Einstein's Discovery of General Relativity, 1905-1915

By cjohnson | November 29, 2005 2:42 am

Busy day of meetings related to business of three separate committees. (The day started well, at about 6:00am, with writing and then giving a two hour class on string theory techniques….) But it’s all tiring and time-consuming. Sigh….

….But then the day ended wonderfully. We had Tilman Sauer of the Einstein papers Project give the final colloquium of the semeser, and it was entitled “Einstein’s Discovery of General Relativity, 1905-1915”. It was conceived as an event in celebration of the World Year of Physics or Einstein Year. The abstract:

Ninety years ago, on 25 November 1915, Einstein published the gravitational field equations of general relativity, the so-called Einstein equations. This event marks one of Einstein’s most significant achievements, even in comparison to his three most famous papers of his miracle year 1905. It also presents the end of a long and winding path that began soon after Einstein published his theory of special relativity as an unknown patent expert in 1905. At the end of this path he had risen through the ranks of academic hierarchy to being a member of the Prussian Academy of Sciences in Berlin. The experimental confirmation of his theory by a British eclipse expedition in 1919 then irreversibly catapulted Einstein to world fame, making him the first celebrity in the history of science. In the talk I will give an account of Einstein’s search for a theory of gravitation and a generalized theory of relativity in those years. I will show how an analysis of some of Einstein’s research notes helps us understand his heuristics, and will also comment on his competition with the mathematician David Hilbert in the final days of the discovery of general relativity.

(We can argue about whether he really was the first celebrity in the history of science -Galileo springs to mind- but I agree that the scale and scope was truly and unprecedentedly global in Einstein’s case, given modern communications, etc…. but we can discuss this maybe some other time…..)

Most of the focus of events for this year has been on Einstein’s “Miracle Year” of 1905, in which he wrote a series of five fantastic papers. But it so happens that November the 25th marks the 90th anniversary of his presentation of the field equations of General Relativity. So today, the 28th, was a good day to celebrate that event.

Let me point out the website for the Einstein papers project, and the associated online archive which is a collaboration with the Albert Einstein archives at the Hebrew University, which is here. It is a wonderful resource, and I should also mention the Einstein papers project’s books that the project releases containing the writings of Einstein, with historical commentary.

I thought it was an excellent colloquium, and the perfect end to the semester’s events. A good sign of how well-received it was by the audience (it was a full house again) is the fact that I had several hands up for questions -from students!- before the applause died down and before I could ask “are there any questions?”. Normally I have to beg, cry publicly, promise favours, or threaten violence (ok, I exaggerate…a bit), to get a student to ask a colloquium question, so that was just great.

One of the most valuable aspects of the talk for all to see and contemplate was the very process of theoretical physics research. The picture is of Einstein struggling along over the decade to try to construct the theory, trying what Sauer describes as a “physical approach” sometimes, and a “mathematical approach” at other times. It is excellent to see how he wrestled with the ideas, and how he made mistakes, wrong turns, missteps. How he turned away from the right answer in the wrong direction (he actually had the correct linearized field equations right there on his notebook pages in 1913…..two years earlier, and then turned away!), and how he learned from those around him, incorporating into his ideas what seemed good to him from wherever he could.

It was a good reminder of the truth of how this kind of process goes. We are often told (in our own recent struggles to construct a radical new theory of Nature), that we are wandering around blindly, and that we are not guided by a shining light along some elegant path to the answer like Einstein was. Well, it was not so elegant at times. He struggles along as best he could, and sometimes very inelegantly….he made guesses, and invented ad hoc “reasons” for his guesses that sometimes were just plain nonsense (in retrospect). He published paper after paper, (sometimes with collaborators) with half-baked and sometimes wrong-headed stabs at the answer. (For example, in an attempt to justify one guess (developed with Grossman in 1913), he spent a good couple of years on a quest to support the idea, in which he was willing to give up general covariance (that which we now believe to be at the core of gravitation) as simply incompatible with physics.)

It was not until the middle of 1915 (after taking his dog-and-pony show to Goettingen, the house of David Hilbert, Felix Klein, and Emmy Noether among others) did things begin to crystallize. The big climax was a series of four papers in November (each separated from the other by a week: the 4th, 11th, 18th, 25th!) that he -bit by bit- put things together, including getting the computation for the perihelion of Mercury’s orbit right (finally, after getting it wrong a number of times before). It is amusing to note that his computation of the latter was based on his penultimate version of the field equations -which was still incorrect- which were luckily correct just for that case (the terms that modify things to give the correct equations actually vanish for that particular computation…the equations in vacuum are much simpler than with sources).

(Yes, he did talk a bit about the so-called controversy over whether Hilbert published the correct field equations five days earlier. Well, he actually derived a variational principle which is equivalent to Einstein’s equations (actually, he was thinking only of the case of electromagnetic sources), and there is some question about the date. But his misses the point entirely…..Hilbert came into that game rather late, and was able to see more clearly the correct mathematics…..but we must not forget that he was able to build on all that Einstein had done over several years, putting all the right tools, principles and other pieces into place….nor must we forget Einstein’s great pains to compare what he was doing to Nature when he could, trying to derive observable consequences a several points. I digress. In addition to the books and other materials on the site already mentioned (see Princeton University Press for the collections of papers in several volumes) I recommend Pais’ wonderful Einstein biography “Subtle is the Lord” for discussion of this too, including the wonderful flurry of postcards they were exchanging in November as they kept dashing off papers to their respective academies to be rapidly published.)

This is an excellent lesson that these struggles can take a long time, and you cannot know how close you are to the end. Ten years could easily have been twenty…or more. This is what I meant in previous posts and comments when I say without embarrasment that it is too early to condemn the program of research into string theory. Nobody knows if it is right or wrong. Screaming loudly on blogs here, there, and elsewhere, and making spectacles in, and appeals to, the popular press won’t change that fact. I personally do not think that it is yet ready to compare to Nature. We don’t understand it at all well enough yet. Although, it would be nice if we were lucky, and we do need guidance from attempts to make comparisons, and so this is why it is important to have stringy and string-inspired phenomenological programs within the field. But we should not be surprised if those programs are not yet conclusive, since after all, we do not even understand the theory well enough to say what it is. Rather, we should be encouraged -given the tantalizing hints that the theory has given us so far- that we might be onto understanding something rather profound that arises in Nature when you combine gravity and the quantum. We shall see, but let’s not be hasty. One day, I hope, we will get it into the right shape to make a set of predictions that we can challenge with experimental and/or observational data. And then we will know, one way or another if it is right or wrong. (And in the meantime, the other benefits of this program of research in physics and mathematics have been numerous, and will no doubt continue to accumulate.)

This look over Einstein’s shoulder in his ten year struggle is also an excellent lesson that these battles are worth it in the end. I’ll close with the wonderful opening lines of his letter to his (dying) mother, in September 1919**:

Dear Mother,

Today some happy news. H. A. Lorentz telegraphed me that the English expeditions have recently verified the deflection of light by the sun.

-cvj

(**For those who don’t know, those expeditions went to South America (Brazil) and to Principe, an island off the Western coast of the African continent to witness a solar eclipse which allowed them to see that the distant stars that can be seen by looking near the edge of the sun, are slightly out of position because the gravity of the sun deflects the light from them. The deviation -and its actual amount- was predicted by Einstein’s 1915 theory.)

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  • Moshe

    Clifford, I remember looking through Einstein notes when they were first displayed in the Israel museum near the Hebrew university in Jerusalem (back in 99 I think). I was impressed that I could understand things (language has not changed too much, similar to the dead sea scrolls I saw there also…). Also, I was surprised to see how messy they were…

  • http://blogs.discovermagazine.com/cosmicvariance/clifford/ Clifford

    Yes, that is a rather nice feature isn’t it? I like that too.

    -cvj

  • Jack

    Just a tiny correction: we no longer believe that general covariance is at the core of GR, though Einstein did. We now know that special relativity and even Newtonian gravity are generally covariant — see Misner et al. I’m not just picking nits here, it’s a good example showing how things that seem absolutely fundamental can turn out to be unimportant when a theory is better understood — this is relevant to cvj’s point about our [lack of] understanding of string theory. Already we’ve learned that “strings” are not as basic as we thought [there are branes], and we can expect similar upsets. After all, and I say it as a real Einstein fan, Albert didn’t really understand GR very well; he even thought that special relativity can’t handle accelerated motion, that the “singularity” in the static form of deSitter was a problem, etc etc etc. Probably we are all saying things just as silly about string theory. This is why I think people are wrong when they say that one of our problems is that we “don’t know the basic principles ” of string theory. On the contrary, all that stuff about principles will be understood *after* we get the theory to work. That’s how it was with SR and GR.

  • http://blogs.discovermagazine.com/cosmicvariance/clifford/ Clifford

    Jack:-

    This is why I think people are wrong when they say that one of our problems is that we “don’t know the basic principles ” of string theory. On the contrary, all that stuff about principles will be understood *after* we get the theory to work. That’s how it was with SR and GR.

