Testing the TK Tar Baby

[Liberty]

Flawed concepts of fundamentals will prevent the interested student from being able to understand further ideas that depend on a proper underpinning. To get the more complicated ideas, like "what is voltage" or "what is current" , one absolutely must have a grasp of some very basic concepts, and if these concepts are misunderstood... or even DENIED.... then further understanding of even seemingly simple things like relative voltages and how current flows and in which direction will be severely impeded. Please bear with me while I review some of these vital fundamental concepts.

Electric charge is fundamental, and is a conserved quantity. It is the interaction between charges of opposite polarity, and the motion of these charges, that comprise quantum electrodynamics (QED) in its entirety. QED is the "standard model" of electricity, electronics, electromagnetism, electrostatics, ion chemistry, molecular bonding... all of that is covered by QED and is understood well enough under that model so that we can calculate.... CALCULATE... based on a few fundamental quantities, the behaviour of any electrical circuit (and much more). The basic relationships amongst charge, motion, and force are contained in what is perhaps the most "sacred" and elegant set of equations in all of mathematical physics: Maxwell's Equations (ME). These equations take as input charge and motion (relative direction and magnitude) and return forces, directions and rates. Using ME and the further math that is derived from them, like Ohm's Law and KCLs, we are able to PREDICT with incredible accuracy the behaviour of circuits, devices and systems of these things. That is why circuit simulators actually work accurately: they are based on QED, which describes Charge, Motion, and Force.

Notice that ME don't talk about electrons at all. Charge, Q, is independent of its carrier in its relationships described by ME. Physicists have also been able to determine through an elegant (and huge) set of experiments that Charge is Quantized, that is, it comes in little discrete packets that have a smallest size and every Unit Charge is the same as every other. And they come in two flavors, Positive and Negative, and due to an accident of definition (thanks to Ben Franklin for a hundred years of confusion)  it happens that it is the electron, a particle, that carries the Negative Unit Charge. And it also turns out that the Unit Charge is inseparable from the electron; take it away somehow and you no longer have an electron at all, but some other particles from the PZ (particle zoo) and some energy. (The standard model of particle physics (PP) is properly called _The_ Standard Model with capital initials.)

So ME describe the motions and interactions and forces involved in MOVING CHARGES and how they effect each other. Charge is conserved; it takes energy to move things against opposing forces... but the charge is not the energy.

Now.... how do these Unit Charges happen to move, if they are attached to physical things like electrons and atoms that exist in solids like copper metal?

Well, it turns out that METALS, due to the structure of the electron shells around the individual atoms... have a lot of so-called "free electrons" that can be thought of as a kind of electron "gas" that is free to move around inside the metal's lattice formed by its atoms. These electrons are charged, each carrying its own little Unit Charge, and although the entire chunk of copper is "neutral" or balanced wrt P and N charges, the negatively charged electrons in the "conduction band"-- that electron gas-- are free to be pushed around however the forces applied make them go. In a copper wire, for example, it's like a bunch of little mutually repulsive pingpong balls in a tube, just big enough so the balls are free to move along the tube but can't push past one another. The balls are the electrons, the charges are what makes them repel each other.

So... if you push one of the balls in one end of the tube, this "wave" of mutual repulsion travels down the tube, as one ppball pushes the next one in line, never touching but transmitting the push through the mutual repulsion of the Unit Charges that are "stuck" to each electron. The electrons themselves need not move either far nor fast !! The repulsion of the charges causes the Last Electron at the far end of the tube to get pushed OUT at practically the same instant as you are pushing your First Electron IN to the tube at your end, even though you've only pushed yours in a tiny bit. The FORCE you use to push in is transmitted by the charge repulsion all the way down the line to the far end and thence to whatever that electron is going to push against.

