1997 William J. Beaty        
Here's the result of an epiphany I suffered regarding the nature of energy. I don't know if others use these concepts regularly, but I've never see them in the books I've encountered. I found them to be devestatingly enlightening, almost as much fun as discovering philosophy in college. (I don't know if this is just an ego effect because *I* thought of them myself, or because they inherently have that much merit.)


When I turn a crank that winds a spring, I do some work.

When I turn a crank that's connected to a long shaft that winds a spring, the "work" I've done is somehow instantly conducted along the shaft from the crank to the distant spring. Yet the shaft just turns. Is there a way to reveal the "work" that flows along the shaft from my fingers to the spring?

When an auto engine drives the tires, all the work that is done by the engine is somehow instantly conducted along the drive shaft. Yet all I see is a shaft which turns. By looking only at the spinning shaft, I cannot tell if the engine is sending "work" to the tires, or if the engine is turned off, and therefor the car is coasting and sending "work" from the tires to the engine, and therefor pumping the cylinders. In both cases the shaft just spins.

Ah, but what if I SUDDENLY turn the crank? Or what if the engine SUDDENLY starts up with a jerk? Then, if I have fast eyes, I will see one end of the shaft twist a bit while the rest stays still. A wave of "twisting" will race down the shaft. Finally the far end will begin turning. So, the shaft doesn't simply turn, also there is a wave of "something" that moves from one end of the shaft to the other. The stuff that moves is wavelike, so I can only see it when the speed of the engine suddenly changes.

OK, another situation now. If I scrub a brush upon the floor, I perform work. The floor gets hot. If I lay a very long pole upon the floor, attach the brush to the far end, then grab the other end of the pole and push it back and forth, I do work upon the brush and the brush heats up. Ah, but what if the pole is 100km long? Then whenever I push it forward, the distant brush doesn't instantly move. Instead, at my end, the pole's substance compresses and also moves forward, which compresses the next part which also moves forward, and after a long time this wave of "work" finally reaches the brush. The brush moves against the floor and work is done (the floor and the brush get hot.) But that moving wave of motion/ compression within the pole... is sound! It's sound of very low frequency. For example, if I push the pole back and forth a few times per second, then I essentially am transmitting very LOUD sound along the pole, where this sound has a pitch of several cycles per second. And if my 100km pole is wood (carved from a very tall tree!), then as that wave of "work" moves from my hand to the distant scrub-brush, it flows at the speed of sound in wood.

But... this means that mechanical energy.... is the same as SOUND! I can't hear it because the frequency at which I'm pushing the brush is deeply subsonic. (If I pushed it back and forth 100 times a second, I might hear my "work" as a humming sound that escapes from the pole.) Or, if I should push the pole constantly ahead instead of back and forth, then it's even harder to think about: it has become "DC sound" instead of "AC sound." But even if I pull the brush backwards at a constant rate, there's still "something" moving in the other direction. "Something" is created in my arm, moves rapidly through the pole, and is finally absorbed by the distant scrub-brush. If I push/pull the pole fast enough, there will be no mistake that I am actually broadcasting sound waves to the distant brush. By rubbing upon the floor, the brush absorbs the waves and becomes hot. If the pole is short, the same thing happens: I send sound-wave energy to the brush. And finally, if I grab the brush directly, I'm still sending "sound" into the brush as I scrub the floor. The act of scrubbing the floor is an acoustic event! :)

Being in electronics, I automatically want to plot all this on a frequency graph. I will place normal sound in the middle of my graph (30HZ to 20KHZ), and below this I place NOT subsonic sound, but instead "mechanical energy" or "work." At 0HZ I place "constant motion." Just above zero I place "transient motions and oscillating motions". Too weird. At the bottom of the acoustic spectrum, sound becomes "everyday work."

Returning to the automobile drive shaft, I see that its twisting and rotation is also a type of sound. It is shear-wave sound, "torsional" sound. Solids are able to support transverse sound waves as well as longitudinal waves, so the work/sound that flows within the drive shaft is torsional sound waves of zero frequency. Well, not exactly zero, since the spectrum of the sound/work is that of a pulse with minutes-long or hours-long duration. To be *exactly* zero in frequency, the car would have to drive along for an infinite period of time.