    Indeed…. this could well be the way things turn out. The lesson here is that people like to romanticise and “clean up” the recollection of the process of research into the great things that have gone before, and forget that how we do things now bear a lot more (and perhaps instructive) resemblance to what has gone before than is often acknowledged.

    Cheers,

    -cvj

  • http://feynman137.tripod.com/ Science

    The general relativity consistent gauge boson radiation causing gravity and electromagnetism is DISPLACEMENT CURRENT. Catt shows that Maxwell got his interpretation of this ‘displacement current’ wrong, by ignoring the time it takes light speed electricity to flow along the capacitor plates. His co-authors Drs. Walton and Davidson mathematically worked out how the transmission line theory of Heaviside can be applied to explain the charging curve of a capacitor, which is compared to reality and is a correct prediction. Catt’s error follows from Heaviside’s false idea that

    [snip]

    [snip-cvj]

    ….see more here.

  • http://arunsmusings.blogspot.com Arun

    . This is what I meant in previous posts and comments when I say without embarrasment that it is too early to condemn the program of research into string theory.

    I’m sorry, but the comparison between Einstein’s decade-long struggle with General Relativity and the wandering through the darkness of string theorists don’t seem at all appropriate. Who are the Greene and the Kaku of the nascent General Relativity? Where are Einstein’s periodic press releases telling the world of his progress towards the theory of Everything, which is just around the corner? It seems to me that if one wants to live by the press, one should not squeal when the press turns negative.

  • http://www.damtp.cam.ac.uk/user/gr/ damtp_dweller

    It’s a pity that there seems to be so much comment spam these days.

  • http://feynman137.tripod.com/ Science

    dam dweller, are you referring to your own comment, then? Science is not a matter of pet theories, but experimantally verified fact, no matter who does it 😉

    In quantum gravity, the big error in physics is that Edwin Hubble in 1929 divided the Doppler shift determined recession speeds by the apparent distances to get his constant, v/R = H. In fact, the distances increase while the light and gravity effect are actually coming back to us. What he should have done is to represent it as a variation in speed with time past. The whole point about space-time is precisely that there is equivalence between seeing thing at larger distances, and seeing things further back in time. You cannot simply describe the Hubble effect as a variation in speed with distance, because time past is involved! Whereas H has units s-1 (1/age of universe), the directly observed Hubble ratio is equal to v/t = HR/(1/H) = RH2 (and therefore has units of ms-2, acceleration). In the big bang, the recession velocities from here outward vary from v = 0 towards v = c, and the corresponding times after the big bang vary from 15,000 million years (t = 1/H) towards zero time. Hence, the apparent acceleration as seen in space-time is

    a = (variation in velocity)/(variation in time) = c / (1/H) = cH = 6 x 10-10 ms-2.

    Although a small acceleration, a large mass of the universe is involved so the outward force (F = ma) is very large. The 3rd law of motion implies equal inward force like an implosion, which in LeSage gravity gives the right value for G, disproving the ‘critical density’ formula of general relativity by ½ e3 = 10 times. This disproves most speculative ‘dark matter’. Since gravity is the inward push caused by the graviton/Higgs field flowing around the moving fundamental particles to fill in the void left in their wake, there will only be a gravitational ‘pull’ (push) where there is a surrounding expansion. Where there is no surrounding expansion there is no gravitational retardation to slow matter down. This is in agreement with observations that there is no slowing down (a fictitious acceleration is usually postulated to explain the lack of slowing down of supernovae).

  • fh

    Two more crucial differences between String Theory and GR development: GR development started out with Einstein deriving physical predictions (bending of light among other things) from a physical assumption (the equivalence principle: Gravity is spacetime curvature).

    Real physics was on the table before the development of the theory incorporating these principles actually began. To say that physical predictions only came after the theory was understood is clearly wrong, and while the understanding of GR was certainly rudimentary, the equivalence principle (as opposed to general covariance), and the idea that gravity is spacetime curvature was there as a guiding light from the start though.

    Secondly, and far more importantly, Einstein and a small number of collaborators were working on this theory. Not the vast majority of the theoretical physics community of the time. This, above all, is worrysome. There is a real danger that it’s momentum is maintained by social dynamics, rather then by scientific criteria.

    Given how much in the dark we all are, and given that none of us has a physical guiding principle like Einstein did, we should be looking at a far wider class of ideas, instead of developing one particular one to such an incredible complexity and intricacy that we can no longer tell wether we are lost in a realm that is physics or mathematics.

    (Disclaimer: As you might have guessed I’m a starting loopy student, so the above also reads: Gimme more funding!!!)

  • http://cowgrazes.blogspot.com Kaushik

    There is a charisma that surrounds einstein that I havent seen in any other scientist. To the world he is a reflection of genius inspite of the fact that a very large chunk does not understand GTR. A friend of mine put itquite nicely when he asked me- in physics what are the two major theories of the century? – Relativity and Quantum mechanics. On one side you have Einstein who developed Relativity and on the other side you have this whole bunch of amazingly brilliant people- Schrodinger, Dirac, Pauli, Bohr, Born…….and now equate (to a first degree approximation? – come on its not as bad as a spherical cow!!)
    RL Stevenson put it beautifully when he said “The heights by great men reached and kept were not attained by sudden flight bu tthey while their companions slept were toiling upwards in the night”- true to the 10 years Einstein spent before GTR bore fruit. String theory?- no comments. I have no clue as to what it is but I know that there is no experiment so far that can verify it. Is seeing believing?

  • http://blogs.discovermagazine.com/cosmicvariance/clifford/ Clifford

    fh:-

    To say that physical predictions only came after the theory was understood is clearly wrong, and while the understanding of GR was certainly rudimentary, the equivalence principle (as opposed to general covariance), and the idea that gravity is spacetime curvature was there as a guiding light from the start though.

    That’s very nice, but wrong. The equivalence principle is not enough. Please read again what I wrote about him struggling to get the field equations right. And note when he got the perihelion of Mercury right. 18th November 1915. He got it wrong several times in the ten years before that…..he had the wrong equations. Equivalence, and curved spacetime alone will not get the numbers right.

    Arun:-

    Who are the Greene and the Kaku of the nascent General Relativity? Where are Einstein’s periodic press releases telling the world of his progress towards the theory of Everything, which is just around the corner? It seems to me that if one wants to live by the press, one should not squeal when the press turns negative.

    Try to separate out the irrelevant. To say that our field “lives by the press” is frankly, ridiculous and laughable. I’m talking about the science done by hundreds of people, not the PR done by a dozen. Science is not PR. You (and others) might consider not condemning hundreds of people’s efforts by your reaction to the statements of a relative few people that you have a hard time with (for whatever reasons). (Also, nobody responsible that I know of claims that the result is “just around the corner”. If they do, it is manifestly not a credible claim. Nobody knows….”that’s why it’s called research”…to quote Einstein.)

    It’s a bit like if someone from the field of condensed matter physics appeared on TV or in the newspaper and talked (perhaps in an over glossy way) about the program of solving some interesting and exciting problem in their field. Let’s say you don’t agree with them for whatever reasons (to do with you, them, or whatever). I hope you don’t then condemn the entire field of condensed matter, and all condensed matter theorists in the same bitter tones……

    Cheers,

    -cvj

  • http://blogs.discovermagazine.com/cosmicvariance/sean/ Sean

    I think fh is right. Not that you get all of the physical predictions from the equivalence principle, obviously; Mercury’s precession is something you couldn’t get. But you do get a prediction for gravitational redshift, which you later realize is the first-order approximation to the exact GR result.

  • http://blogs.discovermagazine.com/cosmicvariance/clifford/ Clifford

    I don’t. You get some predictions, but they are incomplete. A first order approximation is not the result. As another example, equivalence tells you that you get deflection of light, but it does not tell you by how much.

    [Update: Further, the gravitational redshift was not actually measured until way after 1915, wasn’t it? So it did not actually serve as a guide in the development of the field equations…..]

    -cvj

  • Arun

    If you don’t tell the public that a Greene or Kaku is overly optimistic, but rush to say a Peter Woit is overly pessimistic, then somewhere, somehow, if not truth, then at least balance is lost.

    Anyway, ’nuff said. Are the wrong Einstein papers on-line anywhere? It might be fun to take a look.

  • http://blogs.discovermagazine.com/cosmicvariance/clifford/ Clifford

    Sean….as I’m sure you know, the gravitational redshift result was Pound-Rebka, 1959, using the 1957 Mossbauer effect.

    Wiki article.

    So I claim that this fits the rough analogue rather well. This cannot be claimed as a guiding light for developing the field equations if it was not even measurable until 45 years later!

    Cheers,

    -cvj

  • http://blogs.discovermagazine.com/cosmicvariance/clifford/ Clifford

    Arun, there is a range of opinions out there in the public eye. Read this blog for example. There is a limit to what can be done, as you know. I can’t force the press to cover balanced, reasoned statements in any field of science…… it does not sell newspapers.