All of this and much more is contained in precise mathematical relationships described in ME. They can be calculated, and give values that agree with experiment to an amazing degree of precision and accuracy. THIS is what is meant by a MODEL, in the physics and math sense. It agrees with observation, it makes predictions that can be checked by experiment, and most importantly it contains a means... mathematical relationships.... to quantify those predictions precisely and accurately. Models are accepted, to the degree with which they conform to experiment. When experiments and measurements become so precise that they reveal that the current model in use is not complete, then PERHAPS someone can come up with a new, better model... but that model has to be both CONSISTENT with what is previously known and also make BETTER, more precise or accurate or additional predictions of the behavior of experiments. That's what is meant by a MODEL, and that's what is needed for a better one to replace an old one: it really DOES have to be better, and it really DOES have to make numerically calculatable predictions that not only describe ALL previous behaviour that the old model did, quantitatively, but also must do its new thing too.

Enough for now. Thank you for your attention, and please think about Charge. Charge is fundamental and conserved; voltage, current, induction, capacitance, and all the rest emerge from the interactions of Unit Charges with one another.

Next: the Hydraulic Analogy.

Hi TinselKoala,

I am curious and have a question.  (I enjoyed your description above).  My question is about the movement of electrons vs. movement of charge or electrical potential.  How do we know that electrons actually move like ping pong balls, instead of the charge moving from electron to electron?  I know (or I think I know this) that electrical potential always wants to equalize difference in potential.  If distance and/or resistance between a difference in electrical potential is low enough, then the difference in potential will tend to equalize.  Can you please give me your view and understanding on this? 

Thank you,

Liberty

[TinselKoala]

Hi TinselKoala,

I am curious and have a question.  (I enjoyed your description above).  My question is about the movement of electrons vs. movement of charge or electrical potential.  How do we know that electrons actually move like ping pong balls, instead of the charge moving from electron to electron?  I know (or I think I know this) that electrical potential always wants to equalize difference in potential.  If distance and/or resistance between a difference in electrical potential is low enough, then the difference in potential will tend to equalize.  Can you please give me your view and understanding on this? 

Thank you,

Liberty

Hi Liberty and thanks for your question.
You are asking, I think, how we know that (first that electrons even exist as individual entities) the electrons move like pingpong balls in my analogy, instead of just transferring that Unit Charge, or simply Charge, along between more or less stationary electrons. Right?
Well, that's a complicated issue. The proof of the existence of the electron itself and its carrying the unit charge is given by electrolysis experiments, where exact ratios of input and output chemical ion species exactly correspond to the current (charge per unit time) doing the electrolysis. In addition electrons themselves, and current-carrying beams of them, are very common in electronics... but not so common as they used to be, when every television set had one or three or four of them constantly painting pretty moving pictures for us all day long.
The issue of the conduction band electrons moving sedately in the metals at essentially the speed of sound, while transferring charge at the speed of light, is something that perhaps people like Feynman understood... but I just have to take their word for it, since the explanation is consistent with the things I do think I understand.

Now...voltage, tension, potential difference, and charge. I think you are asking about what voltage is, and why and how it tends to equalize,  overcome resistance, and cause current to flow. Right?
This is a topic that I will be covering in the next little mini-essay, so that the HA analogies to voltage and current will make sense. Please hold your question until I've had a chance to deal with the issue of voltage and what it is and how it relates to the fundamental conserved and quantized Charge. I hope that's acceptable.

I really appreciate your interest and questions, and also that you wait until I have actually been able to cover some small details before asking them.

As an aside, I'm glad to entertain questions but this is not the place for challenges or alternative theories. I am, I hope obviously, trying to clarify some pertinent points having to do with the CURRENT, most successful physical model that humans have ever invented: Quantum Electrodynamics, and its relationship to common ordinary circuit behavior. QED predicts, from first principles, the results of experiments with great reliability and precision. Some of the predictions and calculations of QED are so precise that they have as many as thirteen or more significant digits of precision. If the Moon is 384500 km away exactly... that is six sig digs of precision. Add another seven digits to the right of the decimal point.... and we are talking about knowing the Earth-Moon distance with a precision to the ten-millionth of a kilometer, or one ten-thousandth of a meter, or one tenth of a millimeter... about the diameter of a coarse human hair. THAT is how accurate and precise some of the predictions of QED are.
So.... if you've got something better.... it's gonna take some convincing, for me to believe it, and this isn't where it's gonna happen.

