Talk:Special relativity/Archive 15

Relativity Wikiproject
I've suggested at the proposed wikiprojects page that a relativity wikiproject be created. If interested, you can add your name to the list and check out the plan for the project at WikiProject Relativity. MP  (talk) 12:58, 29 October 2006 (UTC)

Sign Convention
Have we formed a consensus on the sign convention? From other articles, it looks like the signature is mostly -+++. That's definitely the one I prefer -- spinors notwithstanding. It's also the predominant one in current GR literature. This is important. Most notably, it affects many components. We need to decide on one convention, and stick to it thoroughly. Among other things, we need to make sure that it carries through in expressions for components of the four-current, for example. --MOBle 16:18, 20 November 2006 (UTC)
 * I think we just need to make clear what convention is used in the article and to what one needs to pay attention to if one switches from one to the other convention. We also need to get rid of c everywhere. You can do the unit conversions before and/or after you use an equation. It is better to explain these issues so that readers can learn and understand it, instead of protecting the reader against having to deal with changing conventions, changing units etc. etc. Count Iblis 16:42, 20 November 2006 (UTC)
 * I have reasons to prefer +---, but I admit this it is non-standard. I advise choosing conventions on the signature (which should be -+++ unless of good case can be made for doing otherwise) and whether c should apprear in the equations or not.  In the later case, I usually omit c, but given that people are using this article to learn about SR I feel that it's omission only will make a difficult subject even harder to handle. --EMS | Talk 17:21, 20 November 2006 (UTC)
 * About c, we could define x_{0} to be c t instead of t as is done now in the "Physics in spacetime" section. People reading that part of the article surely are able to understand how to put back c and if you put x_{0} = ct that's going to help. Count Iblis 17:37, 20 November 2006 (UTC)
 * Landau & Lifshitz, Jackson, Bjorken & Drell, Peskin & Schroeder all use +---. I think +--- is thus pretty standard, or at least it is certainly not non-standard. Peskin & Schroeder say that their conventions follow nearly all recent field theory texts.LeBofSportif 18:07, 20 November 2006 (UTC)
 * Hmm... This might be true. I admittedly come with a bias for the GR convention.  (Anyone giving a GR talk without spinors and with +--- would be laughed out of the room.)  I think the newest version of Jackson may have switched to the "reasonable" -+++.  I like the idea of using x_0=ct.  However, as the anon seems to be pointing out, it is more standard to use upper indices on coordinates.  (I also like the anon's use of $$d\sigma$$.)  --MOBle 18:13, 20 November 2006 (UTC)
 * Using upper indices on coordinates is the correct thing to do. To obtain a scalar (such as $$ds^2$$) from a tensor with subscripted indices (such as the metric tensor $$g_{\mu\nu}$$) you need to use tensors with superscripted idices (such as $$x^\mu$$).  Personally, I prefer to name my coordinates (i.e., [x, y, z, t]) and let that be that. --EMS | Talk 18:50, 20 November 2006 (UTC)
 * It will be particularly unkind to the majority of readers to use anything else but the usual units of physics (x, y, z, t). No more than that is required to explain SRT, and it is good practice to keep the standard physics units -- which includes c in m/s. IMO all physics articles in Wikipedia should keep the international units standard. Harald88 22:34, 20 November 2006 (UTC)
 * I'll take issue with this, but only slightly. In more advanced articles (and especially GR-related ones), c becomes a bothersome nuisance.  So I would permit some flexibility in terms of whether to omit c or not.  OTOH, for any article where a firm understanding of relativity is not a necessary prerequisite (such as this one), I agree 100% with Harald that omitting c is unkind.  People need to be brought in one step at a time.  This article necessarily covers a lot of ground for readers trying to get a handle on SR.  Bringing in anything which is not absolutely necessary truly is a disservice to the readers. --EMS | Talk 04:32, 21 November 2006 (UTC)
 * For the first half of the article, roughly till "The geometry of space-time" that's ok. But in the later sections, defining x0 = ct will help. Now you have c^2 (c^(-2)) covariant (contravariant) metric tensor. The people who are going to read that stuff will be helped by eliminating c. Also, note that in the section "Electromagnetism in 4D" c has been set to 1. And I don't think anyone wants to switch to SI units and insert the conversion factors epsilon_0 and mu_0 everywhere there :) Count Iblis 14:08, 21 November 2006 (UTC)