    But there is a ton out there. You’re just getting annoyed by the stuff you don’t like and ignoring what does not bother you. The lack of balance is partly in your own filtering.

    Cheers,

    -cvj

  • http://blogs.discovermagazine.com/cosmicvariance/sean/ Sean

    Do you really think that the prediction of gravitational redshift was not a prediction because it was only an approximation to the exact result? fh is saying something true: before Einstein had the field equations, he had the principle of equivalence, which was enough to lead to some predictions all by itself. None of those predictions had been tested at the time, obviously (thus “pre”-dictions). And the EP certainly guided his thinking.

    String theory does not have something like the EP, a rough physical principle that gives some new predictions even before the entire theory is put into place. That’s okay, sometimes you’re not so lucky. We have to work with what we have.

  • http://blogs.discovermagazine.com/cosmicvariance/clifford/ Clifford

    Sean,

    What I really think, and what I am saying was that Einstein could have been totally wrong…he had no way of knowing -in the period 1905-1915 that what he was doing was not total nonsense. What I am saying is that you (and fh) can’t say that EP was a clear guide except with the benefit of hindsight. It over-romanticizes the scientific process he went through to make it seem as clear as all that. It was a struggle…a mess. The redshift was not measured until 1959! He got the 43 degrees of Mercury’s perihelion only at the end of his struggle to get the equations……

    At any time before November 1915, he could have turned out to be totally wrong. That is the lesson, and the -rough- analogy I am painting.

    I did not claim that string theory has an equivalent of the EP….but my point is that the importance of the EP as a guide is over-stated, given that it took 45 years to get the verification of the basic prediction of the EP.

    -cvj

  • http://www.damtp.cam.ac.uk/user/gr/ damtp_dweller

    Quoting the Pound-Rebka experiment as providing acceptable experimental evidence for general relativity is dangerous. In particular, it does not provide verification of the theory. In fact, the PR experiment provides evidence that the local inertial frames of special relativity and Newtonian theory are equivalent; it does not substantiate general relativity on its own.

  • http://blogs.discovermagazine.com/cosmicvariance/sean/ Sean

    Obviously. New theories can always be wrong, and they are always a struggle — nobody would dispute that. But as a matter of historical fact Einstein was guided by the principle of equivalence, a rough idea that did give new predictions. Which is what fh said in the piece you quoted.

  • http://blogs.discovermagazine.com/cosmicvariance/clifford/ Clifford

    With respect, you’re totally missing the point. Read his/her post again.

    Cheers,

    -cvj

  • Thomas Larsson

    Ivan Todorov discussed the history of GR, and Einstein’s and Hilbert’s roles, in physics/0504179.

  • Dissident

    #17: (relatively) low energy supersymmetry?

  • http://eskesthai.blogspot.com/2005/11/foundations-of-mathematics.html Plato

    Good piece of work Clifford…

    the benefit of hindsight

    how so very true…past and present getting mixed up.

    ….some who can go back and change things(?), then we find we are now in new reality where this one no longer exists..we wouldn’t be aware would we:)

    So it is necessary to get it historically right, is it not?

    It then gets added to the consistancy of views on this subject.

  • Belizean

    Sean & fh,

    I have to side with Clifford on the question of whether guidance by a principle can be known to be beneficial a prioiri.

    Remember, Einstein was also guided by Mach’s Principle. [The stars revolving around me is equivalent to me rotating in such away as to observe the same motion of the stars.]

    A belief in Mach’s Principle — a physically reasonable idea — could only have retarded Einstein’s efforts.

  • Elliot

    It is pretty interesting to see how many of the threads her migrate to:

    1 Some type polical/social discussion with everyone sticking to their guns (left vs. right)

    2 Some discussion of the value of studying/not studying string theory with everyone sticking to their guns (pro vs. con)

    This is not a criticism but an observation on the dominant “meta-themes” on this blog.

    Elliot

    BTW anybody else see Brian Greene on the “Colbert Report” last night. It to my mind it certainly punctuated the challenge String theorists confront in “explaining” their work to the general public. Colbert was jamming on him pretty hard.

  • http://blogs.discovermagazine.com/cosmicvariance/clifford/ Clifford

    Elliot. I think you’ll find that there are several other thread topics too. But yes, those are two common fixed points.

    I missed Brian’s appearance, but did hear about it. Probably will catch a repeat one day.

    Cheers,

    -cvj

  • http://www.damtp.cam.ac.uk/user/gr/ damtp_dweller

    A belief in Mach’s Principle — a physically reasonable idea — could only have retarded Einstein’s efforts.

    It turns out that Mach’s principle isn’t necessarily a barrier to deriving general relativity. For example, some recent papers have shown that one can actually derive general relativity and all of its consequences without presupposing the existence of spacetime simply by regarding Mach’s principle as fundamental.

  • Cygnus

    I generally almost no clear idea, of what string theory is except for some popular science stuff so most of what I say is subject to that disclaimer. Nonetheless, I would side with Clifford on this one.

    The fact that you do not have some EP like guiding principle in string theory is no reason to attack it. I mean if you look at the early development of Quantum Theory it was quite ad hoc, and unclear as to what we were doing until much later in it’s development. In fact so was the case with QED, and Quantum Field theory as well.

    It is however important that other approaches are also explored parallely, and that while we may not yet have a strong physical guiding principle now, we should at least have reason to believe that the theory will give is one.

  • http://www.damtp.cam.ac.uk/user/gr/ damtp_dweller

    For all those who are interested, you can catch last night’s interview with Brian Greene on the Colbert Report here.

  • http://arunsmusings.blogspot.com Arun

    I do have a different question. Suppose arxiv.org existed in Einstein’s days. Now, after his 1905 papers, arxiv.org would probably have tolerated any number of wrong papers between 1905 to 1915, when Einstein finally got GR right. But suppose Einstein1 made the 1905 publications, and we were lucky enough to have an equally bright Einstein2, maybe a couple of years younger, who immediately started work on melding gravity and special relativity; and went through much the same travails as the real Einstein did.

    My question to the physicists here is would Einstein2 be tolerated on arxiv.org?

  • fh

    I completely agree with what Sean said.

    A physical guiding principle can turn out to be wrong (see Mach’s principle), but Einstein had one and was guided buy it. Maxwell had Faradays lines of force. Lorentz had the Ether, and so on.

    My point was that a physical principle with physical consequences was on the table before even the linearized field equations were known.* (Next to a host of other physical principles that turned out to be wrong).

    At the time EP was not a guiding principle to a correct physical theory, I didn’t mean to imply that, but it was a guiding principle to a potential (and elegant) physical theory.

    As far as I can tell String Theory does not have such a principle. Does that mean it is not worth studying? Not at all! However, I think to use Einstein as an example for the absence of physics from a theory until late in it’s development is not correct.

    In a way it’s funny Loop and String people both cite Einstein for pointing out why, by historical precedent, they are more likely to be right and the others to be wrong. I wonder if Einstein was thinking about how Newton had arrived at his results when deciding what path to take…

    *If you assume that Gravity is described by “accelerated inertial systems” you get gravitational redshift and bending of light by the sun. Thus you have two physical predictions that need to be part of any theory that is based upon this physical principle. Einstein first wrote about this in 1907, in 1911 he derived numerical predictions. Both before even the linearized equations were known. In fact in 1907 he also conjectured that a theory based on this principle might succeed in explaining the perihelion of Mercury.
    (Unfortunately I can not find a precise reference for the 1907 arguments, anybody?)

  • http://blogs.discovermagazine.com/cosmicvariance/clifford/ Clifford

    Ahhh, the benefits of 20/20 hindsight. Sigh.

    -cvj

  • JoAnne

    fh, Very well said! I completely agree with you and Sean. A physical guiding principle, right or wrong, with physical consequences is a very powerful tool in the development of a theory, right or wrong.

    Cygnus, the development of quantum theory, and QED in particular, is one of the best examples of experiment and theory working together hand-in-hand. QED is arguably one of the best physical theories we have and correctly predicts electromagnetic phenomena to parts per mill. During its development it sought explanations for and predicted new phenomena such as Compton scattering, pair production and annihilation, bremstrahlung, radiative transitions of atoms, and anomalous magnetic moments. The theory was formulated on Maxwell’s and Dirac’s equations and used experiment as a guiding principle.

    However, even for the elegant and well-understood QED, exact expressions for scattering amplitudes or transitions are not known. The best we can do is approximate the exact result as a perturbative series, where each successive term is (hopefully!) smaller than the previous. In most cases, the first order approximation works darn well.

  • http://blogs.discovermagazine.com/cosmicvariance/clifford/ Clifford

    I don’t understand how my statement got turned into “there need be no guiding principle”…..I don’t get it. What I’m saying (once again) is that the positive role of the guiding principle is only determined after you’ve done working out the theory and shown that it makes contact with experiment. Beforehand, it could be simply a wrong principle! Further, we tend to read history and forget this….because few bother to read the history of all the great principles and their associated theories that turned out to be wrong.

