Relativity
in brief... or in detail..
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Relativity
in brief... or in detail.. |
The original references - and some caveats and conventionsThe key works cited by or used in writing Einstein Light are:
Galileo is easy reading for a non-physicist: indeed the Dialogue is probably more often read by philosophers and historians than by physicists. Although the Principia (as Newton's work is commonly called) is rather heavier going in general, the section on relativity is clear. Compared with Galileo, Newton's and Maxwell's works are not only less accessible to a non-technical reader, but also quite unfamiliar to a physicist, because the nomenclature and emphasis has changed considerably. (Newton uses geometry much more than would a modern physicist, in part because he assumed that all educated readers would know geometry — one of the quadrivium — and this was his way of communicating with a general audience.) Einstein's paper is also both difficult for a non-scientific reader and somewhat unfamiliar in nomenclature for a physicist. In all cases, with the possible exception of Galileo, the novice reader would probably be better advised to consult an introductory physics text rather than the original works. In this brief presentation, we cite only a small number of physicists. Science, however, is usually the result of many researchers working independently or in collaboration. Those listed above are undisputed greats, but the advances they made built upon the work of others. For instance, a few months before Einstein's celebrated paper introducting Special Relativity, Poincaré had published the transformation equations, from which flow many of the results of Special Relativity. Poincaré names the transformation equations for Lorentz because, the preceding year, Lorentz had described the length contraction (Lorentz-Fitzgerald contraction) and time dilation described in module 4 of this presentation. Poincaré expresses the principle of relativity thus "It seems that this impossibility of demonstrating absolute movement is a general law of nature." These authors in turn draw on the earlier work of Larmor. Further, in this link Macrossan argues that the Lorentz transformations — the heart of relativity — were presented in 1897 by Joseph Larmor. (One could also note that of Einstein's papers of 1905, the one that was most cited in the following years, was that on molecular diffusion. This paper was preceded by a similar analysis reported in the previous year by William Sutherland.) As we note in our discussion of Maxwell's equations, of the four equations collectively known as Maxwell's equations, each bears the name of earlier researchers who had done the work on the individual effects: Faraday, Ampere and Gauss, not to mention Coulomb. It should be mentioned, too, that the versions of Maxwell's equations we know owe a lot to Fitzgerald and Larmor. Today, science is a vast structure, to which individual researchers add small parts, and occasionally do some rebuilding. Newton's famous quotation "If I have seen further, it is by standing on the shoulders of giants" may have been sarcastic. For today's scientists, who can see out to cosmological distances, down to the interior of nuclear particles, and with fabulous detail and subtlety into the vast range of problems between these scales, the quotation could be well applied. So, great though these thinkers certainly were, it is important to note that they built on the work of others. Important, too, to recognise that all of them were wrong about some things. It is important in science to maintain a healthy skeptical attitude to authority, as did Galileo (or at least Brecht's Galileo, the only one I know). He was not awed by Aristotle, nor Einstein by Newton. You do not need to be wiser than Aristotle to understand mechanics better than he did. Students must be ready to understand more than their teachers, or else we make no progress. (Finally: This presentation concerns only special relativity, not general relativity. Nevertheless, I cannot resist recommending a lovely paper by Sam Drake: The equivalence principle as a stepping stone from special relativity to general relativity: A Socratic dialog.) Taking liberties with the original referencesIn this very condensed presentation of relativity, I am taking certain liberties in presenting the views of those involved. My aim is to save you time, and to make it easier. This involves a potentially dangerous compromise. Einstein himself is reported to have said that every explanation should be made as simple as possible, but no simpler. This is an extremely important point. When discussing something complex, a simple statement could easily be made so simple as to be untrue. If you suspect that I am erring on the side of simplicity, then I urge you to consult the original references listed above. Meanwhile, here is an example of one of my shortcuts:Galileo's characters in the Dialogue do not mention juggling, nor do they say explicitly that there is no way that a sailor in a smoothly moving ship can tell whether the ship is moving or not. What they do say takes up much of the second day of the Dialogue. For instance, Salviati says: "Motion exists as motion and acts as motion in relation to things that lack it, but in regard to things that share it equally, it has no effect and behaves as if it did not exist. Thus, for example, the goods loaded on a ship move insofar as they leave Venice, go by Corfu, Crete, and Cyprus, and arrive in Aleppo, and insofar as these places (Venice, Corfu, Crete, etc.) stay still and do not move with the ship; but for the bales, boxes, and packages loaded and stowed on the ship, the motion from Venice to Syria is as nothing and in no way alters their relationship among themselves or to the ship itself; this is so because this motion is common to all and shared equally by all; on the other hand, if in this cargo a bale is displaced from a box by a mere inch, this alone is for it a greater motion (in relation to the box) than the journey of two thousand miles made by them together*." And so on, at very considerable length. It's wordy, but it gives insight into the culture of the time. Don't trust me, borrow a copy from the library — it's a good read.
