Goddalehundi Bharathraj - Academia.edu (original) (raw)

Drafts by Goddalehundi Bharathraj

This is a brief analysis of some errors in Einstein's Relativity theory. Specifically regarding, ... more This is a brief analysis of some errors in Einstein's Relativity theory. Specifically regarding, (i) Energy - Momentum balance during light emission process, (ii)Reflection of light as seen from moving frames, (iii) A consequence of Lorentz time transformation which causes material objects in relative motion to dematerialise and display an illusory super-luminal wave, (iv) An asymmetry in the measurement of mutual distance between moving inertial frames, (v) About misconceptions in application of electromagnetism, (vi) Error in equating inertial frame with free falling frame and (vii) Error in equating uniformly accelerating frame with a frame at rest under gravity.

#einstein #physics #relativity #space #time #light #michelson #morley #lorentz #poincare The Ti... more #einstein #physics #relativity #space #time #light #michelson #morley #lorentz #poincare

The Time Dilation and Length Contraction are apparent effects. They are not real. And they do not occur because the speed of light is constant for all observers. It happens because light speed is constant relative to the source. This might indicate that when a pion is moving the delay in receiving signals from it enhances, we just receive the information late. It is not the same as enhanced life time of a pion.

Kepler summarised the available (2D)observational record of planetary orbits and periods into thr... more Kepler summarised the available (2D)observational record of planetary orbits and periods into three simple laws. Newton further reduced them into one little equation... Newton henceforth setup the idea that the entity md^2r/dt^2 called Force is somehow more fundamental than other physical quantities and a physical interaction essentially involves a law governing the evolution of md^2r/dt^2. This idea was then extended to include all other kinds of physical interactions, fluid mechanics, electro dynamics, etc.

Newton successfully applied the equation inspired by Kepler's celestial laws to explain terrestrial objects such as the parabolic trajectory of cannonballs, the period of a pendulum, ... Yet he was not successfull in extending his equation to explain the precessions in Moon's orbit. And it was found that Newton's equation produce unstable solutions when extended to 3 or more interacting objects. And it produces ill-posed equations in 3D because the observational base used by Newton to derive his equation is limited to a flat 2D space with 2-body type interactions where one of the interacting mass is extremely heavy compared to the other. The primacy of md^2r/dt^2 established through Newton's laws of motion and the universality of the form of gravitational(or any other physical) interaction established through Newton's law of gravity remains unquestioned. But there are good reasons to reassess that stance. For example under uniform gravitational acceleration condition observed near Earth's surface we see that in case of Brachistochrones and Inclined planes md^2r/dt^2 = g is not valid. In contrast the form of graviational potential energy remains fixed, P = −mgy or P = P0 − mgy. Infact starting from Kepler's laws we can not only derive Newton's law of gravity but also the Energy(E) conservation equation. ...

Einstein's Equivalence principle is wrong. Here we briefly see how. If Einstein was to have a ha... more Einstein's Equivalence principle is wrong. Here we briefly see how.

If Einstein was to have a happier thought he would have realised that when we throw away(or disengage) some mass from an accelerating frame like a spaceship the acceleration of the frame increases. Because now the same fuel burn will be accelerating a lesser mass. But in case of gravity throwing away some mass from the frame at rest does not alter the state of acceleration of the frame. Hence the two cases are not equivalent.

Using the Energy Conservation and Angular Momentum Conservation Equations on the Sun-Moon-Earth 3... more Using the Energy Conservation and Angular Momentum Conservation Equations on the Sun-Moon-Earth 3-body System with gravitational interaction, we can easily find the 18.6 Year periodicity of regression of nodes of Moon's orbit and find a period of 1.4 Lakh Years for the Precession of Earths orbit around the Sun. Perhaps this is related with the Milankovich Ice Age cycle.

