A 737-B has just reached cruising altitude for its trip from California to Colorado. In one row toward the back an older man in the middle seat leafs through the airline magazine. Through the window his wife watches the Sierras slide by beneath them. In the aisle seat a younger man opens a book and begins to read.

“Pardon me”, says the senior citizen, recognizing the sky blue cover, “Halliday and Resnick, right?”

The other smiles and, closing the well-worn book to expose the front cover of PHYSICS For Students of Science and Engineering, Part II, by Halliday and Resnick, replies:

“Yes, I guess this one’s been around for a long time. Were you an engineering student by any chance?”

“As a matter of fact I was. Arizona State. Electrical Engineering. I’m retired now, though.”

“I’m a double E as well. University of Colorado.”

“Really! Our three children are all CU grads. So how come you’re reading Halliday?”

“Actually, I’m trying to figure out, one more time, just how electromagnetic waves physically propagate the way they do. As I’m sure you remember, we can mathematically model them traveling as sine waves, and predict accurately how they’ll behave in just about all situations, but nobody’s ever been able to fully explain how and why the physical process actually occurs as it does. What causes E waves to behave that way and so forth.”

Pleasantly surprised, the older man replies: “Hmmm. Yes, it’s interesting you should say that. As a matter of fact, I’ve been meaning to take another look at E waves myself. I don’t mean to say I’ve got them completely figured out as yet, but I do have some ideas that just might help us to better understand them.”

Even more surprised, the younger man says, politely, “Oh, really?”

“Yes. I think so, anyway. Have you been able to make any progress?”

“No, But there’s got to be an explanation somehow, somewhere. If you’ve some new ideas I’d like to hear them.”

“Well, before I get to them let’s make sure we’re on the same page here. If you remember, at the very beginning of the book the authors talk about studying electromagnetic waves on two levels. The first level has to do with learning them well enough to solve practical engineering problems. Which is of course what the book’s about. They do mention, however, that there remains a deeper understanding of the universe that no one’s yet fathomed. One that connects electromagnetic theory and quantum theory and all the rest of the universe together into one seamless, completely understandable reality. It sounds to me like you want to know not only the mathematical how of E waves but the philosophical why as well.”

“Yeah, I know. I’m probably asking too much. And I ought to be satisfied like most people to just learn how to use the theory and let it go at that. My problem is that I’m doing some antenna design work right now and it keeps reminding me I don’t really know what I’m doing. Or, I suppose I should say, we don’t know what we’re doing. And, while simple antenna design, which is all I’m doing, is mostly cookie cutter sort of stuff any more what with computer software and all, when something doesn’t make complete sense to me I start to get uneasy about the whole situation. Because somewhere down the line I know I may be leaving myself open to making some big mistakes simply because I didn’t understand what was going on well enough from the beginning. So, from time to time I’ll whip out old Halliday and Resnick here, or sometimes check out some other source looking for maybe a slightly different explanation of E waves; hoping to find some deeper meaning to it all. Some fundamental reason why electric and magnetic waves work the way they do, that none of us understand yet. So, yeah, I guess I want to know not just the how, but the why.”

“I know exactly what you mean. I feel the same way. As do many others. I don’t recall his exact words, but I remember reading somewhere about the physicist Richard Feynman commenting on the unfathomable strangeness of electromagnetic waves. So, if you don’t mind, what I’d like to do is make a suggestion or two about an entirely different way to look at electromagnetic waves. Mind you, I’m no bona fide scholar on this subject, so I might just be whistling in the dark here. I only have an undergraduate degree, and, as a matter of fact, I didn’t complete the requirements for that until I was 37. So, like I say, I certainly could not be categorized as a scholar. However, for reasons which are a bit complicated, some personal investigations I’ve been working on recently, sort of as a hobby you might say, on the origin and nature of time led me just last year to realize that maybe we haven’t been able to figure out electric and magnetic waves because we keep thinking of them as sine waves interacting at right angles to each other. When, in reality, the two sine waves might just be two slices, so to speak, of a continuously advancing electromagnetic helix.”

“Hold on a minute! I’ve never heard that one before. I’m not sure I follow you.”

“Of course. That’s understandable. After all, for generations we’ve been taught that electromagnetic waves travel as sine waves like you said. And the two dimensional mathematics has always worked perfectly for us in every respect. Thus there’s never been any reason to think they propagate any other way. Except for one thing. We don’t understand the cause and effect relationships--the mechanics, if you will--responsible for the propagation of these waves. So maybe, as you young people say nowadays, we need to get outside the box.”

“Outside the box?”

