Tom Palmer

For phillip1882-- I am a "retiree" from this thread, but I have to reply to your recent posting. Back in 2005 I had submitted a number of postings, a few of which happen to address concerns you mentioned. You might want to go back and read them. Posting #157 is entitled "The Final Theory - NOT (Part 2)" and deals with the fact that in a vacuum bodies fall at the same rate regardless of their mass. Posting #223 is entitled "Origin of the tides," and my follow-up Posting #241 ("Re: The origin of tides") included an explanation of the tidal twin-bulge phenomenon. I would also like to suggest that you read posting #154 ("The Final Theory - NOT"). I hope you find these postings helpful. Best regards. Tom Palmer

:rolleyes: I can only agree with you, Beagleworth. I can't say I was totally thrilled with that ridiculously large margin of error, either. But one thing about cutting-edge experiments: other laboratories always try to see if they can duplicate—and then improve on—any published results. Or discredit them—physics can be a competitive, even cutthroat, business sometimes. So perhaps some day soon we'll have better numbers. But in the meantime, you're certainly entitled to any doubts you might have. By the way, thank you for your kind thoughts on my "Galveston" post. Tom Palmer

Just a sad sidebar to the main “text” of our discussion. We’ve all been shaken by the horrors of Hurricane Katrina, and now the looming menace that the people of Galveston, Texas, face as Hurricane Rita approaches. As news reports are currently recalling, this is a horrible déjà vu for that beleaguered city. Back on September 8, 1900, Galveston was devastated, experiencing the worst loss of life the U.S. has ever suffered from any natural disaster—over 6,000 dead. While the fierce winds of that Category-4 hurricane (or “tropical cyclone,” as hurricanes were then known) were certainly a significant factor, the deadliest factors were the flood waters and storm surges. Galveston was particularly vulnerable to high water because it is an island, and on that night a 15½-foot-high storm surge rolled over the island, battering and essentially drowning it. There have been more ferocious hurricanes since, but there was one unusual circumstance that made this one the most brutal of them all. It had occurred during a proxigean tide. This may or may not prove anything one way or the other as far as our discussions go. But I find it ironic that we had just been discussing this exotic force of nature when media reports suddenly reminded us of its terrible potential for tragedy. I guess it is a sobering reminder that there is a human dimension to the “technical” points we discuss. Tom Palmer

Steve, I was working on a reply to your request for help in visualizing the “speed-of-light-equals-speed-of-gravity” example I had posted. I was getting pretty deeply into vector increments and the like, and I doubt it would have been very “visualizable” by the time I would have finished it. Last night, just before dropping off to sleep, a nice visualizable example popped into my head. :rolleyes: Have you ever heard a jet plane going overhead, only to discover that the plane itself seemed to be well ahead of where the sound seemed to be coming from? Of course, this is easily understood once we realize that sound travels far more slowly than light. At any given moment, we are seeing the plane where it was just microseconds ago, thanks to the incredible speed of light. But at that same moment, we are hearing the plane via the sound produced several long seconds ago. (This is the same reason we see the lightning before we hear the thunder.) The sound being heard at the present moment “points” to that part of the sky where the plane was when the sound was produced. You could say that the planes’s optical image is always ahead of the plane’s “sonic image,” which lags behind due to the slower speed of sound. The farther away the plane is, the greater the disparity between the two “images.” (“Optical” will here be understood to include all forms of electromagnetic radiation.) Similarly, a planet should have a “gravitational image” as well as an optical image. At any given moment, our hypothetical spacecraft is receiving an additional “tug” from the planet’s gravity. This tug is toward the direction of where the planet was when those particular gravitons or gravitational waves or whatever were emitted by the planet’s mass, and with a strength inversely proportional to the square of our present distance from where the planet was at that earlier time. In other words, at this present moment the astronaut and his instruments optically see the planet in a particular direction and at a particular distance. At that same moment, however, his instruments “see” the planet at some particular direction and distance based on the direction and strength (hence distance) of its gravitational pull on the spacecraft at that moment. If this “gravitational image” lags behind the optical image, then gravity must be slower than light. If it stays ahead of the optical image, then gravity must be faster than light. However, if the optical and gravitational “images” always coincide, then light and gravitation must both share the same speed. And that is what appears to be the case. By the way, the hyperlink I included in my previous post (#252) didn’t work, as you may have already discovered. However, my flash of enlightenment last night also told me why, so now the link is fixed and should work fine if you still want to read the article “Gravity and light move at the same speed.” Again—hope this helps. Tom Palmer