In part-I of Rediscovering Gravity we saw that Newton's Laws of Motion and Newton's Law of Gravit... more In part-I of Rediscovering Gravity we saw that Newton's Laws of Motion and Newton's Law of Gravity do not have universal validity. But Energy conservation principle is universally valid. Here we touch upon the errors with Einstein's Equivalence principle. Then discuss the proper expression for projectiles on the surface of Earth(fit to launch ICBMs) and And move on to a Fatio-LeSage type dynamic gravity without the mystery of action at a distance.

Kepler(supposedly) kicked off modern science with the discovery of Planetary Laws. They are the v... more Kepler(supposedly) kicked off modern science with the discovery of Planetary Laws. They are the very first empirical laws of Physics. Newton partially identified the universal nature of Kepler's work and mathematically put (Mass of)Sun at the center of the solar system. He connected Kepler's laws with Galileo's observation of the same rate of fall of all objects(independent of Mass) on Earth surface. Since there was no clear grasp of concepts like Energy conservation and Angular momentum conservation at his time, Newton's analytical method remained a bit more complicated than necessary(where it is applicable) and erroneous in most cases. Perhaps, Newton tried hard to conceal that, all we need to do is apply calculus on Kepler's laws to understand the underlying dynamics. If he really did discover calculus then why was he reluctant to show off the far more easier and superior technique?. A point to be noted is, a rudimentary form of Indian(+Arabic?) calculus/number system started floating in European continent from 1100 AD onwards. In this article we see that the first time derivative of Kepler's I law, along with the application of II law gives the Planetary Energy conservation equation. We can use this as the basis to solve the generalized 3-body problem also. Along the way we see that the term Inertia coined by Galileo to explain the height conserving property of balls rolling down inclined plane has to be properly interpreted as energy. That is, Inertia = Energy. Hence we should replace Newton's I law by Energy conservation principle. We also see that F = ma is not a correct definition, the correct definition should be F = Gradient of Kinetic Energy. In certain cases the two definitions match, most often they do not.

The Cycloid solution to the Brachistochrone problem proposed by Johann Bernoulli, Newton, Jacob B... more The Cycloid solution to the Brachistochrone problem proposed by Johann Bernoulli, Newton, Jacob Bernoulli, Leibniz, L'Hospital etc and later cloaked in formal looking Calculus by Lagrange actually shows that in this case the acceleration is Non-Newtonian. It is strange that neither Newton or Lagrange pointed it out. The Brachistochrone solution does not follow Newton's Second Law.

The correct way using Energy and Angular Momentum Conservation Equations

Contrary to Georg Cantor's conclusion in this article we see that in the limiting case when the s... more Contrary to Georg Cantor's conclusion in this article we see that in the limiting case when the size of the set of all natural numbers tends to infinity, the size(cardinality) of the set of natural numbers becomes the same as the size of the set of all real numbers in the domain (0,1). We also see a 1-to-1 correspondence function between the set of natural numbers and the binary form representation of real numbers in (0,1). Going further we see that the size of the set of natural numbers is larger than the size of its own power set. Another paradox amongst the zoo of infinity paradoxes.

We need to reboot the entire thought process about dealing with the Riemann Zeta series and start... more We need to reboot the entire thought process about dealing with the Riemann Zeta series and start from saner grounds.

There is a basic problem with Bohr's Model. This mechanism can not explain electron jumps longer ... more There is a basic problem with Bohr's Model. This mechanism can not explain electron jumps longer than 1 angular momentum level at a time. Like line spectra observed by Angstrom, Lyman, Paschen, Pfund, etc and summarised by Balmer and Rydberg. Because in Bohr's scheme an electron jump from some energy level n to another level m is not only associated with a change in Energy of the electron {∆E = E_m – E_n = hcR*(1/n^2 – 1/m^2)} but it should also be associated with a change in angular momentum of the electron {∆A = A_m – A_n = h*(m – n)}. A single photon has a unit Angular Momentum (h), so in order to get rid of h*(m–n) units of Angular Momentum, an electron has to release (m–n) photons. But in case of the above mentioned line spectra the whole energy ∆E is carried away by only 1 photon with 1 unit angular momentun (h). So where is the rest of h*(m–n–1) units of angular momentum going?. Perhaps there is a change in angular momentum level of the electrons by only 1 unit and the energy changes by several units. Bohr's simple circular orbits can not explain it and looks like Arnold Sommerfeld needlessly complicated/obfuscated the issue. What is needed is a room for orbits with multiple energy levels possible at the same angular momentum. The function between Energy space and Angular momentum space is not 1-to-1 but many-to-1 .. https://www.academia.edu/36778930/Neo_Classical_Atoms_Molecules_and_Nucleus..

