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C. K. Raju

Publications and source records attributed to C. K. Raju.

11 recordsLinked to original sources
arXiv2013

Teaching mathematics with a different philosophy. Part 1: Formal mathematics as biased metaphysics

We report on a pedagogical experiment to make mathematics easy by changing its philosophy. The Western philosophy of math originated in religious beliefs about mathesis, cursed by the church. Later, mathematics was "reinterpreted", in a theologically-correct way, using the myth of "Euclid" and his deductive proofs. The fact of the empirical proofs in the Elements, was, however, contrary to this myth. The discrepancy was resolved by Hilbert and Russell who rejected empirical proofs as unsound, reducing all mathematics to metaphysics. We explain why that formalist metaphysics is anti-utilitarian and culturally biased, not universal. Historically, most school-level math originated in the non-West with a practical epistemology, but was absorbed in the West after superimposing on it an incompatible Western metaphysics, still used to teach it. This has made mathematics needlessly complex. Accordingly, math can be made easy and more universal by reverting to a more practical epistemology.

math.HO↗
arXiv2013

Teaching mathematics with a different philosophy. Part 2: Calculus without Limits

The example of the calculus is used to explain how simple, practical math was made enormously complex by imposing on it the Western religiously-colored notion of mathematics as "perfect". We describe a pedagogical experiment to make math easy by teaching "calculus without limits" using the new realistic philosophy of zeroism, different from Platonic idealism or formalist metaphysics. Despite its demonstrated advantages, it is being resisted because of the existing colonial hangover.

math.HO↗
arXiv2013

Stability of 2-body orbits in retarded gravitation theory (RGT)

The recently formulated retarded gravitation theory (RGT) explains the non-Newtonian velocities of stars in spiral galaxies, *without any new hypothesis*, and may hence be tested even in the laboratory. However, doubts have been expressed that those higher rotation velocities in RGT may be due to instabilities. We resolve these doubts by solving the full functional differential equations of RGT for a model 2-body planetary system. The solution is stable and closely agrees with the Newtonian solution for this planetary case. Thus, the big difference between RGT and Newtonian gravity for a spiral galaxy is not due to any instability in RGT.

physics.gen-ph↗
arXiv2013

Retarded Gravitation Theory

We propose a Lorentz-covariant theory of gravity, and explain its theoretical origins in the problem of time in Newtonian physics. In this retarded gravitation theory (RGT), the gravitational force depends upon both retarded position and velocity, and the equations of motion are time-asymmetric retarded functional differential equations. We explicitly solve these equations, under simplifying assumptions, for various NASA spacecraft. This shows that the differences from Newtonian gravity, though tiny within the solar system, are just appropriate to explain the flyby anomaly as a v/c effect due to earth's rotation. The differences can, however, be large in the case of a spiral galaxy, and we show that the combined velocity drag from a large number of co-rotating stars enormously speeds up a test particle. Thus, the non-Newtonian behaviour of rotation curves in a spiral galaxy may be explained as being due to velocity drag rather than dark matter. RGT can also be tested in the laboratory. It necessitates a reappraisal of current laboratory methods of determining the Newtonian gravitational constant G. Since RGT makes no speculative assumptions, its refutation would have serious implications across physics.

physics.gen-ph↗
arXiv2008

Radiative Damping and Functional Differential Equations

We propose a general technique to solve the classical many-body problem with radiative damping. We modify the short-distance structure of Maxwell electrodynamics. This allows us to avoid runaway solutions as if we had a covariant model of extended particles. The resulting equations of motion are functional differential equations (FDEs) rather than ordinary differential equations. Using recently developed numerical techniques for stiff FDEs, we solve these equations for the one-body central force problem with radiative damping with a view to benchmark our new approach. Our results indicate that locally the magnitude of radiation damping may be well approximated by the standard third-order expression but the global properties of our solutions are dramatically different. We comment on the two body problem and applications to quantum field theory and quantum mechanics.

