Tom Bethel has been riding an anti-relativity-theory hobby horse for years. He has recently published an article questioning the theory of relativity in the American Spectator. I have never met Mr. Bethel. I am sure he is a fine fellow; but he should stick to subjects he knows something about. Bethel apparently learned what he knows about physics (obviously very little) from a now-deceased friend of his named Petr Beckmann. Bethel tells us that Beckmann was an engineer. I have enormous respect for engineers—as engineers. But knowledge of engineering in itself no more qualifies a person to talk about fundamental physics than does knowing about baseball or butterfly collecting.
To a non-scientist, maybe there is not much difference between electrical engineering and fundamental physics—they both deal with equations and with electromagnetic phenomena, after all. But that is like saying that because a civil engineer who designs bridges is dealing with gravitational forces and doing calculations involving them he is therefore also competent to discuss the ins and outs of Einstein’s theory of gravity.
Bethel refers to a $2,000 prize that awaits anyone who can disprove a certain one of Beckmann’s crackpot ideas about relativity theory. I will offer a prize of my own. I will pay Tom Bethel $2,000 out of my own pocket if he takes the following courses at a first rate research university and passes them with a grade of A- or better: Classical Electrodynamics I and II (at the level of either Griffith’s book or Jackson’s book), General Relativity, and any course that covers the Dirac equation and relativistic field theory. If he succeeds in doing that, he will at least know what he is talking about when it comes to relativity. Why is it that so many people think they can talk intelligently about extremely technical subjects without knowing anything about them?
To a person who has only cracked open a book on relativity theory written for laymen, relativity seems strange, complicated, unwieldy, and ugly. That is because the way it is often explained in such books (in terms of moving clocks and meter sticks, etc.) obscures what is really going on. One has to get to a certain level of mathematics and physics knowledge to get a clear picture, just as one has to reach a certain elevation in hiking in the mountains before the vistas open up and one sees clearly the lay of the land.
Donald Rumsfeld spoke about the “known unknowns” and the “unknown unknowns”. The world is full of people who think they know something about physics, but haven’t even the barest inkling of what it is that they don’t know.
There is a certain kind of humility that is not only a Christian virtue, but a necessary condition of remaining sane. I barely know the rules of football. I played touch football (very badly) as a child. I don’t follow the sport. Would I feel myself competent to advise Charlie Weis on what plays to call? I have never taken lessons in flying any kind of airplane. Would I climb into the cockpit of a 747 and try to fly it solo to London? I know nothing about accounting or tax law. Would I try to do Donald Trump’s taxes? I have never taken any courses in medicine. Would I try to do a heart transplant? The answer in every case is no. Why? Because I am not crazy. Competence in theoretical physics is no less difficult to achieve than any of those other skills.
November 6th, 2009 | 2:36 pm
You got it easy. I teach Political Science for a living. Try and find me an individual who doesn’t consider themselves an expert on just about every aspect of politics (even if they can’t name the Senators for their state or a single member of the Supreme Court.)
That being said, crackpots are the price we pay in an open society. It beats the alternatives.
November 6th, 2009 | 3:14 pm
Odd, I’ve read both Jackson and Beckmanm’s books and liked each: the Electrodynamics and History of Pi. But I know Beckmann is the one who tries to turn science into politics…
November 7th, 2009 | 12:18 am
Beckmann’s book “A History of Pi” was fun to read, when I came across it back around 1970. The author seemed intelligent but grotesquely opinionated. In the context of a whimsical book on the intertwining of the math connected to the number pi and general history, that was quite tolerable. In a more serious treatment of either history or science/math, his prejudices would quickly become annoying.
Beckmann’s dismissal of Aristotle (by comparing his prose as dense gibberish compared to the clarity of Archimedes) stands out as a pinnacle of philistinism. He couldn’t even begin to imagine that Aristotle was dealing with fundamental categorical issues which we take for granted — groundwork which made possible the confidence in mathematical analysis we and Archimedes (living a century after Aristotle) have in common.
November 7th, 2009 | 9:13 am
Ha, Rich, that’s similar to the experience that theology teachers have. Someone might not know Aquinas from Anselm or Q from Thomas – maybe they even unwaveringly affirm that God is that being which is really, really big and really, really loud – but boy do they have it all figured out!
November 7th, 2009 | 11:31 am
For a long time I was a reader of the American Spectator – back in the 90′s. And I was finishing a degree in Physics at the time. It was so embarrassing to read these occasional nutty-science articles of Tom Bethel.
He may be a good writer, and have some area in which he has expertise. But science is definitely not one of them. It’s really amazing that the Spectator continues to publish this junk.
November 7th, 2009 | 9:47 pm
Steve, thanks for taking Bethell to task (spelled with two Ls, btw). I just blogged on him (and Carver Mead) a few days ago.
One small thing: I don’t imagine Bethell would come out ahead monetarily if he took two courses at a major research university and you only gave him $2000. Have you checked the prices lately?
LG
November 7th, 2009 | 10:18 pm
Absolutely outstanding! I dealt with some of Bethell’s nonsense in an article I did years ago when he claimed, based on an ‘anonymous’ source (via ‘face on Mars;’ crackpot Tom Van Flandern), that Einstein supposedly fudged his GRT field equations to get the perihelion of Mercury. He is so utterly blinded by his hero worship of the late Petr Beckmann, that it never occurred to him to pass the latter’s material by some physicists with training in GRT.
November 7th, 2009 | 10:38 pm
What’s fascinating, and in the end kind of sad, is that Bethell’s (and Beckmann’s) resistance to relativity is ultimately egotistical (purely subjective). Because for whatever reason they cannot comprehend it, they assume that no one else can either and that it’s perfectly legitimate to dredge up any objection to it, however ill founded. (When Beckmann couldn’t get any physicists to agree with his arguments on the newsgroups, he started flame wars attacking them for ideological reasons.)
Professor Barr deserves our heartfelt thanks for calling this bluff.
November 8th, 2009 | 12:50 am
MR BARR DOESN’T KNOW THE FIRST THING . . .
I have never met Mr. Barr but in contrast to his speculation about me, I am not sure that he is a fine fellow. I hope he is, but I have my doubts. He thinks the way to dispute with people he disagrees with is to hurl insults at them — not the mark of a fine fellow.
When I read his piece about my article, I began to think Mr. Barr was describing himself. He shows no understanding of relativity at all. I mean really none. Maybe he took a course on it once but maybe he already forgot it. On the basis of his post, I doubt if he could be teaching the subject.
He seems to think that esoteric knowledge of the higher math is needed to understand relativity. “One has to get to a certain level of mathematics and physics knowledge to get a clear picture,” he says. Well, that’s true. And in the case of special relativity that level is high school algebra. From his post, I assume that Mr. Barr doesn’t know that. And if he doesn’t, he just doesn’t have a “clear picture” of the subject.
Does he think that all those Easy Einstein books, attempting to explain relativity to laymen, are pointless because they use plain language? Of course not. What he means is that if they agree with Einstein they are right and if they disagree (as in my case) then they are bound to be wrong.
Let me tell you what I think of Mr. Barr — and I mean this literally, not insultingly. I don’t think he knows the FIRST THING about science. And that includes physics. He may know obscure things about particle physics and some unfalsifiable ruminations about string theory with a lot of impressive-seeming symbols on the blackboard. One might say that he know the last things; the newest things, the trendy things. But he doesn’t know the FIRST THINGS.
The first thing is that the truth or falsity of a scientific theory is not established by a consensus of experts or by the letters after one’s name. It is established by reason and by the testing of theories, which themselves must be falsifiable in principle.
Einstein’s special theory does undermine the first things of physics — space and time. They no longer exist independently of us but depend on the motion of the observer. Space contracts, time dilates, depending on the observer’s motion. Einstein achieves this dramatic result with two postulates and high school algebra. The question is: Are those postulates correct? Does subsequent experiment confirm them? Maybe not.
As to the $2000 reward that Mr. Beckmann and a physicist at U. Conn. offered jointly, I herewith offer it out of my own pocket to Mr. Barr right now. All he has to do is look into the journals for a certain experimental result and provide the page and date of the journal.
Let me remind his readers of Petr Beckmann’s “crackpot idea” on which this reward was based. It is very simple. Einstein postulated in his special theory that the speed of a light is a constant (with respect to the source and the observer). Beckmann said that is wrong — the experiments say no. There is a difference between the speed of light to the east and the west, measured on the Earth’s surface.
The reward goes to Mr. Barr if he can point to an experiment which does indeed show that the speed of light is the same, to the west and the east, to within 50 meters per second.
It may not be easy for Mr. Barr to collect, however, because experiments have already been published showing this east-west light- speed difference. The best known was by Hafele and Keating, published in Science magazine in 1972. I am sure Mr. Barr knows how to look it up. There are other experiments but I won’t bore the readers.
If Mr. Barr cannot understand the importance of this issue, then he could consult with the famous physicist Clifford M. Will, who addressed it himself and at one point was under the impression that he would be able to collect the reward. He was unable to.
The reward was first offered in Science magazine in 1990, and an article in the L.A. Times was also written about the offer.
So how about it, Mr. Barr? The issue is important, because we are talking about the possible falsification of a famous theory here.
Mr. Barr’s inability to spell my name is not reassuring, as to his concern for accuracy. And his identification of Petr Beckmann as an “engineer” strikes me as borderline dishonest. Barr is the only person who ever called him that. Beckmann was very much a physicist, who taught electrical engineering at the Univ. of Colorado after he came to the United States.
The most important thing that Mr. Barr needs to learn, however, is that in science you cannot triumph over an opponent by flourishing credentials or pointing to a consensus,or by using insults. You have to address the issues with facts and arguments. It will be difficult for Mr. Barr to do this, maybe because he is unfamiliar with them. But the greater drawback is that — as far as special relativity is concerned — the facts are against him. Atomic clocks were needed to discover this, long after Einstein’s death. But Mr. Barr should at least make the effort.
–Tom Bethell
November 8th, 2009 | 12:05 pm
Poor clueless Barr!
I’m sure that Prof. Barr is a “nice Christian gentleman” and I’m glad to know [from googling his name] that he’s written a book on “Modern Science & Ancient Faith” which I’m sure I’ll enjoy reading (except that, as the “best” reviewer at Amazon.com complained, he’s uncritically accepted the questionable Copenhagen Interpretation of QM). but I’ll hereby publicly bet Prof. Barr $1,000.00 that he wrote his put-down of Bethell’s new book PRIOR to even glancing at the book’s Table of Contents, much less having read it carefully from cover to cover [which took me 8.3 hours in a single sitting because it was so enthralling that I couldn't put it down!]. Poor Prof. Barr hasn’t waked up to what Kuhn has documented about Paradigm Shifts in basic science, and he is pathetically wasting his time pursuing conventional “Supersymmetric Grand Unified Theories” without realizing that what he seeks was published long ago!! [I'm referring to 'ignored but well qualified authors in reputable journals,' with complete citations.] I’ll bet Prof. Barr another $1,000-to-$1 in his favor that if he goes to my website and reads CAEFULLY my paper “3.5 of the ’5 Great Problems of Physics’ Have Already Been Solved!” that his cheeks will be burning red with shame for having publicly dissed a genuine truth seeker from a philosophically naive and subject-matter abysmally-uninformed viewpoint!. (See my BassBio2008 on my website to confirm that I’m adequately credentialed that Barr can’t say I shouldn’t opine on things that I have no expertise in.)
November 8th, 2009 | 6:48 pm
Goodness, was that rant from Tom Bethell, or is it a practical joke? Hell hath no fury, etc..
No doubt Barr can defend himself, but it’s worth pointing out that he’s apparently a professor of physics who has taught Relativity at the graduate level: http://web.physics.udel.edu/about/directory/faculty/stephen-barr
It’s very precious to have to hear how absurd is is to consider Petr Beckmann an engineer, not a physicist. I suppose the fact that his degrees were in engineering, and that his occupation was to teach Engineering isn’t sufficient cause? Anybody familiar with science departments knows physicists don’t teach in engineering dept’s except under very very unusual circumstances… maybe as a temp job for a particular class.
The fields of Physics and Engineering are very very different, diverging notably halfway through an undergraduate program. The math requirements for Physics, especially at the graduate level, are much much higher. And engineering students, when they do delve into physics, tend to hit the more practical highlights, and leave the broad theoretical basis untouched. If you were to compare the text and syllabus of Electrodynamics taught to Electrical Engineering students and to Physics students, this would be very clear.
Every physicist can accumulate a file of earnest, unsolicited tracts from would-be theoretical physicists. They arrive free in the mail (and now, the inbox). Many of the authors are engineers. The authors are usually well-meaning, and can produce many pages of realistic-looking ‘research’. You’d have to wade through a sea of stuff to get at the errors and misunderstandings.
The thing is – it’s not worth it. Science is far from perfect, and the scientific consensus is in most cases flawed or incomplete. The point, though, is that there is a lovely process for testing alternative models: publication and peer review. If a reputable scientist has a solid argument, let him defend it among his peers. Beckmann didn’t sway physicists in his Usenet days. And he certainly never published any research in physics journals that supports his alternative to Relativity.
November 9th, 2009 | 9:16 am
Hmm. It appears that disputes among physicists, like poets, are so vicious because the stakes are so small.
November 9th, 2009 | 11:14 am
‘Cept is isn’t a dispute among physicists.
Mr. Bethell writes: Einstein’s special theory does undermine the first things of physics — space and time. They no longer exist independently of us but depend on the motion of the observer. Space contracts, time dilates, depending on the observer’s motion.