First, Steve, I should mention that the example I quoted there is a good indication that the speeds of gravity and light are equal, but in strict scientific terms does not constitute proof that gravity travels at the speed of light, or count as a “measurement” of that speed. In fact, the speed of gravity has been a hot topic among physicists because it depends on the speed of gravitational waves (general relativity), and these would be so exceedingly weak as to be undetectable—although precise measurements from binary pulsars have provided intriguing evidence of their existence. However, ingenuity triumphed, and now we have a bona fide measurement to back up Einstein’s assertion. You can find a brief summary of it at http://physicsweb.org/articles/news/7/1/2 ("Gravity and light move at the same speed"), and more detailed accounts at other sites. Hope this helps. Tom Palmer

Hello, everybody. I just discovered in my “physics” file an old draft that I never actually posted—why I didn’t, I have no idea. It was from back on August 16. I’ll post it now, out of order, rather than let it go to waste. For what it’s worth, here it is.—Tom Palmer Questor, you touched on a point that I’ve been itching to discuss: The “speed of gravity.” As you know, I have many objections to McCutcheon’s way of sidestepping, dismissing or “disproving” evidence which appears to support standard theory rather than his own theory of everything. But when I read that first chapter, one of the things that particularly outraged me was—as it appeared to me, at least—his cunning deception about the speed of gravity. First, he informs the reader that in Newton’s view gravity is instantaneous—that is, if body A suddenly changes position, body B will “feel” the resulting gravitational effect at that same instant, regardless of its distance from body A.. Now, it’s true enough that this effect is implicit in Newton’s model—and this keeps the equations simpler than they would otherwise be. McCutcheon then informs the reader that in Einstein’s general theory of gravitation, gravity requires time to traverse distance, which is true. His opinion: “However, this is only a proposed solution since the actual speed of gravity is unknown—no direct tests have been done to determine it.” (p. 26) First of all, that jest ain’t so. A space probe, as it approaches a massive planet like Jupiter or Saturn, speeds up just as one would expect, so the distance separating the planet and the probe is continuously changing. If the gravitational effect of this continually changing position (with respect to the probe) didn’t propagate at exactly the speed of light—and neither more nor less—the cumulative effect would eventually become strikingly evident in the growing disparity between the visual images and ranging measurements of the planet’s apparent (i.e., “optical”) location, on the one hand, and the changing rates of gravitationally-induced acceleration of the probe on the other. McCutcheon really doesn’t want to concede that Einstein might have been right, and so implies that his ‘finite speed of gravity’ view is unsatisfactory and is yet unproven. He concludes: “So, we have the choice of Newton’s simple and intuitive theory, which violates the speed-of-light limit, or Einstein’s complex and mysterious theory, which offers an unproven solution to this violation.” Despite its starting out with a correct statement, that is a truly terrible sentence (alas, just one among many). For one thing, it implies that neither theory is really satisfactory, and therefore only McCutcheon’s can be right—Hobson’s choice. For another, it alleges that the Newton and the Einstein theories are fundamentally different and hopelessly at odds (“simple and intuitive...violates...etc.” versus “complex and mysterious...unproven solution...etc.”). This allegation is simply not true. The truth of the matter is that Newton’s theory can be derived as an approximation of Einstein’s general theory of relativity in the limit of infinite light-speed in a Euclidean (“flat”) spacetime. As such, its general validity for lower-speed (“non-relativistic”) phenomena has been abundantly confirmed. In fact,“approximatibility” (new-word alert!) is the general case when comparing the relationship between an older theory which was reasonably valid within certain limits, and its newer, more precise, more broadly applicable replacement. Old theories never die—they just get upgraded. Tom Palmer

Steve, Thanks for the reply and the quotes about tides from McC’s book. Before I weigh in with my thoughts, please be assured that it is McC who is on the hot seat here, not your estimable self! In fact, it is only thanks to you that I can even do this. Repeater makes a good point when he asks I thought the same thing when I read McC’s quote. In line with Repeater’s observation about lunar gravitation being the simpler explanation, it may suffice to note that a proxigean tide—the granddaddy of them all, a spring tide on steroids—will only occur when the moon is nearest the earth (and on the same side of earth as the sun). So the proximity of the moon (further enhanced by the solar contribution) at this time obviously has a great deal to do with the exceptional magnitude of the resulting tide. I see nothing in McC’s rationale that would, or even could, account for the uncommon intensity of a proxigean tide. I have every confidence that he could—or perhaps somewhere in those seven pages even has—come up with a way around it. He’s good at that sort of thing. But it would likely be just another ad-hoc conjectural complication. As I had mentioned, the beauty of gravitation theory is that it explains all the tide varieties in one fell swoop, all with the same simple “GmM/r**2.” Another hurdle McC must surmount: The “tidal bulge” has a twin—another almost-identical bulge occurring simultaneously on the opposite side of the earth. Notice how the inverse-square law of Newton’s equation so nicely accounts for the twin-bulge phenomenon. The oceans are fluid, highly deformable. The solid earth, on the other hand, is a coherent, essentially rigid body. The side of the solid earth facing the moon is closer to it and thus more strongly attracted than the opposite side of the earth, which at the equator is 8,000 miles farther from the moon—giving a significant gravitational force differential. But since the solid body of the earth is not very deformable, both the near and the far sides (and everything in between) will only move in tandem. (The solid earth does have a slight deformability; that is why there are also very weak “earth tides” and even “atmospheric tides.”) So the solid body of the earth as a single indivisible entity moves as a whole, in accord with its gravitational average, which would be about the same as the pull felt at its midpoint, the center of the earth. The water on the side facing the moon is roughly 3 percent more strongly attracted than the “averaged-out” solid earth, so the oceans move toward the moon while the solid earth lags behind, thus creating a frontal water bulge. Meanwhile, back at the ranch—on the other, far side of the earth, the water is roughly 3 percent less strongly attracted to the moon than is the earth’s solid body. So this time, the solid earth as a whole is the more strongly attracted of the two, while the far-side oceans lag behind, thus creating another water bulge, antipodal to the frontal one. It is basically simple, but hard to explain (as you can see from my labored attempts). Please let me know if you need further clarification. Thanks again. Tom Palmer