physics.class-ph↗
arXiv2008

On Time. 6b: Quantum Mechanical Time

The existence of small amounts of advanced radiation, or a tilt in the arrow of time, makes the basic equations of physics mixed-type functional differential equations. The novel features of such equations point to a microphysical structure of time. This corresponds to a change of logic at the microphysical level. We show that the resulting logic is a quantum logic. This provides a natural and rigorous explanation of quantum interference. This structured-time interpretation of quantum mechanics is briefly compared with various other interpretations of q.m.

physics.gen-ph↗
arXiv2008

On Time. 5b: Electromagnetic Time

We formulate the 2-body problem of electrodynamics using functional differential equations, and explain the peculiar features of these equations which indicate a paradigm shift in physics. We examine the possible empirical existence of advanced interactions using various absorber theories of radiation. Functional differential equations were connected to quantum mechanics in a subsequent paper in this series and in later publications.

physics.gen-ph↗
arXiv2008

Distributional Matter Tensors in Relativity

This paper uses products of distributions to obtain new junction conditions for relativistic shocks. In general, the shock is accompanied by a surface layer, and the new conditions generalize both Taub's jump conditions for shocks, and those of Israel and Kuchar for surface layers. In the non-relativistic limit, the surface layer is present only when the fluid is viscous or thermally conducting--a situation where the classical Rankine-Hugoniot conditions do not apply. Thus, our conditions properly extend all previous conditions, and provide complete Cauchy data needed to solve the full Navier-Stokes equations downstream of the shock. Since the associative law fails for our product, the residual uncertainty regarding the association of factors must be eliminated empirically. This is equivalent to fixing the correct initial_form_ of the equations (such as the ``conservation form'' in the Euler case)

physics.gen-ph↗
arXiv2008

A new mathematical model for molecular dynamics 1: Molecular basis of memory

Proteins have been empirically linked to memory. If memory relates to protein structure, then each conformation would_functionally_ code only one bit, making it difficult to explain large memories. Nor is there a simple way to relate memory to protein dynamics on current molecular dynamics (MD), which is memoryless. Here we point out that MD may be modified to involve memory ab initio without any new hypothesis: simply replace the electrostatic (Coulomb) force by the electrodynamic force--which is more accurate. We now need to solve functional differential equations (FDEs), instead of the ordinary differential equations (ODEs) currently solved in MD. Unlike ODEs, retarded FDEs are history-dependent: so memory is already present even at the level of interacting sites within molecules. The resulting increase in computational complexity is within the reach of current computers. While Amdahl's law does pose a challenge to parallelised time-stepping with this model, the compute-intensive part--the force calculation--may still be carried out in parallel. Thus, reformulating MD to use FDEs is feasible, and this could help to understand the possible dynamical basis of memory.

physics.gen-ph↗
arXiv2005

The electrodynamic 2-body problem and the origin of quantum mechanics

We numerically solve the functional differential equations (FDE's) of 2-particle electrodynamics, using the full electrodynamic force obtained from the retarded Lienard-Wiechert potentials and the Lorentz force law. In contrast, the usual formulation uses only the Coulomb force (scalar potential), reducing the electrodynamic 2-body problem to a system of ordinary differential equations (ODE's). The ODE formulation is mathematically suspect since FDE's and ODE's are known to be incompatible; however, the Coulomb approximation to the full electrodynamic force has been believed to be adequate for physics. We can now test this long-standing belief by comparing the FDE solution with the ODE solution, in the historically interesting case of the classical hydrogen atom. The solutions differ. A key qualitative difference is that the full force involves a `delay' torque. Our existing code is inadequate to calculate the detailed interaction of the delay torque with radiative damping. However, a symbolic calculation provides conditions under which the delay torque approximately balances (3rd order) radiative damping. Thus, further investigations are required, and it was prematurely concluded that radiative damping makes the classical hydrogen atom unstable. Solutions of FDE's naturally exhibit an_infinite_ spectrum of _discrete_ frequencies. The conclusion is that (a) the Coulomb force is_not_ a valid approximation to the full electrodynamic force, so that (b) the n-body interaction needs to be reformulated in various current contexts such as molecular dynamics.

quant-ph↗