MetaFrizzics

There is a philisophical trap here, involving sloppy semantics. Quantum measurements measure 'states', but only at individual points in space-time. That is, 'events' according to GRT or even local SRT. But what people usually mean by 'alive' is an ongoing 'state' that is more like a whole (possibly continuous and infinite) series of 'events' or space-time locations, like a worm-line or time-line tunnel. The quantum measurement can only determine the cat was 'alive' or 'dead' at some specified instant or space-time coordinate set.

Is that a serious offense? or just a misdimeanor? I am not trying to be funny, (at the moment anyway). I just thought a bit of spice could be fun.

Same way the pink panther does: He pulls a cord in his chest to inflate his torso. (I'm leaving the 'pun' response alone). After watching Alien the second time (I forgot how slow and boring most of the plot-dragging was) I was stunned at the use of a camera aperature (about 50 mm in size) from the 50's as a worthless airlock throughout the Larger spaceship that could not close or make a seal by design. Oh come on, what about her shower scene at the end? Am I the only one who stood at attention for that?

What is it that we want from a gravity wave? A detectable effect. A transfer of energy (through field and/or particle exchange). And that's just what Newton gives us, if we'd only listen. Balanced forces do no work. But unbalanced forces cause energy exchange and motion. Oscillating forces cannot be balanced, except by precise counter-forces or by drowning in a sea of random counter-force. For instance, for a diatomic gas, Newton gives us the effect of a 'virtual particle with 720 degree spin without all the effort of Pauli spin matices etc. If only those German physics students like Heisenberg hadn't been 'Ocktoberfesting' so much, we might have been spared the grief of Quantum Mechanics. What!?! Quit drinking? Drown this traitor!

Its not the velocity of the particle, but the angular velocity of a rigid system of particles that generates the radiation. What kind of spin is he trying to put on this now?

For instance, (1) the Centre of Mass 'method'/approximation says that a spinning, free-falling non-spherical body acts as though its mass were concentrated at its centre. (2) However, the error in the approximation means that a rotating body presents a fluctuating gravitational force upon all nearby objects, oscillating at the frequency of relative rotation to the nearby object. (3) The fluctuating force exerts a stress and does work on the surrounding objects. This causes micro-variations in the location of mass nearby when the field strength of the nearby object is large in comparison to neutralizing or averaging counter-forces. So what this guy is saying is that nearby spinning objects act as inexpensive vibrators!

The perfect book for someone with a high-school education is About Vectors by Hoffmann (Dover reprint <$10) This little gem takes a reader with no real grasp of vectors at all, right to tensors (last chapter). The book is in a class by itself, superior to Div, Grad, Curl, and All That by Schey. Either of these books is almost a prerequisite to squeaking through 1st or 2nd year Engineering, but About Vectors really lays all the key (and controversial) topics before the student in a lively and friendly way with thorough but not too wordy discussions that are easy to understand. pm me if you want help with getting up to speed. Vectors are critically important for virtually all of Mechanics and Electrical Engineering (Electronics). By the way, Vectors were almost singlehandedly invented by Heaviside, who took Maxwell's messy and impenetrable Electromagnetic Theory based upon quaternions, and reduced Maxwell's original 12 - 20 equations to an efficient four! (The ones everyone thinks are Maxwell's!) In the process, Heaviside virtually invented the whole field of Electrical Engineering, as well as Vectors, by deconstructing quaternions into bite-size and practical pieces, and inventing nine out of ten electrical terms, like resistivity, permeability etc. If you want to understand things, ignore Maxwell and grab Heaviside.

Yes. Since the Centre of Mass 'method' and Sphere Theorem are only approximations, they also implicitly predict gravitational waves. Therefore the existance of GW is not a strong proof for General Relativity. Comments? Next he'll say Newtonian gravity bends light too!

forensic scientist: "for-en-sick' - a scientist willing to accept money from a lawyer.

Actually, Hawking's idea is complex and confusing: He began searching for a Quantum Gravity theory:

I'm probably a bit slow this morning, but I fail to see the significant difference between the two models. It seems you are saying that the field acts as a 'conveyer belt' rather than a 'pressure' difference applied to the ends of the wire. That is, the field I suppose penetrates everything instantaneously, and hooks directly into every electron, transmitting energy directly, not through 'collision'. But it seems hard to deny that from this perspective the voltage difference is essentially a uniform field, and the 'motion' of the energy at C is simply a different inertial frame, measuring the transport of a different 'substance'. The electrons still maintain an equilibrium of 'equal spacing' via collision or rather repulsion of their own electrostatic fields. There is some 'gas-like' compressibility which we observe, in the bunching of charges in a capacitor for instance, and of course impurities causing non-uniform motion (friction) for the electrons, which is countered by 'collision-like' bumping that keeps things moving. I have noticed others complaining about both the 'water' analogy and the 'pressure' analogy. But they seem extremely useful for people learning the basics of electricity and electronics, and cause no serious perceptual crippling. After all, new concepts can be (and can only be) introduced when students are ready, having mastered simpler ones. psst!...Metaphrizzie = outpatient... apply meds.

