Two Dimensional Gravitational Lensing Does Away With the Need of Dark Matter

Spiral galaxies invariably have stellar rotation curves that are constant, or flat, with increasing distance from the galactic center. If Newton's inverse law of attraction were at work, the rotational velocity would steadily decrease as we move away from the galactic center. One way to speed up the outer regions would be to encase them in a halo of matter that would be necessarily "dark" since we do not perceive them. There would therefore be halos enshrouding the galaxies that would lead to an inverse law instead of an inverse square law of attraction.

Flat Rotational Curves Could be due to Gravitational Lensing

MOND has been very successful in accounting four the Tully-Fisher relation which is a correlation for spiral galaxies between how fast they are rotating and their luminosity. Below a critical value of the gravitational acceleration, Newton's inverse square law goes over into a inverse law. MOND has been criticized insofar as the new law does not conserve angular momentum. But the basis for such a criticism is that the geometry is three dimensional.

How LIGO Redefines the Meaning of Quantum Uncertainty

To avoid the negative consequences of Heisenberg's Uncertainty Relations (HUP), LIGO borrows from Braginsky et. al. to introduce what is supposed to be novel developments like the Standard Quantum Limit (SQL) and Quantum Non-Demolition (QND) experiments that supposedly beat the HUP. Yet, we know that HUP stands in the "defense" of quantum mechanics, to use a colorful expression borrowed from Feynman.

How LIGO Domesticates Heisenberg's Uncertainty Principle

The measurement of "ripples" in spacetime by shaking two pairs of mirrors by 1/1000 th the diameter of a proton---or 1 billionth of 1 billionth of a meter certainly enters to domain of quantum measurements which is fully protected by Heisenberg's Uncertainty Principle (HUP) involving conjugate variables like position and velocity, and energy and time. The more uncertainty, measured in terms of the variance, of one the less there is in the other. 

Last Minute Update!

There is going to be a Dover Edition reissue of my book

                                  Nonequilibrium Statistical Thermodynamics

originally published by Wiley-Interscience (1985), that will hit the bookstalls early next Spring. It can already be pre-ordered on Amazon for the April 17th release date.

Pre-orders can be made at

Last Minute Update!

My new book, 

                                             Seeing Gravity

will be in all the bookstalls early next year, being published by World Scientific Publishing Company.

Where Lies the Optical Properties of Matter in General Relativity?

In the December 12 1936 issue of Nature, Ludwik Silberstein publishes a letter entitled "Minimal lines and geodesics within matter: A fundamental difficulty of Einstein's theory."

The issue Silberstein address was that Einstein equates geometry $G$ with a material tensor $T$ so that one should know what the other is talking about. Otherwise, you would be equating apples and oranges. 

Now according to Einstein's generalization of the Minkowski indefinite metric, 


Why Black Holes Don't Exist in the Schwarzschild Metric, and How to Create One

We are told to imagine that within the Schwarzschild radius, a particle will spiral in to its doom hitting the singularity in an undetermined amount of time. All this comes from extrapolating the Schwarzschild metric beyond its domain of validity, $r<2GM/c^2$. This is undoubtedly why Karl Schwarzschild did not find any such sucking in of material, and why he went beyond his outer solution to create an inner solution for $r<\surd(G\varrho)/c$, where $\varrho$ is the density and $1/\surd(G\varrho)$ is the Newtonian free-fall time.