 * Of course I see nothing wrong with simplifying equations where appropriate, as long as it is correctly done and clearly indicated. :-) Harald88 21:05, 24 November 2006 (UTC)
 * I haven't added to a discussion page before so I'm sorry if I mess up the insetion. Anony is right. This section is a mess. Instead of addressing all points though, I’ll just give my input on the sign convention. When doing physics there are many conventions that are left up to the choice of the practitioner. Many conventions are very standard, but some still have no general consensus. In relativity there is a sign convention for the metric that is somewhat not agreed on, but I will argue should be +---. First I will give you the ONLY reason that it is sometimes taken to be -+++ and then show why this is a bad choice. In non-relativistic Euclidean physics the line element describing distance along a path is given by $$d\sigma $$ in $$d\sigma ^{2} = dx^{2} + dy^{2} + dz^{2}$$ In special relativity there is an invariant interval between events which can be described in terms of an invariant line element ds, which looks much like this with the exception that it must include a time differential with the opposite sign of the other terms in order to be invariant. In other words $$-(dx^{0})^{2} + d\sigma ^{2}$$ where $$x^{0} = ct$$ is invariant, but also $$d\sigma ^{2} - (dx^{0})^{2}$$ is invariant.  So the question is then which way should we define $$ds^{2}$$. Minkowski unfortunately chose the former merely for the only reason that the interval would look more like the Euclidean line element that he was used to dealing with. Which led him to the erroneous(which I will demonstrate) conclusion that time is an imaginary spatial coordinate.  This was the wrong thing to do and is unfortunately carried on in too many papers and texts involving relativistic metrics.  Here’s the first reason. Squared lengths of vectors for real physical quantities become negative. The inner product of four-vectors A and B involves the metric $$A \cdot B = g_{\mu \nu }A^{\mu }B^{\nu }$$ So for example the squared length of the momentum four-vector in special relativity is $$p \cdot p = \eta _{\mu \nu}p^{\mu }p^{\nu }$$ and with the +--- convention that yields a positive result $$ \eta _{\mu \nu}p^{\mu }p^{\nu } = (\frac{E}{c})^{2} - (p)^{2} = (mc)^{2}$$ It is nice that the mass is the length of the momentum four-vector and not imaginary times mass,  which would have been the case if we chose -+++. As another example consider the velocity four-vector. $$U \cdot U = g_{\mu \nu }U^{\mu }U^{\nu }$$ With the +--- convention the length of the velocity four-vector is the speed of light. $$g_{\mu \nu }U^{\mu }U^{\nu } = c^{2}$$ This yields an elegant interpretation of relativity that all things travel in 4d spacetime at the speed of light, merely rotated in direction in spacetime by four-forces. Thats why four-force is always perpendicular to four-velocity. $$g_{\mu \nu }F^{\mu }U^{\nu } = 0$$ It would be awfully inconvenient if the interpretation had to be that all things traveled through 4d spacetime with imaginary velocity because we chose -+++ for no good reason.  Heres the second reason.  It leads to the erroneous interpretation of time as an imaginary spatial coordinate instead of associated imaginary with the spatial coordinates with which it now obviously belongs. Consider for a moment the 2x2 identity and the three Pauli matrices. The square of the 2x2 identity is identity is $$\sigma _{0}^{2} = \sigma _{0}$$ The square of any other Pauli matrix is minus one times identity. $$\sigma _{i}^{2} = - \sigma _{0}$$ Lets see how these would affect physics if we let them serve as a component of an orthonormal basis with the 2x2 identity associated with time. It is not imaginary that is associated with time. It is imaginary in the Pauli matrices that is associated with space. A displacement vector $$\mathbf{ds}$$ in space and time with these associations is $$\mathbf{ds} = \sigma_{0}(dx^{0})\mathbf{e_0} + \sigma_{x}dx\mathbf{e_x} + \sigma_{y}dy\mathbf{e_y} + \sigma_{z}dz\mathbf{e_z}$$ and the square of that displacement vector without using the metric this time as its effect is imbedded in the Pauli matrices is $$(\mathbf{ds}^{2}) = \mathbf{1}ds^{2} = \mathbf{1}((dx^{0})^{2} - dx^{2} - dy^{2} - dz^{2})$$ Minkowski associated imaginary with the wrong coordinate, BECAUSE he chose the wrong sign convention.WaiteDavid137 17:56, 24 December 2006 (UTC)