    I repeat again: You can’t know for sure until the end. Until you’ve compared with the experiments. Einstein could have turned out to be wrong. The Equivalence principle’s basic physics prediction was only verified 45 years after he wrote his field equations.

    JoAnne,

    What were the guiding principles in the development of Dirac’s theory, and of QED in general? Yang-Mills?

    You say:

    The theory was formulated on Maxwell’s and Dirac’s equations and used experiment as a guiding principle.

    Experiment as a guiding principle is sort of a tautology, imho. What other principles were paramount in the developer’s minds? I don’t think it is as clear as is being made out. If we whitewash the history of ideas (good and bad) in this way we lose a lot…particularly ideas about how to proceed in the present time.

    It only seems clear with hindsight. See Pais’ book “Inward Bound”, for example. And the forthcoming book by Van Nieuwenhuizen on the history. It is not as neat and tidy as people make out, and we are doing our students a disservice by making it seem so neat and tidy.

    -cvj

  • http://blogs.discovermagazine.com/cosmicvariance/clifford/ Clifford

    fh said:

    In a way it’s funny Loop and String people both cite Einstein for pointing out why, by historical precedent, they are more likely to be right and the others to be wrong. I wonder if Einstein was thinking about how Newton had arrived at his results when deciding what path to take…

    That is not what I am doing. I said nothing about likelihood of being right or wrong. Rather I said that we cannot know a priori. That’s in fact 180 degrees in the opposite sense, and crucially so.

    Cheers,

    -cvj

  • Moshe

    Interesting discussion, I think that some theories have basic, almost axiomatic general principles, and I agree with Clifford that often they are discovered long after the fact. Some theories do not have such central principle, they just happened to be correct :QED comes to mind, I am not sure I would call gauge invariance such principle, and I don’t think it was a guiding principle in the development of the theory.

    Most extreme example is quantum field theory: the guiding principle of the subject (namely Wilsonian renormalization group) was discovered decades after it was already mainstream physics and a part of every particle physicist’s education.

    Not having such guiding principle does not equal “absence of physics”, one is not prevented from using physical intuition and reasoning. String theorists can probably do a better job explaining how the physics of gravity and quantum mechanics guides us, indeed makes string theory seem almost inevitable. This physics certainly provides more guidance than historical analogies…

  • http://blogs.discovermagazine.com/cosmicvariance/clifford/ Clifford

    Not having such guiding principle does not equal “absence of physics”, one is not prevented from using physical intuition and reasoning.

    Thanks Moshe! Very clearly put.

    -cvj

  • JoAnne

    Clifford, I’m afraid we disagree. As I said, I think guiding prinicples, RIGHT OR WRONG, are a very powerful tool. And, stating that experiment is a guiding principle is not a needless repetition – it is the way science is done and is a crucial tool in the development of theories. I realize that I may sound like I am harping on this point, but I feel that this most important point continously gets lost in these discussions.

    Moshe, it is statements such as “String theorists can probably do a better job explaining how the physics of gravity and quantum mechanics guides us, indeed makes string theory seem almost inevitable.” that ruffles the feathers of your non-stringy colleagues.

  • http://www.math.coumbia.edu/~woit/blog Peter Woit

    I’ve seen quite a few attempts by string theorists in recent years to justify the lack of any progress towards a predictive unified theory by very strained historical analogies. In this one, I don’t see how you can sensibly compare a research program conducted mostly by one person with a small number of collaborators, which in the course of ten years completely reached its goal of having a precisely formulated, predictive and falsifiable theory with another one, which after more than 20 years effort by thousands of people is now much farther from any hope of success at predicting anything than it was when it started.

    As for complaints of “making spectacles in, and appeals to, the popular press”, I’m not sure what you have in mind. There has been and continues to be a huge amount of that done by string theorists, with little criticism from their colleagues, virtually none of it in public. If you’re making a start on that, great.

    The press coverage of string theory until the past couple years has been grotesquely overoptimistic and one-sided. This has started to change and it has become much more balanced recently. Some string theory partisans have reacted to this not by putting up an honest defence of their program, but by attacking the competence of anyone critical of the theory (for some of the more laughable examples of this during the past week, see Greg Kuperberg’s comments on Gerard ‘t Hooft over at Dave Bacon’s blog, or Lubos’s claim that the author of the recent Slate piece has the intelligence of a dog). This tactic isn’t going to work.

  • agm

    Clifford, I think it is clear that you and Sean, Joanne, and fh disagree about the utility of a guiding principle. What’s hard to understand about scientists disagreeing about how to do science?

    May I ask why you are so strong in what appears to be an opinion that a guiding principle is not useful because you can’t know one is there except in hindsight? I’m not sure that this is the statement you meant to make, but it is what the discussion in the thread has turned into.

    Sean, Joanna, fh, what’s less-than-optimal about Clifford feeling that such a guiding principle isn’t necessary for all physics research? Personally I feel that there must be some sort of physical guidance, touchstones with the real world, but that doesn’t mean that I should expect everyone to feel that way. Why do you feel that way?

    These are useful issues of conduct and philosophy, so thanks for discussing them.

  • http://blogs.discovermagazine.com/cosmicvariance/clifford/ Clifford

    Peter…funny that you read it that way…I was referring to both pro- and anti-string people when I said “making spectacles in, and appeals to, the popular press”. Read the sentence again.

    How interesting that you only took it one way.

    And also, you seem to (as you have before) ignored the statement I wrote: “And in the meantime, the other benefits of this program of research in physics and mathematics have been numerous, and will no doubt continue to accumulate.”

    How interesting that you should have missed that. Again.

    Cheers,

    -cvj

  • Jack

    First of all, cvj is clearly right. :-)
    I’m afraid that many of us have this comforting picture of Einstein et al being “guided” by some simple principles. In fact, most of the principles he worked with were wrong. He thought that gravity was the same thing as acceleration, whereas we know that gravity is spacetime curvature and the curvature tensor is either zero or not, independently of whether you are using an accelerating frame. [Yes, the principle of equivalence is wrong — unless you re-define it to the point where it is unrecognizable.] He thought that the principle of covariance is the mathematical expression of the EP, which is also wrong. He believed in Mach’s principle, which denies the existence of a linear connection on a flat spacetime and is therefore also wrong. Miraculously he came up with a correct theory! How? Well, as cvj keeps trying to say, Albert was groping in the dark. It was ten years of total confusion. All these wrong “principles” were just a sort of psychological crutch to keep him going while he tried to do various technical things which didn’t work. When he made the mistake of taking his “principles” too seriously, he really got stuck — see the incident of the “hole argument”.
    The lessons here are : as cvj says, there is a strong tendency to romanticize the past and to use this fictitious past as a way to attack string theory. If only those foolish string theorists would latch onto some basic PRINCIPLE like *real* physicists then they would get somewhere, just like Albert! Whereas the evidence suggests that Albert would have been a lot better off paying no attention to “principles”.
    Second point: if you are going to teach physics “historically” [a bad mistake in my opinion, but anyway….] then make sure that you find out the REAL history, not “history as it ought to have been according to our vague memories of what we were taught as undergrads”.

  • http://blogs.discovermagazine.com/cosmicvariance/clifford/ Clifford

    agm, JoAnne,

    I’m sorry about what follows, but this is really frustrating. This seems to happen again and again….from thread to thread. I write something….really clearly, I thought… and still people just seem to pick only some of the words, and leave the others! I repeat and reemphasize in comments…..still it seems to go unread.

    agm says:

    May I ask why you are so strong in what appears to be an opinion that a guiding principle is not useful because you can’t know one is there except in hindsight?

    Where did I say that a guiding principle is not useful? I never said that. I can’t repeat it all again….please read my comments again. Sorry.

    JoAnne says:

    I’m afraid we disagree. As I said, I think guiding prinicples, RIGHT OR WRONG, are a very powerful tool. And, stating that experiment is a guiding principle is not a needless repetition – it is the way science is done and is a crucial tool in the development of theories. I realize that I may sound like I am harping on this point, but I feel that this most important point continously gets lost in these discussions.

    I say…where is the disagreement? I’ve been saying again and again how important experiment is! Just because I’m a string theorist and not an experimenter or phenomenologist does not mean that I don’t put experiments first and foremost in the study of Nature. I’ve been saying how experiments are important again and again, and again, and again, and again…………..

    Ok. I’m going to lie down now. Have a glass of milk. Maybe something stronger…..

    Sorry.

    -cvj

  • http://eskesthai.blogspot.com/2005/11/foundations-of-mathematics.html Plato

    Maybe the guiding principal was something buried in Einstein’s past (meme)? How would you know unless you were Einstein? :)

    So I’ll say, “maybe it was the compass,” something unseen, and interest instigated, but there.

    Maybe that was the guiding principal? Fussy fuzzy :)

  • fh

    Besides agreeing to disagree, I just wanted to point out that the paragraph about likelyhood of being right was not specifically directed at you or your point, but more of an aside. Should have made that clear, sorry.

