DrRocket

I have not accomplished this seemingly impossible feat. It has been explained to you several times, by several people, precisely why you are wrong. I have no intention to continue to attempt to explain physics to someone who is so blatantly proud of his state of ignorance and who refuses to learn either the subject itself or the language (mathematics) in which it is spoken. Either acquire a physics book and learn something about the subject, or remain in your present state. It is your decision.

Turn the question around, and ask what a center would mean ?

Angry ? Nobody is angry. You have the right to be as silly and obtuse and you please. It certainly is no skin off my nose. While most engineers read "FFT" as the "Fast Fourier Transform" mathematicians also know it as the "Finite Fourier Transform" because that is what it really is -- the Fourier transform on a finite abelian group. The exact nature depends on the arbitrary choice of the number of points involved, the order of the cyclic abelian group. Now why would you expect the Fourier transform of some sampled data on [math] \mathbb Z/ n \mathbb Z [/math] to tell you anyrhing at all about the distribution of prime numbers in [math]\mathbb R [/math]?

Unless you can determine WHY LTI places the noted limits on the angle of incidence of the radar beam, you are in danger of finding yourself actually arguing that you were traveling faster tnan the alleged 84 MPH. That does not strike me as a winning strategy. One possible reason might be the potential to pick up reflections from the wheels, portions of which woul be moving much faster than the body of the car. A lot would depend on the geometry of the wheels and the details of the laser beam. If the officer testifies and is believed that he aimed for a flat spot, like the front license mounting surface, that nullify this approach. The real reason would have to come from LTI. I would not pin my hopes on that. Failure to recalibrate and certify the device after repairs strikes me as your best argument. If the gun has been checked in the interim your goose is cooked. You said you were accused of traveling at 84 MPH . The ticket is usually written for something less than the recorded speed (this looks suspiciously like the cop wanted to keep the excess below 20 MPH). Any experienced cop can tell the difference between 65 MPH and 84+ MPH by eyeball. How fast were you really going ?

Classically one can determine the position and velocity of every particle in a closed system at some point in time and predict the behavior of the system at all subsequent times, although the equations are difficult for more than two bodies and must be solved numerically. . This is a reasonably accurate model for macroscopic bodies. It is how the positons of the planets are calculated. However, this model is not completely accurate and fails badly at the atomic level. Quantum mechanics tells us that exact determination of the simultaneous position and velocity of a particle is not possible. This is known as the Heisenberg uncertainty principle. At the atomic and sub-atomic level this effects is very important. It applies to macroscopic bodies, but in that case the uncertainty is very swmall and the classical model is a good approximation.

Fourier analysis is a huge area. Unfortunately a lot of what is written on the subject in physics and engineering books is just wrong. The better books on the subject require a strong background in real and complex analysis and quite a bit of functional analysis.. Rudin's book on Real and Complex analysis has a lot of good information. That is not surprising since he also wrote the classic Fourier Analysis on Groups, which is required reading for every specialist in harmonic analysis. Another excellent book is An Introduction to Harmonic Analysis by Yitzhak Katznelson (a PDF copy was once avvailable at Katznelson's web site). I was also once available as an inexpensive Dover book -- you might find one on the used book market.

Fourier analysis is a huge area. Unfortunately a lot of what is written on the subject in physics and engineering books is just wrong. The better books on the subject require a strong background in real and complex analysis and quite a bit of functional analysis.. Rudin's book on Real and Complex analysis has a lot of good information. That is not surprising since he also wrote the classic Fourier Analysis on Groups, which is required reading for every specialist in harmonic analysis. Another excellent book is An Introduction to Harmonic Analysis by Yitzhak Katznelson (a PDF copy was once avvailable at Katznelson's web site). I was also once available as an inexpensive Dover book -- you might find one on the used book market.

I have had a few decades of experience with both mathematics and real applications, including fluid dynamics. I stand by my statement. The good applied mathematicians that I knew left and went into the actual areas in which the applications themselves were found. The remainder, in their own words, neither prove theorems nor solve problems that anyone cares about. I am sure that there exceptions, and exceptional schools. Courant and Friedrichs did good work on gas dynamics for instance. But in general the best applications of mathematics come from the physicists and engineers who work in the applied areas, and mathematics comes from mathematicians. This in no way contradicts your statement that collaboration is beneficial. I have seen productive collaborations between real mathematicians and physicists, chemists and engineers. I even know of pure mathematicians with substantial education in engineering.

wrong Now go read a physics book.