Thanks, Steve, for the offer of the book loan. I appreciate it, but I wouldn’t want to put you to that effort or expense. And there’s no need to transcribe—perhaps illegally—the seven pages about tides. All I’m really after is the bare-bones conceptual foundation of McC’s “non-gravitational” explanation of the tides. Specifically, I would like to know how, within the parameters of his model, he can explain all of these observationally-verified facts: 1. Although precise Tide Tables for particular locations are complicated by local factors (e.g., coastal variations), the tides basically “follow the moon.” Although occurring twice daily due to the rotation of the earth, this diurnal pattern is continually drifting in sync with the lunar cycles. 2. The stronger tides (“spring tides”) occur when the sun, moon and earth are in a line, and therefore when there is a new moon or a full moon. 3. The weaker tides (“neap tides”) occur when the sun and moon are closer to right angles with respect to the earth. 4. The strongest tides of all are the rarer “proxigean tides,” and these always occur when the moon is unusually close to the earth (at or near its closest perigee—the “proxigee”) and the moon is between the sun and the earth (i.e., new-moon phase). All these facts are readily explained by basic gravitational theory—in fact, are required by it— and it is not surprising that, in the second volume of his Principia, Isaac Newton was the first to demonstrate this. It is important to note that in gravitational theory all of these phenomena share the same basic, straightforward explanation. Newton didn’t have to find a different way to explain each one. Any competing theory will have to be able to do the same thing. Not separate, custom-made explanations, but one simple all-encompassing explanation, in the spirit of “Occam’s razor.” And there is one other constraint on McC’s non-Newtonian alternative. If, as I understand it, McC explains the tides as arising from the wobble of the earth’s axis, then he has the burden of explaining why it is that the tidal cycles are many orders of magnitude out of sync with that slow wobble, while at the same time they are in such precise synchronization with the solar-lunar cycles. The main component of the “wobble” is the precession of the equinoxes. I hope McC doesn’t attribute the tides to the torque from it, because it takes about 25,800 years to complete a single cycle. Other, lesser effects add their own contribution; the largest of these “nutations” does arise from the moon’s gravitational effect on the earth’s bulges. However, that fact cannot reasonably be of much use to McC, for this oscillation has a period of about 18.6 years. Another very slight component is the so-called “Chandler Wobble.” It has a period of 435 days. That is approximately 14.5 months, and so of little use, I would think, to McC. There are other, even smaller, corrections as well. All of the “world-wide wobblies” taken together have a minuscule effect on the length of the day (the variations adding up to only a few milliseconds). Some are so tiny that they have yet to be detected. I hope McC states his conceptual bases in such a way that you won’t have to hunt through those seven pages trying to chase down each piece of the puzzle. If his theory really works, the same one answer should be sufficient to meet all of these challenges. And keep in mind that, under the doctrine of “fair use,” you are legally permitted to quote brief passages from the book. Thanks again for the offer. I’ll look forward to your thoughts. Tom Palmer

