|
For those of you who already understand electromagnetic retardation, you may skim the first few paragraphs. For those of you who “think maybe” you understand it, or know you don’t, read the first paragraphs carefully and bear with me—it’s worth the exercise.
Consider a long, uniformly charged rod at rest in “thought experiment space” (I’m picturing something the size and shape of a spear handle). At a point P many rod lengths away from the rod and near, but not on, an imaginary line drawn through the long axis of the rod, we place a charge detector. The detector tells us the magnitude and direction of the electric force due to the rod at the point P at a time t. Looking more closely at the rod itself, we realize that the portion of the rod closest to point P (let’s call it the front)—because electromagnetic interactions take place at the speed of light—posted (or sent out) its contribution to the measurement taken at P a tiny bit later than the portion contributed from the very back end, just late enough so that both contributions arrived at P at exactly the time t.
Indeed, every portion of the rod, from back to front, sent out its contribution slightly in advance of the portion in front of it. Also, given where we picked P to be, even though the rod is uniformly charged, the back is farther away than the front, so though the signal starts sooner at the back, it is weaker when it gets there.
That little time delay is retardation, but as long as the situation is static (no relative motion) the details about exactly when each portion sent out its contribution don’t matter. Since the measured value is independent of time, the speed of electromagnetic propagation could just as well be instantaneous, or three rods per fortnight—it won’t make any difference.
Now let’s assume the rod was approaching P, in motion along its long axis. Again we make our measurement at P at time t, at the instant the position of the rod is the same as in the static case. Now things are a bit different. As in the static case, the contribution from the back had to leave sooner than from the front to arrive at P at the same time. However, with the rod moving, the back end was not where it was in the static case, but farther away from P. Being farther away, the contribution is also smaller. So despite being the same charged rod in the same position in both cases, the motion affects what is measured at P. (The astute reader will have noticed that I ignored the magnetic field associated with moving charges. I ignored it, but I haven’t forgotten it.)
To finish out this thought experiment, let’s assume the rod is uncharged, but simply massive, and ask what Newton’s gravity law tells us about the forces due to gravity at the point P. Well, it’s much simpler—it doesn’t matter one bit whether or not the rod is moving because Newtonian gravity is instantaneous: the field in both cases will be the same. However, even though the “speed of gravity” hasn’t been definitively measured (see here: http://wugrav.wustl.edu/people/CMW/ SpeedofGravity.html), it is generally assumed that it propagates at the speed of light, and I would be shocked if it didn’t. If the speed of gravity is the same as the speed of light (or any other non-infinite speed), then matter in motion must behave at least somewhat analogously to charges in motion, and at minimum, retarded effects must be present.
Dr. Oleg D. Jefimenko sent me a copy of his latest (and unfortunately, last) book at the very end of 2006, which he had signed and dated on December 28. I read it the first time shortly after it arrived, and knew that eventually I would write about it, either as a straight review or in the context of a larger issue. I didn’t want to discuss it immediately because I had talked quite a bit about Jefimenko in my January/February 2006 Alternate View, “Length Contraction.” A few years later I reread it thinking maybe it was time to write about some of Jefimenko’s recent work, but then the global warming stuff started heating up and I got distracted. I was also faced with the question of just how to approach it. I had already talked enough about retardation, and this book just represented the application of that concept to gravity. That makes almost the entire book an exercise in pure theoretical physics and heavy on the math (even though it’s just vector calculus in retarded form). Some of the implications of the math were fascinating and perfect for a science fiction venue, so I absolutely had to talk about those sometime. But I hoped to do so in the context of “here’s a result found in this book” as opposed to “here’s a book and this is one of the things you’ll find in it.”
Then fate stepped in and forced the issue. I think Jefimenko’s work on gravity is important enough that it needs wide dissemination, so the sooner after his death I discuss it, the better one’s chances of obtaining his book. I don’t expect it to replace General Relativity; indeed, I think GR is already on the right track. But the fact is that if the speed of gravitational interactions is limited to the speed of light, then in the ordinary cases in which GR reduces to Newtonian gravity, it reduces to Jefimenko’s extension, not Newton’s original.
Jefimenko’s book, with full title, is Gravitation and Cogravitation: Developing Newton’s Theory of Gravitation to Its Physical and Mathematical Conclusion (ISBN: 0-917406-00-1). It is a continuation of a project begun by Oliver Heaviside in a paper from 1893 called “A Gravitational and Electromagnetic Analogy.” You can find the paper online here at http://www.electretscientific.com/author/heavisid.html. This is an unedited version of the original, except that Jefimenko did us all the favor of having “converted some formulas and all vector equations appearing in the article to modern mathematical notation.”
