An Introduction to Information Theory: Symbols, Signals and Noise, by John R. Pierce, says the following:
While linearity is a truly astonishing property of nature, it is by no means a rare one. All circuits made up of the resistors, capacitors, and inductors discussed in Chapter I in connection with network theory are linear, and so are telegraph lines and cables. Indeed, usually electrical circuits are linear, except when they include vacuum tubes, or transistors, or diodes, and sometimes even such circuits are substantially linear.
Because telegraph wires are linear, which is just to say because telegraph wires are such that electrical signals on them behave independently without interacting with one another, two telegraph signals can travel in opposite directions on the same wire at the same time without interfering with one another. However, while linearity is a fairly common phenomenon in electrical circuits, it is by no means a universal natural phenomenon. Two trains can’t travel in opposite directions on the same track without interference. Presumably they could, though, if all the physical phenomena comprised in trains were linear. The reader might speculate on the unhappy lot of a truly linear race of beings.
Thinking about this from a physical perspective, I was wondering how it is that telegraph wires are linear, in the sense that two telegraph signals (in other words, two electric currents) can travel in opposite directions on the same wire, at the same time, without interfering with each other?
I was naively thinking about the wire as a single-lane, two-way road. In this analogy, the cars would be able to travel in either direction, but not at the same time. As I understand it, in solids, movement of electrons produces an electric current, so the electrons would be the cars. Given the author's explanation of linearity, what is going on here with the electrons that allows this concurrent, two-way flow of current?
I didn't find anything on the Wikipedia page for linear circuits that clarifies this physical property of linearity.
I would greatly appreciate it if people could please take the time to clarify this.
P.S. I do not have a background in electrical engineering, so a basically-worded explanation is appreciated.
EDIT: Based on comments from the previous thread, I understand that my analogy would be more accurate if I represent the electrons as double-sided bumper cars, and then imagine the two-way lane that they inhabit as filled with these cars, so that movements in either direction (electric current in either direction) is represented by a sequential "pushing/nudging" motion, like a wave, that is perpetuated by each car "bumping/nudging" into the one in "front" of it (in the direction of the current).
EDIT 2: I see many answers that are telling me that the core of my misunderstanding comes from the fact that I assume that electric current and signal are the same thing. And these answers are correct, I was assuming that electric current and signal are the same thing, because the author keeps implying that they are the same thing in the text (or he fails to clearly differentiate between the two)! See the following excerpts from the same chapter:
While Morse was working with Alfred Vail, the old coding was given up, and what we now know as the Morse code had been devised by 1838. In this code, letters of the alphabet are represented by spaces, dots, and dashes. The space is the absence of an electric current, the dot is an electric current of short duration, and the dash is an electric current of longer duration.
The difficulty which Morse encountered with his underground wire remained an important problem. Different circuits which conduct a steady electric current equally well are not necessarily equally suited to electrical communication. If one sends dots and dashes too fast over an underground or undersea circuit, they are run together at the receiving end. As indicated in Figure II-1, when we send a short burst of current which turns abruptly on and off, we receive at the far end of the circuit a longer, smoothed-out rise and fall of current. This longer flow of current may overlap the current of another symbol sent, for instance, as an absence of current. Thus, as shown in Figure II-2, when a clear and distinct signal is transmitted it may be received as a vaguely wandering rise and fall of current which is difficult to interpret.
Of course, if we make our dots, spaces, and dashes long enough, the current at the far end will follow the current at the sending end better, but this slows the rate of transmission. It is clear that there is somehow associated with a given transmission circuit a limiting speed of transmission for dots and spaces. For submarine cables this speed is so slow as to trouble telegraphers; for wires on poles it is so fast as not to bother telegraphers. Early telegraphists were aware of this limitation, and it, too, lies at the heart of communication theory.
Even in the face of this limitation on speed, various things can be done to increase the number of letters which can be sent over a given circuit in a given period of time. A dash takes three times as long to send as a dot. It was soon appreciated that one could gain by means of double-current telegraphy. We can understand this by imagining that at the receiving end a galvanometer, a device which detects and indicates the direction of flow of small currents, is connected between the telegraph wire and the ground. To indicate a dot, the sender connects the positive terminal of his battery to the wire and the negative terminal to ground, and the needle of the galvanometer moves to the right. To send a dash, the sender connects the negative terminal of his battery to the wire and the positive terminal to theground, and the needle of the galvanometer moves to the left. We say that an electric current in one direction (into the wire) represents a dot and an electric current in the other direction (out of the wire) represents a dash. No current at all (battery disconnected) represents a space. In actual double-current telegraphy, a different sort of receiving instrument is used.
In single-current telegraphy we have two elements out of which to construct our code: current and no current, which we might call 1 and 0. In double-current telegraphy we really have three elements, which we might characterize as forward current, or current into the wire; no current; backward current, or current out of the wire; or as +1, 0, -1. Here the + or — sign indicates the direction of current flow and the number 1 gives the magnitude or strength of the current, which in this case is equal for current flow in either direction.
In 1874, Thomas Edison went further; in his quadruplex telegraph system he used two intensities of current as well as two directions of current. He used changes in intensity, regardless of changes in direction of current flow to send one message, and changes of direction of current flow regardless of changes in intensity, to send another message. If we assume the currents to differ equally one from the next, we might represent the four different conditions of current flow by means of which the two messages are conveyed over the one circuit simultaneously as +3, +1, -1, -3. The interpretation of these at the receiving end is shown in Table I.
Figure II-3 shows how the dots, dashes, and spaces of two simultaneous, independent messages can be represented by a succession of the four different current values.
Clearly, how much information it is possible to send over a circuit depends not only on how fast one can send successive symbols (successive current values) over the circuit but also on how many different symbols (different current values) one has available to choose among. If we have as symbols only the two currents +1 or 0 or, which is just as effective, the two currents +1 and - 1, we can convey to the receiver only one of two possibilities at a time. We have seen above, however, that if we can choose among any one of four current values (any one of four symbols) at a time, such as +3 or + 1 or - 1 or - 3, we can convey by means of these current values (symbols) two independent pieces of information: whether we mean a 0 or 1 in message 1 and whether we mean a 0 or 1 in message 2. Thus, for a given rate of sending successive symbols, the use of four current values allows us to send two independent messages, each as fast as two current values allow us to send one message. We can send twice as many letters per minute by using four current values as we could using two current values.
And this textbook doesn't assume any prerequisite physics or electrical engineering knowledge, so it seems unlikely that readers would be able to differentiate between signal and electrical current -- especially given the fact that the author seems to constantly imply that they are the same (or fails to, in any clear way, separate the two for people without such a background).