  • http://blogs.discovermagazine.com/cosmicvariance/clifford/ Clifford

    agm…. (cvj sits up from drunken stupor for a minute):

    I do appreciate your trying to clarify, by the way. I’m just a bit frustrated by revisionist history of how science proceeds. It is never as clear at the time as it seems with hindsight. I did not say that principles were not useful. Rather, I said that principles are not always going to lead to a right answer. Furthermore, often the principles don’ emerge until after the heory was developed, such as in much of QFT. You can only know this sort of thing at the end of the process, not during it. So this means that the model of “lone genius being guided by shining light to answer” that we often get presented with is misleading. Einstein wandered in the dark for many years on GR, with no way of knowing if his principle was on the right track. Happily, he was. But all I am saying is that it was by no means a direct path to the answer…..current long and hard research paths for big goals like GR (such as into string theory or otherwise!) should not be considered as new modern endeavours with no precedent. A clear precendent is the struggle for GR. Another precedent migh be the struggle for (name your favourite elegant but ultimately wrong theory). We cannot yet know. So even if we had something that you would call a principle…it may or may not help. It is nice to have (and one should use them when one has them, along with all sorts of other physical intuition), but you can only know it was nice to have for sure after the fact of building the theory and testing it against experiment..not before.

    Back to lying down.

    -cvj

  • fh

    PS, Clifford, since I missed your last comment when writing my last, maybe there is no real disagreement here, but it seems there is little point in trying to clear up what then is merely semantics. So perhaps rather agree to misunderstand each other, at least for the moment, then agree to disagree.

    Jack,
    rather bold move to give Einstein posthumous advice on how he should have conducted his research more efficiently, if I may quote:

    “Ahhh, the benefits of 20/20 hindsight.”

    😉

  • http://blogs.discovermagazine.com/cosmicvariance/clifford/ Clifford

    fh…. right. ok. The frustrating thing is that I said all of this in my main post and in my comments early this morning. I’ve said nothing new since then, in fact.

    -cvj

  • Moshe

    JoAnne, I am sincerely trying very hard not to ruffle any feathers, really! So maybe “inevitable” is a poor choice of words, but my point still stands, we are strongly guided by physics in what we are doing, and also in what we are not doing, and we do have good reasons for this (and others have their own good reasons, which obviously I found less convincing, but I still wish them good luck…). It is logically possible to be enthusiastic about what you do without insulting other people, isn’t it?

  • fh

    I think I never disagreed with what I think you thought I disagreed with. Particular the “things are muddy and Einstein was groping in the dark” bit. My (our?) point is that things were muddy and AE was in the dark despite having an (in hindsight even right) principle. So how lost would he have been without any principle at all?

    (there are other tangential points like flasifiability, if in 1912 someone had meassured a solar eclipse and found that light does not bend in the gravitational field AE could/would have stopped the entire effort, having a principle from which you can get some physics also helps to avoid wasted efforts…)

    However, let’s put it in another way, is there historic precedent for a succesfull physical theory developed without either a physical principle or experimental data? Perhaps Yang Mills theory? They had a physical principle (neutron/proton SU(2) IIRC) but it was known to be wrong/only approximate at the time.

    If not perhaps String Theory (which despite having no physical principle is certainly full of physical intuition) might set the precedent, who knows.

  • http://blogs.discovermagazine.com/cosmicvariance/clifford/ Clifford

    fh:- Despite what people say, String theory has access to a wealth of experimental data, and they are a very useful guide indeed.

    -cvj

  • fh

    “Despite what people say, String theory has access to a wealth of experimental data, and they are a very useful guide indeed.”

    Oh could you elaborate?

  • http://blogs.discovermagazine.com/cosmicvariance/clifford/ Clifford

    Oh,simple….everything that has already been established experimentally! And the nature of the theories that currently apply well to Nature. These are very important for shaping any new theory. We must not forget that.

    I’m going to get beaten up for saying this…but I don’t care. It is important, and true.

    -cvj

  • http://eskesthai.blogspot.com/2005/11/foundations-of-mathematics.html Plato

    yes please…I haven’t seen much of this lately….from what has been implied by anti-, it was all theoretical? :) I need something “concrete” to hang my hat on.

  • http://blogs.discovermagazine.com/cosmicvariance/joanne/ JoAnne

    Moshe, Yea, it was the “inevitable.” It’s amazing how things come out differently when they are read versus heard. Something we are all learning on this blog…

    Here’s another one for you. I recently found out that condensed matter physicists get their feathers ruffled when particle physicists use the term “New Physics.” (A term which I use all the time to describe possible physics beyond the Standard Model.) They think all physics research is “New Physics,” otherwise it is not worth doing, and thus think we are insulting them when we use the phrase.

    But I digress off the topic, which I’m not sure of anymore anyway….

  • http://blogs.discovermagazine.com/cosmicvariance/clifford/ Clifford

    My point is that we are not making up string theory out of whole cloth. It has a very firm foundation in what has gone before. What has already been understood. This is also true for other approaches too…but it must not be forgotten all the same.

    -cvj

  • http://eskesthai.blogspot.com/2005/11/foundations-of-mathematics.html Plato

    oops, I confused “access too” as support for, the experimental validation of string/M theory….I thought we might be headng for the 21 century thing that dropped into the minds of 20th century people, or something like that:)

    Somebodies surely twisting time around here? :)

  • fh

    Hehe, in that sense Einstein had experimental data ‘en mass’ for Special Relativity and GR. As you well know it’s not what I meant with the question either.

    I think Witten put it that way as well some time ago, by saying the underlying principle of String Theory is to unify GR and QM. And as Rovelli points out in his book, this constraint is so tight that we do not have the problem of choosing between many candidate theories that fullfill it, but of finding even a single one that would. Alas, then LQG is working from the same underlying principle and I would resist calling it the underlying principle (underlying experimental data) of String theory, rather it’s the underlying principle (underlying experimental data) of all flavors of Quantum Gravity research, and in some sense even of all of physical research at all times past and future.

    Ok, enough for tonight, being European I have to sleep a bit. I hope this exchange was not to annoying. :)

    cheers
    frank

  • http://blogs.discovermagazine.com/cosmicvariance/clifford/ Clifford

    But he did…he did! That’s important! It is also where the equivalence principle came from…what had gone before.

    -cvj

  • http://eskesthai.blogspot.com/2005/11/foundations-of-mathematics.html Plato

    ….so your saying, that if you want to be good at drawing a historical “guiding principle” you have to know how to weave, or knit? :)

  • Moshe

    JoAnne, there is no topic I believe…or rather it is back to the same old topic again…but this is very useful, because it is often surprising to compare what you mean to how you are interpreted, especially by people who don’t know you personally and therefore cannot put you words in context. I usually try to be precise, but sometimes things get by one’s filters…

    (and on topic, I find many times, often from students, a sense of surprise at how tightly constrained the framework is, how everything hangs together just right, and every little change makes the whole thing fly apart. This was what I was trying to clumsily express…)

  • Jack

    fh said:

    “things were muddy and AE was in the dark despite having an (in hindsight even right) principle. So how lost would he have been without any principle at all?”

    He would have been better off saying: “Hey, maybe spacetime is not flat and this is what gravity is! Now let me see if I can play around with semi-Riemannian geometry and get out something like the Poisson equation….” Instead of all that junk about Equivalence, general covariance, accelerated reference frames blah blah blah. He would have saved at least 5 years if he had proceeded in this string-like manner. :-)
    “Principles are Crap” — my teacher.

  • http://eskesthai.blogspot.com/2005/11/foundations-of-mathematics.html Plato

    “math symbology” on knitted sweaters never fail I hear? :)

  • http://www.math.coumbia.edu/~woit/blog Peter Woit

    Clifford,

    Actually I read your sentence correctly the first time, and thought that, given the long history of overselling of string theory in the press, it was pretty absurd to hear a string theorist complain about a string theory critic going to the press. I initially wrote a comment saying this, but then thought better of it, given the ambiguity of what you wrote. So I deleted the criticism of you, and replaced it with the phrase you seem to have missed “I’m not sure what you have in mind”.

    Now that it is clear what you have in mind, I’ll go back to my original version of the comment, and elaborate. Over the last twenty years of absurd overselling of the theory I haven’t seen any string theorist publicly complain about this. Now that critics are getting more equal time, all of a sudden they see the press discussion of this topic to be problematic. Funny how that works.

    As for the extent to which I’ve personally made spectacles in or appeals to the popular press, I should explain some history. About five years ago I first finally decided that, given the overwhelming hype surrounding string theory, someone should write up an account explaining the problems of the theory for an audience of physicists and mathematicians. The result was posted on the arXiv and submitted to Physics Today (where it was more or less treated as the work of a crank). I made no further attempts to publish it, but was contacted by an editor of American Scientist who had seen it on the arXiv and asked if they could publish it, which I agreed to. I then started work on a book manuscript, containing both criticisms of string theory as well as history and more positive material, again aimed at physicists and mathematicians, hoping to publish it with an academic press. When I had nearly finished it, an editor from Cambridge University Press stopped by my office when he was visiting Columbia, so I gave him a copy to look at. Publication by Cambridge was ultimately thwarted by two anonymous string theorist referees.