Yeah, and he enjoys the wrestle as well! I'll never forget the funniest joke I ever saw above the urinal:"Why are you looking here? The joke's in your hand."

Hmm. Nobody calls me bitch. No really: I have to pay someone $20 for that.

First they cancel my show, and now any clown can talk out of my butt with a remote control radio transmitter! Cripes!

Recommended Books: Fourier Series Georgi Tolstov 1962 - Dover reprint $10 (thorough account with proofs and applications: older text) 1 Trig Fourier series 2 Orthogonal systems 3 Convergence 4 Trig series with Decreasing Coefficients 5 Operators on Fourier Series 6 Summation of Trig Fourier 7 Double Fourier Series / Integrals 8 Bessel Functions & Fourier-Bessel series 9 Eigenfunction Method & Physics Intro to Theory of Fourier's Series & Integrals -Carslaw 1950 -Dover $10 1 Rational / Irrational Numbers 2 Infinite Sequences & Series 3 Functions of Single Variable Limits Continuity 4 The Definite Integral 5 Infinite Series (single variable) 6 Arbitrary parameters 7 Fourier's Series (with Deirichlets Cond.& Poisson) 8 Nature of Convergence & Fourier Constants 9 Approximations Gibb Phenomenon 10 Fourier's Integrals (w Sommerfeld's discussion) Appendices Harmonic Analysis & Lesbesque's Theory of Definite Integral Fourier Integral & Certain Applications - Norbert Wiener 1958 Dover $10 1 Plancherels Theorem (Hermite Functions) 2 Tauberian Theorem 3 Special Tauberian Theorems 4 Generalized Harmonic Analysis P.S., let me know if all this effort was worth it for anyone....thanks!

This is partly a semantics issue. Objects get renamed when we want to distinguish sub-categories of an object based upon differences in origin or history, as well as other factors. This is a legitimate way of making the amount of precision necessary to limit the scope of scientific statements. If we can distinguish one electron from another via energy levels and certain conclusions about their origin based upon trusted theoretical constraints, then we can give it a special name for convenience. Flexibility is key.

Here's a link to a handy intro to the nuts and bolts of Fourier for signal processing: Fourier Notes Six nice pages on technique with C+ code Fourier Theorem Handout Java Applet that lets you see and hear Fourier Analysis in Action! YOU set harmonics, see the resultant wave! (Caution: if your soundcard gets stuck on, you may have to reboot or turn off speaker temporarily.) Nice intro to Fourier Square Wave & pics Hardcore Fourier Analysis Website **** University Level Lecture Fourier & ADD EEGs (yikes!) How to use an FFT Spectrum Analyser Nice Lecture introducing the Delta Function 34 page PDF file on Fourier Analysis - nice and meaty! ****

Sure I'll help you. The Fourier Transforms and integrals are actually really easy. Start with the Fourier Theorem: (It's brilliant, and really useful in electronics, especially audio etc.) Simple version: Any repeating waveform (of any shape) can be broken down into sine waves, which when added back up result in the original funky waveform again. What is so awesome and elegant is that the frequencies of all the (smaller) sinewave components are all multiples of the original frequency of the funky wave. So, a sawtooth wave from an electric organ is made up of the original note, plus a note an octave higher (2xf) and a bit of the note an octave + musical 5th higher (3xf) and some amount of the note 2 octaves higher (4xf = 2x2xf) etc. All of these little sounds added to the original note create the complex wave shape you hear (and the speaker gets electronically as a voltage). This means the lowest 'harmonic' in a fancy shaped wave is just the sinewave of that same frequency as the fancy wave. To get all the possible shapes (these have to be actual sensible functions) of wave, you simply adjust the phase and amplitude (volume) of each harmonic to create the shape (and the distinct tone or timbre of an instrument). Thus a flute might be an almost pure sinewave, while an oboe could be a sawtooth. The difference is in the loudness and relative phase (synchronization) of the harmonics (sinewaves at various multiples of the frequency.) What use is this knowledge, or ability to convert a complex wave back and forth between two or three ways of viewing it, writing it down etc? Let's see: If we make an 'additive' synthesizer, we have sinewave oscillators controlled by a keyboard (and ganged to each other to act as harmonics). This is literally a 'Fourier Analysis' synthesizer!. Similarly, An AM radio signal can also be broken down into or viewed as a carrier plus side-bands of sub/super-harmonics. The audio is encoded in the overall amplitude envelope, but it is also contained in the sidebands. Its another way of looking at the same thing: Radio >> Fourier The varying radio carrier can be viewed as a set of sinewaves of various frequencies and amplitudes. In this case the Fourier Analysis method would view the 'period' of this wave *not* as the radio frequency, but as the lowest component of the audio signal!