Thanks, Buffy, for cutting me more slack than I probably deserve. That last sentence of yours really hit the nail on the head. With no discernible progress, despite some powerful refutations you and others have posted, exasperation can indeed "slip out"---and did. But I do need to apologize to other posters who are just trying to figure out where the truth lies. Honest, I wasn't mad at you folks---I'm mad at Mr. McCutcheon, but you're the ones who got dumped on. As other recent postings acknowledged, you are mostly gentle, noncombative individuals who have been impressed with "The Final Theory" and are simply trying to see that it gets a fair hearing. Mr. McC, on the other hand, is anything but "gentle and noncombative," and my characterization of his animus to Newton et al. as "scornfully dismissive" is something I firmly stand by. Believe me, you're nicer than he is. Beagleworth, I especially want to apologize to you. You came on board, you said, in part because there was a tone of civility in our discussions. I hope you will stay. Boerseun, I notice that I misspelled your name, and am sorry about that. I think I got it right this time. Afrikaans isn't exactly my strong suit. There was one paragraph in my diatribe that nobody quoted (though Buffy touched on it), and it is really the heart of what I was saying: <<As I said, I sometimes despair. I despair because, despite the fact that some pretty powerful and decisive disproofs of McC have been posted, it didn't seem to make any difference. Is anyone really listening? A few, at least, have sought clarification on some of our points, and I respect them for that.>> "It didn't seem to make any difference. Is anyone really listening?" Buffy has put some potent arguments out there, but they're just lying there, unanswered. And back on my posting #154, I put out what I thought was a pretty fundamental failing of McC's "mass-is-irrelevant" claim, along with some heavy supporting evidence. I thought it might get some strong reactions, but---apart from a much-appreciated thumbs-up from Buffy---I can't say that it did. But then, no one is under any obligation to answer any particular point; after all, I've passed on answering some questions that my postings did manage to elicit, and I'm grateful to Buffy for fielding some of these. But here is a point I hope one or more of you will comment on. I understand that McC attributes the lunar tides to the known wobble of the earth's axis---and not at all related to the moon's gravity. Is this what he actually says? If not, what does he say? If it is what he says, do any of you out there want to undertake the unenviable task of trying to justify it? Some of the questions that have been raised in this thread are imponderables that, without a rigorous mathematical treatment, cannot really be decided one way or the other. But the question of the origin of tides is clear-cut and specific, and should at least be basically resolvable without recourse to the math. In a spirit of mutual respect---let's have at it! Any takers? Tom Palmer

I heartily second the motion. I sometimes despair that anything will get resolved in this thread, but every now and then cooler heads prevail. CraigD, Boersun, ColdCreation, and my friend and resident slayer Buffy, and doubtless others I have missed--all of you solidly enough grounded in real physics to see through the arrant nonsense of "McCutcheonism" (or, more accurately, "McBaloneyism"). And friend Repeater, who genuinely wants to know the truth, wherever it lies--and deserves better than the pseudo-intellectual obfuscations coming from the pro-McC camp. So, for those who remain committed to McC, I offer you words of comfort: I confess--every physicist knows in his or her heart that Mr. McCutcheon, and he alone, has found the true and ultimate "Final Theory of Everything and Then Some," and that our own wacko theories are all wrong. I admit it--we who uphold conventional physics have been thoroughly deluded and are mere pawns in a vast supergalactic conspiracy dedicated to crushing scientific truth and promoting a bogus physics whose only justification is the flimsy excuse that modern physics has given humankind incredible, unimaginable wonders and sent out probes to touch other worlds. Obviously, all of that counts for nothing. It may be tactless to be so blunt, but the time has come to say it: The extent to which you were convinced by McC was in inverse proportion to your knowledge of present-day physics. He was counting on your unfamiliarity with the nuts and bolts of modern physics. "Frankly, my dear," you have been suckered. Please don't feel too hurt by this sting of this statement, for you are not alone. I was once suckered by an unscrupulous roofing contractor named Andy Kutscher. Mr. Kutscher is now cooling his heels in a state "facility" for such as him. It is only coincidence that "Kutscher" and "McCutcheon" have a somewhat similar ring, but there is a certain irony in it for me. As I said, I sometimes despair. I despair because, despite the fact that some pretty powerful and decisive disproofs of McC have been posted, it didn't seem to make any difference. Is anyone really listening? A few, at least, have sought clarification on some of our points, and I respect them for that. So, to all of you who still want to live in McCutcheonville---here is your assignment: Get yourselves a real physics book that is geared to the general public, and start boning up. And don't let that McCutcheon-induced skepticism keep you from seeing the validity of what you read. Healthy skepticism is fine, but not the scornful dismissiveness he "taught" you to have. Really, you should never have let McC into your heads before you first took this step, but perhaps it isn't too late to combat the infection. I have progressively tired of fighting this battle, and I thank Buffy and others who have posted their intelligent, insightful replies. You have fought the good fight---keep it up. Tom Palmer