    Other editors at a couple of academic presses then advised me that an academic press would not be able to publish my manuscript since it was “too controversial”, i.e. there would be too much heat from string theorists. Only then did I start exploring publishing with a trade publisher. A literary agent advised me that the best thing to do was to remove much of the more technical material, after which it would be quite salable, something I was loathe to do. Finally Roger Penrose put me in touch with the British publisher Jonathan Cape, and they were willing to publish the book despite the inclusion of more technical material.

    I don’t have an agent or publicist, and don’t spend any time contacting people in the press trying to get them to write articles criticizing string theory. Instead I write a blog not intended for the general public, one where I put up material I think other mathematicians and physicists might find interesting. I’m gettng more and more phone calls and e-mail from people in the press who are writing something about string theory and want to get both sides of the story. If they seem to be responsible and have some idea of what is going on, I talk to them and tell them what I think about the scientific issues as honestly and clearly as I can. You’re welcome to your opinion that this behavior is “making spectacles in, and appeals to, the popular press”, but it’s out of line.

  • http://blogs.discovermagazine.com/cosmicvariance/clifford/ Clifford

    Peter…. This is rather funny, actually. I don’t see your name anywhere in my post. Not all conversation about a dissenting view about string theory refers to you. Sorry if you thought you had a monopoly! …. 😉

    Cheers,

    -cvj

  • http://www.math.coumbia.edu/~woit/blog Peter Woit

    Clifford,

    One more thing. No, I didn’t miss the part about the benefits of string theory to math and physics, it’s just that I have a very different point of view on them than you do. While they are non-trivial, they are not as great as you think, and they have come at the cost of an immense amount of damage to the subject of theoretical physics.

    Didn’t think you’d like that or it was an argument worth entering into today, but don’t want you to think you’re being ignored.

  • http://www.math.coumbia.edu/~woit/blog Peter Woit

    Clifford,

    Glad to hear it’s those other guys that are the bad attention seekers, apologies for any misunderstanding.

  • http://blogs.discovermagazine.com/cosmicvariance/clifford/ Clifford

    “an immense amount of damage to the subject of theoretical physics”

    Gosh. Peter….we’ll just have to disagree. I don’t see the subject as damaged. I see it as extremely healthy and exciting. It is sad that you think that. I’m sorry you think that, in fact. Sounds like your path through the subject went through some unpleasant darkness. I sympathize, for what its worth, and can see how that might very much colour your view of the field…..

    Best,

    -cvj

  • http://blogs.discovermagazine.com/cosmicvariance/clifford/ Clifford

    Peter….it’s always the other guy…. right? 😉

    -cvj

  • http://eskesthai.blogspot.com/2005/11/foundations-of-mathematics.html Plato

    .it was nice to hear this from you Peter…. :)you and Clifford with the rest of the gang are doing a good job of informing… putting aside the religious context of evangelistic attitudes we sometimes wear… has done wonders and cleared some of the fog to reveal a better truth :)

  • http://eskesthai.blogspot.com/2005/11/foundations-of-mathematics.html Plato

    um, that the truth about um…..:)

  • http://www.math.coumbia.edu/~woit/blog Peter Woit

    Clifford,

    Thanks for the concern but you don’t need to worry, I’ve been treated very well by life in general and academia in particular, undoubtedly better than I deserve, and much better than most people who try to make a career for themselves in theoretical physics.

    As for theoretical physics being “extremely healthy and exciting”, well I guess we finally do have experimental evidence for multiple universes.

  • http://eskesthai.blogspot.com/2005/11/foundations-of-mathematics.html Plato

    Frequency……the aurora borealis allows me to visit you for a “time” Peter. You should not mock me..:)

  • Thomas Larsson

    What were the guiding principles in the development of Dirac’s theory, and of QED in general? Yang-Mills?

    It may be worth recalling the Maxwell story. After having collected a lot of old laws under one hat (Ampere, Faraday, Biot-Savart,…) JCM found that his equations would be more symmetric and beautiful if he added an extra term (the displacement current, I believe). In modern language, his guiding principles were gauge and Lorentz invariance.

    A more recent success story is the application of conformal field theory to 2D critical phenomena, where there is a clear guiding principle: conformal symmetry on the quantum level. What is important is the distinction between classical and quantum symmetries; everything of interest involves a non-zero central charge. In contrast, checking the symmetries of the action, which is all one does in higher dimensions, is a purely classical operation. After all, Noether’s theorem predates QM.

    My own guiding principle is gauge and diffeomorphism symmetry on the quantum level, in analogy with CFT (and yes, gauge anomalies can be consistent, cf. the free subcritical string). This is why I discovered the multi-dimensional generalization of the Virasoro algebra. However, I cannot lay claim on the multi-dimensional affine algebra, although I did rediscovered it independently, since it was written down by Kassel already in 1985. Incidentally, it has appeared in string theory, cf hep-th/9511185.

  • http://eskesthai.blogspot.com/2005/11/foundations-of-mathematics.html Plato

    Layman here.

    I have question then about the term (Axiomization), and the relationship to Dirac? Be kind here.

    I am thinking of Feynman as well leadng from Dirac’s example and the toy models of interactive relations.

    Axiomization:A mathematical axiom is Axio
    – a “first principle”,
    – a basic assumption,
    which a mathematical theory is based on.

    If we are looking for what could emerge from “first principles” would this concept be the first inclination of “physics and math” as having a common bond, as to origination?

  • http://golem.ph.utexas.edu/~distler/blog/ Jacques Distler

    It may be worth recalling the Maxwell story. After having collected a lot of old laws under one hat (Ampere, Faraday, Biot-Savart,…) JCM found that his equations would be more symmetric and beautiful if he added an extra term (the displacement current, I believe). In modern language, his guiding principles were gauge and Lorentz invariance.

    Have you actually seen Maxwell’s equations in the form he wrote them down? He didn’t even have vector-calculus notation, let alone something that would make Lorentz symmetry manifest. And as to gauge-invariance, that’s another historical anacronism on your part.

    The Displacement Current term was invented for consistency. “Beauty” (or those other fancy principles you cite) had little to do with it.

  • http://www.amara.com Amara

    It’s here:
    MAXWELL, J. C. (1865): “A Dynamical Theory of the Electromagnetic Field”. Philosophical Transactions. 1865 London, Vol. 155, S. 459 – 512

    It’s surprisingly readable (I skimmed it yesterday.. I want to go back and read it in full).

  • http://countiblis.blogspot.com Count Iblis

    Jacques: ”The Displacement Current term was invented for consistency. “Beauty” (or those other fancy principles you cite) had little to do with it.”

    Indeed, without that term you don’t have conservation of charge.

  • http://golem.ph.utexas.edu/~distler/blog/ Jacques Distler

    Indeed, without that term you don’t have conservation of charge.

    More specifically, if you have a dielectric medium (for Maxwell, the æther was a dielectric medium), and a changing electric field, then you have a “displacement current” as the polarization of the dielectric changes in time (positive charges flow in one direction, negative in the other). Ampère’s Law is inconsistent in the presence of a capacitor, if the charge on the capacitor (⇔ electric field in the gap) is changing in time. This is fixed if we include the displacement current on the RHS of Ampère’s Law.

  • http://golem.ph.utexas.edu/~distler/blog/ Jacques Distler

    [I fixed the font problem in previous comment Jacques. -cvj]

  • Joe

    A couple of points from memory. Hopefully someone will either set me right or provide a reference to back me up.

    It may be worth recalling the Maxwell story. After having collected a lot of old laws under one hat (Ampere, Faraday, Biot-Savart,…) JCM found that his equations would be more symmetric and beautiful if he added an extra term (the displacement current, I believe).

    I believe that the displacement current was the final step. In the beginning he very consciously set aside the theories and set to work on absorbing all the experimental results. (Maxwell was very important in bringing experimental physics in to universities.)

    Have you actually seen Maxwell’s equations in the form he wrote them down? He didn’t even have vector-calculus notation, let alone something that would make Lorentz symmetry manifest.

    If I recall correctly it was as bad as a different letter for each component of each field. However, I believe that Maxwell had got as far vectors and vector differential operators. The problem was that nobody else understood that language at the time of publication.

  • Joe

    OK, returning from the bookshelf anyone who’s interested in Maxwell’s derivation of his equations can consult chapter 5 of Malcolm Longair, Theoretical Concepts in Physics. He quotes the preface to Maxwell’s Treatise on Electricity and Magnetism:

    before I began the study of electricity I resolved to read no mathematics on the subject till I had first read through Faraday’s Experimental Researces in Electricity.

    When Maxwell published his first paper on EM in 1856 everything was done with partial derivatives. It was not until 1870 that he published a paper defining “slope” (now “gradient”), “curl” and “convergence” (opposite of “divergence”).