This is what is known as a 'black bicycle rim'. The rim collapses, swallowing the spokes, which stretch toward the threshold of the outer rim. Then suddenly, time stops, as the air leaks out of the tire. Hawking showed that such objects are really 'gray rims', since they leak air molecules via 'broken-glass tunnelling'. Incredibly, the probability that there will be dogdoo on the outer surface approachs 1 as the cyclist approaches C.

Whatever effects you are seeing might have to do with an artificial light source like a Sodium street-lamp flickering at 60 cps. What were the conditions of your observation? Have you ever tried shaking your hand in front of a TV set with other lights off? Or watched a car-wheel go backwards on film or Television? this has to do with frame-effects, not light speeds.

Okay, I looked at your picture, but now what? What exactly is the claim here? Usually one has to do a model of the earth moving around the sun and mark some angles showing predicted bending of light rays through the aether from some North-Pole star. Or do you have some other light source in mind for the experiment?

Actually the answer here is simpler than it appears: First let's talk about 'normalization', a habit that physicists do without thinking that confuses almost everyone. Here's an example. Newton's gravity Force = Gm1m2/d^2 One way I might simplify this is to just leave out m2, and call it potential energy or something instead of force, because I want to generalize or talk about the contributions from everything else except the 'testmass', isolating those components. For a series of experiments or discussions, I might also completely simplify the equation, by just setting both masses at '1' (one unit of mass in some choice of sizes). Now I can also set G (the Gravitational constant) to '1' also, by choosing the right unit of distance to work with. After all this clowning, I have now 'normalized' the equation for the task at hand, and gotten to the essential (simplified) law of gravity: F = 1/d^2 ........( G x m1 x m2 = 1 x 1 x 1 = ...1 ! ) viola! It is now clearly the simple Inverse Square law. (Notice that masses don't usually change, nor do the units we have chosen, so the only variable is distance, in an appropriate choice of units.) Now I can talk about a series of experiments, as long as everyone has figured out from the simple form I am using that I have automatically assumed the masses are all '1', and the units appropriately match. Feynman has done something quite similar in your example. He has noticed that the mass is proportional to the density, and that it is constant, and he has assumed that the actual 'mass' for the discussion is just '1' unit in some appropriate scale, and now he can just directly substitute in 'rho', the density. This is possible, because normally (with the full blown version) he would have had to multiply the number of units X the density to get the real mass in an arbitrary object. With the mass = 1, there is no calculation required. Its just now 'rho', or whatever the variable is called that is holding the density value (in the proper units). Feynman just skipped a step without thinking out loud and left thousands of beginners frustrated for the next 20 years.

I read recently of a test where 90% of electrical engineering grads couldn't calculate the speed of electrons in a wire, and had hopelessly inaccurate ideas about it. An important point to note is the idea of 'drift'. Since all electrons (and holes) are identical, how do we tell what has actually moved? Another important idea is the idea of 'compression' or build-up. In some sense electrons are 'incompressible', and can be imagined to act like mutually repulsing 'magnets' that keep a certain distance apart from each other. This image comes from classical electrostatics. The 'billiard ball' model can be helpful to explain the motion: Imagine a wire is a long 'tube' full of billiard balls. If you push a billiard-ball in one end, then one pops out the other end, pretty much instantaneously (if there is no spaces). So this can explain why the transmission of electrical effects seems instantaneous, while the actual electrons are not believed to move very far or very fast at all along the wire. Especially with A.C. it is unlikely that a specific electron moves very far if at all for many cycles. On the other hand, static electricity experiments and capacitors show that electric charges *do* act like a 'compressible' gas in many circumstances, crowding at one end or another in a wire or plate, and having varying densities. Superimposed upon these ideas is the idea of 'free electrons' or holes that can 'wander' in a kind of random 'Brownian' motion through the substance, like gas particles in space. But a key idea to come away with is that actual individual electrons (if they really exist) probably don't travel very far or fast relatively speaking, compared to the 'voltages' (i.e., pressure changes) which are transmitted great distances and very rapidly (approaching the speed of light).