Hi, Repeater, Thanks very much for your posting. First, Roger and the cheese. A splendid illustration of potential energy! I wish I could carry out this same experiment so as to speak with some assurance on the matter—but I can’t. You see, our little pet is Rosie the guinea pig. (Actually, I should say “was”—sadly.) So there are at least two factors preventing me from duplicating your success. Factor One: Guinea pigs, as far as I know, aren’t into cheese—just lettuce, carrots, pumpkin seeds, etc. Factor Two: Guinea pigs have no tails. Many years ago, wife Fay and I had two white mice, Dynamo and Geronimo. Unfortunately, it never occurred to me that our little “Mo”s held the secrets of the universe in their little rodent tails. (I’m sure that, by this point, everyone else on this thread is thoroughly grossed out.) Re your request for references on the increased weight attributable to potential energy. First, I should clarify in what sense this is true. When the two magnets (the “system”) are pulled apart, energy has been added to that system—obviously. Energy is conserved, so where is that energy that I just put into the system? One of the counterintuitive things about potential energy is that, strictly speaking, you can’t really assign it a particular point location in space, because it is “energy of position.” It exists by virtue of the relative positions of—in this case—the two magnets after they’ve been pulled apart. Sprinkle some iron filings on the table in the space separating them, and the filings will immediately arrange themselves in a neat, unmistakable pattern displaying what Faraday called “lines of force,” showing that something is definitely going on in that separation. A study of these patterns, and the behavior of the magnets themselves when finally released to snap back together, both confirm that the farther apart the magnets are pulled, the greater the total potential energy that has been added to the system. And that makes sense, because we have been progressively adding energy to the system, and it has to be somewhere. However, that energy should manifest itself as a very slight increase in the weight of the system. We have empirical evidence of this in the atomic nucleus, which I had discussed right after my remarks on magnets. Here, the “weight” of the potential energy is, in effect, determined by measuring the mass of the nucleus as a whole, then measuring the mass of the individual components after they have been separated. I had alluded to Hiroshima and Nagasaki, and there is no better (or, in another sense, worse) example of the power of unleashed potential energy becoming all too kinetic and radiative. And it had all been successfully figured out in advance because the theory behind it was evidently right. A uranium-235 nucleus absorbs a slow neutron and becomes the highly unstable isotope U-236 as a result. The instability means that the nucleons are not as tightly bound anymore. The U-236 nucleus achieves greater stability by splitting into two smaller nuclei— barium-141 and krypton-92. Three (sometimes two) more slow neutrons are also released, which continue the chain reaction. The barium and krypton nuclei are more stable, hence more tightly bound. That is, their nuclear potential energies are less than the potential energy that had existed in the more loosely bound U-236 nucleus. The forces inside a nucleus are enormous, far exceeding anything else in the world, so we’re talking a heap of energy here. So if you add up the masses of the barium nucleus, krypton nucleus, and the two or three slow neutrons, it comes out a little less that the mass of the original U-236 nucleus. And the whole world trembles at that “little less.” It is, in effect, a potential-energy difference that expresses itself in the release of powerful gamma radiation, and also in the enormously high kinetic energy of the resulting nuclei. However, you were interested in experimental evidence of a weight gain in the two magnets when pulled apart, and on that I can’t deliver. The above example assures scientists that it is there, as do the evidences of the energy spent to create potential energy (e.g., pulling the magnets apart) . Here’s why I can’t give you direct evidence for potential energy from magnetism or gravitation. It’s a quote I’m copying in here from a science website: <<Everyday matter is given its stability by chemical bonds between its atoms and/or molecules. However, such chemical bonds are much too weak, the associated binding energies much too small to result in measurable mass defects - typical values are in the range of a hundredth of thousandth or even of a millionth of the mass of an electron. The forces binding protons and neutrons together to form atomic nuclei are considerably stronger, with binding energies that are a few million or even billion times larger than those of chemical bonds. In consequence, mass defects correspond to the masses of a few dozen or even a few hundred electrons. That is well within the range of precision mass measurements.>> So the numbers themselves tell us that the quantities of potential energy in non-nuclear situations are simply too small to be measured currently. Even though the indirect evidence tells us the magnets would weigh more when separated, I’m sorry I confused the issue—I should have saved my remark about “detectable and measurable” for the paragraphs following. My best regards to Roger. Give him an extra piece of cheese for me. Tom Palmer

Buffy—now it’s my turn to say “Wow!” Your response to Questor’s concerns was absolutely masterful, and everything you said was right on target. To tell the truth, I was getting a little weary, and was not particularly looking forward to making the effort. Thanks to you, the job has been taken care of. It was outstanding, and better than anything I would have come up with. You really nailed the fallacies in McCutcheon’s objections to the Big Bang, and especially the all-important point that the BB shouldn’t be thought of as an “explosion.” That misconception trips up a lot of people—though most of them aren’t as anxious to trip over it as Mr. McCutcheon was. I’m especially glad you addressed the matter of elliptical orbits—I had hated to leave that part out but just wasn’t motivated enough to get into it. And another good point you made: That orbits do degrade in time due to occasional encounters with other matter. In fact, I seem to recall reading once that the moon is gradually losing orbital energy through the interactions that produce the tides. I’m also glad you mentioned angular momentum. One thing that has been consistently missing from the discussions is momentum—linear and angular—and their conservation laws. Everybody has been hung up over energy (which McCutcheon seems to confuse with “power,” even using the terms interchangeably), as if it were the sole dynamic quantity. I’m sure you know this already, but I’ll mention it for the other readers: In relativistic physics, time and the three dimensions of space are wed in four-vector union, and it is only the so-called “invariant space-time interval” that is independent of coordinate system. Among its analogues are energy and the three components of momentum (and their corresponding invariant). So in relativistic physics, treating energy alone—à la McCutcheon—and leaving out momentum (or vice versa) will guarantee failure. But, considering what McCutcheon has done with energy, I shudder to think what he would do with momentum. You made many other equally commendable points, Buffy, but I’ll hold it here. Again—a superb job. You really know your physics and cosmology. Tom Palmer