Taking liberties in the animations: caveats and conventionsScaling. People cannot walk and cars and trains cannot go fast enough for relativistic effects to be appreciable. Even in airliners, the effects are extremely small and difficult, though not impossible, to measure. So, at that level, the animations we supply are obviously unrealistic. Nevertheless, while we ask you to suspend disbelief long enough to admit such speeds in these cases, we have endeavoured to keep the effects involved approximately to scale. In some cases, the animation software has interpolated frames, so results will not always be accurate to the nearest pixel, but they are close.Optical aberration. The convention we adopt in the animations is that, although the speed of light in the animation has been slowed down, the speed of light from the screen to your eyes has its normal value. A consequence of this is that the images of high speed cars and rocket ships represented are those that would be measured, rather than those that would be seen or photographed*.
Illumination. A further convention is that the space ship is illuminated by light from a source that is travelling with it. This is for two reasons. First, in deep space and at that speed, the light source would have to have to do that for us to see the object. Second, and more importantly, the objects that we actually do see travelling at great speed and at right angles to us are stars. These of course are their own light source, and so they have a relativistic red shift that is not explained by the classical Doppler shift. What does light look like? Representing light itself poses a problem. Of course we have deliberately 'slowed it down' in the animations. However, viewed from the side, a beam of light in vacuum or clean air is invisible. So our representation as little red blobs is misleading in those regards, and we seek your forgiveness. They do give the idea of speed, and they do give the idea of time-of-flight, which are the important concepts here. Accelerating rockets. The rocket ships in module 5 have the feature that their mechanical energy, in our frame, increases linearly with time. This does not happen in any real space craft, whose energy, momentum and speed are complicated functions of time. The red shift is qualitative (to make it quantitative requires assumptions about the spectrum of the illumination and albedo and it wouldn't add much).
Taking liberties with the historyThese are unintended: please report any serious errors. Neither the author nor the producer is a historian.We heartily recommend the web site of the Museo Galileo. * "il moto in tanto è moto, e come moto opera, in quanto ha relazione a cose che di esso mancano; ma tra le cose che tutte ne participano egualmente, niente opera ed è come s'e' non fusse: e cosí le mercanzie delle quali è carica la nave, in tanto si muovono, in quanto, lasciando Venezia, passano per Corfú, per Candia, per Cipro, e vanno in Aleppo, li quali Venezia, Corfú, Candia etc. restano, né si muovono con la nave; ma per le balle, casse ed altri colli, de' quali è carica e stivata la nave, e rispetto alla nave medesima, il moto da Venezia in Soría è come nullo, e niente altera la relazione che è tra di loro, e questo, perché è comune a tutti ed egualmente da tutti è participato; e quando delle robe che sono in nave una balla si sia discostata da una cassa un sol dito, questo solo sarà stato per lei movimento maggiore, in relazione alla cassa, che 'l viaggio di dua mila miglia fatto da loro di conserva." |
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