[TinselKoala]

Charge and current; charge and voltage; current, voltage, resistance: Ohm's Law.

Sen no Rikyu, a tea-master, wished to hang a flower basket on a column. He asked a carpenter to help him, directing the man to place it a little higher or lower, to the right or left, until he had found exactly the right spot. "That's the place," said Sen no Rikyu finally.
The carpenter, to test the master, marked the spot and then pretended he had forgotten. Was this the place? "Was this the place, perhaps?" the carpenter kept asking, pointing to various places on the column.
But so accurate was the tea-master's sense of proportion that it was not until the carpenter reached the identical spot again that its location was approved.

[MileHigh]

Nobody could adjust the picture on a colour TV like me!  lol  The sweet spots.

[TinselKoala]

Charge and voltage; charge and current; current, voltage, resistance: Ohm's Law.

First: Charge and voltage, charge and current.

OK, I hope everybody had a nice break and that we are all back again, ready and eager to find out what a Koala thinks voltage is.

Let's all play a little game. Come with me, you brave class of three hundred warriors, down the hall to a small 30-desk classroom.

Out here in the hall, I'll tell you the rules and the reward. I have here ten Benjamins, totalling ONE THOUSAND DOLLARS in cash, and a guaranteed "A" for the course, for the last person remaining at the end of the game. And here are the rules. I'll be sending people into the room one at a time. If anybody actually TOUCHES anybody else, your are both out and have to exit the room, you get no money and of course you fail the course. Trapdoors have been provided in the floor so that you just vanish and don't disturb the rest of us.

OK... got the picture? You are acting like a bunch of repulsive little identical negative Unit Charges, confined to the space within a finite volume of conductor like a "gas" of nonbound conduction band electrons in a lattice of bound metal atoms (the desks). But you cannot under any circumstances allow yourselves to touch each other, or you lose your chance at the ten Bens and the easy A. The first thirty people inside can of course find seats at the desks and sit down and stop moving if they like, but the same no-touching rule still applies and of course you can't have two people at the same desk.

Right. Now I'll send a few people into the room and let them mill around. There, that was easy, there was nothing in the room preventing or pushing back and the three people are in there milling about with plenty of room and no pressure and can even find safe seats and stop moving.

Notice how I snuck that word in there... pressure.

Let's continue to send people in, one or a few at a time. Pretty soon that little classroom has a lot of nervous people in there, under considerable _pressure_ to avoid one another, and this pressure is caused by nothing other than their mutual desire to stay away from each other as far as possible (because that is how to minimize your chance of touching somebody else and knocking you both out of the running.)

Of course we aren't letting anyone out the entry door. And everybody is pretty good at the game, nobody gets eliminated, so the pressure continues to rise as we send more and more people into the room. In fact... we notice that it even takes more and more work to send each additional person into the room, because all the little bubbles of space around each repulsive person have to shrink and jostle with each new entry, and that pressure pushes back against the newcomers at the door.

But wait... somebody inside found the door in the party wall that leads to the next... empty... classroom, and people immediately begin spilling out that door into the area where the pressure is much less and they can get comfortably far from each other again. Now I can send even more people in through the entry door because the pressure in the original small room is decreased. In fact, if I am careful, I  can actually balance the RATE at which I send new people in, to the RATE at which people find the other door and exit into the less full classroom next door. In this case, obviously (I hope it's obvious, anyway) the pressure in the original room doesn't change, because the number of people doesn't change, because I am adding at one end just as fast as they are subtracting at the other end.

OK? Got the picture of the Voltage Game?