It is good to hear from you again, Buffy from Oakland (or is it Sunnydale?). Thanks for the vote of confidence. :) Thank you, too, Questor, for your questions. I’ll try to hit them all (though not in order). I’ll just go a little crazy here, let the juices flow, and hope that the results will be at least marginally coherent. :) You asked, “What is the energy source that has propelled the earth around the sun for billions of years at a constant speed?” I’d like to clear up, if I can, a glaring misconception Mr. McCutcheon has attempted to plant in the minds of his readers. He portrays a source of gravity (such as the sun) as if it were continuously pouring out energy from some mysterious “bottomless well” of the stuff (and magnets, ditto). Then, as this emitted energy supposedly flies off into the unknown, a new wave of emitted energy takes its place, and so on, ad infinitum. He implies (quite correctly) that this is ridiculous, but that his model (quite incorrectly) sets thing right again. What he has done here is to set up a straw man, which he then proceeds to knock down. In no way, however, does his “straw man” actually represent what is believed about the gravitational field today or in the last 300 years. Energy is not continuously generated by a gravitational source. Rather, the gravitational field itself contains potential energy, and that energy stays put in the gravitational field until another body “converts” it to kinetic energy. (It’s a little tough to explain without the math.) Consider a two-body system such as the sun and the earth. Both are orbiting their common center of mass (about which I wrote previously) . This is a stable, self-sustaining system. Over the eons, it has achieved equilibrium. The gravitational energy which “drives” the motions of the bodies never leaves the system, nor does any “new” energy come in. It is a fallacy to think that new energy must constantly be supplied as old energy purportedly leaves. If the average radius of the earth’s orbit were to become progressively longer, then that would indicate “new” energy being added to the system. That it remains the same means that no “new” energy is coming in, but also that it is not losing its present energy, either. Remember the law of inertia: “A body will preserve its velocity (i.e., speed and direction) so long as no force in that same direction acts upon it.” This is a modern restatement of Newton’s first law of motion (though Galileo and his pupils, and later Decartes, also did their part). Up to Galileo’s time, Aristotle’s notion had been dominant. Aristotle had taught that it takes force to keep a body in motion. He really blew that one, and it wasn’t his only blunder. But you can see why this misconception lasted so long. Down here on the earth, any moving body gradually slows down and eventually comes to a halt. Of course, we now realize that friction and air resistance are the energy thieves who drain the body’s kinetic energy, gradually converting it to mostly heat energy (which still involves motion, but at the molecular level). As long as nothing is “stealing” that body’s energy (or adding to it), it will continue in motion at a constant velocity. And there is no friction or air resistance to slow the earth’s passage through empty space. So it is able to hang onto its energy for orbit after orbit after orbit. In physics, “velocity” indicates both speed and direction. This inertial velocity of the earth is therefore a vector quantity. However, the earth is in the sun’s powerful gravitational field, so there is another vector to consider: the pull of the sun. In a circular orbit, this second vector is always at right angles to the inertial velocity vector. Try to picture this: The earth’s orbital velocity can only keep it moving in a straight line at any given instant. But the sun’s gravitational field simultaneously pulls it directly toward the sun. The vector sum of these two forces in that instant is a diagonal “compromise” vector. In that instant, the earth doesn’t go straight ahead, as its velocity would like, nor does it head directly for the sun, as the sun’s field vector would like. Rather, it goes in an in-between direction. Since the sun’s gravity did succeed in getting it a little closer to the sun than it had been, you might think that we’re all going to be getting very warm very soon. But not so. Because while the earth was getting a little closer to the sun, that other, “straight-ahead” vector was going at right angles to the direction of the sun, and therefore the earth actually ended up a little farther from the sun than it was the instant before. In a circular orbit, these two effects—the sun’s field pulling us toward the sun, the earth’s inertia simultaneously pulling us at right angles away from the sun—mutually cancel out, exactly. So we didn’t really get a little closer to the sun in that instant, but stayed at the exact same distance, but in a slightly different orbital position. So I lied—so sue me. It’s a little more complicated for an elliptical orbit, but the same thing basically happens there, too. It’s hard to put into words, but the mathematics of it is beautiful—though one needs a background in differential and integral calculus to perceive that beauty. (Incidentally, Newton invented calculus—as Leibniz did also, independently—and he did it in order to do the math for his Principia.) Questor, you also asked: “What is the source of the energy that produces gravitational pull? Why does it not dissipate?” As you might see now, the question should be “Why would it be expected to dissipate?” Potential energy is not like radiation energy, which cannot be held in one place. It’s just that a body which is a certain distance from, say, the earth has an implied potential energy available to it by virtue of its position. In other words, a certain amount of energy had to have been expended to counteract the earth’s pull and get that body out to that particular distance away from the earth in the first place. The body will now reclaim that energy (unless some countering force prevents it) by accelerating toward the earth, converting that potential energy into kinetic energy. As for the question: “Since the orbit is elliptical and the earth is closer to the sun at times, why does the greater mass of the sun not pull the earth into it?”—I haven’t discussed elliptical orbits because they are more complex, even though the same basic principles we have considered apply to them, too. It might be helpful, though, for me to mention that the earth’s orbital velocity becomes greater, the closer it gets to the sun (and again slows as its distance increases). You are right—it takes a greater orbital velocity to counteract the greater pull near the sun. The beauty of this is that the energy of the sun’s gravitational field is naturally greater closer to the sun (just as its brightness is greater). So the earth has more potential energy available to convert to kinetic energy at those close encounters, and so speeds up. Then, as it heads back out to the far end of the orbit, the earth slows again, in effect returning the excess kinetic energy to the potential-energy field. The process is repeated on the next orbit, and on and on. No new energy, just the same old energy endlessly recycled. And why not? The remaining question: “Since Pluto has such a small mass and is in an orbit, why does it not escape the pull of the sun's gravity?” Remember, a gravitational field will give all bodies at any particular distance the same acceleration regardless of their masses. If Pluto were to suddenly lose most of its mass (also losing the kinetic energy of the vanished mass), it would still continue to move in its same exact orbit. Remember, too, that gravitation obeys an inverse-square law, which means that it never dies out completely, no matter how far out a body is. And since the nearest star is over four light-years away, there is no other “sun” in our neck of the woods to woo Pluto away from old Sol, even though the sun’s pull is exceedingly feeble that far out. In fact, there are substantial bodies in the remote Kuiper Belt (where shorter-period comets originate), and in the Oort Cloud. One such body recently discovered is believed to be more massive than Pluto, and it may currently be three times farther out than Pluto. Hope this helps. Tom Palmer