On his Electret Scientific Co. author webpage (http://www.electretscientific.com/ author/author.html) Jefimenko described his current research interests this way: “I am also working on the generalization of Newton’s gravitational theory to time-dependent systems. By analyzing causal gravitational relations, I find that there is no objective reason for abandoning Newton’s force-field gravitational theory in favor of a metric gravitational theory . . .” This is a significant claim, and whether or not it is correct, since we use Newton’s theory all the time, the least we should learn to do is apply it in a way that doesn’t treat gravity as instantaneous. He goes on to say: “I base such an expansion, or generalization, on the existence of the second gravitational force field, the ‘cogravitational, or Heaviside’s, field’ (except for a numerical factor, the cogravitational field is the same as the ‘gravimagnetic’ field of the general relativity theory). This field was first predicted by Oliver Heaviside in his 1893 article ‘A Gravitational and Electromagnetic Analogy.’”
The “gravimagnetic” field is more often called the gravitomagnetic field. It is a force created by moving masses that acts only on other moving masses. I did a quick Google search on the term and it turned up a lot of crap, but this link yields a brief, accurate description: http://www.aip.org/pnu/1996/split/pnu295-2.htm. It says: “A gravitomagnetic field, according to the theory of general relativity, arises from moving matter (matter currents) just as an ordinary magnetic field arises from moving charges (electrical currents).” This is why I said above that I hadn’t forgotten that moving charges create magnetic fields—because moving masses also produce a force analogous to magnetism, in both GR and the generalized Newton’s theory. Wikipedia isn’t always a good source, but for a bit more information, this entry seems okay: http://en.wikipedia.org/wiki/Gravitomagnetism.
Recall that Jefimenko said there’s “no objective reason for abandoning Newton’s force-field gravitational theory in favor of a metric gravitational theory. . . .” If true then in principle experimental results will allow us to discriminate between the two theories, but I’m not holding my breath waiting for that to happen. It’s hard enough just trying to measure the gravitational constant “big G” to high accuracy. And the full theory of generalized gravity predicts several other forces besides the first two (for instance, the “gravikinetic” force, associated with accelerating masses) which makes it even more complicated than it looks at first glance. It will be awhile before we can make predictions numerically accurate enough to check one against the other. That having been said, perhaps we can look to the heavens and see if the generalized theory might explain some phenomena that we as yet don’t understand too well.
As I skim through the pages I am once again astounded by the number of examples worked out for simple systems moving at ordinary velocities (much less than c), and the implications of them. For instance, the title of chapter 14 is “Torque Exerted by a Moving Mass on a Stationary Mass” and therein Jefimenko applies the generalized theory of gravitation to multiple examples of this phenomenon. Example 14-3 (p. 244 and following) derives the torque for a point mass moving in a circular orbit, analogous to a planet revolving around a star. The result shows that a planet exerts a torque on the star, making it rotate faster in the same sense that the planet is revolving. Since a star is not solid, planets in her equatorial plane would cause the equatorial region to rotate faster than the polar regions. Jefimenko, having “looked to the heavens” before us thinks this effect may explain why the equator of our own Sun rotates faster than at the poles.
Chapter 7 is called “Differential Equations for Gravitational and Cogravitational Fields; Electromagnetic Analogy.” This chapter shows how very similar the generalized theory of gravitation is to Maxwell’s electromagnetism. Jefimenko puts the value of this as simply as one can: “An important consequence of this similarity is that many methods and techniques originally developed for solving electromagnetic problems can be used for solving problems involving gravitational and cogravitational interactions.” (p. 119) It is not so simple as substituting one Greek letter for another, however. For instance, there is a gravitational induction analogous to electromagnetic induction, but is there anything analogous to assorted magnetic materials? Or dielectrics? Or even an ordinary conductor, let alone a superconductor? Jefimenko is well aware of this and quite clear that we are speaking of an analog here.
To even things out, we have chapter 19 called “Gravitation and Antigravitation.” Here we find “gravitational equations depicting ‘nonlinear’ gravitational effects (that) do not have their electromagnetic counterparts.” (p. 138) Unfortunately, though I could hack out a brief description of what’s in the chapter, I can’t do it and have it make sense to you without your first reading the previous 18 chapters. Suffice to say that the generalized theory of gravitation allows for the existence of stellar and intergalactic antigravitational mass configurations. This is not about ordinary matter being put into some magical shape that makes it repel other matter. Rather, it is that the net gravitational field in free (empty) space, like between galaxies, can be repulsive rather than attractive.
What might we see if we consulted the heavens about that possibility? Cosmic acceleration perhaps?
Copyright © 2010 Jeffery D. Kooistra
Home | Address Change Form | What is Analog? | Forum | Submissions |Links | FAQ Page | Contact Editors | Privacy Policy | Advertising
Copyright © 2011 Dell Magazines, A Division of Penny Publications, LLC
Report problems on this site to Webmaster
|
