Now that it’s 2006 and the Einstein Centennial year is behind us, along with any number of popular articles implying that Einstein was right about everything, perhaps it’s time to go about clearing up some confusions about just how it is that Einstein’s Universe really works. For as it turns out, and has been long known by physicists (just not by that many), some of those things “everyone knows” about what relativity says “just ain’t so.” And in this column, I’m going to get set things straight about relativistic length contraction.
When I was growing up, the popular books on Einstein’s special relativity (SR) theory said quite clearly that when objects move, time slows down and the object gets shorter (and mass increases, but I’m not going there at all this column). They said that when an object, like a spaceship, is moving at a very high percentage of the speed of light, then the “time dilation” becomes pronounced and it’s possible to go to a star 20 light years distant and yet only age a few years. And they said that if someone was looking at your spaceship while it was crowding lightspeed, they’d see it contracted in the direction of travel, so that a 1000-meter long spaceship might look like it’s only 100 meters long.
We’ll leave the facts (such as they are) about time dilation to another column, but in the case of length contraction, it is not at all the case that the spaceship will necessarily look contracted. In fact, if the spaceship is coming toward you, it will look longer, and if it’s going away from you, it will look much shorter than the relativistic length contraction suggests it should. And the fact of the matter is that this reality was known certainly by 1960, since it was published in the American Journal of Physics then, and the findings have never been in dispute.
Indeed, let’s see what a couple of modern books have to say about this matter.
One of them is an educated layman’s book called Simply Einstein: Relativity Demystified by Richard Wolfson (1). Ironically, given the title, Wolfson has very little to say about the issue, just a few paragraphs worth. But a couple of sentences from pages 116-7 go like this: “However, that doesn’t mean you see the object contracted.” And: “Remarkably, the object appears not contracted but rotated!” (Italics in original.)
The other is a graduate level well-respected textbook called Classical Electrodynamics (3rd Ed.) by John David Jackson, one of the most respected references in the field of E&M (2). Jackson has nothing to say about the subject except in the suggested reading section of chapter 11, the chapter on special relativity. On page 567 it reads: “Another neglected subject is the appearance of rapidly moving objects. This fascinating topic illustrates how careful one must be with concepts such as the FitzGerald-Lorentz contraction.” He then lists five journal references on the subject.
An exceptionally straightforward account of what you can expect to see when observing a moving object is “Observation of Length by a Single Observer,” by Roy Weinstein (3). (Note: Jackson neglected to mention this one, but to me it looks like it is the most accessible to the educated layman, and it is the one from 1960 that I mentioned above.) Weinstein does a good job of describing how Einstein’s measurement method requires two observers with synchronized clocks, one noting the position of the front, and the other the position of the back of say a moving rod, at the same time. (As it turns out, it isn’t even possible for anyone to actually do this measurement.) The difference between the position of the front and back is then found, and this is defined to be the length of the moving rod.
Weinstein says (p. 608 of ref. 3): “As a result of (the usual length contraction equation), educators from Einstein to Gamow have concluded that an observer sees the rapidly moving rod contracted. An observer seeing the meter stick, however, are words describing a particular experiment, and it is easily seen that the experiment consisting of a single observer viewing a rod is not the experiment described by the Lorentz-Fitzgerald contraction.” (No, I didn’t screw up earlier—Jackson uses “Fitzgerald-Lorentz.”)
Weinstein demonstrates that what you actually see depends upon how fast the rod is moving and whether or not it is approaching or receding from you. In the former case, you see the front of the rod at one time and the back of the rod from a time earlier than that because of the light speed delay, so the rod looks longer. In the latter case, you are seeing the front of the rod from an earlier time, but since it’s now moving away, earlier means it is closer to you, so the rod looks shorter.
You may have heard that fast moving objects look rotated, but this is only somewhat true for objects sufficiently far away—if you’re within five feet of a passing ten-foot rod, there’s no way it can look rotated.
Bear in mind that how the object looks is almost entirely a classical effect, due simply to the finite speed of light. Weinstein says that the only time a single observer can see the Lorentz-contracted length of the rod is when he’s at right angles to it. But if this is true, why do we need two observers? Can’t we just have one observer taking his measurements when the rod is dead center? Of course, judging when the rod is “dead center” isn’t going to be easy, since the receding front will look closer to you than the approaching back even when you’re “really at” the midpoint. Even with two observers, for each to be exactly orthogonal to the respective front or back of the rod when the measurements are made, they’d have to know ahead of time what the measurement was going to be so they could position themselves accordingly. Absent that knowledge—well, you’d need an infinite number of observers with an infinite number of synchronized clocks to get the measurement right, although the observers wouldn’t be able to agree on what the answer is.