Charge is fundamental, charge is conserved, charge is quantized, charge is attached to physical carriers of some kind, charge comes in two flavors, and like flavors of charge repel like. (And of course opposites attract.) I haven't really mentioned the two flavors much but if you like,  you can think of the negative flavor as the Unit Charge on the electron, and the positive flavor as some place where an electron _should be_ along with its negative charge, but isn't.... so any negative charges wandering by will fall into that "hole". Ultimately, the positive charge that attracts the negatively charged electron comes from the positively charged protons in the atomic nucleus, but this charge waay down there in the center of the atom makes itself felt at larger range by the action of the "holes" in the electron orbital shells where one should find electrons in a neutral (unionized, unbonded) atom, but where the normally present electrons have been knocked away by adding energy to them or are elsewhere participating in an interatomic bond.

Now... in the Voltage Game, the people are of course the electrons and their Unit negative Charges. Mutually repulsive, the lot of them. And there is a measurable pressure from packing the repulsive charges together in a tight space. And there is even a "suction"... a RELATIVE suction... that causes a flow of these repulsive little charge carriers into the other reservoir where the pressure is lower. You could even view this relative suction as a negative pressure, as long as you remember where your reference pressure value is. It makes no difference to the behaviour of the people at all, all they know is that they don't want to touch.

The PRESSURE, or the suction or the tension, is of course VOLTAGE. The Voltage arises from the mutual repulsion of a lot of like charges confined to a volume of a conductor. The more charges you pack in there, the higher the voltage. The higher the voltage the harder it is to pack additional charge in there, and the more eager the charge that IS in there is to escape to some region...any region.. where the pressure is lower. It's not that easy to get an A in my classes!

And the FLOW of the unit charges into the other room, or into the first room, is of course CURRENT. And we measure a flow by its RATE, that is a count of the flowing things PER a unit of time. If I have seventeen schmoos passing me every second, then I have a RATE of seventeen schmoos PER second, and by multiplying by the number of seconds I am interested in I can count the total number of schmoos that have passed my measurement point during that interval. Conversely, if I count, say, ten thousand schmoos every ten seconds, then I know that I am seeing an average RATE of a thousand schmoos per second. Same with the Unit Charges and the Current, except we are measuring, usually, negative unit charges bound to electrons, one each, passing our measurement point.

Right? With me so far? Good.

So it's not very convenient to keep saying "a bunch of schmoos per second" all the time, so a bunch of boffins, to a man, got together one rainy afternoon and decided to name all these complicated units after revered scientists of the past, and they decided that the Rate of Electron (or negative unit charge) flow was to be called, for ever after, the Ampere, after  André-Marie Ampère (1775â€"1836), the French mathematician and physicist who is considered to be the father of electrodynamics. (They also named the Volt, the unit of electrical pressure or tension, after the Italian physicist Alessandro Volta (1745â€"1827), who invented the voltaic pile, an early form of chemical battery.)

So the Ampere, then, refers to the Rate at which unit negative charges flow past your measuring point, per second. Well, then, how many negative charges have to flow by in a second to make one Ampere? A great many. A very great many, in fact. One whole Coulomb of negative charge has to flow per second to make one Ampere of current.

Well, that's helpful you say, what the heck is a Coulomb then when it's at home?

Well, it's a quantity of charge of course. How much? It's the quantity of charge carried by 6.241 × 10¹⁸ electrons. So that many unit negative charges passing your measurement point in one second is an Ampere of current. It doesn't really matter what the charge carriers are; if you had a beam of protons carrying their positive charges going by at 1 Coulomb per second (but of course counting positive charges now) you would also have a current of one Ampere in your proton beam. (And you'd be attracting a lot of attention, too.)

OK, that is at least a Coulomb of information for you to meditate upon and digest, so we will pause here for dinner. Thanks for your attention; this is a difficult part of the story here but in order to go further it is absolutely vital to understand where and how Voltage (electrical pressure or tension) arises and that Current is the flow of charge, lots of little unit negative charges all flowing past your point.

Next will be Voltage, Current, and Resistance: Ohm's Law.