    But in the context of this discussion the most remarkable thing is the “physical model” that led to his equations. First he treated B as stream lines of an incompressible fluid. This led him to conclude that magnetism was an essentially rotational phenomenon. In order to allow these vortices to rotate he then had to introduce “ball bearings” or “idler wheels” into the aether. When these bearings come loose, they carry a current. This can happen even in vacuum and accounts for the displacement current!

    This was a remarkable scheme informed by engineering experience and mathematical virtuosity. It led to the correct equations but we all know what happened to it the physical picture. I’m not sure whether theory or experiment comes off better. Draw your own conclusions.

  • http://feynman137.tripod.com/ Science

    Displacement current is supposed to flow between the plates of a vacuum-dielectric to complete the continuity of current while a capacitor charged/discharged: http://www.ivorcatt.org/icrwiworld78dec1.htm

    However, only energy flows this way, and Maxwell’s models (both elastic aether and gear cogs with idler wheels) screwed up by ignoring the fact that electricity needs to spread ALONG the first capacitor plate before anything reaches the other one.

    By treating the capacitor as a Heaviside-type TRANSMISSION line Catt’s co-authors Drs. Walton and Davidson derived the correct charging curve for the capacitor as a series of steps: http://www.ivorcatt.org/icrwiworld78dec2.htm

    This gets rid of Maxwell’s aetherial displacement current. Dr Woit says above he worries about damage to theoretical physics from string theory, but consider:

    ‘Maxwell discussed … in terms of a model in which the vacuum was like an elastic … what counts are the equations themselves and not the model used to get them. We may only question whether the equations are true or false … If we take away the model he used to build it, Maxwell’s beautiful edifice stands…’ — Richard P. Feynman, Feynman Lectures on Physics, v3, c18, p2.

    Even the greatest scientists make errors!

    ‘a) Energy current can only enter a capacitor at the speed of light.

    ‘b) Once inside, there is no mechanism for the energy current to slow down below the speed of light…’

    – Ivor Catt, Electromagnetism 1, Westfields Press, St Albans, 1995, p5.

    Displacement current is radio wave energy, it doesn’t need to oscillate when flowing at light speed from one charging conductor to another! Transmitted between spinning charges it constitutes the gauge bosons of electromagnetic and gravitational forces: the different ways the series of capacitors that are fundamental charges in atoms add up by this background field gives rise to gravity and electromagnetism: http://feynman137.tripod.com/

  • David

    I sympathise with Clifford’s analogy between Einstein’s long struggle to develop GR and the current struggles of string theorists, and I sincerely wish them best of luck. It would be a massive advance for physics if the string program ends as successfully as Einstein’s did; something that we would all celebrate. As for the chances of this happening, I leave that debate to the experts (and it has been a pleasure to follow the debates on this on this blog). But I can’t help mentioning, as Peter Woit has already alluded to in #40, a place where this analogy breaks down: the bandwagon situation with regards string theory.

    Manifestations of this situation include peculiar phase transitions in the careers of some people, who go from being struggling nobodies to feted hot shots after switching to ST and publishing a few papers on it, and cases of people switching to ST because “well, you know, that’s the way things are going” (an actual quote from an acquaintance who switched to ST during one of his postdocs. It worked out well for him; he landed a faculty job at a good university a few years after making the switch). I don’t think string theory itself is to blame for this situation. It seems more the result of a “follow the leaders” culture in present day particle physics; the “leaders” just happen to be doing string theory. But in any case, for whatever reason, empirical evidence suggests that the career prospects of people doing formal theory things are significantly improved if their topic happens to be string theory.

  • agm

    Clifford, fh, thanks for elaborating. I really don’t understand the disagreement, mainly because I don’t think there is one way to do physics, but I wanted to know more about what you thought.

  • X^2

    Man, there is so much contradicting information on here that it is hard to make sense of anything. I thought blogs such as this were supposed to serve as a medium for which the public (here an undergraduate in mathematics) could look into the worlds of the physicist and gain insight into what the main theories were? Not bickerings and contradictions…but wait, they do serve the alternate purpose of showing how very well human and hence, just as susceptible to collapses into childishness, (layered in proper and polite talk, and in the case of Lubos, not even) physicists and academics are. As a youngster who looks up to you guys, I must say, you all do not set a very good example. 😛

  • http://blogs.discovermagazine.com/cosmicvariance/clifford/ Clifford

    X^2:- Reading stuff on the web is no substitute for going and doing the research yourself and forming your own conclusions. So you’ve read the arguments…this is healthy. Go and look at Einstein’s papers – I’ve given several links- go and look at Maxwell’s papers…other things we referred to…….. form your own opinions and don’t expect us to form them for you…..

    In other words, the key information you got from here is those references, and the important fact that physics is a living, breathing, vibrant subject that is worth arguing passionately about over a hundred or more years after a piece of work was done.

    I do hope that you see the value of that.

    Cheers,

    -cvj

  • X^2

    I dont even see how it is possible to do physics without a guiding principle, if there is none then what seperates it from the random stabs into the illogical that is most religions?

    I think it is inevitable that there must always be some guiding idea, even if it is only in the form of an analogy or a hunch and not based on any physical principle. From what I could pull from Clifford (who had been made to repeat himself such that it is no longer clear what he meant) is that based on the discraded litter that comprises the landscape of most attempts at a phyiscal theory, that (overattatchment to) something so subjective as a guiding principle is insufficient and often retarding in the making of a proper and correct theory.

    But then I suppose that is what makes those Einsteins, Plancks, Newtons and Greens so great, they were able to intuitize correctly and move ever in the general correct direction. Starting with a most base of foundational principles and sketching and developing, based on a need to explore and make sense of some inexplicable area of nature. Or perhaps they were simply just lucky, a bit of both perhaps?

    —-

    Is Mach’s Principle Wrong? I see people who say it is not wrong and others who say it is. Based on my very limited knowledge, it is my belief that it should not be wrong. It is a very strong thing, I feel. Is it something like the axiom of choice in terms of its consequences and provability?

  • http://blogs.discovermagazine.com/cosmicvariance/clifford/ Clifford

    Ah.. so you did get something out of it! great! Keep reading! Read some of the original papers…..students today only read the neat and tidy presentations in textbooks….read a few of the classic orginals…please!

    Cheers,

    -cvj

  • http://eskesthai.blogspot.com/2005/11/paul-dirac-and-geometrical-thinking.html Plato

    So a first principle needed to be established for a guiding principle, and this was the geometry that runs through it all, consistantly?

  • Thomas Larsson

    Distler #77

    OK, you are right that Maxwell was not a good example. My second example is a much better example of a successful guiding principle; conformal invariance leads to highly nontrivial predictions once you allow for conformal anomalies.

    This example also shows how important it is to consider symmetries on the quantum level. The most striking lesson from 2D gravity is that the trace of the metric becomes physical after quantization. How this manifests itself depends on the formalism. In lightcone quantization, the Hilbert space becomes unexpectedly large since you cannot factor out conformal transformations due to the anomaly. Alternatively, you can save proper conformal invariance by explicitly introducing the trace of the metric as the Liouville field. Either way, a gauge component of the metric has become physical.

    The obvious generalization to 4D gravity is that there is more to the metric than the two graviton polarizations, and that any approach to quantum gravity which ignores this will run into serious problems. Provided, of course, that we take the lesson from 2D gravity seriously.

  • http://countiblis.blogspot.com Count Iblis

    Thomas,

    I don’t really see the physical significance of all this. Consider e.g. percolation in two dimensions, which is a fairly trivial model with central charge zero. You can map this to all sorts of interesting 2d models (xxz spin chain, loop models, coulomb gas etc. ). Using the techniques developed for conformal invariance you can then calculate correlations in the percolation model. E.g. The associated Coulomb gas has central charge different from zero and yet can be used to calculate nontrivial correlations in the original percolation model.

    But if the model refers to a physical system, then it’s just percolation. The fact that it happens to be conformally invariant may not be of any relevance for the physics.

  • http://golem.ph.utexas.edu/~distler/blog/ Jacques Distler

    This example also shows how important it is to consider symmetries on the quantum level. The most striking lesson from 2D gravity is that the trace of the metric becomes physical after quantization. How this manifests itself depends on the formalism. In lightcone quantization, the Hilbert space becomes unexpectedly large since you cannot factor out conformal transformations due to the anomaly. Alternatively, you can save proper conformal invariance by explicitly introducing the trace of the metric as the Liouville field. Either way, a gauge component of the metric has become physical.
    The obvious generalization to 4D gravity is that there is more to the metric than the two graviton polarizations, and that any approach to quantum gravity which ignores this will run into serious problems. Provided, of course, that we take the lesson from 2D gravity seriously.

    We have discussed this many times before, and I still maintain that you are wrong.