If I grab a chair and lift it, the wood in my hand moves first, then it pulls the next bit of wood which moves, which pulls the next, and eventually the whole chair is rising. But the work I did was broadcast to all parts of the chair as sound, as subsonic energy which travels at the speed of sound in wood.

This can't be the whole story, since it doesn't apply to situations where no energy is flowing, right? For example, a moving mass has no twist and no stretch, so there is no "DC sound" involved. Or, a compressed spring has no motion, so work/sound is not moving within it. But this is familiar to me. Sound waves contain both compression and movement, they have both Kinetic Energy and Potential Energy. At a low, nonzero frequencies we can say that sound and mechanical energy are the same. But at zero frequency, we have a sort of "unification" of separate energies going on. The very slowly-changing "sound wave" slows to a stop, and can exclusively end up as motion-energy, or exclusively as compression-energy. So, the mechanical KE and PE concepts connect directly to the rest of the stuff above, they are simply the two (dual) facets of sound waves. Mass at a height can appear on my sound spectrum. So can a spinning flywheel They are both plotted at 0hz.


So, all this stuff was hiding in the plot of the sound spectrum all along. It was just mislabled "subsonic" or "infrasonic." Instead the label should have said "work" or "mechanical energy." I wonder, is there anything weird in the other direction? Ultrasound, hypersound, what's up there? In a physics encyclopedia on "Hypersonics" I find an interesting tidbit. If we send sound waves through a solid object, and raise the frequency higher and higher, something interesting happens. The speed of sound decreases as the wavelength shortens, and the speed of sound becomes about zero when the wavelength equals the crystal lattice spacing. There is a classic demo of this, with an air track and a row of carts connected by springs. If the end cart is wiggled too fast, the "wiggle" moves through the line of carts very slowly. HMMMM! That sounds familar. High-frequency sound that oozes through solids like syrup? Where the sound is stuck as standing waves between individual atoms of the material, and where individual atoms seem large and cause scattering of the waves? If a chunk of solid is "infected" with this intensely loud and slowly-moving hypersound, and if another piece of solid should touch the first one, then the slow hypersound will ooze into the other object until (if the objects are equal in size), the sound occupies twice the volume and is half as loud.

So... Heat is a form of sound?!

Or should I say "heat" is sound, since many educators believe that the word "heat" causes misconceptions. I'll say it this way: thermal energy within physical objects is actually a very loud screech of hypersonic whitenoise. When a hot object is touched to a cold one, "phonons" of sound start pouring between them.

Think about frictional heating. My scrub-brush from before, when it dragged across the floor, must have "twanged" the individual atoms in the floor and in the bristles, and the sound frequency was so high that it moved slowly into the floor and into the bristles. Work/sound was converted to heat/sound by friction, in the same way that a slow subsonic movement of a fingernail can be converted into high frequency noise when that fingernail moves across the teeth of a hair comb. Nonlinear stick-and-slip events have connected the low-frequency realm of work/sound to the high-frequency realm of heat/sound.


Being on a roll, I look around for other things to "unify." Thermal energy isn't really so simple as I've described above, because atoms within a hot object can transmit energy as IR photons as well as by the "incoherent hypersound" method. I wonder, is the wavelength of the thermal-photons the same as the wavelength of the "heat vibrations"? I don't know. I suspect that it is. Anyway, take a closer look at those "hot" atoms. One atom in a warm solid can bash another one, which bashes a couple neighbors, and "heat" travels as sound waves. But one atom can also bash just the electron shell of another atom, and generate waves in the EM field.