Actually, Augustine wrote that “With the motion of creatures, time began to run its course. It is idle to look for time before creation, as if time can be found before time.”
De genesi ad litteram, Book V, Ch. 5:12. And Aquinas, too, noted that time is “nothing but the numbering of movement by ‘before’ and ‘after.’ For since succession occurs in every movement, and one part comes after another, the fact that we reckon before and after in movement, makes us apprehend time, which is nothing else but the measure of before and after in movement.”
IOW, there is no time [or space] in the absence of matter. Space is the extension of matter; time is its motion. Einstein was really a sort of post-modern Aristotelian, under the skin.
November 9th, 2009 | 2:01 pm
I don’t claim to be a fine fellow. I only claim to know what I am talking about.
I quite agree with Mr. Bethell that insulting people is not the right way to dispute with them. What Mr. Bethell fails to grasp, however, is that I neither had nor have any intention of “disputing” with him about relativity theory. One cannot have an intelligent dispute with someone who lacks even a rudimentary knowledge or understanding of the subject. It would be farcical for an economist, for instance, to engage in a “dispute” with someone who knew next to nothing about economics about the merits and demerits of the value added tax, or the gold standard, or the validity of the law of comparative advantage. What would be the point of “disputing” with someone who thinks physics is just a bunch of “impressive seeming symbols on a blackboard”?
Mr. Bethell doubts that I could be teaching relativity. For the record, I teach a one-semester course in General Relativity for advanced graduate students every two or three years. I also teach Special Relativity at the graduate level (as part of a course in Classical Electrodynamics) almost yearly.
Mr. Bethell thinks one can understand relativity with only a knowledge of high school algebra. Even for special relativity, to have an adequate understanding, one needs somewhat more math than that. One also needs to have a good background in college level physics. For General Relativity, one needs differential geometry, which itself requires several semesters of calculus.
Are all those “Easy Einstein” books pointless?
No. But they give one a superficial knowledge. Superficial knowledge is better than no knowledge — as long as one is aware that it is superficial.
Mr. Bethell thinks that since my profession is to do research in theoretical particle physics, perhaps I only know “obscure things about particle physics”, but don’t know the basics of physics. Wow. That is like saying someone can be a concert pianist without knowing the musical scales or the basics of playing the piano.
As far as Petr Beckmann is concerned, I looked up his publication record before I said anything about him on Firstthoughts; and what I found is that Beckmann published in electrical engineering, not physics. He was not a physicist.
A point about physics: To say that “space contracts” and “time dilates” is a misleading way of stating what relativity really says — in fact, it is a complete misconception. The correct way to understand the “Lorentz contraction” of objects when they move is that when one looks at an object from a different “angle” in four-dimensional space-time, it looks shorter or longer. That in itself is no more mysterious than the fact that when one looks at one’s TV set from a different angle in three-dimensional space it looks bigger or smaller: The screen looks bigger when viewed face-on than when viewed from a slant. Someone moving with respect to an object sees it from a different angle in space-time than does someone at rest with respect to it.
(I am sure that this is the first time anyone has explained this basic fact about special relativity to Mr. Bethell, despite his years of deep immersion in Easy Einstein books.)
November 9th, 2009 | 3:20 pm
To Bill Daugherty,
The stakes here are that a person who writes regularly for a respected conservative journal is embracing in a very public way utterly crackpot ideas about science. That tends to bring discredit on conservatism. If Bethell weren’t writing for the American Spectator, I wouldn’t care, and neither would anyone else.
Is it vicious to call a crackpot idea a crackpot idea?
November 9th, 2009 | 4:44 pm
Dear Matthew M.
You hit several nails on the head. Thanks.
Steve Barr
November 10th, 2009 | 8:39 am
Prof. Barr
My little attempt at witticism fell flat, which I might have foreseen if I had given it a moment’s reflection. I apologize.
Wild Bill
November 10th, 2009 | 8:46 am
[...] at the website of the conservative magazine First Things, a physicist named Stephen Barr takes on Tom Bethell for his anti-Einsteinianism–which has been published, let us not forget, by [...]
November 10th, 2009 | 2:54 pm
Strange to see this kind of discussion with so much emotion and so little reasoning involved. I would just like throw into the comments section some interesting aspects regarding the subject.
1. In Physics a theory always comes in pairs with a measurement system. It is no surprise that metrology advanced so much at the same time that Einstein and others reasoned about a new theory about space and time.
2. A scientific truth is always relative to the scientific methods used to define the fundamental unit standards. As Poincaré once said: “no given way of measuring time is more true than another”. There are methods that are more convenient, more ubiquitous and that lead to more elegant theories capable of explaining all the acquired data.
3. In face of the current SI system of units, the standard second and meter, the velocity of light is constant by definition. If one reaches, in the laboratory, a different result, he must logically end with the conclusion that the apparatus used is mis-calibrated. Of course that the present experimental units of time and meter are mere conventions, and can be revised.
4. Finally I would just like to say, that if one reads Einstein himself talking about special relativity, one will see that clocks and rods are all over his texts… In my opinion this is good. If one forgets to connect theories with measurement processes, then one enters the field of Mathematics and not Physics. The beauty about Physics is that once and a while, you stop tweaking with paper equations and start tweaking with the experimental standards of fundamental units. Maybe we are reaching one of these points again.
November 10th, 2009 | 5:06 pm
I am going to be abroad for two weeks so will not be able to look at this till Thanksgiving or after. Notice the obsession with credentials above. One ought to address the issue raised, not the letters after a person’s name.
Mr. Barr is wrong if he thinks that time dilation and space contraction are a matter of mere “appearance” to the observer. No it is supposed that these things are real, not merely appearing differently to the observer. And it all depends of the speed of the ref. frame with respect to the OBSERVER. So it is relativity that introduces an unacceptable subjectivity into the subject. The observer should merely observe.
Incidentally, length contraction has not yet been detected in any experiment. “Time” dilation has been; but in this instance it is CLOCKS that slow down when they plow through the gravitational field, and the slowing of clocks has been construed as the slowing of time, to fit with Einstein’s claim.
That is merely one of the issues that Petr Beckmann brings out in his Einstein Plus Two. Another is that there is an ether, or luminiferous medium, but not the Maxwellian ether. It corresponds to the local gravitatonal field and therefore is non-uniform. Many things fall into place once that is understood.
I also discuss all this in plain language in my recent book: Questioning Einstein: Is Relativity Necessary?
I argue that general relativity gives the right results but by a roundabout method and the same results can be achieved by classical physics. Special relativity has (I argue) been falsified by experiment.
I do mention (and repudiate) in my book the late Tom Van Flandern’s more outre ideas.
When I was working on this book, I consulted with and exchanged emails with physicists who know far more about relativity than Barr seems to. Their names are given in my preface. They do not necessarily agree with me, but at least they are willing to respond calmly and argue in a rational, non-angry manner.
Does anyone on this blog have a response to the finding that there is an east-west light-speed differential? Someone should look up Hafele and Keating in Science magazine and see for themselves.
I won’t be able to look at this blog for two weeks but I will be back, and I shall be interested to see if the above defenders of the faith can respond rationally and without using words like crackpot. Mr. Farrell has long been a specialist in this regard.
Has Mr Barr read Beckmann’s book, Einstein Plus Two? Suggest he might look it up. Also: What knowledge of this subject would PB be deprived of if he “only” had a degree in electrical engineering and not physics? Serious question, hope for serious answer. And with particular ref. to the way these fields were subdivided in Czechoslovakia in the 1950s.
BTW, global warming has also been certified as true beyond doubt by all manner of scientific panels. Do we go along with that?
Sorry but this is very rushed; no doubt typos etc. Going to the airport.
Tom Bethell
November 10th, 2009 | 6:07 pm
Hey, people that eagerly bought/read/gave 5 stars on amazon to even tho you didn’t read “The Politically Incorrect Guide to …” do you get it yet?
Bethel doesn’t know, he doesn’t care, and he thinks you’re complete morons who will lap up anything that makes you feel righteously angry and superior to the “eggheads.”
Strong assertions of opinion are irrelevant to the truth. Never before have people had more ability to find out facts for themselves, but never before has the amount of deliberate lies and misinformation – the business Bethel happens to be in – been greater, either.
Politically Incorrect Guide fans need to either find a reliable source of filters for information or smarten up themselves.
I love the offer – Bethel makes $2000 from the audience for one Glenn Beck show.
November 10th, 2009 | 9:13 pm
Einstein proposed that the field of Ricci tensors, i.e., the gravitational field constituted what he called the “relativistic ether.” Around 1920 IIRC. Ludwik Kostro discussed this in Einstein and the Ether.
November 10th, 2009 | 11:05 pm
It is not a question of credentials, Mr. Bethell. It is a question of knowledge. One could understand relativity without credentials, or have credentials and not understand relativity. My criticism of you is not that you lack credentials, but that you lack knowledge. You reveal your lack of knowledge by the things you say about relativity. I discussed Beckmann’s credentials only because you held him up as an authority. It is you who referred to his credentials as an electrical engineer; and I merely pointed out the total irrelevance of that. The problem with you is not your lack of credentials, but that you quite literally don’t know what you are talking about.
You reveal again your lack of knowledge by saying that the “observer” plays a role in relativity theory. You are confusing relativity theory with quantum mechanics. In the traditional (Copenhagen) interpretation of quantum mechanics, the “observer” as such indeed does play a fundamental role. In relativity theory, however, what is important is not observers (in the sense of sentient beings)but “reference frames”, which are essentially just coordinate systems — i.e. ways that the coordinate axes are oriented in space-time. This is simply a matter of space-time geometry and how it is coordinatized. Yes, some books talk about different observers’ reference frames. But that is a loose way of talking.
It is clear from things you have written in the past and from your present statements that you think relativity theory is somehow subjectivist. That is a misconception common to people who have naively misinterpreted things they have read about relativity, but have no real understanding of the theory. There is nothing subjective about relativity, any more than there is about Newtonian physics.
In both relativity and Newtonian physics, some quantities are “relative” (with respect to reference frames, not to “observers” as minds) and some quantities are “absolute”. For example: In Newtonian physics spatial and temporal separation are absolute, whereas in relativity they are both relative and “space-time distance” is absolute. On the other hand, in Newtonian physics the speed of everything — including light — is relative; whereas in relativity the speed of light is absolute! In BOTH Newtonian physics and in relativity, velocity is relative and acceleration is absolute.
So, you see, it is not that in relativity things are all relative and in Newtonian physics they are all absolute. In both theories — indeed in all theories of physics that could be written down — some things are relative and some things are absolute.
But, again, this has nothing to do with observers as minds. It has to do with frames of refernce, i.e. axes of coordinate systems. It is a matter of geometry.
I could in five minutes prove this all to you on a blackboard, Mr. Bethell, using those funny little “impressive looking symbols”. But you would have to know what those funny little symbols meant.
The idea of “relative” quantities and “absolute” ones can be illustrated in a purely Newtonian context by considering a ladder. If I take a ladder and hold it vertically, there will be a certain vertical separation between the rungs. But if the ladder is tilted against a wall, say, the rungs will have — truly have, it is not a mere illusion — a smaller vertical separation between them. So “vertical separation” is “relative” to the angle between the ladder and the direction one defines to be “vertical. What is absolute (in the sense that it does not depend on the orientation of the ladder in three-dimesnional space) is the actual distance between the rungs. There is an exact mathematical analogy with what happens in relativity. In relativity, the separation between two events in the x direction, y direction, z direction, or t direction are relative to the way one orients the x,y,z, or t axes (i.e. the three space axes and one time axis). What is absolute is the “spacetime distance” between the two events.
Just as there is nothing mysterious or subjectivist about the “relativity” of the “vertical spacing” of the ladder’s rungs, so there is nothing subjectivist in relativity theory
about the “relativity” of x, y, z, or t separations.
There is some strangeness in relativity, most of it having to do with the fact that the geometry of spacetime is “Minkowskian” rather than “Euclidean”. But that is not relevant to the question of subjectivism.
Incidentally, Einstein, who certainly understood relativity well, needless to say, was the farthest thing in the world from a subjectivist. He firmly believed that there is a single truth about physical reality. It was the role of “observers” in the Copenhagen interpretation of quantum mechanics that was the reason he rejected it.
I am saying all of this not for Mr. Bethell’s benefit, since if he hasn’t understood relativity properly after reading about it for decades, nothing that could be said in a blog post will make any difference to him. I am saying this for the enlightenment of any readers of First Things who are still be reading all this and might care about these matters.
November 11th, 2009 | 8:57 am
Dear Prof. Barr:
I understand your position. It is an orthodox position, coherent with the mainstream view by the scientific community.
Nevertheless, I’m curious to hear your opinion on the conventionalist view of science and in particular relativity theory.
As you may know, even though the “history of science” taught in universities all over the western world tends to ignore it, many scientists shared a conventionalist point of view about relativity while it was being developed.
When you say for instance that ‘the geometry of space-time is “Minkowskian” rather than “Euclidean”’, do you accept the fact that this is only so, as long as one maintains the current (experimental) conventions about how to measure time and space? Or do you go beyond this point and settle it as a metaphysical truth, above the ground of experimental observation?
For me, it is quite clear that one could easily invent a new standard clock that once adopted would readily reject special relativity and Minkowskian geometry as an adequate representation of space-time. That this clock could bring more benefits than disadvantages in the human pursue of scientific knowlegde, is a different matter.
Historically, the theoretical birth of relativity, the shift from astronomical to atomic timekeeping processes, and the birth of radio signaling for geodesic purposes, all happened more or less simultaneously and helped to shape the current experimental and theoretical concepts of time and space.
