Pradip Kumar Chatterjee | Indian Association for the Cultivation of Science (original) (raw)
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Papers by Pradip Kumar Chatterjee
Arxiv preprint quant-ph/0412144, Jan 1, 2004
- Gravitationally induced wave function collapse 6) Bohmian Approach [11] 7) Many Worlds Interpr... more 5) Gravitationally induced wave function collapse 6) Bohmian Approach [11] 7) Many Worlds Interpretation .
Arxiv preprint physics/0509219, Jan 1, 2005
Quantum Mechanics of photons leads to a theory of Quantum Gravity that nicely matches the experim... more Quantum Mechanics of photons leads to a theory of Quantum Gravity that nicely matches the experimental results of varying fine structure constant, obtained from many-multiplet Quaser absorption systems and atomic clocks. The variation of that constant is due to quantum gravity of photons, created by their non-zero invariant mass. The photon mass is obtained from a Klein-Gordon scalar tachyon. This led to a Lorentz symmetry-breaking and varying speed of light theory in complex spacetime manifold. In essence, Quantum Mechanics includes quantum gravitational potential in the guise of Quantum potential. The greatest surprise lies in showing that Quantum Mechanics naturally leads to open bosonic string whose troublesome tachyonic vibration is taken in its stride. Quantum Mechanics also proves Sen`s second conjecture and space-tearing. Length melts into dimensionless number at the Planck scale. Quantum-mechanical analog of the classical equation E=Mc 2 has been derived and a dispersion relation demonstrates Lorentz noninvariance in Quantum Mechanics.
Preprint version (4)., Jun 9, 2013
Since division by zero is not a valid mathematical operation in real number field, Heisenberg unc... more Since division by zero is not a valid mathematical operation in real number field, Heisenberg uncertainty relation implies that particle position cannot be absolutely precise. The same result follows for momentum also. The real line is deleted from the eigenvalue spectra for position and momentum. The real line therefore vibrates briskly between two D2-branes. At low energy, a string is perhaps to-and-fro vibration of probability pulse of D0-brane along an extra imaginary dimension. A Lorentz-violating term in rest energy of a particle feeds the extra energy needed for particle spin. Inertial frames and Dirac delta function are found incompatible with the uncertainty relation.
Preprint, version (1), Jun 22, 2013
" Minimal imaginary momenta of quantum particles available in non-unitary quantum mechanics ge... more "
Minimal imaginary momenta of quantum particles available in non-unitary quantum mechanics generate spin of the particles. The D0-branes of a universal constant mass comprise the lowest vibration mode of quantum vacuum. Spin of a particle is just orbital angular momentum of D0-brane(s) of mass equal to mass gap circling along a loop of imaginary radius. For three distinct directions of spin component, each orbit picks up a distinct unit of pure quaternion basis. The interpretation becomes relatively untangled when each unit of pure quaternions is found related to one of the three Pauli spin matrices. An important revelation is that spin in quantum mechanics requires Lorentz violation. Lorentz-violating energy term feeds the energy required for spinning of the D0-brane. Impossibility of a non-composite spin-0 object existing as a truly elementary particle has been examined.
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Preprint : version (3), Apr 23, 2013
""Non-unitary relativistic quantum mechanics and supersymmetry derived from Heisenberg's uncertai... more ""Non-unitary relativistic quantum mechanics and supersymmetry derived from Heisenberg's uncertainty relation lead to a probable candidate for quantum gravity. D0-branes cupped inside Riemann spheres studded on the space-time fabric are probable building blocks of nature. Apart from finding theoretically the astronomically observed value of cosmological constant, and attempting to resolve the coincidence problem, it also derives some well-established results of string theory and loop quantum gravity. It also provides strong mathematical and physical support for Maldacena conjecture. While tweaking the formula for quantum black hole entropy, it is observed that the second law of thermodynamics breaks down in singularity-free black hole physics. This in turn perhaps gives onto the results concerning no loss of information in a black hole and no preferred arrow of time. Re-examining Pauli's theorem, "time" has been established, hopefully, as an operator in standard quantum mechanics. Possible hiding places of violations of equivalence principle and Lorentz symmetry have been explored, and these now offer testable predictions for quantum gravity. Particle spin is now gleaned as rotation of the particle along a circumferential path or a motion along the great circle on a 2-sphere surface constrained with a radius of one imaginary unit. This non-classical spinning is a model for non-Higgs mechanism, and probably generates particle mass. Electric charge in Planck scale is found to equal square root of particle mass/energy. The core principle of superstring theory, supersymmetry, is found to emerge from the "heart" of quantum mechanics : The uncertainty principle. Supersymmetry also allows physics to dissolve into mathematics at transplanck scale. This allows to solve about 200 years old Clausen’s paradox and some unresolved identities of number theory. It also sheds light on Baker’s theorem and Schanuel’s conjecture in Transcendental number theory. A fundamental mass constant or "mass gap" reaped from vacuum energy may allow a peek into a "space-time-matter"-less primary theory where all fundamental interactions meld in nature. Physics perhaps mingles with mathematics in this confluence of transphysical zone of transcendental numbers. Two quantized formulas from general relativity gives off gravitons as well as two purely quantum gravity equations. This template tries to create a road map to find quantum gravity analogs of various equations of general relativity. Some other overlapping topics of current interest are also discussed to add more clarity.
Key words: Cosmological constant problem, quantum gravity, string theory, supersymmetry, mechanism of particle spin, Lorentz symmetry violation, violation of equivalence principle, quantum electro-gravity, quantum black holes, singularity theorems
PACS numbers : 98., 04., 12., 11., 03.