Ignore photons and think of electromagnetic waves. An atom whose electrons and nucleii do not move as one single object is going to generate an electrostatic field and a magnetic field. If the atom wiggles like a single entity, it can wiggle its neighbors through its chemical bonds and transmit sound. But if the atom's electrons/protons wiggle separately out of phase, then electromagnetic fields of just that same frequency are being broadcast, and they can wiggle the electrons and protons of a neighboring atom's separately. I still haven't found out if the sound spectrum of "heat" has the same general frequency distribution as the IR thermal spectrum, but I've convinced myself that it probably is similar. Thermal vibration can move as *mechanical* wiggles of charges in phase, or as field-wiggles coming from plus and minus atomic charges that wiggle out of phase. When the opposite charges wiggle in phase, it's called "sound", and when they wiggle with non-zero phase, it's called "electromagnetism." Heat can flow as phonons or photons, Heat is a strange combination of light and sound.


Hold on there. This work/sound stuff applies to wires! So, what if I go back to the scrub brush experiment and replace my 100KM wooden pole with a 100KM copper bar? If I had some way to push on just the copper protons without pushing on the electrons (or maybe vice versa), would I perform some work on the column of charge within the rod. I therefor would send a wave of electromagnetic "work/sound" along the rod?! This wouldn't be a pure EM wave, because it would be connected with physical particles. As before, if I push the electrons and protons together as one, I produce sound (mechanical work,) but if I push the electron-stuff separately from the proton-stuff in the copper, I get travelling compression waves in the electron-sea of the rod, and this causes transverse e-fields and magnetic fields to flow forwards within space around the rod. It seems that sound and electromagnetism are conceptually joined inside of matter. If matter was entirely made of totally neutral particles, maybe our universe would have a distinct "mechanical/acoustic" facet and an "electromagnetic" facet. They would be like two separate realities which existed independantly and never interacted. Put simply: electric charge is what joins electromagnetism-work to sound/mechanical-work. It keeps the universe from splitting into separate, non-interacting "realities."

There's a problem with the above electron-pushing idea. If we try to move an object's electron-stuff forward, it requires immense values of electrical potential (voltage.) Once I calculated the voltage involved with pushing the electrons a few cm forwards in a wire without pushing the protons too. (Assume it is a capacitor where you've moved Avagadro's number of electrons across a capacitor having a few picofarads value.) To physically move the electrons of a rod by a perceptable amount, GAZILLIONS of volts are required. There is a well-known solution to this problem: connect the rod into a circle. Then it becomes possible to push the electron-sea along like a drive-belt without having to create any separated charges anywhere.

So, rather than using a 100KM copper rod, I use TWO parallel 100KM copper rods, with the ends joined at both ends. I want to push the electron sea, so I stick a motor at one end of the rods (connected in series with the link between the rods.) I stick a generator at the other end. Now, if I suddenly start cranking the motor, I push electrons into one rod and suck them from the other. A wave of "work" (of charge compression and motion) starts at my end of the rods, travels along the rods, and ends up at the far end, where it moves the generator. Does it move at the speed of light? I don't know. Electrons have nonzero mass, so I would think that the wave of compression moves at a bit slower than c. Regardless, I'd better make my rods a million KM long, so that it takes a few seconds for my "work" done upon the generator shaft to appear on the distant motor shaft.

(Aside: wouldn't it be cool to build a simulator that did this? Have a pair of motor/generators each connected to a programmable power supply, with a computer measuring the current and back-emf, and then simulating a one-second bidirectional time delay between the two? It would give people a FEEL for electromagnetic wave propagation along transmission lines.)

Electromagnetic work/stuff can travel along wires very much like work/sound moves through a drive-belt system. If I look closely, I'll find populations of compressed electrons and rarefied electrons generating e-fields, and populations of moving electrons generating b-fields. If I wiggle the DC generator shaft instead of turning slowly, I send some "sound wave" electromagnetism from one end to the other. People call this stuff "electricity", as in "kilowatt hours of electricity", or "quantity of electricity sold by the electric company." But it really is electromagnetism, and the energy is in the fields surrounding my two rods, and not inside the rods.