Do you accept that all the conventions involved in the above mentioned processes are the fundamental reason for validating relativity?
Even though one might accept living in an objective world, the knowledge obtained by science might only be a dual and quite useful convention after all: one made of experimental standards and measurement processes, and made also of elegant mathematical theories that fit the current observations.
Why do you think that modern discussions on the physics of space-time often neglect the experimental aspects of the subject as second order issues to be addressed at latter times?
Thank you.
November 11th, 2009 | 11:34 am
Dear Mr. Ramos,
You ask, “do you accept the fact that [the Minkowskian nature of space-time] is only so, as long as one maintains the current (experimental) conventions about how to measure time and space? Or do you go beyond this point and settle it as a metaphysical truth, above the ground of experimental observation?”
Neither. The fact that space-time has a Minkowskian geometry is neither a matter of convention nor a metaphysical truth. It is a fact about reality that we learn through empirical investigation. In that sense, it is like the fact that I have a nose. The fact that I have a nose is one that does not depend on arbitrary conventions. (Though the way this fact is expressed in English, using a word spelled n-o-s-e, obviously depends on conventions of language.) The fact I have a nose is not “a metaphysical truth above the ground of experimental observation” either. One cannot deduce that I or you have a nose by metaphysical reasoning; one must make an observation to find out.
The birth of relativity theory and the grounds for its acceptance had nothing at all to do with new developments in the way scientists measured time or space. The experiment that most influenced Einstein’s thinking was one that had been done decades before Einstein was born by Michael Faraday. Faraday had showed that the current induced in a coil of wire was the same whether one moved a magnet toward the coil or the coil
toward the magnet. This suggested to Einstein that the laws of electromagnetism obeyed the “principle of relativity” — i.e. the principle that physical effects always depend on the relative velocity of two things, and not on the “absolute velocity” of one thing.
The Michelson-Morley experiment, which was done in the late 1800′s was not a major influence on Einstein’s thinking — he saw it as evidence in favor of his theory, but it was not what led him to develop his ideas. (Despite Bethell’s notion that this is some recent revisionist history, this has been well-known for a long time. Michael Polanyi emphasized this back in the 1950′s.)
It is not appreciated by many people outside of physics that Einstein was not trying to be a revolutionary. His motives were actually quite conservative. He was trying to preserve two of the pillars of then-existing physics that seemed to be at odds with each other. One of those pillars was the “principle of relativity” of velocity, which was a principle obeyed by Newtonian mechanics. The other pillar was the theory of electromagnetism developed by James Clerk Maxwell in the mid 1860′s based on the earlier experimental and theoretical work of many other scientists. These two pillars had been standing for a long time, but they seemed at odds, because the equations of Maxwell’s theory did not seem to satisfy the relativity principle. The fact discovered by Faraday about coils and magnets that I mentioned above was a vital clue for Einstein, because it suggested to him that Maxwell’s Equations somehow DID obey the relativity principle. Einstein came to the realization that if this was true, then space-time must have a different geometry than had been assumed.
That, in a nutshell, is the story. Einstein was not thinking so much about recent measurements, but rather about long-established theoretical ideas and how they could be reconciled with each other. Those long-established theories were based on experiments and observations, to be sure, but one’s that had been done much earlier.
All this illustrates why one really should have a thorough knowledge of electromagnetism to appreciate what is going on relativity theory.
That is why I suggested to Bethell that he take some courses on electromagnetism at the level of either Griffiths’ or Jackson’s textbook.
I hope this answers your questions.
.
November 11th, 2009 | 4:02 pm
I write to correct one statement made by Tom Bethell in his November 8 post. He stated that the Hafele-Keating experiment published in Science in 1972 supported Beckmann’s theory of an east-west difference in the speed of light. This is incorrect. The experiment had nothing to do with the speed of light. What was measured was a difference in the time accumulated on an atomic clock, which first traveled around the world eastward, and then made a similar trip westward. On returning home, after each trip, the traveling clock was compared with an identical clock that stayed in the laboratory (the clocks were Caesium-based standards, the best available at the time). All the trips were flown on commercial flights (these were the pre-TSA days!), each totaling around 45 hours in flight. Because the clock flew at high altitudes where gravity is a bit weaker than on the surface, Einstein’s general relativity predicts that its rate should differ compared to the stay-at-home clock. And because it traveled at different speeds (an eastward moving clock moves slightly faster relative to inertial space than a westward moving clock) special relativity predicts additional differences in its rate. Accurate logs of all altitudes and airspeeds were recorded. When the clock returned to base and was compared with the home clock, there was a difference in accumulated time between eastward and westward trips, and between each trip and the home clock. But the differences were in total agreement, within the measurement errors, with what was predicted by general and special relativity, given the itineraries. No light signals were ever used, so the experiment said nothing about the speed of light. The results agree completely with relativity.
Finally, Mr. Bethell implies that I tried to collect the reward and failed. This is false. I have written about experiments that confirm the isotropy of the speed of light, both in the scientific literature and in my books, but have never paid serious attention to the musings of Mr. Petr Beckmann.
November 11th, 2009 | 4:05 pm
Dear Prof. Barr:
I thank you for your time addressing my questions, and also for your good humor answering me. If I may, I will try to return to you with the same good humor (both philosophically and technologically) by kindly disagreeing with you.
You say: “The fact that space-time has a Minkowskian geometry is neither a matter of convention nor a metaphysical truth. It is a fact about reality that we learn through empirical investigation. In that sense, it is like the fact that I have a nose.”
Well, at the level of “I have a nose” (I do too) I would put the fact that “I have a(n atomic) clock and a light beam”.
Both are physically tangible empirical facts that can be investigated. Minkowskian geometry is not, it is an abstract mathematical tool.
Now, if one uses those physical objects (not the nose of course) in a carefully arranged procedure to attribute 4 real numbers to world events, one finds out that Minkowsky geometry is very useful. This is so because the 4 real numbers obtained for world events depend on the velocity of the chosen physical objects, now raised to the status of space-time standards for measurement purposes. And Minkowsky space allows us to directly calculate what our standard instruments measure for these same events when animated with any possible (constant) velocity. As a bonus, as you said, we find out that electromagnetic phenomena is easily and elegantly expressed in terms of space and time when measured against these standards.
Now “I have a nose, but I also have an elbow.”, that is, I’m free to choose a clock that does not rely on atomic processes. And, of course, I may not define the meter as “the distance traveled by light in a definite amount of atomic time”, even knowing that this has proved to be so convenient, both technologically and theoretically.
So I may define radically new concepts of space and time, that can equally address the real world events placing them in adequate reference frames. With these new reference frames, maybe Minkovsky algebra is not so useful anymore, (the new clocks and rods might react differently when animated with velocity). But I could find other algebras. Maybe Electromagnetism cannot be expressed through Maxwell equations anymore. I could find new equations.
What would remain as a matter of empirical evidence, would be that, by choosing atomic clocks and light beams as time and space standards, measured data in a large range of natural phenomena is adequately addressed by means of Minkowsky algebra.
This suffices to say that, as you may have already noticed, I believe in physics as a rigorous convention, (in a way similar to a language, composed not of mere consonants – mathematical symbolic theories – but also of experimental vowels – physical standards). A convention that is the most well equipped piece of human knowledge able to address in a predictable way the natural phenomena.
But I agree with you in one respect: In what regards to persistence in time, both my nose and the fact that “space-time is Minkowskian” are facts condemned to cease their existence somewhere in the future.
November 11th, 2009 | 10:19 pm
I thoroughly enjoyed Tom Bethell’s book. He does not refute relativity but merely explains the results it predicts in a different and more clear manner. Surely any physicist can appreciate this on its own merits or simply tell us why it is a wrong with his explanation. He explains clearly everything you have mentioned in your comments.
a lowly electrical engineer
November 12th, 2009 | 9:18 am
Dear Mr. Brodie,
I do not see how it is possible that Mr. Bethell could be “clearly explaining” in his book the same things that I am saying in my comments here, given that he flatly contradicts me on important points. Several of the things he has said here are simply wrong. I have pointed out some of these errors, and Prof. Clifford M. Will (above) points out another one. (I should note that Prof. Will is a noted expert on General Relativity — that is his field of research.) It is hard to see how Bethell could have given a clear exposition of relativity in his book, when his understanding of it (as manifested here) is so superficial and, in fact, erroneous.
Dear Mr. Ramos,
I must confess that I cannot tell what you are driving at, so perhaps we should leave our exchange where it is.
November 12th, 2009 | 12:47 pm
Mr. Bethell writes:
Does anyone on this blog have a response to the finding that there is an east-west light-speed differential? Someone should look up Hafele and Keating in Science magazine and see for themselves.
I have Hafele and Keating here in front of me. Both of them. They published two articles in that issue of Science: Volume 177, 14 July 1972.
The first article is called, Around-the-World Clocks: Predicted Relativistic Time Gains:
The abstract is as follows:
“During October 1971, four cesium beam atomic clocks were flown on regularly scheduled commercial jet flights around the world twice, once eastward and once westward, to test Einstein’s theory of relativity with macroscopic clocks. From the actual flight paths of each trip, the theory predicts that the flying clocks, compared with reference clocks at the U.S. Naval Observatory, should have lost 40 ± 23 nanoseconds during the eastward trip, and should have gained 275 + 21 nanoseconds during the westward trip. The observed time differences are presented in the report that follows this one.”
Bear with me: the second follow-up article is called Around-the-World Clocks: Observed Relativistic Time Gains, and the authors conclude thus:
“In conclusion, we have shown that the effects of travel on the time recording behavior of macroscopic clocks are in reasonable accord with predictions of the conventional theory of relativity, and that they can be observed in a straightforward and unambiguous manner with relatively inexpensive commercial jet flights and commercially available cesium beam clocks. In fact, the experiments were so successful that it is not unrealistic to consider improved versions designed to investigate aspects of the theory that were ignored in the predicted relativistic time differences (1). In any event, there seems to be little basis for further arguments about whether clocks will indicate the same time after a round trip, for we find that they do not.”
Given Professor Will’s excellent summary of the experiment above, I would ask Mr. Bethell a couple of questions:
1. how exactly he would derive this “differential” he is talking about from an experiment that was designed to test general relativity?
And 2. is this differential also demonstrated by the several updated repeats of the experiment since it was first done? My recollection is, and I’m sure Prof. Will is the best person to ask about this, that the later experiments confirm relativity to even greater accuracy than HK, but if Mr. Bethell can site papers in the recent literature (Science, Nature, Journal of Physics etc) to the contrary, I’d be interested to check them out.
Mr. Bethell also makes a reference to an experiment(s) he says (or argues) falsifies special relativity. Might he point out which experiment this is?
Now, I’m sure Mr. Bethell would agree that one claimed falsification of a theory’s prediction should be verified independently more than a few times before the scientific community changes its mind.
Even granting, for the sake of argument, that Beckmann’s theory can claim Hafele Keating post-facto, can Mr. Bethell descibe de novo experiments that would establish predictions specific to Beckmann’s theory alone that could not be explained by Einstein?
November 12th, 2009 | 2:46 pm
Dear Prof. Barr:
I apologize for any inconvenient I might have caused you. I was merely trying to express a humble conventionalist point of view about relativity, and trying to discuss it with a professional theoretical physicist.
Conventionalism belongs to the domains of Philosophy of Science. I leave you with a quote from Poincaré, written in 1898, in “La mesure du temps”, which I believe holds adequate to the subject:
“We have not a direct intuition of simultaneity, nor of the equality of two durations. If we think we have this intuition, this is an illusion. We replace it by the aid of certain rules which we apply almost always without taking count of them. [...]
We therefore choose these rules, not because they are true, but because they are the most convenient, and we may recapitulate them as follows : “The simultaneity of two events, or the order of their succession, the equality of two durations, are to be so defined that the enunciation of the natural laws may be as simple as possible. In other words, all these rules, all these definitions are only the fruit of an unconscious opportunism.” ”
May I suggest you Peter L. Galison’s book: “Einstein’s Clocks, Poincaré’s Maps: Empires of Time”?
Best wishes for the success of your career,
Sincerely,
Hugo
November 12th, 2009 | 8:16 pm
Have you read the book or are you arguing on Mr. Bethell’s comments? The issues appear to have disintegrated into personal attacks by all parties.
The book simply says most relativity questions disappear if we assume an ether of the gravitational field. It explains light bending, all interferometer experiments, GPS satellite problems, etc. Is this not true? where does it fail?
a simple reader of books,
Ben Brodie
November 12th, 2009 | 9:57 pm
Dear Dr. Brodie,
You call yourself “simple”, and a “lowly” electrical engineer. You could have called yourself a “first rate” electrical engineer and I would have believed you. Don’t put yourself down!
You ask whether I am arguing based solely on Mr. Bethell’s comments here. No. I have read two articles by Mr. Bethell about relativity. One was published in National Review (if memory serves) years ago, and the other on the American Spectator website just a few days ago. But even if I had not read those articles, what Mr. Bethell has said here would be quite sufficient to show to anyone expert in the subject that he is deeply confused about relativity. (Cf. the devastating comments made by prof. C.M. Will above.)
Did I engage in a “personal attack” on Mr. Bethell? I said that he does not know what he is talking about when it comes to relativity theory. That is just stating a fact, and a fact that it is important for his readers to understand. Suppose a man of very limited historical knowledge wandered in off the street and started to give history lessons to unsuspecting high school students. And suppose a real history teacher, who knew his stuff, told the students that the fellow did not know what he was talking about. Would that be a “personal attack” or just responsible truth telling? Aren’t we all opposed to that kind of “political correctness” that is afraid to call things by their proper name? An impostor is an impostor, and ought to be exposed as such.