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Arxiv preprint quant-ph/0412144, Jan 1, 2004
- Gravitationally induced wave function collapse 6) Bohmian Approach [11] 7) Many Worlds Interpr... more 5) Gravitationally induced wave function collapse 6) Bohmian Approach [11] 7) Many Worlds Interpretation .
Arxiv preprint physics/0509219, Jan 1, 2005
Quantum Mechanics of photons leads to a theory of Quantum Gravity that nicely matches the experim... more Quantum Mechanics of photons leads to a theory of Quantum Gravity that nicely matches the experimental results of varying fine structure constant, obtained from many-multiplet Quaser absorption systems and atomic clocks. The variation of that constant is due to quantum gravity of photons, created by their non-zero invariant mass. The photon mass is obtained from a Klein-Gordon scalar tachyon. This led to a Lorentz symmetry-breaking and varying speed of light theory in complex spacetime manifold. In essence, Quantum Mechanics includes quantum gravitational potential in the guise of Quantum potential. The greatest surprise lies in showing that Quantum Mechanics naturally leads to open bosonic string whose troublesome tachyonic vibration is taken in its stride. Quantum Mechanics also proves Sen`s second conjecture and space-tearing. Length melts into dimensionless number at the Planck scale. Quantum-mechanical analog of the classical equation E=Mc 2 has been derived and a dispersion relation demonstrates Lorentz noninvariance in Quantum Mechanics.
Preprint version (4)., Jun 9, 2013
Since division by zero is not a valid mathematical operation in real number field, Heisenberg unc... more Since division by zero is not a valid mathematical operation in real number field, Heisenberg uncertainty relation implies that particle position cannot be absolutely precise. The same result follows for momentum also. The real line is deleted from the eigenvalue spectra for position and momentum. The real line therefore vibrates briskly between two D2-branes. At low energy, a string is perhaps to-and-fro vibration of probability pulse of D0-brane along an extra imaginary dimension. A Lorentz-violating term in rest energy of a particle feeds the extra energy needed for particle spin. Inertial frames and Dirac delta function are found incompatible with the uncertainty relation.
Preprint, version (1), Jun 22, 2013
" Minimal imaginary momenta of quantum particles available in non-unitary quantum mechanics ge... more "
Minimal imaginary momenta of quantum particles available in non-unitary quantum mechanics generate spin of the particles. The D0-branes of a universal constant mass comprise the lowest vibration mode of quantum vacuum. Spin of a particle is just orbital angular momentum of D0-brane(s) of mass equal to mass gap circling along a loop of imaginary radius. For three distinct directions of spin component, each orbit picks up a distinct unit of pure quaternion basis. The interpretation becomes relatively untangled when each unit of pure quaternions is found related to one of the three Pauli spin matrices. An important revelation is that spin in quantum mechanics requires Lorentz violation. Lorentz-violating energy term feeds the energy required for spinning of the D0-brane. Impossibility of a non-composite spin-0 object existing as a truly elementary particle has been examined.
"
Preprint : version (3), Apr 23, 2013
""Non-unitary relativistic quantum mechanics and supersymmetry derived from Heisenberg's uncertai... more ""Non-unitary relativistic quantum mechanics and supersymmetry derived from Heisenberg's uncertainty relation lead to a probable candidate for quantum gravity. D0-branes cupped inside Riemann spheres studded on the space-time fabric are probable building blocks of nature. Apart from finding theoretically the astronomically observed value of cosmological constant, and attempting to resolve the coincidence problem, it also derives some well-established results of string theory and loop quantum gravity. It also provides strong mathematical and physical support for Maldacena conjecture. While tweaking the formula for quantum black hole entropy, it is observed that the second law of thermodynamics breaks down in singularity-free black hole physics. This in turn perhaps gives onto the results concerning no loss of information in a black hole and no preferred arrow of time. Re-examining Pauli's theorem, "time" has been established, hopefully, as an operator in standard quantum mechanics. Possible hiding places of violations of equivalence principle and Lorentz symmetry have been explored, and these now offer testable predictions for quantum gravity. Particle spin is now gleaned as rotation of the particle along a circumferential path or a motion along the great circle on a 2-sphere surface constrained with a radius of one imaginary unit. This non-classical spinning is a model for non-Higgs mechanism, and probably generates particle mass. Electric charge in Planck scale is found to equal square root of particle mass/energy. The core principle of superstring theory, supersymmetry, is found to emerge from the "heart" of quantum mechanics : The uncertainty principle. Supersymmetry also allows physics to dissolve into mathematics at transplanck scale. This allows to solve about 200 years old Clausen’s paradox and some unresolved identities of number theory. It also sheds light on Baker’s theorem and Schanuel’s conjecture in Transcendental number theory. A fundamental mass constant or "mass gap" reaped from vacuum energy may allow a peek into a "space-time-matter"-less primary theory where all fundamental interactions meld in nature. Physics perhaps mingles with mathematics in this confluence of transphysical zone of transcendental numbers. Two quantized formulas from general relativity gives off gravitons as well as two purely quantum gravity equations. This template tries to create a road map to find quantum gravity analogs of various equations of general relativity. Some other overlapping topics of current interest are also discussed to add more clarity.
Key words: Cosmological constant problem, quantum gravity, string theory, supersymmetry, mechanism of particle spin, Lorentz symmetry violation, violation of equivalence principle, quantum electro-gravity, quantum black holes, singularity theorems
PACS numbers : 98., 04., 12., 11., 03.
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