All the preceeding replies notwithstanding, decay doesn't do much for the picture. Assuming that you have not tossed general relativity out the door, energy as well as matter, is included in the stress-energy tensor that determines gravitation. So unless not only the matter, but also the energy that is associated with decay "disappears", gravity marches on. If both the matter and energy disappear, you have a local violation of general relativity. That would be a big deal indeede. If general relativity is off the table, then we are back to ajb's question, "What replaces GR ?"

" That's not right - that's not even wrong” – Wolfgang Pauli Where in the world are you getting such ideas ? You desperately need to read a physics book. Try The Feynman Lectures on Physics.

Most calculus texts are awful. One exception is Michael Spivak's book. Believe it or not, you will have an advantage later on by learning your calculus at a university rather than in high school. I had a conversation on this very subject with a very senior engineering professor at MIT, and he was of the same opinion. Teaching yourself calculus and learning it in high school exposes you to the risk of learning to bevfacile in manipulating symbols, but not understanding what they really mean. That is because they don't really tell you why calculus works in a calculus class. That comes in a class on real analysis. Your university instructor will understand real analysis. It is important that the instructor understands why calculus works even though you may not be exposed to proofs in the introductory classes. Any decent university mathematician can prove all of the basic theorems of calculus off the top of his head. Despite recommendations for books like "Advanced Engineering Mathematics" or "Mathematical Methods for Physicists", I would avoid them until you have a solid understanding of calculus. Arfken's book is as good as any when you reach that stage, but you will likely use whatever text is required by your instructor at that time. Kreyzig's "Advanced Engineering Mathematics" IMO is bloody awful -- and I taught from it. I also know one of the guys acknowledged in the autrhor's introduction -- he reviewed the draft for the publisher and recommended that the book not be published. Once you get past calculus, find a copy of Spivak's Calculus on Manifolds. It is the best and most readable introduction to calculus of several variables available. It is quite thin as well, an altogether wonderful little book. As far as trigonometry goes, any college algebra and trigonometry test should be fine. Do a search at Amazon or Alibris and find a good buy. They are pretty much interchangeable. If you have been exposed to the basic trigonometry functions and identities you will do fine. You may find that you understand trig better after having taken calculus.

I also own that book. There are better books. Zee's Quantum Field Theory in a Nutshell, and the books of Ryder, Zeidler, Peskin & Schroeder, Weinberg, and Glimm & Jaffe leap to mind. It is the only Kaku book that I own. I will never own two.

An excellent and classic treatise, now in the sixth edition. It is serious mathematics, so if you are looking for something light, look elsewhere. If you are serious it is very good. There are no exercises, so don't expect any. The sixth edition has an introduction by Andrew Wiles who was inspired in his younger days by the fourth edition. If it is good enough for Wiles, it should be good enough for anyone. Beware of the sixth edition papeerback binding. I recently bought this updated edition, and the cover fell off on first opening (it was a new book). It cost me another $38 to have it rebound in hardback by a local bindery.

Wrong. It is not even just frame relative. It is relative to a choice of ground point within a frame. Why ? If one of them is moving fast enough, relative to the star, the energy in any single photon can be made arbitrarily large (blue shifted) by making that speed sufficiently close to c. no Where are you getting this stuff ? Just making it up as you go along ? I give up.

Yes, but so what ? ?????????? no Don't thoink about the complex processes involved in nuclear reactions and radiation. Just note that the total energy (aka relativistic mass times c^2) of the star is dependent on the reference frame.

Right here: You are making nonsense sentences. Until you take the time to learn the requisite mathematics communication is impossible. Mathematics makes very precise use of terms, and the terminology in probability is just as precise as that in other branches. Unfortunately many terms have everyday meanings that are suggestive of the technical meaning, but still they don't mean what you think. For instance "probability 1" does not mean that the event must occur, only that it occurs "almost surely" and "almost surely" means except on a set of measure 0. "Measure 0" has a precise meaning as well, but you will need to learn some more mathematics to understand it. The biggest problem is using probability theory in the complete absence of a probability space. There is no meaning in that situation.

You need to learn some mathematics.