In this article we take a closer look at the inner and outer regimes of a Rankine vortex. The inn... more In this article we take a closer look at the inner and outer regimes of a Rankine vortex. The inner regime (ala Eye of the cyclone) is where the angular velocity is conserved and we observe the Coriolis effect. The outer regime is where the angular momentum is conserved and we do not see the Coriolis effect. We derive the particle trajectories observed under both the regimes.

Inner Vortex: We get circular trajectories with all the possible trajectories of the family themselves being bound within a circular region (like the trajectories within the eye of a cyclone).

Outer Vortex: We get straight line trajectories with all the possible trajectories of the family being tangents to the circular region at the center. So there is a hole or gap at the center where no trajectories extend (like the trajectories outside the eye of a cyclone).

This has deep repercussions on understanding phenomena at various scales in physics especially magnetism. Because there is a correspondence between Coriolis effect in Mechanics and Lorentz effect in Electromagnetics.

Updated 13th December 2018..... Updated (for 'Superballs') 16th December 2018..... As long ... more Updated 13th December 2018.....

Updated (for 'Superballs') 16th December 2018.....

As long as we have “elastic collisions” with only Linear Energy and Linear Momentum conservation we can never get “irreversibility”. The “no-slip” condition seems to be the crux of this irreversibility. The total energy and the linear momentum of the system is conserved, but angular momentum is not conserved.

The usual exponential decay (with e, the Base of Natural Logarithm) of particle density with resp... more The usual exponential decay (with e, the Base of Natural Logarithm) of particle density with respect to energy levels proposed by Boltzmann does not hold up to scrutiny!. In fact the base of the exponential function depends on the ratio of Number of Particles to Number of energy levels.

In this we need not really assume that E (Energy level of the individual charge) is discrete. E a... more In this we need not really assume that E (Energy level of the individual charge) is discrete. E and hence emission frequency can be continuous. But we need to assume the emission happens in discrete steps. That is, a rotating charge will emit the whole energy in a 1 single step. That is the discreteness necessary.

The maximum possible effect of CO2 is raising the surface temperature by 2.7% only, even if the w... more The maximum possible effect of CO2 is raising the surface temperature by 2.7% only, even if the whole atmosphere is made of CO2. This effect is not enough to explain even the observed 288 K surface temperature on Earth.

The usual radiative equilibrium equation(used by climate scientists) predicts that the averge sur... more The usual radiative equilibrium equation(used by climate scientists) predicts that the averge surface temperature of moon should be around 270 K(or -3 C) with an albedo of 0.11. But the observed surface temperature of moon is less than 200 K. This is a huge discrepancy of 70 K between theory and observation. This discrepancy arises because of wrong radiative equilibrium equation which disregards rotation and disregards the nature of the surface.

I develop the correct model of radiative balance and provide the first correct method to model the surface temperature of moon (which is devoid of ocean/atmosphere) and also derive the "correct" average surface temperature of earth (~288 K) by considering proper air-sea interaction. On Earth the effect of the atmosphere as a whole is to rise the temperature of the ocean surface from about 225 K(or -50 C as observed during snowball earth scenario) to 288 K (as observed in present times), that is a total rise of 63 K.

In light of this we can conclude that the 'greenhouse effect' theory needs to be reinvestigated empirically in a proper way. The previous model based estimates of that effect may be way off the mark. The climate scientists have got even their ABC's wrong. Perhaps also make solar-like panels to trap the backradiation, because according to the prevalent energy balance we receive ~340 W/m2 of greenhouse-backradiation as opposed to ~170 W/m2 of solar radiation at the surface. And backradiation is more reliable because it is available at night as well.