Why feel sorry for Mr. Bethell? There has been nothing stopping him for all these years from really learning some physics. He has the money to pay tuition and take some courses in physics. All across the country, tens of thousands of students are learning college-level and graduate-level physics. He could have become one of those people. He has chosen not to.
He wants to be regarded as knowledgeable, without doing the hard work required actually to become knowledgeable. R-E-S-P-E-C-T has to be E-A-R-N-E-D.
November 18th, 2009 | 12:17 am
Dear Mr. Barr,
Thank you for responding to this guy. Tom Bethell is not a bad writer when he sticks to his strengths, but like Richard Dawkins trying to play the philosopher, Bethell seems way out of his depth when discussing relativity theory. Of course, he doubts that Shakespeare was quite himself and that HIV causes AIDS.
In other words, he makes conservatives and libertarians (and Christians) look like idiots, and like so many people in the “conservative man of letters” crowd, he seems unbothered by the ignominy this draws down upon his moral and philosophical allies. Thank you for taking him on.
November 22nd, 2009 | 4:44 pm
I have not read Mr. Bethell’s book yet but I will over the Thanksgiving holiday. I have no way of knowing whether Mr. Bethell’s criticisms are sound but I will say he is at least correct in being skeptical of relativity as a whole. It is not a valid theory. If Mr. Barr thinks that relativity is completely valid, he is incorrect. I have a $500 contest of my own on my website http://www.sciencewithoutfiction.com where I demonstrate two different ways that relativity is not valid.
November 26th, 2009 | 9:03 pm
I am accessing this through someone’s laptop and can only make a short reply. I will reply to the comments by Clifford Will and M. Farrell on the issue of the Hafele Keating experiment in greater detail in a couple of days. I do not have access to my own books and papers.
November 26th, 2009 | 9:47 pm
I am accessing this with someone else’s computer and wll reply in more detail in a couple of days. I don’t have any books or papers here. Especially I shall respond to the arguments by Clifford Will and Mr Farrell about the Hafele Keating experiment. I shall be glad to have the opportunity to do so as it is important.
Mr Barr is under the impression that he has corrected certain errors in what I have written. What is he referring to? His own claim that the observer plays no role in special relativity? He is quite wrong about that.
Space and time are transformed –by what are called the Lorentz Transformations — in a reference frame that is moving. Moving with respect to what? To the OBSERVER. Or, if Mr Barr prefers, to the reference frame of the OBSERVER. (I agree that sentient beings have nothing to do with it and I never said they did.)
If Mr Barr wishes to take issue with this claim, then let him. I shall be back in a of days with numerous citations and references supporting my claim that Lorentz transformations are observer referred; including quotes from Einstein himself. If Mr Barr really wishes to contest this point, his knowledge of special relativity is, as I have suspected, seriously defective.
As to the Hafele Keating result, it’s true that the authors were able to make it approximate the claim of special relativity; but only at the cost of violating the cardinal rule, or first postulate, of relativity theory: Thou shalt have no preferred reference frames. They concluded the only way they could get the result to come out right was to refer the motion of the atomic clocks to an Earth centered, non-rotating inertial reference frame; a privileged reference frame. But special relativity is not allowed to have preferred reference frames. Its results are supposed to be symmetrical: When I move, I observe your clock to slow down; and when you move you observe my clock to slow down.
Contest it is you like, Mr Barr, but you are threatening to sink deeper into an error generated by your own unjustified self confidence.
Minkoski’s views about the rotation of spacetime formed no part of Einstein’s 1905 special relativity. It was a subsequent mathematical interpretation that tended to make things harder to understand. Not easier. I stand by my claim that SPECIAL relativity involved only high school algebra.
Mr Barr, can you give me a ref. to the well known claim that SPACE contracts in the moving reference frame? (And yes, moving w.r.t. the observer.) I have seen those drawings of foreshortened space ships. Are there any experiments that confirm space contraction? Perhaps Mr Will can help out here. . .
November 26th, 2009 | 11:19 pm
A brief reply here to Mr Will’s idea that I “implied” that he tried to collect Petr Beckmann’s $2000 reward offer and failed. That is not what I said. I think I said, above, that he was at one point under the impression that he might be able to collect.
Anyway, here is what happened. Let the reader judge. The reward was offered, and published in Science magazine in 1990. To collect it, the winner had to cite an experiment showing that the speed of light is the same to the east as it is to the west, to within 50 meters per second. (This was the “musing” of Mr. Beckmann, to which Mr Will never paid “serious attention.” We see it is highly relevant to our discussion here.)
A reporter for the L.A. Times read the offer and contacted Clifford Will and suggested he might be able to collect. Mr. Will is reported to have responded that he knew about the offer, but it had a time limit. The experiment had to have been done before a given date. Since then, however, there was apparently some new experiment whose results would allow him to collect the reward.
The L.A. Times man reported this back to Howard Hayden, then a professor of physics at the University of Connecticut, who had shared with Petr Beckmann in making the offer in the first place. (Since then, Hayden has retired.) Hayden then mailed a “special offer to Clifford Will,” updating the offer to the present time. But he never heard back from Mr. Will.
I describe the episode in my book.
If that does not accord with Mr Will’s recollection, perhaps he could let me know.
Tom Bethell
November 27th, 2009 | 3:05 pm
Let us first examine this paragraph from Mr. Bethell’s recent post:
“Space and time are transformed –by what are called the Lorentz Transformations — in a reference frame that is moving. Moving with respect to what? To the OBSERVER. Or, if Mr Barr prefers, to the reference frame of the OBSERVER. (I agree that sentient beings have nothing to do with it and I never said they did.)”
Mr. Bethell, you are caught by your own words. You did in fact quite clearly say that sentient beings have something to do with reference frames, when you said (and this a direct quote from your Nov 10 post):
“And it all depends of the speed of the ref. frame with respect to the OBSERVER. So it is relativity that introduces an unacceptable subjectivity into the subject. The observer should merely observe.”
When you say that reference frames of OBSERVERS introduce “subjectivity”, you are talking about the OBSERVER (capital letters yours) as an entity that has “subjectivity”, i.e. is a “subject” of knowledge, i.e. a sentient being.
In any event, reference frames do NOT have to refer to an observer. If you had ever actually done real calculations in relativity, and solved actual relativity problems (whether of the elementary homework type or the harder kinds often encountered in research) you would know that as often as not one is calculating in reference frames that have nothing to do with any kind of observer, such as the frame of reference of a particle moving near the speed of light through the atmosphere, or the frame of reference of an astrophysical object that has no life anywhere near it. Again, a reference frame is simply a set of axes for coordinatizing space-time. (Of course, it is obvious that when a human being makes a measurement of the location of something in space-time, it is often convenient for him to make use of some system of coordinates — convenient, but not necessary. Usually, the most convenient frame of reference is that in which his experimental apparatus is at rest — i.e. the “rest frame” of his laboratory, i.e. the “lab frame”. I will refrain from picking apart all the nonsense in the rest of your post — life is too short to spend it thus.
I have only one other thing to say. My field of research is theoretical particle physics. The very language of my field is “relativistic quantum field theory”. The so-called Standard Model of particle physics is a relativistic quantum field theory. It is utterly impossible to become a respected researcher in my field without a thorough mastery of both quantum mechanics and relativity theory. And I do research in it, Mr. Bethell. Some of my papers are very well-known in the field. (According to the SPIRES HEP database, at the moment one of my papers is categorized as “famous”, 11 as “very well-known”, and 22 as “well-known”, based on the number of times they are cited by other researchers.) By what miracle am I able to do highly regarded research in a field of which, according to you, I do not understand the basics?
Doubtless you will say that I am citing my “credentials”. No. Again, it is a matter of knowledge and demonstrated mastery, not degrees. There is an easy way to test whether you are knowledgeable enough to discuss these matters. We could do the test right here at a time convenient to both of us. I could pose to you on this website some elementary homework problems in special relativity — standard textbook questions, such as I assign to my students. These would be problems that average undergraduate students who have learned special relativity are expected to be able to do in about 20-30 minutes (though an expert could do them in five minutes or less). You would have 30 minutes to do each problem and post the answer here. Are you game?
Until such time as you agree to subject yourself to this public test of basic knowledge and understanding I will refrain from further comment on anything you say on this subject.
November 30th, 2009 | 12:54 am
THE OBSERVER IN RELATIVITY THEORY
The special theory is largely concerned with what happens to particles and bodies in an inertial reference frame that is moving. It is deduced (although not necessarily observed) from the postulates of the special theory that time dilates, length contracts, and mass increases in moving frames.
Moving with respect to what? The reference frame of the observer.
As Jeremy Bernstein said in his book Einstein (1973): “A moving electron or any massive object becomes more massive when it is motion with respect to an observer than when it is at rest with respect to the same observer.” [p. 94, Penguin Modern Masters]
The same sentence can be rewritten substituting changes in time and length for mass.
Question: Does Mr. Barr accept that or not?
If he does not, he’s in danger of going up against the entire relativity establishment.
If he does, why on Earth is he making such a big deal by insisting that my reference to observers shows that I believe “sentient beings” are involved? I do not, nor does Jeremy Bernstein. Observations are made by cameras, telescopes and atomic clocks. That he keeps harping on this point is odd, even suggesting that he may not be familiar with the frequent references to “the observer” in relativity theory. He seems determined to show that, one way or another he has caught me out in an error and that I do, too, believe in a role for sentient beings. To be sure, my use of the word “subjective” was ill chosen. It was used in blogging haste and did not imply a belief that sentient beings do any of the observing.
All I can say is readers of this blog must be saying to themselves: “C’mon, Professor Barr, this is a mere denialist amateur. Can’t you come up something better than that . . ?”
HAFELE KEATING: DEVASTATING RESULTS
I want to say something about the Hafele Keating experiment and the comments by Mr. Will and Mr. Farrell, which Mr. Barr finds “devastating.”
In a way, the experiment really was devastating—to Einstein’s theory. But both Will and Farrell carefully avoid explaining why that is so. Special relativity predicts that a moving clock will run more slowly than an identical stationary clock. The Hafele-Keating papers giving the results of atomic clocks flown around the world in opposite directions were published in Science magazine in July 1972. Before that, preliminary analysis by Hafele was published in Nature arguing that “the standard answer that moving clocks run slow . . . is almost certainly incorrect.”
In an article published in AJP in 1972 [vol 40, 81-82] before the Science articles came out, Hafele noted a “quite remarkable feature” of the theory was that of “directional dependence” for time dilation, and this “seems to have been largely overlooked in the past.” Right. It was overlooked, because Einstein’s theory had never predicted any directional difference for time dilation. In Science, the authors reported, the flying clocks “lost time (aged slower) during the eastward trip and gained time (aged faster) during the westward trip,” This was by comparison with a reference atomic clock at the U.S. Naval Observatory in Washington.
The difficulty that this created for special relativity (SRT) was patched up by deciding that the stay-at-home clock at the Naval Observatory was “not suitable” to be considered as inertial because it moves around in a large circle along with the rotating Earth. It was non-inertial. Therefore the flying clocks had to be compared with a different reference frame. This turned out to be the “hypothetical coordinate clocks of an underlying non-rotating (inertial) space.”
(It’s true that the Observatory clock was non-inertial, and therefore disqualifying as a test of special relativity. But so were the clocks flying around the world. There wasn’t an inertial frame anywhere in sight, so the whole experiment could have been disqualified as a non-valid test of SRT. But because a way was found to bring the results seemingly into line with Einstein’s theory, the experiment was admitted into the canon of SRT-confirming experiments. Clearly also the publishing arrangement was intended to give readers a warning or heads-up that some unexpected results were coming up, but not to worry because they had found a way to minimize or disguise the problem.
From the point of view of Einstein’s theory, the problem was that a preferred reference frame was brought to the rescue — something not hitherto permitted in special relativity. All inertial reference frames are supposed to be equivalent to one another. The speed of light is supposed to be the same in all frames, no matter how the observer’s frame moves. But the east-west difference in atomic clocks rates showed that the speed of light indeed was not the same in all reference frames.
So the underlying theory of relativity was changed in an important way that has not been acknowledged. One might say that it was adapted to the real world. No longer was it motion with respect to the observer that causes time dilation. It was motion with respect to a real block of space within which the earth is embedded and rotates.
This use of a preferred reference frame violated the rules of relativity, but it did bring the theory into line with Petr Beckmann’s theory, in which the local gravitational field is equivalent to the luminiferous medium. Motion through this field causes clocks (not time) to slow down. When the clocks are moved to a higher altitude, the gravitational field becomes more attenuated, and there the clocks speed up (much as planes encounter less air resistance and therefore save fuel when they fly higher).
Thus does Beckmann’s theory give the same results as general relativity, but in a much simpler manner; bending of starlight is explained by Fermat’s Principle, no need for “curvature of spacetime,” etc.
(As Edward Teller told me when I interviewed him at the time of a memorial event for Petr Beckmann in 1993: “What does it mean if three dimensional space, and even more horribly four dimensional space-time, is curved? That you won’t understand very readily.” George Gamow said the same thing.)
So the new reference frame gave “time dilation” results that are in agreement with “theory,” but it was no longer Einstein’s theory; it was Beckmann’s. (Or better, the altitude corrections were in agreement with Einstein’s general relativity; but the moving clocks’ east-west corrections were not in accordance with special relativity.)
The same problem applies to the analysis of GPS. When the GPS clocks are put into orbit, they have built-in altitude corrections that are in accordance with the general theory but a built-in orbital motion correction that again uses the same preferred reference frame we find in Hafele-Keating. Results agree with experiment and GPS works but the moving-clock corrections are not properly derived from special relativity.