It is only evidence of kinetic energy of the football relative to the thrower or of the thrower relative to the football. There is no such thing as absolute kinetic energy. Potential energy is only meaningful relative to some reference. That is the point. Gravitational potential energy relative to the round is one natural choice, but not the only choice. To make sense of potential energy a choice of "ground state" is needed, and that can be arbitrary. Potential energy and kinetic energy are not absolute. Energy is relative. Even in relativity, while speed of a photon is the same in all reference frames, the frequency depends on the frame, and energy is proportional to frequency.

But you have no a priori idea what that finite number will be. Even a probability zero event can occur a finite (or actually infinite) number of times in infinitely many trials. So, your logic doesn't help.

From the Wiki link to the Drake equation: " As T.J. Nelson states:[24] The Drake equation consists of a large number of probabilities multiplied together. Since each factor is guaranteed to be somewhere between 0 and 1, the result is also guaranteed to be a reasonable-looking number between 0 and 1. Unfortunately, all the probabilities are completely unknown, making the result worse than useless. Likewise, in a 2003 lecture at Caltech, Michael Crichton, a science fiction author, stated:[25] The problem, of course, is that none of the terms can be known, and most cannot even be estimated. The only way to work the equation is to fill in with guesses. [...] As a result, the Drake equation can have any value from "billions and billions" to zero. An expression that can mean anything means nothing. Speaking precisely, the Drake equation is literally meaningless..." From Feynmam: "The first principle is that you must not fool yourself and you are the easiest person to fool." -- Richard P. Feynman You are fooling yourself. Your approach is going nowhere. Fast.

There is no such thing as "speed of time". "Speed of something" is "change in something"'/"change in time". "change in time"/"change in time" = 1, always. What relativity tells us is that observers in relative motion to one another have different notions of both time and space -- time and space are not the absolute notions of everyday experience, but are dependent on the observer. What is invariant is a more abstract notion -- spacetime and the "spacetime interval" ([math](spacetime \ interval)^2 = ( \Delta t )^2 - (\Delta x)^2 - (\Delta y)^2 - (\Delta z)^2[/math]). The spacetime interval is neither time nor space, but a combination of both and it is differences in how that interval is partitioned into time and space separately that result in the "time dilation" and "length contraction" of elementary special relativity. Lorentz transformations preserve the spacetime interval, but change the partition. Speed is relative between the reference frames of two observers. Observers will agree on the speed of light. There is nothing magic about it being light. If you look carefully at the physical derivation of the Lorentz transformations, you will find that if you postulate that some phenomenon, any phenomenon, propagates at some speed "x" in all inertial reference frames, the you get the Lorentz transformations with "x" in place of the usual "c". There can be only one such speed "x". One the notes the experimental fact that light propagates at "c" in all inertial frames, and, voilà, you have special relativity in the usual form. "Mass", in the form of "relativistic mass depends on the observer. You cannot determine the speed of an object relative to you by measuring the mass, but you can if you know the ratio of the relativistic mass to the rest mass. For macroscopic objects you can do this if you replace "rest mass" with "invariant mass", which is relativistic mass in center-of-momentum coordinates. "Mass" is not the well-defined concept that you might think. There are several notions of mass, all valid and all different. There was a thread on this topic recently. As a result I had a conversation on the subject with a local prize-winning (not the Nobel prize, but a nice one anyway) high-energy physicist friend. He went so far as to point out that not only are rest mass, invariant mass and relativistic mass all valid and useful in their place, but also even in Newtonian mechanics it is a happy, but not logically required, coincidence that inertial mass and gravitational mass are equal. There is no such thing as "absolute rest". That is fundamental to special relativity.

I am more than a little bit familiar with the theory of probability. Probability theory is the most misapplied discipline in mathematics. You are attempting to misapply it. You do not have a mathematical problem. Your idea is going nowhere.

Then some revision of the Standard Model will be required and "Gravimotion" will still be rubbish.

Texas is a neat place. The University of Texas has a first-rate physics department (Weinberg is there). Norris is also impressive -- my brother studied at his dojo in California years ago. But one reason that Chuck Norris retired from karate competition was that he did not think he could match the ability of Bruce Lee. Bruce Lee was extraordinary in terms of both speed and power. Top, really top, karate masters are phenomenal. I have seen this guy up close and personal. You can't even see him move when he is in high gear. And while he is fast, you should see Nakayama.