“Yes. In this case the sine wave box. What I’m saying is, we might be thinking of electric and magnetic waves more or less exclusively in terms of constantly interacting sine waves when the whole electromagnetic wave front actually travels through space as a continuous, constantly rotating, three-dimensional helix.”

“Like I said, I never thought about it that way.”

“I know. I only stumbled on the idea because of, again, some other thinking I’ve been doing about quantum mechanics and time. And I’ll say again that I don’t know if there’s any truth to this idea about the helix or not. It’s going to take somebody better at math than myself to develop a mathematical model to prove it. But I think if it can be done, it might help us to have a clearer picture of E waves, and much more besides. That’s why I think you might be interested. At least it’ll give you something to think about. And, who knows, if you’re better at the math than I am, maybe you can work it all out and surprise the heck out of everybody. Wait a minute, to show you what I mean (pointing to the folded sheet of notebook paper the young man is using as a bookmark) can we write on that?

“Sure.”

“OK then. First, if you don’t mind, draw me a simple sine wave traveling from left to right.”

The young man does so. (Fig. 1) “Like that?”

“Good! Now, starting at the same place, superimpose on the sine wave a helical wave also traveling from left to right that’s at the same frequency and amplitude and also in phase with the sine wave you’ve already drawn. Only remember, you only have two dimensions to work with, because that’s all you have with a sine wave. In other words, you want to try to reduce a three dimensional helix, or corkscrew shape, into a two dimensional figure.”

The young man, after several tries, begins to draw another sine wave on top of the first one. (Fig. 2)

Fig. 1	Fig. 2

“I see what you mean. I get another sine wave. Actually, I get the same sine wave.”

“That’s what I’m saying. Graphically, a three dimensional helix reduces to a two dimensional sine wave. And if you can do it graphically, you know you can do it mathematically. By the same token, we ought to be able to go the other way and mathematically expand a sine wave to a helix. Although, like I said, I don’t know how to do it. My whole point here is that if the electromagnetic wave actually does travel helically in the real world, then it seems to me that would have a lot to do with why we can’t fully explain the mechanics of it. We’re basically trying to explain in two dimensions what really requires three dimensions to actually happen.”

“If you’re right, that might have everything to do with it.”

“Maybe, maybe not. It depends on just how deep you want to go with your explanation. If the corkscrew idea works, and if you’re satisfied with the mathematics of how electric and magnetic waves interact to produce an electromagnetic wave, then that’s all you need. But if you truly want to know exactly why electric and magnetic waves interact the way the math says they do, if indeed it could show they travel as a helix, then what we’ve talked about so far isn’t going deep enough. Then you have to start thinking of what Halliday and Resnick said about the deeper meaning of things.”

“Well, yeah, but we may never know where electromagnetic energy comes from and what it really is. Or why it shows up as electric and magnetic waves, let alone why they work the way they do. Which is what I suppose they were talking about.”

“Again, maybe, maybe not. However, that’s actually the kind of stuff I’m working on now.”

“A minute ago you said something about working with time. And now you’re talking about the origin and nature of electromagnetic waves. Just exactly what is it you’re doing?”

Smiling, the older man replies, “What’s that old saying, be careful what you wish for? Actually, there’s a long answer and a short answer to that. As far as the short answer goes, which is probably more along the lines of what you’re most likely to be interested in here, I’ve recently been working on trying to understand the origin and nature of time. Where time comes from, what it really is, how it works, and so forth. You see, I think I can make the argument that our universal time, and by that I mean the time that clocks the evolution of our universe, originates in the quantum world. Actually, it turns out that, if we include some other considerations which I won’t go into here, quantum particles, because of the way they work, and because they are the fundamental components of all matter, might turn out to be the original time generators for the matter which makes up our universe. Further, using these same ideas I can then go on to explain some of the mechanics of the quantum and some of the mechanics of relativity and gravity as well. And, eventually, perhaps, where all the laws of nature come from, and how all these things fit together into an overall theory of the universe. I’m not trying to say I’ve got everything all worked out yet. Far from it. But I’ve been able to make a lot of progress toward a general understanding of how the universe works, at least to the point where everything is starting to make sense. So I think I’m at least on the right track. But I can only do this if I first assume that the big bang begins with pure electromagnetic energy propagating outward in all directions from the original point source, and that it does this helically.”

“If you say so. But, frankly, sir, with all due respect, you’ve lost me completely.”

“I suppose I have. And that’s completely my fault.” (He pauses for a moment) “Look. Let me give you the short tour here just to give you a general idea of what I’m talking about. That is, if you’re still interested.”

“Well, all right. I’m game.”