DrRocket

Have another cup of coffee.

Spacetime is not a dimension. Spacetime is a 4-dimensional manifold, that is a topological structure in which every point has a neighborhood that "looks like" (i.e. is homeomorphic -- topologically equivalent -- to ) ordinary 4-space. In that local neighborhood one can identify 3 dimensions as spatial and one dimension as timelike. This is due to the nature of the metric imposed on spacetime -- its geometry which is more restrictive than its topology. But there are no global coordinates on spacetime. So there is no universal way to distinguish time from space. It is all just spacetime. This takes some getting used to. Now, as ajb said if you consider the world line of a 3- spatial-dimensional body, that is something that has 3 spatial dimensions in some local coordinate system, then that world lline will be 4-dimensional and will be a basically a tube swept out by a 3-dimensional body along a time-like curve. To make sense of all of this you probably need to study a bit more mathematics and become more familiar with and comfortable with the notion of "dimension". It is not mysterious, but it is a bit more abstract than simply thinking of time as the "fourth dimension". Mathematicians work with spaces of various dimensions, including infinite dimensions, all the time and think nothing of it. Laymen tend to make too much of the mystery of dimensions beyond 3 because they have trouble visualizing it. NOBODY can really visualize higher dimensions, but with some experience one can develop an intuition for higher dimensions based on what we know of dimensions 1-3, which we can visualize. There are some tricks for doing it, but they are not easy to explain until you have more background. Even 2-dimensional manifolds can be very difficult to visualize, because they may be impossible to realize in 3 dimensions (the Klein bottle is a simiple example). It may surprise you to learn that in terms of the topology of manifolds dimensions 3 and 4 are the most difficult. In dimensions 5 and above some things are much easier. http://en.wikipedia.org/wiki/Generalized_Poincar%C3%A9_conjecture http://en.wikipedia.org/wiki/Classification_of_manifolds http://en.wikipedia.org/wiki/4-manifold

Airbus is a French company, a competitor of Boeing. There is not much comparison between the handling qualities of a fighter aircraft and a commercial airliner, such as those produced by Boeing and Airbus. The F-14 is old technology. Google the F-22 and F-35 to see what a more modern fighter can do.

Not really though LaPlace did conceive of a black hole in very primitive way through just such an analysis, and formally that solution will give you the event horizon of a black hole. However, classical Newtonian gravity does not apply to light. That requires general relativity. Escape velocity is related to 1) a mass and 2) a distance from that mass. It is the velocity at which the kinetic energy is equal to the energy required to raise an object from the starting distance 2) to infinity against the Newtonian gravity of the mass.

[math]C(x-a)^2 = 0[/math]

What is a "chain of energy" ? What in the world does it have to do with a force ? http://en.wikipedia....rical_generator Generators are a pretty good idea.

In the opinion of Aristotle there were also 4 basic entities -- Earth, Air, Fire and Water. You are just as wrong as he was. But Aristotle had the excuse of the non-existence of modern science. What is your excuse ?

No. But Singer and Thorpe's book is excellent. However, if you have never taken any mathematics beyond, say, high school algebra, you may not find it readable. But then again, you might. While geometry and topology are usually taught to advanced undergraduates or beginniing graduate students (Singer and Thoroe is aimed at undergraduates) there is really no pre-requuisite beyond "mathematical maturity". Unfortunately there is not much that can be done if find the book too imposing at this stage except go back farther and start learning more mathematics. Differential geometry simply requires some background. There is all sorts of stuff on the internet. Some is OK and some is just trash. But you can't go wrong with a book by someone who actually knows what he is talking about. Mathematicians don't come much better than I.M. Singer.

Let [math]n[/math] be a positive integer. Suppose that [math] \sqrt n = \frac {p}{q}[/math] where [math]p[/math] and [math]q \ne 1[/math] are relatively prime positive integers. Then [math]n^2 = \frac {p}{q}[/math] and hence [math]p=n^2q[/math] contradicting the assumption that [math] p[/math] and [math]q [/math] are relatively prime. QED Note that this is really just a slight generalization, with reduced verbage, of the argument that I gave earlier for [math]\sqrt 2 [/math] being irrational. I did not agree on anything. The square root of two is considered irrational because it IS irrational.

The only latitude that is a geodesic is the equator. Wrong. All geodesics are curves (arcs). Very few arcs are geodesics. It is anything topologically equivalent to the set of all points that are some fixed distance from the origin in 4-space. A 2-sphere is anything that is topologically equivalent to the set of all points that are a fixed distance from the origin in 3-space -- like the surface of a globe.\ Dimension refers to the object itself, not the dimension of some space in which you might find it embedded. So a 2-sphere is two dimensional because in small local patches it "looks like" a plane. Apparently you don't understand it at all. This makes no sense. Go read a book on topology and geometry. The book by Singer and Thorpe would be a good place to start.

no no A geodesic is curve. The dimension of the manifold is irrelevant. A geodesic is a smooth curve with the additional costraint that the family of tangent vectors along the curve is parallel along the curve. There is no simple explanation of this. You need to read a book on differential geometry.

I am fond of some little old ladies and would prefer a more reliable source of aid.

vixra is a dead giveaway.