Both the Sagnac experiment (1913) and the Michelson-Gale experiment (1925) showed fringe shifts which undermined special relativity. But it was rescued by saying that that these experiments involved rotation (of a platform in Sagnac; of the earth in M-G). So they were regarded as confirming GRT rather than disconfirming SRT. After Sagnac, Einstein wrote in his 1916 GRT paper that “the principle of the constancy of the velocity of light must be modified.” People tend to overlook that.
The most sensitive Michelson-style interferometer experiment yet done (Brillet and Hall, 1979) showed a fringe shift corresponding to the prediction of Beckmann’s theory. It is hard to detect because it is four orders of magnitude smaller than that expected by Michelson-Morley in 1887. But John Hall (winner of 2005 Nobel in Physics) was looking for something else and he decided that the fringe shift that he had detected was “spurious,” possibly because the axis of the rotating table was not perfectly vertical.
Hall also told me in an interview that special relativity should possibly be considered an unfalsifiable theory because all these experiments are conducted on a “spinning ball,” namely the surface of the Earth. If “you turn up the sensitivity high enough,” he said, you will unavoidably discover non-inertial effects and they in turn will disqualify the experiment as a test of SRT. There speaks a true scientist
Beckmann’s conclusion was that special relativity will eventually have to be discarded; and that general relativity gives the right results by a roundabout method.
And as I discuss in my book, and I am sure Mr. Barr knows, the famous equation E = mc squared was derived first with and then without relativity theory — both by Einstein.
End of discourse. Yes or no answer to my simple question expected from Mr. Barr within 30 minutes on the dot. No problem if he doesn’t want to respond. But I will sit up and pay attention if he points out an error in what I have written.
Tom Bethell
November 30th, 2009 | 5:18 pm
Mr. Bethell would have us believe that he can correctly analyze a very complicated physics problem, namely the one involved in the Hafele-Keating experiment. This experiment involves (a) gravitational effects (i.e. GENERAL Relativity), (b) specifically the gravitational field of a rotating massive body [which is more complicated to work out than the field of a non-rotating body], and (c) objects moving in circular orbits around such a body. To analyze this problem one needs to be able to use the mathematics of General Relativity, which involves tensor calculus and differential geometry in curved four-dimensional space-time. In other words, Mr. Bethell’s “high school algebra” is definitely NOT sufficient. I will bet my silk pajamas that Mr. Bethell could not do the math required to properly analyze this problem in the context of Einstein’s theory even if his life depended on it. (I haven’t analyzed the Hafele-Keating experiment, but I know enough to do it. It would just take me a lot more time than I am willing to spend.)
However, let us suppose that by some miracle Mr. Bethell is able to analyze such a complicated problem in General Relativity. Then it should be utterly trivial for him to do the kinds of simple, standard problems in special relativity that I have challenged him to prove to the world that he can do. The problems I propose that he be tested on are about 50 times easier than the one he is pretending to be able to do. I am also willing to bet my silk pajamas that he will never accept my challenge.
To show my good faith, I will answer his BIG QUESTION The answer is that the statement made by Jeremy Bernstein (“A moving electron or any massive object becomes more massive when it is motion with respect to an observer than when it is at rest with respect to the same observer”) is quite correct as to its substance, but is phrased in a somewhat antiquated way. In the old days, people would say that an object of “rest mass” m moving with velocity v has an energy given by M c^2 (M c-squared), where M is its “mass” when moving at speed v, which larger than its rest mass m by a factor called gamma. In other words the “mass” of the object was spoken of as “increasing” when the object was in motion. That is an old-fashioned terminology, however. Experts rarely use the word “mass” in this way anymore. Nowadays, the word “mass” almost always refers to the rest mass of an object. The “rest mass” is an invariant quantity, it is the same in every frame. So, nowadays people would say that the energy of an object “with mass m” moving at velocity v is given by (gamma m c^2), while its energy at rest is given by just (m c^2). In short, people use the word “mass” to refer to something that stays the same no matter how the object is moving, and say that the ENERGY of the object increases when it moves.
This is not a substantive point. It refers to terminology. I would also note that the word “observer” is quite superfluous here. One could simply say (with less chance of misleading the ignorant) “the energy of an object in a frame where it is moving is greater than its energy in a frame where it is at rest.” That, in itself, is no big deal. The same statement is true in Newtonian physics — but the mathematical expression for the energy is different in Einsteinian and Newtonian physics.
In Newtonian physics the rest energy is zero, in Relativity it is mc^2.
I also agree that one could get another true sentence from Bernstein’s sentence by changing the words “more massive” to “longer”, changing “any object” to “any object of finite length”, and deleting the words “a moving electron” (since electrons are not known to have any length — in our present theory, electrons have no length; they are “point particles”).
BEND IT LIKE EINSTEIN:
I am very amused to learn from Mr. Bethell that Petr Beckmann had the brilliant idea that he could explain the famous “bending of light” by the gravitational fields of massive objects by using only the “time-dilation” effect and Fermat’s principle (also called “the principle of least time”). This is Beckmann’s great idea?!?! (a) Its not original, and (b) it’s wrong — and very, very famously wrong. Everyone who has studied General Relativity knows (except Beckmann and Bethell, it seems — but Bethell has never actually taken a course in General Relativity; right Mr. Bethell?) that with only the time-dilation effect and the principle of least time one can indeed derive an expression for the bending of light — but the expression is wrong by a famous factor of 1/2. The reason is that there are TWO contributions to the bending of light by a massive object: (1) the time dilation effect — which in GR has to do with the “time-time component” of the metric tensor, and (2) an effect that depends on the spatial geometry — which has to do with one of the space-space components of the metric tensor (in saying this I am using coordinates in which the metric tensor is “stationary”). In General Relativity (GR) these two contributions to the bending happen to be equal in magnitude, so that in GR the bending is TWICE what one would find by just taking into account “Beckmann’s” time-dilation effect. In fact, as everyone knows, what was significant about the confirmation that the Sun’s gravity bent starlight was not just that the bending was seen, but that the amount of bending confirmed Einstein’s famous factor of 2.
There is just no way that Beckmann can have gotten the correct answer for the gravitational bending of light from just time-dilation and the least-time principle. The amount of time dilation is unambiguous — it can be derived in several different ways, and there is no room to monkey with that. The “least-time principle” is also unambiguous — it is a very standard exercise in the “calculus of variations” that every person who has taken an intermediate or advanced course in mechanics learns and can do practically in his sleep. Combining these two things, one gets an unambiguous — and WRONG — answer. If Beckmann got the right factor of 2 using only time-dilation, it can only have been by screwing up the math.
Oh, well. What can I say? Why don’t we leave all this to the real, live physicists, not the pretend physicists, hmm?
I repeat the challenge to Mr. Bethell: are you ready to show you can actually do simple physics problems correctly and not just talk about hard ones? I said I wouldn’t respond to you unless you agreed to my challenge. But, really, this was just too tempting.
Mr. Bethell would have us believe that he can correctly analyze a very complicated physics problem, namely the one involved in the Hafele-Keating experiment. This experiment involves (a) gravitational effects (i.e. GENERAL Relativity), (b) specifically the gravitational field of a rotating massive body [which is more complicated to work out than the field of a non-rotating body], and (c) objects moving in circular orbits around such a body. To analyze this problem one needs to be able to use the mathematics of General Relativity, which involves tensor calculus and differential geometry in curved four-dimensional space-time. In other words, Mr. Bethell’s “high school algebra” is definitely NOT sufficient. I will bet my silk pajamas that Mr. Bethell could not do the math required to properly analyze this problem in the context of Einstein’s theory even if life depended on it. (I haven’t analyzed the Hafele-Keating experiment, but I know enough to do it. It would just take me a lot more time than I am willing to spend.)
However, let us suppose that by some miracle Mr. Bethell is able to analyze such a complicated problem in General Relativity. Then it should be utterly trivial for him to do the kinds of simple, standard problems in special relativity that I have challenged him to prove to the world that he can do. The problems I propose that he be tested on are about 100 times easier than the one he is pretending to be able to do. I am also willing to bet my silk pajamas that he will never accept my challenge.
To show my good faith, I will answer his question. The answer is that the statement made by Jeremy Bernstein (“A moving electron or any massive object becomes more massive when it is motion with respect to an observer than when it is at rest with respect to the same observer.”) is quite correct as to its substance, but is phrased in a somewhat antiquated way. In the old days, people would say that an object of “rest mass” m moving with velocity v has an energy given by M c^2 (M c-squared), where M is its “mass” when moving at speed v, which larger than its rest mass m by a factor called gamma. In other words the “mass” of the object was spoken of as “increasing” when the object was in motion. That is an old-fashioned terminology, however. Experts rarely use the word “mass” in this way anymore. Nowadays, the word “mass” almost always refers to the rest mass of an object. The “rest mass” is an invariant quantity, it is the same in every frame. So, nowadays people would say that the energy of an object “with mass m” moving at velocity v is given by (gamma m c^2), while its energy at rest is given by just (m c^2). In short, people use the word “mass” to refer to something that stays the same no matter how the object is moving, and say that the energy of the object increases when it moves.
This is not a substantive point. It refers to terminology. I would also note that the word “observer” is quite superfluous here. One could simply say (with less chance of misleading the ignorant) “the energy of an object in a frame where it is moving is greater than its energy in a frame where it is at rest.” That, in itself, is no big deal. The same statement is true in Newtonian physics — but the mathematical expression for the increase in energy is somewhat different in Einsteinian and Newtonian physics.
I also agree that one could get another true sentence from Bernstein’s sentence by changing the words “more massive” to “longer”, changing “any object” to “any object of finite length”, and deleting the words “a moving electron” (since electrons are not known to have any length — in our present theory, electrons have no length — they are “point particles).
BEND IT LIKE EINSTEIN:
I am very amused to learn from Mr. Bethell that Petr Beckmann had the brilliant idea that he could explain the famous “bending of light” by the gravitational fields of massive objects by using only the “time-dilation” effect and Fermat’s principle (also called “the principle of least time”). This is part of Beckmann’s great idea?!?! (a) Its not original, and (b) it’s wrong — and very, very famously wrong. Everyone who has studied General Relativity knows (except Beckmann and Bethell, it seems — but Bethell has never actually taken a course in General Relativity; right Mr. Bethell?) that with only the time-dilation effect and the principle of least time one can indeed derive an expression for the bending of light — but the expression is wrong by a famous factor of 1/2. The reason is that there are TWO contributions to the bending of light by a massive object: (1) the time dilation effect — which in GR has to do with the “time-time component” of the metric tensor, and (2) an effect that depends on the spatial geometry — which has to do with one of the space-space components of the metric tensor (in saying this I am using coordinates in which the metric tensor is “stationary”). In General Relativity (GR) these two contributions to the bending happen to be equal in magnitude, so that in GR the bending is TWICE what one would find by just taking into account “Beckmann’s” time-dilation effect. In fact, as everyone knows, what was significant about the confirmation that the Sun’s gravity bent starlight was not just that the bending was seen, but that the amount of bending confirmed Einstein’s famous factor of 2.
There is just no way that Beckmann can have gotten the correct answer for the gravitational bending of light from just time-dilation and the least-time principle. The amount of time dilation is unambiguous — it can be derived in several different ways, and there is no room to monkey with that. The “least-time principle” is also unambiguous — it is a very standard exercise in the “calculus of variations” that every person who has taken an intermediate or advanced course in mechanics learns and can do practically in his sleep. Combining these two things, one gets an unambiguous — and WRONG — answer. If Beckmann got the right factor of 2 using only time-dilation, it can only have been by screwing up the math.
Oh, well. What can I say? Why don’t we leave all this to the real, live physicists, not the pretend physicists, hmm?
I repeat the challenge to Mr. Bethell: are you ready to show you can actually do simple physics problems correctly and not just talk about hard ones? I said I wouldn’t respond to you unless you agreed to my challenge. But, really, this was just too tempting.
November 30th, 2009 | 5:39 pm
Oops, somehow I duplicated the above message.
A factor of 2 error — just like Beckmann!!
December 2nd, 2009 | 1:11 pm
I have not finished reading Mr. Bethell’s book yet but I think now would be a good time to chime in on the conversation anyway. From what I have read so far, Mr. Bethell has done a good job of showing that Einstein’s relativity is riddled with inconsistency. Inconsistency in Einstein’s interpretation of his own theory and inconsistent interpretation of experimental results from other scientists. If this is such a solid theory that scoffs at any and all naysayers – then why all of the confusion?? If this theory was as solid as physicists would have you believe, then the arguments would have been wrapped up decades ago and we would all be on the same page by now, don’t you think? Historically, defenders of Einstein have criticized the relativity skeptics by saying that they don’t understand the truly technical aspects and therefore the many nuances that demonstrate the theory’s validity. We shall see about that.
In Bethell’s introduction, Howard Hayden discusses that according to special relativity, the hypothetical scientist traveling with high-speed muons would conclude that muons outside the accelerator have longer half-lives than the traveling ones. He notes that this has not been tested. Actually, Bethell and Hayden should be happy to know that the current GPS system provides that very test and clearly demonstrates that special relativity is not valid.
