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.

bubbles are only for use in GD.

... Only statement I understand the first paragraph. And considering that one' date=' banging my head against a wall would classify as a gravitational wave because it has a detectable effect and transfers energy (even through a particle exchange if one really wants to treat it with QED).

I mean: You want comments on your statement that Newtonian Gravity predicts gravitational waves but you do not say what a gravitational wave is supposed to be - at least not in a way I´d understand.[/quote']

Well, suppose we glue a magnet on a rotating wheel. Most would sense that this is now a dipole antenna generating electromagnetic waves.

 

Similarly, a binary star cluster (two stars rotating) is supposed to generate gravitational waves. Now suppose the binary star pair are for all intents and purposes identical. We have no way of telling one star from the other. Although the pair rotates at one velocity (cycle), the gravity wave generated is actually twice the frequency, since half-orbits are identical states.

 

If such a mass system generates gravity waves, then obviously on a smaller scale so does a diatomic gas molecule.

where does the Incredible Hulk get his extra Mass from?

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?

Perhaps I could understand your statement better if I knew what a gravitational wave is supposed to be...

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!

The Newtonian gravitational potential of a particle at position p is something like V(x)=Gm/|x-p|. I can´t see where the velocity of a particle should play a role in there.

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!

Now go into a room filled with forensic scientists and say that.

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:

In quantum gravity' date=' there is also a certain uncertainty in the geometry of spacetime. ...it becomes important at very small distance and time scales...Hawking suggested progress might be made using Imaginary Time (IT). Imaginary time is related to real time the same way imaginary numbers are related to real numbers.

IT physics is an Alice-in-wonderland version...with particles faster than light and backward in time...Of course when turned into an approximation of QM everything works out....

Hartle & Hawking (H-H) applied the imaginary-time trick to cosmology on a simplified model of the universe...it did possess a singularity under classical GTR. But the QM version had no singularity. Its still open whether the H-H idea can be applied to the real universe.[/quote'] ...just a sample from Readers Companion to A Brief History of Time

A better model is to describe a current using a vertical pipe filled with billiard balls (or a liquid). The billiard balls fall through the pipe because they are responding to the gravitational field.

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.

Never wrestle with a pig. You just get all dirty, and the pig enjoys it!

I'll never forget the funniest joke I ever saw above the urinal: "Why are you looking here? The joke's in your hand."

Recommended Books:

Fourier Series Georgi Tolstov 1962 - Dover reprint $10

(thorough account with proofs and applications: older text)

...readily accessible to students in fields of physics and engineering...(back cover)

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

No one can properly understand FS and Integrals without a knowledge of what is involved in the convergence of infinite series and integrals...

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

There are 3 more or less separate groups of ideas..pertaining to Fourier and Plancherel theorem: the notions of an absolutely convergent Fourier Series and of a Tauberian Theorem; and the concept of the spectrum. ...

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?

I don't understand why Feynman has used p (roe, density) for the length if the mass per unit area is constant. I can see how length wise r^2=p^2+a^2, it's just pythagerous, but how can a length unit be equivalent to p, density?

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'm going to get a scanner' date=' I think I have pretty much considered all the possibilities, so you need to see it.

I do have an additional problem. As I mentioned before I'm reading the Feynman lectures to expand my own knowledge and I've just foudn something that doesn't make so much sense again.

Chapter 15 part 1, Feynman is talking about relativity, and he says that the speed of light waves is unaffected by the velocity of the emitter, which I'm totally cool with, then he says "This is analogous to the case of sound,. the speed of sound waves being likewise independant of the speed of the source".

Erm, that doesn't make sense to me, I thought the Doopler shift was the key thing there to do with sound waves being emitted from a moving source, where it's wavelength and frequency change according to the speed of the source, and therefore the speed of the emitted waves is changed....?[/quote']

 

The simple answer here is that once the 'sound' (impact) is released upon the air molecules (say by a speaker cone striking the air), the speed of the propagation of the motion (think of a bucket-brigade) goes on independantly. The speaker and its velocity are not relevant to how fast the sound actually travels to someplace where it did not exist before.

 

The Doppler Effect in the case of Sound is something totally different: In this case you can think of a long series of repeating strikes. But if the speaker cabinet is moving (say mounted on an ambulance), each time the speaker strikes, it is hitting the air from a new location! So if approaching, the beating of the air arrives sooner and sooner for each 'pop'.

 

If you have a repeating beat that is fast enough, it is no longer percieved as separate beats, but as a musical note (say faster than 20 cycles/beats per second). The musical note from the approaching ambulance sounds like a higher pitched note, since it is getting compressed like groceries bunching up at the end of the conveyer-belt.

 

If the approaching ambulance speed is constant, the note goes up a specific and fixed amount in pitch. It is perceived as a higher frequency sound than the one actually being generated in the frame of reference of the moving ambulance. The sound doesn't actually travel through the air faster than before. The beginning and end of the note travel at a fixed speed through the air.

 

You might think from this that the speed of sound is constant for everyone and that only the pitch or frequency is relative. This is only partly true. The speed of the sound is fixed relative to the air it is travelling through (that is the medium at rest). But the ambulance/speaker is moving through the air.

 

This means that from the speaker's rest-frame (lets say a long train, with microphones at each end and the speaker in the middle) the sound takes longer to go forward than backward, because the air is moving backward. In this case, the beginning and ending of the sound arrive at a different time, depending upon which way the air moves. The pitch is again affected, but for a different reason now. The pitch at the front of the train seems lower because the microphone is receding from the air (and getting the pops at a slower rate).

 

The speed of the sound is affected by the relative movement of the air to the microphone/ear. The pitch is affected by the relative motion of the source regardless of the air motion.

 

If the microphone is on the ground (with air stationary) sound speed is constant, but pitch changes. The approaching sound is higher in pitch, and after the vehicle passes, it lowers in pitch. (pure Doppler effect).

 

mic on ground ------ pitch higher, then lower when passed, speed constant

mic on trainfront --- pitch lower, start and stop delayed. (speed lower)

mic on trainback --- pitch higher, start and stop arrive early. (speed up )

 

I hope this helps. Doppler effects strictly affect frequency (pitch), while

motion of the medium affects the speed of propagation (and pitch too).

 

This is why the Michelson-Morley experiment is important: They were hoping to measure the speed of the aether by finding both frequency AND speed effects for light, but they only found frequency effects! No motion, and no medium!

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).