But there's something else I can do. If I wiggle my DC generator shaft and create a nice AC wave, and if I connect a 1/4 wavelength dipole antenna to the other end of my two long rods, then the travelling electron-compression wave- energy from the generator will flow into the antenna and fly right out into space as radio waves! If I want to do it by wiggling the generator crank at 5 times per second, I just need a very long antenna, a few thousand KM. If I ignore the electrons and the wires for a moment, and concentrate only on the fields surrounding them, I see something interesting. When I wiggle the generator shaft, e-fields and b-fields race out of the generator, surround the pair of rods, then race outwards along them. They move as waves having the same frequency of my generator-shaft wiggling. When they get to the antenna, they pour out into space as EM waves disconnected from any charged particles. By using an antenna, I've removed the obscuring electron/proton concepts, and discovered that the "mechanical" work that travels around in electric circuits is the exact same thing as radio waves! The "work" it takes to wiggle that generator shaft is now flying out into space, not as sound, but as EM ripples. Electrical energy in a circuit is RADIO WAVES, even if it is 60Hz energy, and even if it is 1Hz energy

So, I drag out a plot of the electromagnetic spectrum, and below the AM band I find ELF, VLF, ULF, etc. As with the acoustic spectrum, I see that this is wrong. I can cross out all this stuff at the low end of the spectrum, and in its place write "Electric Power". When the electric company sends "electric power" from its generators to my home, they are sending radio waves. The "electricity" sold by the electric company appears at 60HZ on the radio spectrum. Our culture is truly a radio culture, with everything run by radio waves being ducted along the wires. But no one tells us this. It all sounds like a Nikola Tesla hallucination! When I talk into a telephone, radio waves of approximately 50HZ to 5KHZ race outwards along the space around the phone lines. If I interrupt the pair of wires with a transformer, the waves flow right across the gap. If I connect hundreds of 1:1 transformers end to end, I get more of an idea about the sort of energy that's flowing along that "drive belt" composed of metal electrons. And if I could just put a big enough antenna on the distant ends of those telephone wires, I would need no transmitter. The audio-frequency "electricity" would flow right out into space. When my stereo system sends "stuff" along the pair of wires to the loudspeakers, the "stuff" is ELF radio waves between 30HZ and 20KHZ (higher, if audiophile equipment!) (Note: I did find one wall chart of the Electromagnetic Spectrum published by the Exploratorium museum in San Francisco DOES show 60hz electric energy transmission in the appropriate spot on the "radio dial." Good. It looks like other people are as crazy as I am.)

And following the lure of 0HZ, I look at my flashlight and conceptually I replace the pair of wires with a spinning drive shaft that has a small twist. Zero-frequency electromagnetic sound/work/stuff flows from the battery and into the bulb, where it is converted (by the electromagnetic version of a nonlinear stick/slip fingernails-on-comb-teeth effect!) into thermal/electromagnetic waves called light! Rub a brush on the floor, and the floor fills with hypersound. Rub the electron-sea of a metal against its proton sea, and "hypersonic" (meaning IR) electromagnetic waves bounce around inside. EM is different from sound in this case, since the EM can get out of the hot metal as waves of fields in vacuum, whereas the hypersound can't use vacuum as its medium.

And finally, back to the EM version of the compressed spring and the flywheel. When a ring of metal has its electron-stuff moving, yet its proton-stuff stays still, we have a magnet. When the electron-stuff of a metal is compressed and the proton-stuff isn't (or vice-versa), we have e-fields, separated charge, and "Static Electricity". (I hate that word, it should be 'electricism', so it can unite with 'magnetism' correctly in our heads.) The dual halves of the mechanical version of the work/sound stuff, when at zero frequency, gives us PE and KE, compressed springs and spinning flywheels. They are dual facets of sound, at zero frequency, with symmetry broken. The the dual halves of the electromagnetic work/stuff gives us coils and capacitors, electromagnetic PE and KE, magnets and "electrets." These are the broken symmetry of frozen radio waves.

Work is sound! Electricity is radio! "Heat" is a slow-moving wave of "infection" that's composed of both! Does your brain hurt yet?


Created and maintained by Bill Beaty. Mail me at: .