A couple of years ago, I decided to take a different route than Mr. Bethell’s. I chose to investigate what SR had to say about time dilation (instead of light speed constancy) and soon realized that GPS could be used to test Einstein’s theory. As mentioned in Mr. Bethell’s book, the satellite clocks run at a different rate than the clocks remaining on Earth predominantly due to gravity and velocity which are then corrected with pre-launch adjustments and ongoing corrections from the ground. Hypothetically, if we were to launch a satellite whose clock was gravity adjusted only, its clock would run slower by 7000 nanoseconds per day from our perspective on the ground due to relative velocity. Special relativity says that from the perspective of the satellite, the ground clocks should also be running 7000 ns/d slower. A symmetrical effect, much like the muon example. But in reality, the satellite’s clock is pre-launch corrected and sped up by 7000 ns/d (ignoring gravity for a moment) which should then (if Einstein is correct) produce a net effect of the ground clock now running 14000 ns/d slower from the perspective of the satellite clock. But Einstein’s problem is that once all adjustments are made to get the satellite clocks to be in sync with the ground, the ground is also in sync with the satellites. If they were not synced from both perspectives simultaneously, the current system wouldn’t work. So SR says they should be out of sync but yet they clearly are not!
Now, a lot has been said about not being able to use this rotating frame as a direct test of SR because it is not inertial. In reality it is a very good test for SR. Physicists and engineers use the near 4 km/s velocity of the satellite as the basis for their 7000 ns/d discrepancy. This is SR in a nutshell. The tricky question, however, is what do we do from the perspective of the satellite? The answer is that if Einstein’s theory is even partly correct, the clock altering effects may possibly come from a combination of circumstances (velocity and induced gravity). But even if we give Einstein all of the latitude in the world and assume his induced gravitational field from the centripetal acceleration is altering clock rates through an entirely different mechanism than relative velocity (which I have never seen evidence for) then the rough calculation of the centripetal acceleration (0.62 m/s2) would take back only about 2800 ns/d of the 14000 ns/d and the clocks would still be out of sync by about 11200 ns/d. In other words, much of the clock difference from the perspective of the satellite (ignoring higher gravitational position) comes from the relative velocity component and only a small component (if any) of the net clock difference comes from the non-inertial centripetal acceleration. So the induced gravity of the orbiting satellite affecting the SR test is much ado about nothing. Either way, each corrective update from the ground would surely send the whole system further and further out of sync. I hope you followed all of that. It is very important.
December 2nd, 2009 | 3:21 pm
What Mr. Kennedy says strikes me as utter gibberish.
December 2nd, 2009 | 3:37 pm
I was going to say, “Where do you even begin…??”
December 3rd, 2009 | 4:06 pm
Interesting: No answer yet about how Beckmann could get the correct factor of 2 using only the time-dilation effect.
December 3rd, 2009 | 4:55 pm
Gibberish? Really? Okay – I will do this in steps.
A key feature of special relativity is that two clocks (or frames if you like) in relative inertial motion each experience time dilation from the other’s perspective. So if I get in a rocketship and accelerate to some high constant velocity away from my stationary space station, The observers on the station will see my clocks running slower and at the same time I will see the space station clocks running slower during this constant velocity (inertial) portion of my journey. SR says that this is not an illusion, rather time itself actually slows from the perspective of the other – for each observer simultaneously! As a physicist, I trust you are already familiar with that.
We have all kinds of experimental evidence demonstrating that from the stationary perspective, particles and atomic clocks that were accelerated to a higher velocity experience time dilation. But if SR is valid, then a test to view stationary clock rates from the perspective of the fast-moving object should also verify that the stationary clocks have slowed too. Has this been tested? Are there any papers that cite experimental evidence that this bizarre simultaneous dilation occurs? The answer is: No – because it doesn’t happen.
Since I don’t own a rocketship or live on a space station, I decided to use the current GPS system to test the validity of Einstein’s theory. Because if Einstein is correct, we on the ground would view the satellite’s clock running slower as a consequence of its velocity (ignoring gravity for a moment) while at the same time – the satellite would simultaneously view our ground clocks as running slower. Again, I trust that you are still with me.
This would be a simple test but for one, possibly two problems: Velocity isn’t the only thing that affects clock rates. As you well know, the closer an object is to a gravitational source, the slower its clock will run. This translates to (now ignoring any velocity for a moment) ground clocks running slower than elevated clocks, such as ones on satellites 11,000 miles high. So if we could pretend for a moment that the world were not turning and a satellite was magically suspended motionless 11,000 miles above our heads, we would see the satellite clock running 45,000 ns/d faster than our ground clocks purely as a consequence of being in different gravitational positions. Does this mean then that we can’t use the GPS system as a test? Thankfully, we still can, we just need to compensate for gravity. If we pre-adjusted the satellite clock to run 45,000 ns/d slower (which is the exact gravity compensation) then after it reached 11,000 mile altitude, it would be as if gravity were no longer a factor. It’s like spotting your golfing buddy 4 strokes before you even begin play. If you are normally 4 strokes better than he, the playing field is now level since you spotted him the 4 and the fact that you are better is no longer a factor. The difference has been equalized. With regard to the orbiting satellite and the earth – They are now on equal footing, gravitationally speaking.
This now allows us to isolate and examine the effect of velocity on the 2 clocks. Now if we launch a gravity corrected satellite clock that orbits the earth at nearly 4 Km/s, we should see a satellite clock that is running 7,000 ns/d slower than our control clocks on the ground. If we stay with this example for a moment and also pretend that the satellite’s velocity is inertial, then SR says the satellites should also view the ground clocks as running 7,000 ns/d slower than their clocks. So far all we have been using is simple arithmetic, so I will assume you are still with me. Now what really happens is that the pre-launch adjustments are for both gravity and velocity so there is no 7,000 ns/d clock difference from our perspective. We see the satellite in sync with our ground clocks.
So the question is: if SR is correct, how will the ground clocks be running from the perspective of the satellites? Well with a gravity adjust only, we know SR predicts the ground to be running 7,000 ns/d slower, but with the velocity compensation that speeds up the satellite 7000 that would now put the ground clock as running the original 7000 slower plus an additional 7000 more which is a total of 14,000 ns/d slower from the perspective of the satellite.
Now comes the 2nd possible problem: The satellite isn’t moving inertially. This is not an issue from the perspective of the ground. Physicists actually use SR to compute the clock difference and consider the circular motion no different from any other relative motion. This is in agreement with Einstein’s treatment of comparative clock rates of rotating frames by the way. I’m sure you already knew that too. Where the fun comes in is trying to interpret how the moving satellite (which has a centripetal acceleration) will view the ground with this non-inertial, induced gravity.
One could make the argument that no experiment has ever verified that objects subjected to induced gravity experience an additional time dilation by an entirely different mechanism from inertial velocity, but I’ll tell you what: I’ll assume Einstein is correct on that point and assume the satellite is viewing the earth clocks (which have a relative velocity) that have a fixed distance from the satellite’s induced gravity from its centripetal acceleration. Still with me Steve?
If we count Einstein’s induced gravity’s influence on an otherwise inertial frame, we find that the centripetal acceleration yields a value less than one (A = about 0.62 m/s2, compared to a whopping 9.8 m/s2 here on the surface of the earth) so the noninertial contribution to the total ground time dilation is about – 2,800 ns/d. This means we would subtract out 2,800 from the 14,000 which still leaves a daily ground clock discrepancy of 11,200 ns from the perspective of the satellites if SR is correct. But since the satellites get corrective uploads from the ground about every 12 hours, we know that the clocks are “in sync” from each perspective simultaneously. I’ll say it again: SR says the ground clocks are out of sync from the perspective of the satellites, but the GPS system only works if they are in sync. If this also appears as gibberish to you, I suggest you ask some of your fellow professors to walk you through this.
December 3rd, 2009 | 11:03 pm
Dear Chris, Your step-by-step explanation has indeed made clear what you are trying to do! You are trying to calculate how things will appear in an accelerating frame by first treating it as an inertial frame, and then applying a correction factor. This correction factor you conceive of as a gravitational time dilation factor that arises from the “induced gravity” experienced in an accelerating frame. Unfortunately for you, one CANNOT calculate how things will appear in an accelerating frame in such a way. You are trying to use simple analogies to guess an answer which can only be arrived at through a careful mathematical derivation. It is not simply a matter of applying an extra “induced gravity” time dilation. Your calculation has no resemblance whatever to the correct way of calculating how things look in an accelerating frame.
Besides that — not that it really matters here — you don’t appear to know how to calculate gravitational time dilation. You seem to be under the impression that it is simply proportional to acceleration. (That is evidently how you get the figure of 2,800 ns/d for the “correction”: 2,800 ns/d is to 0.62 m/s^2 as 45,000 ns/d is to 9.8 m/s.) But gravitational time dilation is NOT just proportional to acceleration. For example, at a distance r from a spherical body of mass M, a clock runs slower (relative to a clock at infinity) by a fraction that is (for weak gravitational fields) GM/r, whereas the gravitational acceleration there is GM/r^2 (i.e. r squared, not r, in the denominator.
To be frank, my “fellow professors” — not just at my university but anywhere — would not give such nonsense a moment’s notice — unless you were in their class, in which case you’d find all sorts of red ink written all over it. I, however, take a certain clinical interest in it.
December 4th, 2009 | 12:20 am
For the last four days I have been working on an article more or less non-stop and haven’t had time to look at anything here. (Mr. Barr will be glad to hear that the article had nothing to do with physics.)
I am too tired to think about all this right now but I’ll go through Mr. Barr’s latest tomorrow and do my best to come up with a reply later in the evening.
But I will say this. Can someone please remind me where I said anything about Beckmann claiming he could derive the bending of starlight by use of time dilation and Fermat’s Principle? I don’t think I could have said any such thing because, for one thing, Petr didn’t believe that time dilation was a reality.
Mr. Barr, can you give me a “source” for that? Maybe you are confused or maybe I am or maybe it’s too late at night.
He is likely to be at a disadvantage, however, because taking a look at my own journalistic account of Beckmann’s reinterpretation of relativity is surely beneath his dignity. I doubt also that he would so much as crack a book by Beckmann — an “engineer” as he told us in his initial post. (Beckmann’s book on this is titled “Einstein Plus Two” if anyone wants to look for it. I’m not sure if it is available on Amazon or not, but I’m pretty sure it’s not inexpensively available anywhere.)
To understand what Beckmann is saying, therefore, it seems that Mr Barr will be dependent on what I write here. And if I am his sole source, I must have been the source of his confusion! Oh dear. Must be my fault. I’ll try to explain it more simply tomorrow.
One point that Mr Barr doesn’t seem to have grasped yet is that Beckmann’s theory purports to explain such things as the bending of starlight WITHOUT relativity, general or special. He doesn’t make use of the “metric” that Mr. Barr alludes to. Beckmann’s position is not that GRT is wrong but that it is unnecessary. It gives the right results by a complicated method that can be simplified.
Beckmann rejects time dilation (and space contraction) completely. It’s clocks that slow down — not time — when they pass through the local gravitational field. That is quite different from SRT. Special relativity will have to go, I believe. Its advocates either have to concede that it has been falsified or rescue it by saying that all Earth-bound frames are rotating and therefore non-inertial. If so the theory is unfalsifiable.
One simple bedtime question for Mr Barr: Do you think there is an ether, or luminiferous medium? Or do you agree with Einstein who said in 1905 that such a light medium is superfluous? (Not a trick question, just a request for his thinking on this matter.)
–Tom Bethell
Tom Bethell
December 4th, 2009 | 8:46 am
I’d be happy to tell you where you said this Mr. Bethell. It was in your previous post here. Your exact words:
“[I]t did bring the theory into line with Petr Beckmann’s theory, in which the local gravitational field is equivalent to the luminiferous medium. Motion through this field causes clocks (not time) to slow down. When the clocks are moved to a higher altitude, the gravitational field becomes more attenuated, and there the clocks speed up (much as planes encounter less air resistance and therefore save fuel when they fly higher). Thus does Beckmann’s theory give the same results as general relativity, but in a much simpler manner; bending of starlight is explained by Fermat’s Principle, no need for “curvature of spacetime,” etc.”
So according to your own words, Beckmann explains the bending by (a) the faster clocks at higher altitude and (b) Fermat’s principle. Now the slowing of clocks at low altitude and faster clocks at high altitude is what is called by everyone “gravitational time dilation”. You and Beckmann don’t call it that, but it really doesn’t matter what you call it or how you explain it. What matters for the point I made is only the magnitude of the effect. The magnitude of the effect is precisely known and measured. Moreover, there are several ways to derive the magnitude of this effect (the different rates of clocks at different altitudes), including a very well-known and very elegant argument based on conservation of energy. So even if you explain the slowing of clocks at different altitude in some way different from everyone else, you better come up with the same number for it, or else you will be blatantly violating energy conservation. I repeat: from the effect of the different rate of clocks at different altitudes and Fermat’s principle one does indeed get bending of light — but by half the amount predicted by Einstein’s theory and confirmed by experiment.
I am quite happy to learn of Beckmann’s ideas from your account of them, which I assume to be a fair one. I have not read Beckmann’s book, nor do I intend to do so any time soon — but not because he is an engineer. You would like the readers of FT to think I have contempt for engineers, simply because I said that a degree in Electrical Engineering does not in itself mean that one understands General Relativity or Special Relativity. That is a method of argumentation that is really unworthy of you. Let me reassure any readers of FT who might still be reading this: my late and dearly beloved father was for years Assistant Dean at the Engineering School of Columbia University and instiulled in me a tremendous respect for engineers and engineering. I considered the possibility of going into engineering myself.
