DrRocket

ALL currently accepted models treat spacetime as a manifold (continuous). Attempts have been made to formulate discrete models, but so far none have panned out. The singularity theorems cited in most cases are based on general relativity. Einstein-Cartan theory results in different singularity theorems or no singularities at all, but no current experiment can distinguish between Einstein-Cartan theory and general relativity. Both treat spacetime as a manifold. In short, you are all wet.

This is just plain wrong. Go read the suggested references.

A photon carries no charge. The photon mediates but does not "feel" the electromagnetic force. Read a physics book. Gordon Kane's book on Modern Elementary Particle Physics would be a good start.

Why would anyone in his right mind heat the balance ? Your theory was that the weight of a test mass would decrease with increasing temperature. That is contradictory to physics. A good experimentalist would likely use an apparatus other than a commercial balance. A sane experimentalist would not heat the measuring apparatus any more than absolutely necessary. Try reading a physics book. The Feynman Lectures on Physics would be a good start.

Stiffness is still the driver for in-line rocket design, as I stated. And I am willing to bet that I have been involved in the design of more in-line rockets than have you. In fact we dumped most aluminum structures in favor of composites for weight and stiffness reasons some years back. Isogrids did not work out very well in the trades either.

You can divide by the abstract polynomial x+c in the polynomial ring over the real numbers, and you are not dividing by the zero polynomial, so the operation is perfectly correct. Later you can evaluate the resulting function at x=-c if you like, and if you do it properly you will be dividing by zero.

Wrong. Infinity is quite well-defined in mathematics. In fact there are lots of infinities. Google "cardinal numbers" and "ordinal numbers". Still wrong. Mathematics is subject only to the assumed axioms and logic. It is completely unconstrained by the laws of the universe, though many interesting problems are suggested by physics. You continue to be wrong. It is unknown whether the volume of the universe is finite or infinite. In any case there are no boundaries. Read up on general relativity. Try Gravitation by Misner, Thorne and Wheeler gibberish. What is not just plain wrong (except for the speed of light being c) is nonsensical. Infinity is not unexplained. Neither is it unreachable, in situations where that makes sense, say on the Riemann sphere Try reading Naive Set Theory by Halmos and Lecture Notes on Elementary Topology and Geometry by Singer and Thorpe. Still more gibberish. Read a book on cosmology. Cosmology by Steven Weinberg would be a good start.

General relativity predicts that the interior of a black hole is singular. That is a bit different than "black holes have singularities". The difference is subtle and technical -- a singularity in GR is a failure of spacetime to be timelike geodesically complete. It is generally believed that the singularity indicates a breakdown of the general theory of relativity that may in the future be understood via a theory of quantum gravity, but no one knows for sure. This is consistent with the belief (also unproved) that the singularity is not physical.

Since no one has ever actually defined M-theory, this discussion is a bit pointless.

For in-line architectures, rarely are rocket structures buckling critical. More commonly the driver is stiffness, particularly the first axial bending mode and sometimes a longitudinal compressive mode -- controllability being the issue. In most cases adequate stiffness overcomes buckling concerns.

At the level that you describe there are no prerequisites and the subject (so-called naive set theory) is very simple. The first chapter of any book on abstract algebra or introductory real analysis should be more than enough. Even a chapter on set theory from a high school book should suffice. At the more advanced level of formal axiomatic set theory described by ajb you need a tremendous capacity for tedium. A masochistic streak would also be helpful. Alcohol might ease the pain.

Try using logarithms.

This flat wrong. You don't have a point.

Gravity is NOT based solely on distance and mass. That is true for the Newtonian model, and in a Newtonian model photons do not feel the gravitational force (though there are some rather ad hoc caalculations that pretend to the contrary). In general relativity spacetime curvature, which is the manifestation of gravity, is determined by the stress-energy tensor, which includes mass/energy, momentum and pressure (all forms of energy except gravitational energy). Electromagnetic energy,i.e. photons, are included. But photons have no rest mass and Newton's gravitational law does not apply. Light follows null geodfesics in spacetime, and the Earth has insuffficient mass to significantly affect light at all. Light does not just it the ground, as you can see since your flashlight works as designed. Bumblebees continue to fly. Photons do not accelerate. Their speed is always c, and their direction is always along a null geodesic.

What questions do we need to answer to terminate this ?

At normal speeds and temperatures all of the effects under discussion would be miniscule. Direct measurement would need to consider any number of subtle effects, many dependent on yhe precise nature of the hardware involved. Nevertheless, in principle, relativity shows that invariant mass increases with increasing temperature. To actually perform such an experiment would require a very ingeneous experimental physicist. But ingenuity is the stock in trade of experimentalists. Take a look at the thread on the reported superluminal neutrinos for an example of how subtle and ingeneous some experiments really are, and how difficult and sophisticated the resulting data analysis can become -- that experiment is still very much preliminary and under review.

Wrong. Science answers the question as to how nature works. Why is the province of philosophy and theology. Stephen Hawking lost touch with solid science when he co-authored The Grand Design. M-theory cannot even answer the basic question of M-theory itself, which is "What is M-theory ?"

yep

There is actually, due to relativity, a slight increase in invariant mass with an increase in temperature. At normal speeds and temperatures F=ma has a mountain of experimental support. Your "theory" is groundless.

It is just a matter of integrating the appropriate differential form around the perimeter. http://www.math.ntnu.no/~hanche/blog/planimeter.pdf

Neither one has been clearly, rigorously and umambiguously formulated. Neither has yet made a new verifiable prediction. Nobody knows what M theory really is -- that is the most important open problem in M-theory. Your question is very premature.

See "gravitational slingshot", and for overkill Gary Flandro's "grand tour of the planets".

The electric field is one component of the electromagnetic field. Energy flow is described by the Poynting vector which is the cross product of the electric and magnetic components of the electromagnetic field.

This is a potentially earth-shaking finding, or just a mistake. Before the work is published in a refereed journal it will be VERY thoroughly vetted by experts. That process started today with a presentation to experts in live web cast. The purpose of ArXiv is to put pre-prints of papers into circulation to the scientific community for review and comment on a timely basis, and this e-print has done exactly that. The researchers have acted extremely responsibly. They have established priority and have presented the data and methodology to experts for comment and possible rebuttal. The science community is quite vfamiliar with the archive, and the experiment and its results are now readily available. They have solicited critique, and they will receive it from experts. I also anticipate that the junk filter for their e-mail will be very busy.

What you are faced with is an application of (the general differential goemoetry version of) Stokes theorem. This is sraightforward, but you have missed the point that your problem statement is self-contradictory. It is also clear that you are in way over yoir head. You need to master a great deal of more basic mathematics and physics before you attempt advanced M theory.