Today’s topic will be energy, with particular attention paid to Mr. McCutcheon’s oddly unphysical understanding of it. As he sees it, energy is endlessly pouring out from any source of gravitation or magnetism. We know this, he says, because you will expend your energy to the point of exhaustion trying to separate two strong magnets, but they will win in the end. You’ll run out of energy, but they never will. Here, he is confusing physiological energy with physical energy. To illustrate the importance of this distinction, imagine you have an extra little bone in your hand or arm. Now, this little hook-like bone is so designed that, if you choose, you can position your arm in a way that the hook will “catch” on another little specialized loop of bone. In other words, you could lock your arm and hand in a particular position. So, once you have tensed your muscles to their maximum extent, the “lock” will permit your muscles to relax again, but your arm to retain that tension without any further expenditure of energy. Without the lock, you were in effect having to continually replenish lost energy. That loss was due largely to the body’s restoring forces actively working against the muscle tension, thus requiring a continuing supply of energy to maintain the tension. The lost energy itself ended up in forms such as increased body heat due to a heightened metabolic rate. Now let’s eliminate the physiological factor by substituting a coiled spring for the human muscle. Again—two strong magnets, but this time held apart by the tension of that coiled spring positioned between them. Unlike the human muscle, the spring will prove equal to the task of everlastingly counterbalancing the force of attraction of the two magnets. Mr. McCutcheon’s basic problem seems to be a failure to understand the concept of potential energy, along with the related concept of field energy—he never even once mentions either of them in the fifty-odd pages of that first chapter, where they would be most relevant. (In fact, I get the distinct impression he doesn’t really want to understand them, perhaps sensing that they would throw a very large monkey wrench into his scheme.) Without getting into the quantum-mechanical aspects of the matter, we’ll just look at the simple dynamics of it. First, picture the two magnets as they long to be: devotedly clasped tightly together. Now you, the interloper, seek to disrupt this blissful union. By whatever means, you apply sufficient energy to each magnet to pull them apart, and then you interpose that coiled spring to keep them that way. The spring’s tension is the result of the energy expended to extend or compress it, and that energy still exists in the spring as potential energy. As for the two magnets, the energy you expended to pull them apart is now in the form of potential energy in the electromagnetic field between the magnets. Just as kinetic energy can be called “energy of motion,” potential energy can be called “energy of position.” It works out beautifully for planetary orbits. For example, Kepler’s three laws of planetary motion, of which Mr. McCutcheon speaks so approvingly, are readily explained in terms of gravitational field energy. In an elliptical orbit such as the planets have, the body’s kinetic energy will vary, but its gravitational potential energy always offsets it, so that the sum of a planet’s kinetic and potential energies is constant over time, hence conserved. But back to the magnets. You had to expend energy in order to counteract the force of attraction. You don’t need additional energy to maintain that separation, but you do have to supply energy to bring about the separation in the first place. Here’s an interesting—and very relevant—fact. Excluding the weight of the spring, that pair of magnets now weighs more than it did when the two were tightly together. (Of course, the difference is tiny, and utterly negligible in everyday life.) And that extra weight is, believe it or not, the energy you had to “spend” in order to force them apart. So potential energy is not just a conjuror’s trick to get equations to balance, but a bona fide detectable and measurable quantity. This effect is more pronounced in the atomic nucleus. There, protons and neutrons—collectively, nucleons—are bound via the “strong force,” one of the four fundamental forces (more properly termed “interactions”). But the mass of that nucleus is very slightly less than the combined masses of the bound nucleons as they would weigh in isolation, i.e., unbound. This so-called “mass defect” represents the amount of energy it would take to completely “pull apart” the nucleons until they were no longer within the (very short) range of the strong force. (I’m ignoring the effects of the nuclear electromagnetic and weak interactions here—they don’t materially affect the facts we are discussing.) The basic principle is the same as with the two magnets. Analogously, the magnets could be thought of as the “nucleons” electromagnetically bound together in a “nucleus” until sufficient energy is applied to overcome their mass deficit, which can be thought of as “negative” (or “missing”) energy being restored by an input of “positive energy.” The concepts of potential energy and field energy are very specific. The laws governing them are clear-cut and precise, and these are backed up by two centuries of observational and experimental evidence. Since he declined to even mention them, let alone give them entree into his model, I don’t know how Mr. McCutcheon feels about these forms of energy or the evidence supporting them. But if, as I suspect, he is less than enthusiastic about their validity, there are two cities in Japan where he may find the atmosphere singularly fitting for contemplation of potential energy, binding energy, and nuclear mass defect—and of their more questionable uses. Sixty years this month. Tom Palmer