Still, Weinstein claims that an observer will see the expected contracted length of the rod when he’s orthogonal to the midpoint of the rod as it’s passing. However, he doesn’t derive this—he just adds it in to the classical effects.
The real question is, does length contraction happen at all?
The best discussion I know of which is devoted specifically to the topic is in Oleg D. Jefimenko’s Electromagnetic Retardation and Theory of Relativity (4) where he specifically says that length contraction doesn’t happen. (He also lists for further reading most of the same references that Jackson does, and a few later ones—even in Jackson’s 3rd Ed. his refs only go to 1970 or so. By the way, “Jefimenko’s Equations” are discussed in Jackson.) In the book, Jefimenko derives all of the equations of relativistic electrodynamics just by using retardation (“retardation” is the technical term for explicitly taking into account the light speed limitation of electromagnetic interactions). That is to say, SR is a short cut—albeit a valid short cut in most (but not all) cases. Retardation is more fundamental than SR, requiring no postulates and simply the experimental fact of c-speed EM interactions. (I gave Jefimenko’s book a short review in my April 2003 column. It’s a bit math heavy for the average Joe, but Jefimenko does all the derivations in full using just vector calculus with retarded quantities, so the discussion is about as transparent as it can get mathematically.)
The first sentence of chapter 9 reads: “There is a wide-spread belief that according to relativity theory the length of a body becomes shorter when the body moves. This is incorrect.” By way of proof, in earlier chapters Jefimenko calculates for a line of charge moving in the direction of its length (i.e., the rod is charged), the resultant electric forces measured (experienced) in the rest frame. The motion makes it seem longer than it really is if it’s moving toward you. This is in accord with what Weinstein says happens visually. But in chapter 9 Jefimenko shows that if you try to calculate the correct expression for the field of a moving line charge, putting in the Lorentz-contracted length, which Weinstein does in his paper for the visual appearance, leads to the wrong result.
Cutting to the chase, we have this from pg. 209: “Taking into account that in chapters 6 and 7 we obtained correct relativistic transformation equations on the basis of the retarded length and volume of moving charge distributions, taking into account that Lorentz contraction requires not one but two observers (two points of observation) for its exact manifestation, and taking into account that electromagnetic fields and light propagate with the same speed, we have hardly any choice but to conclude that the relativistically correct visual shape of a moving body is its retarded shape. We then also have a clear answer to why the retarded field theory, without using Lorentz contraction for determining the effective shape of a moving charge, yields relativistically correct fields of the charge. The answer is very simple: as a physical phenomenon the relativistic (kinematic) Lorentz contraction does not exist. And the fact that the several revisions of this concept had no ill effect on relativistic electrodynamics or on any other branch of physics is an excellent indication that the concept does not represent a physical phenomenon in the conventional sense.”
For those of you grinding your teeth right now, what’s worth knowing at this point is that Jefimenko is by no means an “anti-relativist.” He is not at all arguing that relativity is wrong—he is arguing that the correct application of the relativistic transformation equations to the problem of moving line charges (and moving rods) does not support the idea of real shrinkage. He even shows how several so-called “contradictions” in SR, used by some anti-relativists to discard relativity as wrong, are not contradictions at all, but rather a misapplication of the “coordinate transformation machinery.”
Never one to shrink from a controversy, I agree with Jefimenko’s analysis. To disagree with him I’d have to refute some rather straightforward math. But there is nothing wrong with the math (the guy has equations named after him, for Pete’s sake). Also, the rigorous employment of retardation to electrodynamics is a more fundamental way of doing physics than are the postulates of relativity. And as the book shows, retardation predicts the same tested and accepted results for experiments that relativity does.
In that light, it is simply unscientific to continue to think that length contraction is “real” in the sense we were all taught.
The author would like to thank for their inspiration those persons at the Analog forum who were discussing relativity theory around the time this column was coming due.
References
1. Wolfson, Richard, Simply Einstein: Relativity Demystified, W. W. Norton & Company, 2003. ISBN 0-393-05154-4
2. Jackson, John David, Classical Electrodynamics, 3rd Ed., Wiley, 1999. ISBN 0-471-30932-X
3. Weinstein, Roy, “Observation of Length by a Single Observer,” American Journal of Physics, Vol. 28, No.7, Oct. 1960, pp. 607-610.
4. Jefimenko, Oleg D., Electromagnetic Retardation and Theory of Relativity, Electret Scientific Co, 1997. ISBN 0-917406-21-4