At one time, I favored +--- because time is the direction in which the world-lines of particles are extended. However, I subsequently switched to -+++ because it is more similar to non-relativistic physics. In every-day life (and experimental physics), we use the Newtonian viewpoint and just add on relativistic corrections. So the mathematics we use should be designed to make that easy. Theoretical physics is frankly less important. The speed of light in a vacuum c should be retained for the same reason and to conform to the SI units. However, as I did in the section on physics in space-time, I think we should use t (in seconds) as the time coordinate instead of c t (in meters or Plank lengths or whatever). So the c will appear in the metric tensor. JRSpriggs 12:05, 21 November 2006 (UTC)


 * To Count Iblis: I am responsible for the most recent version of "Electromagnetism in 4D". Although c does not appear explicitly in the equations, it was not my intension to set it to one. On the contrary, I intended to use SI units. The speed of light in a vacuum appears implicitly within the $$\eta \!$$s in the constitutive equation and that is the only place that it is needed. And the permeability (electromagnetism) of vacuum is used only in that equation while the permittivity of the vacuum is entirely eliminated. JRSpriggs 04:49, 23 November 2006 (UTC)


 * To WaiteDavid137: Your argument amounts to setting up a straw-man and knocking him down. If you want your changes to this article to be accepted, I have two suggestions: (1) forget about changing the signature, we will never agree to that; and (2) change only one little thing per day because massive changes will almost always include something which offends someone enough to cause him to revert it, and they are hard to check which is offensive in itself. JRSpriggs 06:44, 27 December 2006 (UTC)
 * BS, both about the straw man and massive changes. The only change I recall making to this section was correcting your claim that F = mA doesn't work for relativity, by adding the note that it does still work for four-vectors because in fact as a four-vector equation it works just fine. There are many other mistakes you make in this section, but I only felt like mentioning the sign convention. WaiteDavid137 13:26, 27 December 2006 (UTC)
 * I was assuming that you were the same person as who keeps saying "LETMEFIXYOURCRAP" and trying to change the signature. Excuse me if I jumped to the wrong conclusion there. But my advice applies to anyone.
 * I have no love of imaginary numbers in physics and I think that neither space nor time should be considered imaginary. There is no physical reason why one has to take a square-root of any version of contracting the metric with two copies of an infinitesimal displacement. And if you do want to take a square-root, I suggest changing the sign where appropriate to ensure that you are taking the square-root of a positive number. JRSpriggs 07:56, 28 December 2006 (UTC)
 * But changing the sign as you are suggesting is exactly what going with +--- is doing. Think about your own word on that matter. Maybe you should let him "fix your crap", at the least concerning this matter. Then we can look at the next issue concerning this section. WaiteDavid137 08:26, 29 December 2006 (UTC)

