... In the second place, and more important, nobody knows what entropy really is". Now a number of problems in quantum ...

Measurement of Quantum Fluctuations in Geometry

... enters the apparatus at the top, and eventually is detected on the surface S. Its path is split into beams travelling down and right, sent in those directions and then returned after travelling a distance L out and back. After recombining at the beamsplitter, its arrival is recorded on a detector su ...

... enters the apparatus at the top, and eventually is detected on the surface S. Its path is split into beams travelling down and right, sent in those directions and then returned after travelling a distance L out and back. After recombining at the beamsplitter, its arrival is recorded on a detector su ...

Quantum Gravity and the Holographic Mass

... considerations alone. It then follows that the Schwarzschild solution to Einstein’s field th equations could have been developed in the late 19 Century by computation of tiling Planck quantities independent of spacetime curvature and singularities, near the time when Max Planck in 1899 derived his u ...

... considerations alone. It then follows that the Schwarzschild solution to Einstein’s field th equations could have been developed in the late 19 Century by computation of tiling Planck quantities independent of spacetime curvature and singularities, near the time when Max Planck in 1899 derived his u ...

... considerations alone. It then follows that the Schwarzschild solution to Einstein’s field th equations could have been developed in the late 19 Century by computation of tiling Planck quantities independent of spacetime curvature and singularities, near the time when Max Planck in 1899 derived his u ...

Reciprocal Symmetric Kinematics and Correspondence between

... Planck and Einstein: In 1900 Planck’s hypothesis set a lower limit to energy quantum. In 1905 Einstein suggested velocity has an upper limit. If a quantity has an upper limit, its reciprocal has a lower limit. This suggests a reciprocal relation between Planck’s hypothesis and Einstein’s postulate. ...

... Planck and Einstein: In 1900 Planck’s hypothesis set a lower limit to energy quantum. In 1905 Einstein suggested velocity has an upper limit. If a quantity has an upper limit, its reciprocal has a lower limit. This suggests a reciprocal relation between Planck’s hypothesis and Einstein’s postulate. ...

PH0008 Quantum Mechanics and Special

... Planck suggests ad hoc that the radiation emitted from the walls must happen in discrete bundles (called quanta) such that E=h . Mathematically this additional effect generates an expression for spectrum that fits data well. • The Planck constant is determined empirically from then existing data • ...

... Planck suggests ad hoc that the radiation emitted from the walls must happen in discrete bundles (called quanta) such that E=h . Mathematically this additional effect generates an expression for spectrum that fits data well. • The Planck constant is determined empirically from then existing data • ...

On the theory of light scattering in gases

... additional constraints are imposed on a in formula (3). If a is complex, i.e. a a0 ia00 , the inequality a0 4 a00 is always (in gases, outside of an absorption band) fulfilled. That is why in the calculation of ssc one can assume that a is a real quantity and obtain a (quantitatively) correct re ...

... additional constraints are imposed on a in formula (3). If a is complex, i.e. a a0 ia00 , the inequality a0 4 a00 is always (in gases, outside of an absorption band) fulfilled. That is why in the calculation of ssc one can assume that a is a real quantity and obtain a (quantitatively) correct re ...

Planck Mass Plasma Vacuum Conjecture

... (c2 /rp )(rp /c) = c, and hence the momentum fluctuation ∆p = mp c. But since ∆q = rp , and because mp rp c = h̄, one obtains Heisenberg’s uncertainty relation ∆p∆q = h̄ for a Planck mass particle. Accordingly, the quantum fluctuations are explained by the interaction with hidden negative masses, wi ...

... (c2 /rp )(rp /c) = c, and hence the momentum fluctuation ∆p = mp c. But since ∆q = rp , and because mp rp c = h̄, one obtains Heisenberg’s uncertainty relation ∆p∆q = h̄ for a Planck mass particle. Accordingly, the quantum fluctuations are explained by the interaction with hidden negative masses, wi ...

On an Improvement of the Planck radiation Energy Distribution

... given the additional considerations identified in the cited book). The authors mention that it is only an approximation that the energy spectrum could be considered continuous, under the condition that “the cavity be great relative to the mean radiation wavelength because the energy difference among ...

... given the additional considerations identified in the cited book). The authors mention that it is only an approximation that the energy spectrum could be considered continuous, under the condition that “the cavity be great relative to the mean radiation wavelength because the energy difference among ...

1905, ANNUS MIRABILIS: THE ROOTS OF THE

... “Copenhagen” formulation of QM – why some of the most eminent founders of the quantum concepts (like Einstein, Schrödinger, de Broglie, to name the most famous) never did acknowledge it as the final and complete physical theory of the microscopic world. It should be mentioned that initially there wa ...