Guess this is the final nail in the coffin of Anthropogenic Global Warming. The usual radiative e... more Guess this is the final nail in the coffin of Anthropogenic Global Warming. The usual radiative equilibrium model is wrong. It fails to predict the average surface temperature of even Moon which is devoid of both ocean and atmosphere. The prediction is -3C whereas the average surface temperature of moon is like -120C. We develop the correct model representing the interplay between radiation and planetary surface temperatures.

According to this, the actual warming is not from -18C to +15C(as propagated by IPCC). The actual warming is from -120C to +15C. And each extra 1W/m2 of radiative forcing causes a rise of 0.16C at the Equator and 0.32C rise near the poles. So AGW may not be a very serious concern.

"Earth": The usual discussion about the Greenhouse/Backradiation effect seems to ignore/confuse ... more "Earth":
The usual discussion about the Greenhouse/Backradiation effect seems to ignore/confuse an important consideration. Just by putting more CO2 into the atmosphere we can not keep getting more and more backradiation simply because the power available in the 14-16 micron wavelength band is limited by the temperature of the emitting surface. That is at 288 K Earth surface temperature, there is a total of ~71 W/m2 available in the 14-16 micron band. At present only 45 W/m2 of this available 71 W/m2 is being absorbed by the CO2 in the atmosphere. By increasing the amount of CO2 in the atmosphere we can increase this absorption portion from 45 W/m2 to 71 W/m2, putting more CO2 can not make it absorb beyond the available 71 W/m2. This would be like the saturation limit.

So if we have enough CO2 to absorb all the avaiable energy in the 14-16 micron band we get a maximum rise in the average temperature of 2K. Most of this rise comes due to enhanced minimum Temperature rather than enhances maximum Temperature.

"Venus":
With a Temperature of 750 K the surface would be radiating ~ 17950 W/m2 according to Stefan-Boltzmann Radiation Law. The total energy available in the 14–16 micron wavelength band is 832 W/m2. Thus the maximum available power to backradiation effect is = 832/2 = 416 W/m2. So the net available power at the surface can be maximum = 17948.692 + 416 ~ 18365 W/m2.
So maximum possible Temperature with backradiation = T = (18365/s)1/4 = 754.4 K. Thus the effect of CO2 backradiation on Venus is 754.4 – 750 = 4.4 K.

CO2 backradiation can not create runaway warming even on Venus. It can at best increase the Surface temperature from 750 K to 754.4 K.

#einstein #physics #relativity #space #time #light #michelson #morley #lorentz #poincare The Ti... more #einstein #physics #relativity #space #time #light #michelson #morley #lorentz #poincare

Einstein's Equivalence principle is wrong. Here we briefly see how. If Einstein was to have a ha... more Einstein's Equivalence principle is wrong. Here we briefly see how.

The correct way using Energy and Angular Momentum Conservation Equations

Inner Vortex: We get circular trajectories with all the possible trajectories of the family themselves being bound within a circular region (like the trajectories within the eye of a cyclone).

Updated 13th December 2018..... Updated (for 'Superballs') 16th December 2018..... As long ... more Updated 13th December 2018.....

Updated (for 'Superballs') 16th December 2018.....

CO2 backradiation can not create runaway warming even on Venus. It can at best increase the Surface temperature from 750 K to 754.4 K.

Entropy has nothing to do with Second law of thermodynamics. The term (spatial gradient of pr... more Entropy has nothing to do with Second law of thermodynamics.

The term (spatial gradient of pressure + weight per unit volume) = (∇P + ρ.g) is what determines the times arrow in a thermodynamic system(under gravity), when (∇P + ρ.g) = 0 we get the Hydrostatic equilibrium condition.

When (∇P + ρ.g) ≠ 0, then the system is far from equilibrium... and in the absence of any external energy sources the system will spontaneously always tend to a condition where (∇P + ρ.g) = 0. This is the reformulated II law.