First, my thanks to Buffy from Oakland for her kind remarks—Buffy, I hope I can live up to your expectations! Thank you, too, friend Repeater, for your thoughts—I do understand your feelings on the matter. My last three postings, in quick succession, left me a bit drained, so right now, I’m recharging my batteries. And when you’re about to turn 73, the ol’ recharge takes a little longer than in those long-vanished “days of yore.” Ah, well. That said, I can’t resist a few trenchant remarks on Mr. McCutcheon’s conclusion that, since the acceleration of falling bodies is not dependent on mass, this is somehow a further indication that the very concept of force is “fictitious” (pp. 27, 49 ff.). He says: “If a force were at work here, it would have to be quite a mysterious and unprecedented force indeed to achieve such a feat” (italics his). In truth, gravitation would be more “mysterious” if the rate of acceleration did depend on mass. Rather than simply pontificate on the matter, I will try to illustrate just where he veers off the road and into the ditch (assuming he was ever actually on the road). The gravitational field is generated by mass—or, more precisely, by energy in all forms, though matter (along with hard gamma radiation) is far and away the most concentrated form of energy, as shown by the ubiquitous E = mc^2. Therefore, we can think of any body as an aggregate of tiny little “mass units,” all of equal mass-energy. To make things easier, let’s call them “massons” (not a new particle—I never invent new particles on Saturdays—just a formalism to help visualize the unseen). Here’s the bottom line: When a body is falling, every masson in it accelerates at the same rate, because gravitation, unlike Mr. McCutcheon, doesn’t “see” the whole body as a single entity. Since gravitation deals exclusively with mass (energy), all it sees is a bunch of massons. In fact, it doesn’t even see the “bunch.” Just the individual massons. So it gives each masson the same exact tug. It is utterly irrelevant to the acceleration just how many massons are being tugged, because each one is being independently tugged and given the same acceleration. The fact that they are also bound to one another by internal forces (Van der Waals, etc.) is irrelevant, because they are all falling at the same rate. Even the energy in all the forces—molecular, atomic, nuclear—acting within the body are having their energy massons tugged at that same rate. One rate fits all. Yes, Mark, gravitation is an “unprecedented force indeed,” because no other known force is “driven” by mass/energy alone. So, your attempting to discredit gravitation by contrasting its “mysterious and unprecedented” behavior with that of other forces is pointless—not to mention misleading. :) Tom Palmer