Try it out. Just take a front wheel drive car and drive in reverse.

Proof: Any finite decimal represents a rational number. [math]\sqrt 2 [/math] is not rational. QED Proof that [math]\sqrt 2 [/math] is not rational.: If it were then [math]\sqrt 2 = \frac {p}{q} [/math] where[math] p [/math] and [math] q [/math] are relatively prime. So. [math] 2 = \frac {p^2}{q^2}[/math] [math] 2q^2 = p^2[/math] Therefore [math'p[/math] is even and [math]2q^2 = 4s^s[/math] for some [math]s[/math]. But then [math]q[/math] is also even, contradicting the fact that [math]p[/math] and [math]q[/math] are relatively prime. QED

Like I said, it is precisely the same proof as in the scalar case. Try any book on functional analysis. I haven't specifically checked by you ought to be able to find it in the books by Rudin or Yosida. Really any treatment of Banach algebras. But note this is tantamount to killing a fly with a sledge hammer. You just write down the power series and apply the inequality that I gave your earlier.

A few points. 1. The Schrodinger equation really describes the evolution of the state function over time. It is not a wave equation in the strict sense, and it has nothing to do with standing waves. The Schrodinger equation is completely deterministic and the stochastic nature of QM is not reflected directly in it. However, in order to obtain a measurement of a physical quantity what one does is apply the Hermitian operator correcponding to the desired observable to the state function, which will produce the probability of the measurable being one of the eigenvalues of the operator. It is the interpretation of the Schrodinger equation that results in the stochastic nature of quantum mechanics. 2. Contrary to much that you read the Schrodiinger equation is not the entire story, not by a long shot. The Schrodinger applies only to elementary non-relativistic quantum mechanics. It does not apply to the more accurate and sophisticated quantum field theories, which are relativistic. 3. QM is inherently stochastic. See my earlier post. And this is not a result of the HUP. In fact the real effect of the Schrodinger equation, combined with the operators that represent observables, is simply to describe the time evolution of probability density functions. The HUP simple reflects the fact that complimentary operators do not commute (the order in which you apply them makes a difference). 4. Messiah is a good book. But you might find reading the third voluem of the Feynman Lectures on Physics enlightening. It is accessible and lets you see quantum mechanics through the eyes of a true master of the subject. 5. I tend to like Feynman's perspective: There is no such thing as wave particle duality. Elementary particles are particles. But they are not Newtonian marbles.

What you think or believe is irrelevant. It is what you can support with evidence or prove from established theory that counts. You might consider the fact that one of Einstein's preferred models for the universe modeled space as a 3-sphnere. Wiki strikes again. The second definition is the correct one. On a Riemannian manifold there is always an affine connection, the Levi-Civita connection that produces the metric. A geodesic is only length minimizing locally -- in a sufficiently neighborhood of a point. This is not a good definition, but rather is a consequence of the proper definition noted above. On manifolds that are not geodesically complete there are points that are not connected by geodesics. On other manifolds there may be points connected by more than one, and perhaps infinitely many geodesics. I would sugges that some people in this thread (not particularly you) might want to actually learn some differential geoometry prior to opening their mouths and making fools of themselves.

I have looked at it in some detail. Birkelands experimental work regarding the mechanism behind the aurora borealis was and remains seminal. It is erroneously cited by electric universe wackos as supporting their "theory". His reports from expeditions to measure electric fields associated with the aurora are availablehere. Hans Alfven's book Cosmical Electrodynamics was and is an excellent reference for many aspects of plasma physics. This should come as no surprise as it includes in part the work for which he was awarded the Nobel Prize. EU proponents tend not to be familiar with this book, as it contains actual physics with the associated equations. Hans Alfven's subsequent books Worlds-Antiworlds and Cosmic Plasma, set forth some of Alfven's later notions regarding cosmology. They are basically absurd and fly in the face of physics and observation. One wonders if in later life, Alfven, like Birkeland, was insane. While the early scientific work of both Alfven and Birkeland is indeed of value, it is not germane to the case for the "electric universe" which is just plain trash. Anthony Perat, and his opinions, are not worth spit in the ocean. The entire EU proposition is of similar value.

And that is nearly slanderous towards nonsense. We should all be so cracked.

It is not at all clear that you have any intellectual property. For instance, you cannot patent a fundamental scientific principle or a mathematical formula. That said, I suggest the you first conduct a literature search to determine what is known in whatever field is your specialty, and what relevant research is being conducted and reported. Once you have a reasonable understanding for the current state of the art you might contact the scientist in question and determine if you have a common interest. Theft of ideas is rare among academics, but it does happen. You ought to be able to make an assessment of the scientist in question after speaking with him for some period of time. Then you make a decision and take the consequences just like everyone else. Note even from your brother ?

Proof: 10=1 (mod 9)

Take a look here http://en.wikipedia.org/wiki/Fatigue_(material) Read down far enough to see that applying the ideal gas law and some thermodynamics that the speed of sound in a given gas depends on the temperature and ratio of specific heats (they call it the adiabatic index in the Wiki article, but it is still Cp/Cv). When you change gases the molecular weight also enters the equation.

"If you really catch on to it" then nothing is confusing.

You fail to see a lot of things. That is certainly among them.