As to whether an “aether” exists, it depends on what one means by the word. If one means a medium of the propagation of light (“luminiferous” aether), one could consider the electromagnetic field itself as such an aether. Something that fills empty space (the “vacuum”) and has energy and pressure associated with it? Well, in quantum field theory the vacuum does have things going on it it (vacuum fluctuations), and does contain energy and pressure — the so-called “cosmological constant” or “dark energy”. One could consider that to be an “aether”, if one wished. The important thing however is this: if these things are thought of as aethers, they are aethers with a very special property, namely they are Lorentz covariant. The stress-energy tensor of the “vacuum” is Lorentz covariant, and so is exactly the same in every frame.
The word aether is not used anymore in physics, and that is why there is no precise technical meaning to the term. The precise question is this: in empty space do the laws of electromagnetism (Maxwell’s Equations and the Lorentz Force Law) have the same mathematical form in every inertial frame — i.e. are they covariant? The “Aether theories” of the nineteenth century said no. SR said yes. If that is the question, the answer is yes and the aether theories were wrong.
Let me know when you can get the bending of light — including the factor of 2 just from the altitude-slowing of clocks and Fermat’s principle.
December 4th, 2009 | 10:27 am
One further point. It is Mr. Bethell’s statements and ideas on relativity that I have been concerned to attack. It is logically possible — though it strains credulity — that Petr Beckmann was saying reasonable things and that Mr. Bethell has completely distorted them, and that it is only Bethell’s rendition of Beckmenn that is nonsensical. Maybe by reading Beckmann’s book I would discover that to be the case. But then shame on Mr. Bethell for going around and uttering utter balderdash in Beckmann’s name.
December 5th, 2009 | 3:41 am
I posted a lengthy communique here at about 3: 35 a.m. but it did not show up. Not censored I hope!
December 5th, 2009 | 4:13 am
[Re-posted below, I hope]
WE BOTH LOVE ENGINEERS
First let me deal with the “engineer” issue. Barr wrote at the outset: “Bethel tells us that Beckmann was an engineer.” But, he adds, “knowledge of engineering in itself no more qualifies a person to talk about fundamental physics than does knowing about baseball or butterfly collecting.”
Mr. Barr here strongly implies that Beckmann was not qualified to “talk about” fundamental physics, including relativity theory. He refers, arrogantly, to “Beckmann’s crackpot ideas about relativity theory,” when he hasn’t even opened a book by Beckmann. He really shouldn’t have done that. It was not the hallmark of a scientist.
He now says that I would like readers of his blog to think that he has “contempt for engineers.”
The man cannot think or argue straight. The impression he gave was not that he had contempt for engineers but that he had deliberately misrepresented Beckmann’s credentials in order to make it seem that he was unqualified to criticize relativity theory. Beckmann, in short, was out of his depth and had crackpot ideas. The knowledge that engineers possess no more qualifies them to “talk about fundamental physics” than does the knowledge that butterfly collectors possess.
I never in my life called Beckmann an engineer, which was Mr. Barr’s first mistake. Later, he reveals that he had looked up Beckmann’s qualifications so he actually knew perfectly well that Beckmann taught electrical engineering at the University of Colorado. Further, Barr pretended that I had called him an engineer in order to justify his own mislabeling. I call that dishonest.
Later, I asked him in what way Beckmann’s training in Prague fell short of what is needed to understand “fundamental physics.” He has not done so. Maybe in the interim he took a look at the list of PB’s publications.
I am glad Mr. Barr has a high opinion of engineers. So do I (my grandfather was one). What I particularly admire about them is that they pay their own way and do not depend on government funding. The buildings they build have to stand up without support, which is not always the case with the structures of theoretical physics. (A man I know who teaches astronomy at Caltech was asked by his mother what he thought about when he gazed through a telescope at the heavens. “Funding,” was his one-word reply.)
I am glad that Barr now admits the possibility that Beckmann is saying “reasonable things.” If he is prepared to abandon his (ad hominem) argument against Beckmann being qualified to write a book critical of relativity, then I am prepared to abandon the engineer issue and say no more about it.
Furthermore, Mr. Barr can call me all the names he wants and I won’t mind. Ignorant-denialist-uttering-utter-nonsensical-balderdash. Keep ‘em coming. Water off a duck’s back. I am a journalist.
SCIENCE NOT AN AUTHORITARIAN FIELD
Mr. Barr he has to get over his obsession with qualifications. It is a serious mistake he is making. He seems to think that science is analogous to religion, or more specifically the Catholic Church. The church is a structure based on authority but science is not. You really can’t call yourself a Catholic and go around saying that the Pope is talking nonsense. But there is no analogy to that in science. The whole glory of science is that what someone says about a scientific theory or law is unaffected by his credentials. The denialist’s denial may after all be correct. Mr. Barr probably knows that with his head but his heart clearly rebels against it. (“I am the expert here! Go away you silly little amateurs!” is the attitude that he conveys.)
Secondly, he has to demonstrate some error in what Petr Beckmann is saying. I am sorry that for the time being he will have to depend on my own version of Beckmann’s ideas. But that is a problem that he has imposed on himself.
Now, to the substantive issue that he raises. I wrote above:
“Can someone please remind me where I said anything about Beckmann claiming he could derive the bending of starlight by use of time dilation and Fermat’s Principle? I don’t think I could have said any such thing because, for one thing, Petr didn’t believe that time dilation was a reality.”
He replied:
I’d be happy to tell you where you said this Mr. Bethell. It was in your previous post here. Your exact words:
“[I]t did bring the theory into line with Petr Beckmann’s theory, in which the local gravitational field is equivalent to the luminiferous medium. Motion through this field causes clocks (not time) to slow down. When the clocks are moved to a higher altitude, the gravitational field becomes more attenuated, and there the clocks speed up (much as planes encounter less air resistance and therefore save fuel when they fly higher). Thus does Beckmann’s theory give the same results as general relativity, but in a much simpler manner; bending of starlight is explained by Fermat’s Principle, no need for “curvature of spacetime,” etc.”
“So according to your own words,” Barr continues, “Beckmann explains the bending by (a) the faster clocks at higher altitude and (b) Fermat’s principle.”
Then Mr. Barr writes:
“Now the slowing of clocks at low altitude and faster clocks at high altitude is what is called by everyone “gravitational time dilation”. You and Beckmann don’t call it that, but it really doesn’t matter what you call it or how you explain it.”
CONFLATES SPECIAL AND GENERAL
It is in the last paragraph that Mr. Barr goes off the rails. He conflates the special and the general theories when normally they are kept separate. He even raises the question in my mind that he may be the one who is not competent to discuss “fundamental physics.”
Anyway, could he give me a reference to his claim that “everyone” conflates gravitational (altitude) effects and time dilation (special relativity) effects by referring to “gravitational time dilation”? Does “everyone” include Einstein I wonder? No doubt it is possible to mix them together – e.g. by imagining a clock moving both horizontally and vertically (diagonally, as it were) but it certainly makes things more complicated.
The “slowing of clocks” (as Petr Beckmann explained what is really going on) does not belong to special relativity, and “time dilation” is no part of Beckmann’s theory. That is the point that I hope to convey to Mr. Barr.
In special relativity, time dilates in the reference frame that is moving with respect to an observer. And here we are talking about inertial reference frames in which gravity plays no role.
Mr. Barr may not have grasped the big difference between the claim that a clock is running slow and that time is running slow. Here is the entirely orthodox relativist A.P. French whose book on special relativity is or was used in college courses. After quoting French I will quote Beckmann so that the difference between the two theories is made clear. Beckmann does not agree with French, but French correctly states the Einstein theory:
The claim that “moving clocks run slow” is “misleading,” French says. It
“suggests that some essential change occurs in the operation of the clock itself, that the physical basis of its operation has somehow been modified, whereas it is a central feature of relativity theory that just the opposite is true—that the operation of the clock described in its own frame of reference is completely unaffected.” [French, Special Relativity, p 105]
Beckmann says, on the other hand, that the inner working of an atomic clock really is affected by its motion. To illustrate the point, he asks us to imagine two identical pendulum clocks that are transported around the globe, one to the east, one to the west. If flown eastward the transported clock will read fast, if westward, it will read slow. Time dilation? No, says Beckmann. “The period of a pendulum varies inversely as the square root of the downward force on it, and that force is the vector sum of gravitational attraction and the centrifugal force due to the earth’s rotation.” That force increases when the clock moves east, because its angular velocity about the earth’s center increases, etc. “This is an inherent change, one that an observer traveling with the clock (i.e. at rest with respect to it), could measure by comparison with an equally accurate wrist watch—if it is unaffected by centrifugal force.”
Beckmann cites this as a change in a clock “which might easily be mistaken for a change in the flow of time.” [Beckmann, Einstein Plus Two, p. 78]
Mr. Barr mixes special and general relativity together. Time dilation is explained purely by special relativity, and, as I hope to have shown, it forms no part of Beckmann’s theory. In his theory clocks do inherently slow down as they move horizontally through the luminiferous medium (the local gravitational field of the Earth, in his theory.)
At a higher altitude what Clifford Will calls “gravitational blue shift” takes effect and the “flying clock will tick faster than the ground clock.” This is where the explanation according to general relativity enters the picture. “The two effects, gravitational blue shift and time dilation, tend to offset one another.” [Will, Was Einstein Right? p 56] Which effect predominates depends on whether the clock motion is to the east or the west.
Beckmann argues that at higher altitude the gravitational field is thinner, more rarified, and here clocks really do run faster (than clocks lower down). Clocks moving horizontally really do run more slowly (than stationary clocks) because the field offers resistance to its motion as a clock moves through it.
The ether that Michelson was looking for was thought to be uniform throughout the entirety of space. The most important change introduced by Beckmann is that for him the ether or luminiferous medium is real but NON-uniform. It is denser closer to massive objects. Therefore, if a light beam from a distant star passes by the Sun, it is bent simply by Fermat’s Principle. As the ray approaches the sun it “slews around” slightly (as Eddington put it). It was one of the key things that Einstein’s GR predicted. As the light beam enters the denser field, it also slows down slightly in addition to changing direction. Here everything is explained by classical physics plus a non-uniform luminiferous medium. No need for general relativity or the “curvature of four dimensional space-time.”
(Whether it’s needed for Mercury’s orbit is a complex and interesting question to which I devote a chapter but I won’t go into it here.)
In 1968, Frank Tangerlini published an article in Am J. Physics arguing that a correct value for the gravitational deflection of light could be calculated without general relativity by using Snell’s Law, formulated in the 17th century. (Closely related to Fermat’s Principle.) When a light ray enters a denser medium it is refracted at a certain angle and Snell’s Law demonstrates how the change in angle is related to the change in velocity. (This route was not open to Einstein, who had postulated a constant speed for light as a cornerstone of his theory.) Tangerlini showed that these calculations could be used to give exactly the formula that Einstein used for the refraction of starlight. [Tangerlini, On Snell’s Law and the Gravitational Deflection of Light,” Am J. Physics, Nov 1968, pp 1001-04.] Something similar was done by Tian and Li, also in Am J. Physics, in 1990.
If I have still not given a clear explanation of what Petr Beckmann is about, then that is my fault. I was warned before I wrote this book that for those who have accepted SRT and GRT for decades, and teach it, the whole subject gets cemented into their heads and they are most unlikely to accept anything new. But one has to start somewhere, and there is no harm in trying. For younger people, there is at least a hope. What is that quote (Max Planck?) about scientific theories not changing until department heads die off? There’s a lot of truth to it.
–Tom Bethell
December 5th, 2009 | 2:59 pm
Bethell (just now) “I never in my life called Beckmann an engineer”
Bethell in the American Spectator article: “Petr Beckmann, a Czech immigrant who taught electrical engineering at the University of Colorado”. Not only did I look up Beckmann’s record, I read a few of his papers. I also am aware of what he published early in his life, before he went to Colorado.
Mr. Bethell, I would never say to you “go away silly little amateur”. You don’t rise to the level of a decent amateur. If you were an amateur — which implies someone who really loves the field — you might actually have taken the trouble to learn physics at the required level to talk about its technicalities accurately, instead of taking a purely journalistic approach to it. How often must I say it? It is not a question of credentials but of knowledge and understanding. Every year all over this country tens of thousands of students, some of them probably no more intelligent than you, take real courses in college-level physics and learn quite a lot — and they don’t all go on to become professional physicists. Some become teachers, some even become journalists.
These courses are open to “amateurs” also. There is no excuse — even for a journalist — to talk about things he doesn’t understand.
I am not sure what substantive point Bethell is making about the term “gravitational time dilation”. There is a well-known effect that is normally called “gravitational time dilation” (see Steven Weinberg’s classic textbook, for example, or many other standard texts, or if you’re in a hurry just look at the wikipedia article on “gravitational time dilation”). The effect results in what is called the “gravitational red shift of light” (or the opposite “gravitational blue shift”), it also results in identical clocks at different altitudes registering different times. The effect has been observed and measured. The standard (GR) explanation is that this is a gravitational effect. But even if one has some other explanation of the origin of the effect than the GR one, the magnitude of the effect is not in question, because it has been measured. Moreover, very general theoretical principles that fall well short of Einstein’s theory of gravity imply that such an effect must exist and must have a certain magnitude. You can call the effect something else, if you want. But this effect — the altitude dependence of clock readings — is not enough to account for the bending of light. It does (with the fermat principle) give a bending, but the wrong amount.
I think Mr. Bethell is accusing me of “conflating” special and general relativity, because the word “time dilation” is used for an effect in special relativity, and I am using it for an effect in general relativity (the altitude dependence of clock readings). There is no conflating going on, however. There are two distinct effects: the SR effect is usually called simply “time dilation”, while the GR effect is usually called “gravitational time dilation”. For example, if one looks at Steve Weinberg’s classic book “Gravitation and Cosmology”, one sees in the Index on page 656: “Time dilation (gravitational): 79-85″. If one turns to the pages 79-85, one finds that this is Section 5 of Chapter 3, and is entirely devoted to the purely GR effect of gravitational time dilation. The title of that section is, by the way, just “Time Dilation”.