... “Copenhagen” formulation of QM – why some of the most eminent founders of the quantum concepts (like Einstein, Schrödinger, de Broglie, to name the most famous) never did acknowledge it as the final and complete physical theory of the microscopic world. It should be mentioned that initially there wa ...

Why the Glove of Mathematics Fits the Hand of the Natural Sciences

... Mathematics is the science of the most complete abstractions to which the human mind can attain. As such, it has provoked and inspired more philosophical and scientific questions about its foundations and its relation to the world than any other scientific discipline. The abstractions known as numbe ...

... Mathematics is the science of the most complete abstractions to which the human mind can attain. As such, it has provoked and inspired more philosophical and scientific questions about its foundations and its relation to the world than any other scientific discipline. The abstractions known as numbe ...

THE HIGGS BOSON AND THE FRONTIERS OF PHYSICS Fundacion Valenciana de Estudios Avanzados

... One glorious week in July 2012 when physicists working on the ATLAS One glorious week in July 2012 when physicists working on the ATLAS and CMS experiments at CERN announced that they had discovered a "Higgs‐like particle". These findings have been confirmed in the last year so that IT IS a Hig ...

... One glorious week in July 2012 when physicists working on the ATLAS One glorious week in July 2012 when physicists working on the ATLAS and CMS experiments at CERN announced that they had discovered a "Higgs‐like particle". These findings have been confirmed in the last year so that IT IS a Hig ...

Six easy roads to the Planck scale

... and the basic nature of spacetime must be reconsidered. The arguments are elementary, heuristic, and plausible and as much as possible rely on only general principles of quantum theory and gravity theory. The main goal of the paper is to give physics students and nonspecialists an awareness and appr ...

... and the basic nature of spacetime must be reconsidered. The arguments are elementary, heuristic, and plausible and as much as possible rely on only general principles of quantum theory and gravity theory. The main goal of the paper is to give physics students and nonspecialists an awareness and appr ...

Planck`s law

... radiance, which is always less than or equal to one. The emissivity of a piece of material is in general dependent on its thickness, temperature, the wavelength of the radiation, and the angles of emission and polarization.[6] The surface of a black body can be well approximated by a small hole in t ...

... radiance, which is always less than or equal to one. The emissivity of a piece of material is in general dependent on its thickness, temperature, the wavelength of the radiation, and the angles of emission and polarization.[6] The surface of a black body can be well approximated by a small hole in t ...

Derivation of the Equation E=mc2-v4

... , the work-energy theorem and on Newton's second law of motion. This derivation can be found in most books dealing with special relativity. It is worthy to remark that we derived Einstein's equation without using the above law. So we have also proved that this law, along with the other above mention ...

... , the work-energy theorem and on Newton's second law of motion. This derivation can be found in most books dealing with special relativity. It is worthy to remark that we derived Einstein's equation without using the above law. So we have also proved that this law, along with the other above mention ...

2006-11-14-RAL-Wang - Indico

... Implications on the very small as well as the very large As well as causing quantum matter waves to lose coherence at small scales, the conformal gravitational field is responsible for cosmic acceleration linked to inflation and the problem of the cosmological constant. The formula for relating t ...

... Implications on the very small as well as the very large As well as causing quantum matter waves to lose coherence at small scales, the conformal gravitational field is responsible for cosmic acceleration linked to inflation and the problem of the cosmological constant. The formula for relating t ...

How to use the Cosmological Schwinger principle for Energy

... Making a comparison with a weighted average of ΔS ~ 10 and varying values of a scalar field of 0 < φ < 2π , when one has ηε (−10 −44 sec,0) , and 0 < T ≤ TPlanck ~ 1019 GeV leads to a rich phenomenology , where one could see variations as of a time parameter, and how the wave length, k , evolved, es ...

... Making a comparison with a weighted average of ΔS ~ 10 and varying values of a scalar field of 0 < φ < 2π , when one has ηε (−10 −44 sec,0) , and 0 < T ≤ TPlanck ~ 1019 GeV leads to a rich phenomenology , where one could see variations as of a time parameter, and how the wave length, k , evolved, es ...

13 Black-body radiation and Planck`s formula

... frequencies or, equivalently, wavelengths. We will refer to the wavelength in this section but will convert to the frequency “picture” later on, in Section 2. The notation for the wavelength is λ. Note that the above description has been based on a number of modern concepts, which were not known or ...