Navier-Stokes equation just describes the response of a fluid given a particular value of (∇P + ρ.g), it does not determine the direction in which the pressure gradients further evolve. For that we need an equation which has this (∇P + ρ.g) → 0

The combined gas law PV/T = Constant is actually a statement about Entropy. It turns of PV/T = 2S... more The combined gas law PV/T = Constant is actually a statement about Entropy. It turns of PV/T = 2S/3, where S = Entropy. So, when PV/T = Constant, we get an Isentropic process. In this article we show the much simpler and correct idea of Entropy and its relationship to the Number of particles in the system, Degrees of freedom and most importantly the Idea of "Phase".

With this definition in place we further show the we need to restate Second law of thermodynamics(by removing Entropy from it) as;

The “energy”(not just heat energy) flows from a region of higher average energy per free particle to a region of lower average energy per free particle

This effectively shuts down the Loschmidt-Boltzmann debate in favor of Loschmidt. It shows why the Boltzmann assumption of an Isothermal atmosphere is wrong. The real atmospheres show a vertical gradient in temperature as a consequence of the First law of Thermodynamics. Second law does not stop it because the heat does not flow from the lower atmosphere at higher temperature to higher atmosphere at lower temperature as long as the average total energy (thermal + potential) per free particle at different height remains the same.

This shows that the general solution (with imaginary numbers) assumed for an SHM equation involvi... more This shows that the general solution (with imaginary numbers) assumed for an SHM equation involving e^iwt is not realistic as it always points to a spring-mass system with zero total energy regardless of how large the amplitude or frequency may be. The only realistic solution for SHM is the sinusoidal solution. e^iwt forms introduce spuriousness.

If the springs are relaxed, then it leads to complicated unsolvable mathematical expressions. It ... more If the springs are relaxed, then it leads to complicated unsolvable mathematical expressions. It is a sensitive system which needs certain preconditions to be setup. Check out the Rayleigh wave type particle "orbits" possible on the spring-mass chains.

Still need the "Physics"...

The lighter molecules in a mixture of gases posses higher kinetic energy at every height(z > 0). ... more The lighter molecules in a mixture of gases posses higher kinetic energy at every height(z > 0). Thus they can transfer their energy to the heavier molecules and increase the probability of finding the heavier molecules at greater heights. While doing so the lighter molecules also impart a huge upward bulk velocity to the heavier molecules.

Experimental verification of the new(better than Clausius-Clapeyron) equation relating saturation... more Experimental verification of the new(better than Clausius-Clapeyron) equation relating saturation humidity with air temperature

Derivation of Generalized Lapse Rate for Atmosphere

The equivalence between Coriolis Force and Lorentz Force shows that the Magnetic Field denotes th... more The equivalence between Coriolis Force and Lorentz Force shows that the Magnetic Field denotes the Angular Velocity of a Charge, and Vector Potential denotes the Tangential Velocity.

Easier and more General way to solve the Spring - Mass Systems, using the Energy Method. And a d... more Easier and more General way to solve the Spring - Mass Systems, using the Energy Method.

And a discussion about " Zero Energy Springs " which are the cases in which we get the imaginary solutions.

Proper Derivations of the Vertical Structure of the Atmosphere. Closer to Loschmidt, Better thab ... more Proper Derivations of the Vertical Structure of the Atmosphere. Closer to Loschmidt, Better thab Boltzmann!.

And Formulating the Correct Navier-Stokes Equation...

A better version of the Clausius-Clapeyron Equation especially for Meteorological Purpose

The correct Adiabatic process satisfies the Force balance equilibrium condition and the First law... more The correct Adiabatic process satisfies the Force balance equilibrium condition and the First law of thermodynamics. But we if we insist on using the (wrong) PV^(gamma) = Constant relationship as is specified in the text books then either Force equilibrium condition or the First law goes for a toss.

Here we derive the correct version of Adiabatic process from first principles.

An Introduction to me, thats all.