Mr. Bethell tells me that science is not “authoritarian”. I completely agree. Now let me just make a practical suggestion. Why doesn’t Mr. Bethell (perhaps with the aid of a “credentialed” person to facilitate the effort, or even with a credentialed person submitting it under his own name) just submit a paper explaining Beckmann’s/Bethell’s ideas on relativity, bending of light, or gravity to Physical Review, or Physics Letters, or some other standard refereed journal? I think I know why. If he did it is virtually certain that the paper would be rejected by the referees as unsuitable for publication. In fact, even more likely the editor would not bother to send it to a referee. Certainly Petr Beckmann never published any paper in Phys. Rev., Phys. Lett., etc. containing his gravitation theories.
I guess this refusal of the “white coated priesthood” (Mr. Bethell’s term, I believe) to take Bethell & Beckmann seriously would, in Mr. Bethell’s eyes just show that the whole scientific world is “authoritarian”. So, at least I am not alone in this horrible vice.
I guess I am part of Mr. Bethell’s white-coated priesthood. I think I will end my part of the conversation here. Maybe if Mr. Bethell answers in QUANTITATIVE terms — including the all-important and historically famous factor of 2 — the question I posed to him about Beckmann’s theory, I will return to the discussion. We white-coated types care about numbers. In physics, if you cannot get the numbers to work out, the discussion is over.
i would also be very happy to return to this discussion, if mirabile dictu, Mr. Bethell decides to accept my challenge to show the work that he can calculate and get the right answers even in very simple problems (undergraduate level) in SR, GR —- or for that matter Newtonian physics. The terms of the challenge are described above. (I’ll add a few more here: If he takes such a timed test, and it is proctored to prevent cheating, and he passes it, I’ll pay him $1,000.)
I think the fog of angry denunciations of me as an authoritarian, a bad arguer, a mean-y who calls people nasty names, a guy who doesn’t know my own business, and all the rest are to distract readers from the fact that he won’t accept my challenge, or answer the key question I posed.
December 5th, 2009 | 3:55 pm
where did my reply go?
December 5th, 2009 | 3:57 pm
Oh well, there appears to be a problem with the site. When I get the energy to retype my entire reply to Steve’s statements – I’ll be back.
December 5th, 2009 | 4:18 pm
One more try:
Steve,
Sorry about the delay. I was playing poker until 4am. You are one of the few physicists who have taken the time to understand my argument so that your criticisms can be specific and meaningful. Thank you. It’s much better than what I usually get. Anyway, I finally have my wits about me so here goes:
You said:
To be frank, my “fellow professors” — not just at my university but anywhere — would not give such nonsense a moment’s notice — unless you were in their class, in which case you’d find all sorts of red ink written all over it. I, however, take a certain clinical interest in it.
I say:
Really? Since many in the physics community have been spending their entire careers embracing such nonsense as string theory and its nonexistent extra dimensions, I would have thought they would give my “nonsense” at least five minutes? Oh, well.
You also said:
Besides that — not that it really matters here — you don’t appear to know how to calculate gravitational time dilation. You seem to be under the impression that it is simply proportional to acceleration. (That is evidently how you get the figure of 2,800 ns/d for the “correction”: 2,800 ns/d is to 0.62 m/s^2 as 45,000 ns/d is to 9.8 m/s.) But gravitational time dilation is NOT just proportional to acceleration. For example, at a distance r from a spherical body of mass M, a clock runs slower (relative to a clock at infinity) by a fraction that is (for weak gravitational fields) GM/r, whereas the gravitational acceleration there is GM/r^2 (i.e. r squared, not r, in the denominator.
I say:
I do know how to calculate gravitational time dilation and I actually did it in the most generous way possible for Einstein and his theory still doesn’t hold up. That was my point. I used the gh/c2 formula which is the same formula that Neil Ashby, Robert Nelson and every other GPS expert has used to calculate time dilation. As you surely know, it was originated by Einstein in 1911 and is used to calculate dilation in gravitational fields that are induced by acceleration as well as real gravitational fields. Because this is rotation, you could try using other derivations, but since the distance (h) is in the numerator – I figured I’d give Einstein more bang for his buck, so to speak, rather than use a formula that will calculate a difference less than 2,800 ns/d.
And finally, you said:
This correction factor you conceive of as a gravitational time dilation factor that arises from the “induced gravity” experienced in an accelerating frame. Unfortunately for you, one CANNOT calculate how things will appear in an accelerating frame in such a way. You are trying to use simple analogies to guess an answer which can only be arrived at through a careful mathematical derivation. It is not simply a matter of applying an extra “induced gravity” time dilation. Your calculation has no resemblance whatever to the correct way of calculating how things look in an accelerating frame.
I say:
Again, I am giving Einstein the benefit of the doubt and he still comes up 11,200 ns/d short.
I’m not sure what your exact argument is on this point. Is it that: since there is induced gravity, any time dilation from the relative velocity no longer contributes to the overall clock rate? If that is your argument – then you are not correct. In Einstein’s world of relativity, there are plenty of examples of determining net dilations from multiple factors. The GPS is one example. They don’t suddenly pretend that relative velocity makes no contribution since there are dilation differences from gravity. Both are factored in to get a net total. (See Ashby in particular.) Another example is the turnaround portion of the twin paradox trip. At that point the proper calculation (for an Einsteinian) includes the relative velocity AND the gravitational potential difference from acceleration. If you like – check out Dan Styer’s article in the Am J phys 75 (9) Sept 2007. Although I don’t agree with his premise, at least he represents consistency in the Einsteinian framework on that point.
So to sum up the GPS system, the satellite is whizzing past all of us on the ground and we have a relative velocity from the perspective of the satellite of nearly 4000 m/s. We also (possibly) have an additional minor contribution from a difference in gravitational potential due to a centripetal acceleration.
I will say it one more time: Einstein’s relativity says the ground should not be in sync with the satellites – yet they are.
December 5th, 2009 | 4:20 pm
Steve,
Sorry about the delay. I was playing poker until 4am. You are one of the few physicists who have taken the time to understand my argument so that your criticisms can be specific and meaningful. Thank you. It’s much better than what I usually get. Anyway, I finally have my wits about me so here goes:
You said:
To be frank, my “fellow professors” — not just at my university but anywhere — would not give such nonsense a moment’s notice — unless you were in their class, in which case you’d find all sorts of red ink written all over it. I, however, take a certain clinical interest in it.
I say:
Really? Since many in the physics community have been spending their entire careers embracing such nonsense as string theory and its nonexistent extra dimensions, I would have thought they would give my “nonsense” at least five minutes? Oh, well.
You also said:
Besides that — not that it really matters here — you don’t appear to know how to calculate gravitational time dilation. You seem to be under the impression that it is simply proportional to acceleration. (That is evidently how you get the figure of 2,800 ns/d for the “correction”: 2,800 ns/d is to 0.62 m/s^2 as 45,000 ns/d is to 9.8 m/s.) But gravitational time dilation is NOT just proportional to acceleration. For example, at a distance r from a spherical body of mass M, a clock runs slower (relative to a clock at infinity) by a fraction that is (for weak gravitational fields) GM/r, whereas the gravitational acceleration there is GM/r^2 (i.e. r squared, not r, in the denominator.
I say:
I do know how to calculate gravitational time dilation and I actually did it in the most generous way possible for Einstein and his theory still doesn’t hold up. That was my point. I used the gh/c2 formula which is the same formula that Neil Ashby, Robert Nelson and every other GPS expert has used to calculate time dilation. As you surely know, it was originated by Einstein in 1911 and is used to calculate dilation in gravitational fields that are induced by acceleration as well as real gravitational fields. Because this is rotation, you could try using other derivations, but since the distance (h) is in the numerator – I figured I’d give Einstein more bang for his buck, so to speak, rather than use a formula that will calculate a difference less than 2,800 ns/d.
And finally, you said:
This correction factor you conceive of as a gravitational time dilation factor that arises from the “induced gravity” experienced in an accelerating frame. Unfortunately for you, one CANNOT calculate how things will appear in an accelerating frame in such a way. You are trying to use simple analogies to guess an answer which can only be arrived at through a careful mathematical derivation. It is not simply a matter of applying an extra “induced gravity” time dilation. Your calculation has no resemblance whatever to the correct way of calculating how things look in an accelerating frame.
I say:
Again, I am giving Einstein the benefit of the doubt and he still comes up 11,200 ns/d short.
I’m not sure what your exact argument is on this point. Is it that: since there is induced gravity, any time dilation from the relative velocity no longer contributes to the overall clock rate? If that is your argument – then you are not correct. In Einstein’s world of relativity, there are plenty of examples of determining net dilations from multiple factors. The GPS is one example. They don’t suddenly pretend that relative velocity makes no contribution since there are dilation differences from gravity. Both are factored in to get a net total. (See Ashby in particular.) Another example is the turnaround portion of the twin paradox trip. At that point the proper calculation (for an Einsteinian) includes the relative velocity AND the gravitational potential difference from acceleration. If you like – check out Dan Styer’s article in the Am J phys 75 (9) Sept 2007. Although I don’t agree with his premise, at least he represents consistency in the Einsteinian framework on that point.
So to sum up the GPS system, the satellite is whizzing past all of us on the ground and we have a relative velocity from the perspective of the satellite of nearly 4000 m/s. We also (possibly) have an additional minor contribution from a difference in gravitational potential due to a centripetal acceleration.
I will say it one more time: Einstein’s relativity says the ground should not be in sync with the satellites – yet they are.
December 5th, 2009 | 4:24 pm
Steve,
Sorry about the delay. I was playing poker until 4am. You are one of the few physicists who have taken the time to understand my argument so that your criticisms can be specific and meaningful. Thank you. It’s much better than what I usually get. Anyway, I finally have my wits about me so here goes:
You said:
To be frank, my “fellow professors” — not just at my university but anywhere — would not give such nonsense a moment’s notice — unless you were in their class, in which case you’d find all sorts of red ink written all over it. I, however, take a certain clinical interest in it.
I say:
Really? Since many in the physics community have been spending their entire careers embracing such nonsense as string theory and its nonexistent extra dimensions, I would have thought they would give my “nonsense” at least five minutes? Oh, well.
December 5th, 2009 | 11:52 pm
Dear Chris,
It sounds like you may know how to calculate gravitational time dilation after all, but were making a kind of “a fortiori” argument that might be paraphrased thus “Even if one were to calculate the gravitational time dilation in this (wrong) way, so as to get a bigger effect, it would still not be big enough to save Einstein.”
The Styer article to which you refer sounds very interesting. Thanks for calling my attention to it. From your description of it, it sounds like he shows that in a simple case of the twin paradox, the way things look in the travelling twin’s frame CAN be computed using a gravitational time dilation, where the “gravitation” is due to the traveller’s acceleration. It sounds like he is talking about uniform acceleration in a straight line, and probably using the Rindler metric to describe physics in the traveller’s frame. My guess is that this way of analyzing the problem would be more complicated in the case of the twin moving around the stationary twin in a circular orbit. But maybe it is possible. So what you have been saying makes more sense than it appeared at first. Nevertheless, the way you are doing the calculation is certainly not correct. It is going to be more involved.
I think you are trying to construct a proof that the special relativistic time dilation effect leads to a logical or mathematical contradiction. In that you will surely fail. Whether or not Special Relativity is a correct description of nature, there can be no doubt that it is at least a mathematically self-consistent theory. There is nothing mathematically inconsistent about Minkowski space, and once Minkowski space is assumed, the twin “paradox” follows quite simply.
What this means is that if you manage to analyze the GPS situation using a method similar to (but surely more complicated than)
the method of Styer, you must find what he presumably found, namely that there is nothing inconsistent about the predictions of SR.
Anyway, I encourage you to do the calculation carefully and correctly. If you do, I am sure you will become convinced that SR involves no self-contradiction.
There is an easier way to look at all this, by the way — which, as you know, I am willing to discuss by phone, since that is much easier than tapping away on a keyboard.
I might add that it is refreshing to see that you are actually “putting your money where your mouth is” and attempting a real calculation. It remains, though, for you to do the calculation rigorously and correctly all the way through.
Steve Barr
December 13th, 2009 | 5:39 pm
It dissapoints me to see Mr. Bethell pursuing this argument. I’m a great admirer of his political writings, but it is discouraging to see him charging headlong into a discussion that he is obviously unprepared for (witness his non-answer to Mr. Barr’s challenge.) I understand Mr. Bethell’s contempt for “scientism” and for those people who would use relativity as an argument for moral subjectivism (two completely unrelated things), but it seems totally unwise for him to have persued this course of action. I’ve come to see only recently that many “conservative” critiques of science (evoluton in particular) are really embrassing misfires that make the whole conservative movement look stupid. Now he’s really put his foot in it–writing a book on relativity. I hope for his sake the book is unsuccesful and that this whole business can be forgotten, although the latter scenario is unlikely.
Didn’t it occur to Mr. Bethell at some point in the writing/planning proccess, that he might be dead wrong…and that the overhwhelming likelihood was precisely that he was dead wrong? What was he going to do the minute anyone asked him to prove his ability to discuss the matters in question? Is it possible that Mr. Bethell really does believe that there is some kind of neccesary metaphysical relationship between relativity theory and cognitive relativism? Surely this is an incredibly simple thing to get mixed up about. I can’t believe that Bethell’s thought is that simple but…
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