Suggested addition to Postulates section
Since this is the technical article on SR, I think it might be a good idea to mention in the postulates section that special relativity can and has been derived without the use of the second postulate (that is, certain minimal assumptions about space-time symmetry and smoothness are sufficient). This is not crackpot science, but has been known for quite a while - cited in secondary references such as Purcell's classic Electricity & Magnetism textbook, which refers to the peer-reviewed and oft-cited article David Mermin "Relativity Without Light" (American Journal of Physics -- February 1984 -- Volume 52, Issue 2, pp. 119-124). This is an important observation because it underscores the generality of relativity and deemphasizes the connection between relativity and E&M which, while historically important, is not fundamental to the theory - relativity is not a consequence of E&M, but a higher-order theory describing how _all_ physical theories must behave, after all. The present wording seems misleading (too categorical) in this sense. Alternatively a statement that the two postulates given constitute the _historical_ set, and not the only one possible, might also be sufficient. Anyway, I'm interested in comments and/or objections; I can provide more references upon request. - Anon, Dec 5 2006 —The preceding unsigned comment was added by 134.10.121.134 (talk) 09:44, 5 December 2006 (UTC).


 * I would need to look over the sources for that view. Even so, most references use the Einstein set of postulates, and so it is most appropriate that this page follow suit.  Perhaps a note at the bottom of the article may be appropriate.  However, I have not heard of Merim's article before, but AJP is a well-known and reputable journal. --EMS | Talk 16:46, 5 December 2006 (UTC)


 * There have been several articles that do so, it's indeed rather well known. I would go along with a footnote. Harald88 23:01, 5 December 2006 (UTC)


 * There's a very good online textbook that does this as well. Section 10.8 "Relativity without c" of David Morin's textbook Mechanics and Special Relativity
 * With the principle of relativity alone (without the light speed postulate) you can prove that there is a limiting speed V for objects, finite or infinite.
 * Conclusion on page X-38:
 * Note that all of the finite 0 < V^2 < infinity possibilities are essentially the same. Any difference in the numerical definition of V can be absorbed into the definitions of the unit sizes for x and t. Given that V is finite, it has to be something, so it doesn’t make sense to put much importance on its numerical value. There is therefore only one decision to be made when constructing the spacetime structure of an (empty) universe. You just have to say whether V is finite or infinite, that is, whether the universe is Lorentzian or Galilean. Equivalently, all you have to say is whether or not there is an upper limit for the speed of any object. If there is, then you can simply postulate the existence of something that moves with this limiting speed. In other words, to create your universe, you simply have to say, "Let there be light.
 * Good idea - go for it. DVdm 10:22, 6 December 2006 (UTC)


 * That the universe is Lorentzian rather than Galilean is the main point of special relativity. Before 1900 or so, no one even imagined that Lorentzian was possible or could conceive how it would work. Also the constant which we call $$\frac{-1}{c^2}$$ could be positive (Euclidean), zero (Galilean), or negative (Lorentzian). You did not consider the possibility that it might be positive. JRSpriggs 04:53, 7 December 2006 (UTC)


 * I believe the point here is that all these derivations show that symmetry considerations require a certain mathematical form for coordinate transformations, free up to a constant K; the value of K is then determined empirically to be this or that particular power of c. So, in the end, you _do_ need the observation that c is the invariant velocity - but the logical role of this observation is much more limited than before (it removes a degree of freedom from the theory, instead of providing the very basis for the theory). This is very appropriate as a derivation for SR as it emphasizes _relativity_. Also, sure, the const. could be infinite or negative (i seem to recall the negative case leads to some very absurd conclusions), but at some point you just go out, measure it and conclude it's positive&finite - et voila, you have SR. Anyway, I think we're all saying the same thing. I'll write a possible footnote up sometime this weekend and post it here for discussion. —The preceding unsigned comment was added by 134.10.121.134 (talk) 08:12, 7 December 2006 (UTC).