    1) In the 2D Polyakov formulation (of the string worldsheet), Weyl symmetry is postulated as a gauge symmetry of the 2D gravity theory. In the noncritical string, it is not postulated to be a gauge symmetry and we don’t attempt to quotient out by it. The trace of the 2D metric is physical from the get-go, and that’s that. If the matter theory is classically conformally-invariant, then you get a constraint on the gravitational effective action (which is sufficiently strong to allow you to solve exactly for it).

    2) There are no diffeomorphism anomalies in D=4.

    3) In D=4k+2 dimensions, diffeomorphism anomalies render the gravitational theory inconsistent. Your analogy with the conformal anomaly is a) flawed and b) doesn’t save the theory, even in D=2 (the one case you claim to understand).

    What this has to do with the topic at hand is unclear to me, but since lots of other people are discoursing on their pet “theories” here, I suppose it’s not unreasonable for you to do the same.

  • Thomas Larsson

    Count Iblis,

    I don’t really understand what percolation has to do with anything. For one thing, it is not unitary, since it is not described by the trivial unitary rep with c = 0, but rather by the limit c -> 0 of non-unitary models. IOW, it is not the q = 1 Potts model, which is trivial, but rather the q -> 1 limit. So you need a non-zero, albeit infinitesimal, central charge.

    My point is that the presence of gauge anomalies is the most striking feature of 2D gravity. Exactly how these anomalies manifest themselves depends on the formalism; Jackiw showed that if you start by gauge-fixing Weyl transformations, the anomaly pops up the the diffeomorphism sector instead. By analogy, one strongly expects diff anomalies in 4D gravity as well, but no such anomalies show up neither in string theory nor in LQG. Therefore, I cannot believe in either of these theories.

    The reason why diff anomalies in higher dimensions don’t show up is clear from the representation theory of the multi-dimensional Virasoro algebra. In order to construct representations, one must first expand all fields around a 1D curve, which I call the observer’s trajectory. To introduce and quantize this curve is crucial, because the higher-dimensional analogues of the Virasoro cocycle are always functionals of it. Besides, there is a no-go theorem stating that there are no diff anomalies in 4D if you only quantize the fields.

  • Thomas Larsson

    Distler,

    1) In the 2D Polyakov formulation (of the string worldsheet), Weyl symmetry is postulated as a gauge symmetry of the 2D gravity theory. In the noncritical string, it is not postulated to be a gauge symmetry and we don’t attempt to quotient out by it.

    The whole point with gauge anomalies is that they turn gauge symmetries into conventional non-gauge symmetries, which act in a non-trivial way on the physical Hilbert space. Nobody has ever claimed that an anomalous gauge symmetry should be factored out, except in your imagination. E.g., in the classical noncritical string, conformal transformations are gauge, but after quantization they are not. This is not something that is up to you to postulate, but a mathematical fact.

    2) There are no diffeomorphism anomalies in D=4.

    No theorem is stronger than its axioms, and here the relevant axiom is that the only thing we quantize are the fields. There are certainly diff anomalies in 4D in the sense that the 4D diffeomorphism algebra has non-trivial extensions which generalize the Virasoro algebra. In math speak, H^2(vect(N), M) != 0, where vect(N) is the algebra of vector fields in N dimensions and M is dual to the module of closed (N-1)-forms.

    As I just explained to count Iblis, you need to introduce and quantize a privileged 1D curve in spacetime in addition to the fields, because the relevant anomalies are functionals of this curve. Unless you introduce this curve, you cannot formulate the relevant anomalies. You are not really in the position to question this, because you don’t know how to construct quantum representations of the diffeomorphism algebra in more than 1D.

    3) In D=4k+2 dimensions, diffeomorphism anomalies render the gravitational theory inconsistent. Your analogy with the conformal anomaly is a) flawed and b) doesn’t save the theory, even in D=2 (the one case you claim to understand).

    As I explained above, we are not talking about the same mathematical objects. The difference is simpler to explain for the analogous Yang-Mills anomalies. The current algebra in 3D has two kind of extensions, the Mickelsson-Faddeev extension which is proportional to the third Casimir, and the “central” extension which is proportional to the second. It is the former which describes the anomalies appearing in the standard model. However, I’m discussing the latter, as are the authors of hep-th/9511185. I agree that the MF algebra is almost certainly inconsistent, as I argued in math-ph/0501023, where the distinction is made clear. This has no bearing on other types of anomalies. The crucial issue is not that the symmetry acts trivially, but that it acts unitarily.

  • http://feynman137.tripod.com/ Science

    Maxwell fiddled theory in Part 3 of his paper, “On Physical Lines of Force” (January 1862), getting the right answer (light speed) from wrong working. His elasticity theory is wrong and the predicted speed is really c/2^(1/2). Maxwell quietly corrected the error in a new paper in 1865, getting the same answer, but without the flawed theory. A.F. Chalmers’ article, ‘Maxwell and the Displacement Current’ (Physics Education, vol. 10, 1975, pp. 45-9): “the change was not explicitly acknowledged by Maxwell”. All Maxwell did was to play with equations because Weber had already shown empirically in 1856 that the root of the ratio of electric to magnetic force constants was the speed of light. Maxwell just had to fit a wave equation to this and Faraday’s law, using Faraday’s own theory of 1846, “Thoughts on Ray Vibrations”, and Maxwell had complete flexibility to choose any equation for “displacement current” he liked to get the right answer, but but he took 3 to correct it.

  • http://golem.ph.utexas.edu/~distler/blog/ Jacques Distler

    As I just explained to count Iblis, you need to introduce and quantize a privileged 1D curve in spacetime in addition to the fields, because the relevant anomalies are functionals of this curve. Unless you introduce this curve, you cannot formulate the relevant anomalies.

    Fine. Field theories are not sensitive to these “anomalies.” Theories with a “quantized” privileged 1D curve are. All you need to do is develop such a theory …

  • http://countiblis.blogspot.com Count Iblis

    Hi Thomas,

    Thanks for explaining your point!

    I just used percolation as an analogy. What I wanted to say was that you can look at the same model (e.g. percolation) in different ways and get models with different conformal properties in the scaling limit. E.g. the Coulomb gas representation of percolation has c = 1 (if I remember correctly).

  • Thomas Larsson

    Fine. Field theories are not sensitive to these “anomalies.” Theories with a “quantized” privileged 1D curve are. All you need to do is develop such a theory …

    You can read about it in this book.

  • http://eskesthai.blogspot.com/2005/10/rapping-our-way-to-einstein.html Plato

    Not that I would want to take up such a length to explain, while under moderation in certain areas, I would like too?

    I as laymans view, with a deep interest on the foundations of what Thomas, or any might argue about with Jacque. While it is complex, there is ” axiomatic process” from inception going on and I recognize it.

    I post in 7,8,9 of comment section (They will need time to materialize in about a couple of hours or so) I deal with Peter Woit comments and think this is why such moderation might have been thought about beside the etc, etc, etc?:)

    I do respect the “procedures and validation methods” as guiding principals. Why I mention the “Onion People” :)Without science as a validation process and the offer scientific proof, how could we not see how far we had gone?

  • Ashley

    ok i have a question. i have been having trouble with science and need a lot of help so i dont have to take it again next year. Why dont atoms have any electric charge even though they are made up of charged particles? please help me!!!!

  • http://blogs.discovermagazine.com/cosmicvariance/mark/ Mark

    Ashley. Because they have exactly the same number of negatively charged particles (electrons) as positively charged ones (protons). So as long as you’re not too close to an atom (and by atoms’ standards, we’re almost always far away from them) the two effects cancel and you see something with no charge at all.

  • http://countiblis.blogspot.com Count Iblis

    Mark, I vaguely remember a recent article that derived bounds on the charge difference of protons and electrons. The idea was that a small charge difference would have cosmological effects that were ruled out by WMAP. The new bounds were many orders of magnitude stronger than previously known bounds

  • http://blogs.discovermagazine.com/cosmicvariance/mark/ Mark

    I vaguely recall something similar, but don’t recall the details.

  • http://countiblis.blogspot.com Count Iblis
  • http://blogs.discovermagazine.com/cosmicvariance/mark/ Mark

    Thanks! I knew that I knew the person involved (Pedro Ferreira as it turns out), but still couldn’t remember the article.

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  • M. Ayub Faridi

    In 1905 Einstein merged space and time to get the stage on which Dynamics- spacetime has been played. Introducing the curvature, the merger became “unification” in Einstein’s General Theory of Relativity of 1915. In this process, the original Dynamical concepts were replaced by Field Theoretical concepts for that part of Dynamics to which General Relativity is applied — namely Gravity. However, there was no truly relativistic theory that incorporated gravity and other interactions in a Unified Field Theory. Einstein spent the better part of his life trying to construct such a theory to his satisfaction. Why was he dissatisfied with the unification is apparent in, for example, the Reissner-Nordstorm solution? The essence of the problem is that in the general equations of motion, gravity is incorporated into the left side of equations while the other interactions appear on the right. The left side contains gravity while the right embodies the rest of Dynamics. One might say that, “the seam shows through” here. This problem of unification becomes really acute when attempts are made for the quantistion of field.

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