... frequencies or, equivalently, wavelengths. We will refer to the wavelength in this section but will convert to the frequency “picture” later on, in Section 2. The notation for the wavelength is λ. Note that the above description has been based on a number of modern concepts, which were not known or ...

e3010012

... are solely defined in terms of others. For this reason, we included the Chew boostrap hypothesis as a crucial ingredient, and wrote: All p-branes are made of each-other. This is, in essence, the origins of the dualities in M theory. Pezzaglia [2] using Chew’s bootstrap hypothesis coined the term “po ...

... are solely defined in terms of others. For this reason, we included the Chew boostrap hypothesis as a crucial ingredient, and wrote: All p-branes are made of each-other. This is, in essence, the origins of the dualities in M theory. Pezzaglia [2] using Chew’s bootstrap hypothesis coined the term “po ...

Pilot_waves_of_de_Broglie

... Traveling waves of space quanta (D3-branes) vibrate/oscillate at specific frequencies which correlates with their source and propagate steadily forward at the speed of light. When two or more complementary traveling waves of (3D-branes) space quanta interact, they form a standing wave. The result o ...

... Traveling waves of space quanta (D3-branes) vibrate/oscillate at specific frequencies which correlates with their source and propagate steadily forward at the speed of light. When two or more complementary traveling waves of (3D-branes) space quanta interact, they form a standing wave. The result o ...

the origins of the quantum theory

... orbits’ energies right, Bohr had to introduce some rather ad hoc rules. These he eventually justified by quantization of angular momentum, which now came in units of Planck’s constant h. (He also used an interesting asymptotic argument that will resurface later.) Published in 1913, the resulting pic ...

... orbits’ energies right, Bohr had to introduce some rather ad hoc rules. These he eventually justified by quantization of angular momentum, which now came in units of Planck’s constant h. (He also used an interesting asymptotic argument that will resurface later.) Published in 1913, the resulting pic ...

File - Mr. C at Hamilton

... •In explaining the shape of the black body spectrum, Planck assumed that the electromagnetic radiation came not in continuous waves of energy, but in discrete clumps of energy which we now call photons. •Planck postulated the ‘photons’, at each frequency have a discreteA energy. E = hf, where E is t ...

... •In explaining the shape of the black body spectrum, Planck assumed that the electromagnetic radiation came not in continuous waves of energy, but in discrete clumps of energy which we now call photons. •Planck postulated the ‘photons’, at each frequency have a discreteA energy. E = hf, where E is t ...

Einstein in 1916:" On the Quantum Theory of Radiation"

... In his novel derivation of the Planck distribution, Einstein added the hitherto unknown process of induced emission2, next to the familiar processes of spontaneous emission and induced absorption. For each pair of energy levels he described the statistical laws for these processes by three coefficie ...

... In his novel derivation of the Planck distribution, Einstein added the hitherto unknown process of induced emission2, next to the familiar processes of spontaneous emission and induced absorption. For each pair of energy levels he described the statistical laws for these processes by three coefficie ...

Unification of Gravity and Electromagnetism

... From the derivations above, it seems that the Newton and Coulomb constants, G and ke , have no deeper meaning for two Planck masses other than to manipulate their input into the correct formula for the same force. We could just as well have come up with another formula based on the total rest mass e ...

... From the derivations above, it seems that the Newton and Coulomb constants, G and ke , have no deeper meaning for two Planck masses other than to manipulate their input into the correct formula for the same force. We could just as well have come up with another formula based on the total rest mass e ...

Derivation Of The Schwarzschild Radius Without General

... formula for the temperature of a black hole and (b) the formula for the black hole entropy. In that formulation I used the universal uncertainty principle (UUP) [3] as the cornerstone of the theory along with the Schwarzschild radius formula discovered by Carl Schwarzschild in 1915. The issue was th ...

... formula for the temperature of a black hole and (b) the formula for the black hole entropy. In that formulation I used the universal uncertainty principle (UUP) [3] as the cornerstone of the theory along with the Schwarzschild radius formula discovered by Carl Schwarzschild in 1915. The issue was th ...

Max Karl Ernst Ludwig Planck, FRS (/plɑːŋk/; German: [plaŋk]; April 23, 1858 – October 4, 1947) was a German theoretical physicist who originated quantum theory, which won him the Nobel Prize in Physics in 1918.Planck made many contributions to theoretical physics, but his fame as a physicist rests primarily on his role as an originator of the quantum theory. However, his name is also known on a broader academic basis, through the renaming in 1948 of the German scientific institution, the Kaiser Wilhelm Society (of which he was twice president), as the Max Planck Society (MPS). The MPS now includes 83 institutions representing a wide range of scientific directions.Max Planck's quantum theory revolutionized human understanding of atomic and subatomic processes.