 * OK; how about this for the footnote text:


 * The two postulate basis for Special Relativity outlined in this section is the one historically used by Einstein, and it remains the one most commonly used today. However, other minimal sets of axioms sufficient to derive the theory have been discovered since the publication of Einstein's original paper. In particular, several authors have shown it is possible to derive the structure of Special Relativity from the principle of relativity alone, along with some minimal assumptions about the symmetry and homogeneity of space and time [1][2]. Such derivations yield a theory free up to a constant universal speed K, which must be determined experimentally. Once experiment fixes K=c, the theory matches special relativity exactly. Accordingly, such single-postulate approaches give the full results of Special Relativity while highlighting the importance of the relativity principle. It shifts the role of the constancy of the speed of light from a cause of relativity to a consequence.


 * [1] Relativity without light. Authors:, Mermin, N. David. American Journal of Physics, Volume 52, Issue 2, February 1984, pp.119-124. Online version: http://adsabs.harvard.edu/abs/1984AmJPh..52..119M.


 * [2] A dual first-postulate basis for special relativity. Coleman, Brian. European Journal of Physics, Volume 24, Number 3, 2003, pp. 301-313. Online version: http://www.iop.org/EJ/article/0143-0807/24/3/311/ej3311.pdf


 * Comments would be appreciated. Also, where on the page do you think this would fit best? Finally, I'm new to Wikipedia so the citations etc are probably a bit off; will work on that myself before posting but pointers appreciated if you have the time. —The preceding unsigned comment was added by 134.10.24.172 (talk) 18:02, 11 December 2006 (UTC).

You have not convinced me that you can "derive the structure of Special Relativity from the principle of relativity alone, along with some minimal assumptions about the symmetry and homogeneity of space and time". I do not see any LOGICAL inconsistency between the homogeneity and isotropy of space and either a Galilean or a Euclidean structure for space-time. So I would oppose adding this note, as it is false. JRSpriggs 06:24, 12 December 2006 (UTC)


 * Ah, you're right, there should be a sentence in there that explains that the case K=infinite corresponds to the usual Galilean relativity. Make it:


 * The two postulate basis for Special Relativity outlined in this section is the one historically used by Einstein, and it remains the one most commonly used today. However, other minimal sets of axioms sufficient to derive the theory have been discovered since the publication of Einstein's original paper. In particular, several authors have shown it is possible to derive the structure of Special Relativity from the principle of relativity alone, along with some minimal assumptions about the symmetry and homogeneity of space and time [1][2]. Such derivations yield a theory free up to a constant universal speed K, which must be determined experimentally. For instance, infinite K would correspond to Galilean Relativity. Once experiment fixes K=c, however, the theory matches special relativity exactly. Accordingly, such single-postulate approaches give the full results of Special Relativity while highlighting the importance of the relativity principle. They shift the role of the constancy of the speed of light from a cause of relativity to a consequence.


 * [1] Relativity without light. Authors:, Mermin, N. David. American Journal of Physics, Volume 52, Issue 2, February 1984, pp.119-124. Online version: http://adsabs.harvard.edu/abs/1984AmJPh..52..119M.


 * [2] A dual first-postulate basis for special relativity. Coleman, Brian. European Journal of Physics, Volume 24, Number 3, 2003, pp. 301-313. Online version: http://www.iop.org/EJ/article/0143-0807/24/3/311/ej3311.pdf


 * IMO, treating the K<0 case here is unneccessary - it is a footnote, after all, and it's only marginally relevant, as opposed to the Galilean & Lorentz cases.


 * After further consideration, I decided it was more appropriate to post this on the separate Postulates of SR page. I did so. I also noticed that the overall quality and depth of exposition on the postulates page was somewhat lacking (it wouldn't elucidate anything much to a non-specialist - no context, no "common-sense" discussion - and wouldn't say much new to a specialist. In particular, discussion of the first postulate in galilean vs. special relativity would be nice, along with more indepth discussion of just how surprising the second postulate was/is) . Alas, I need to be working on my thesis right now, not a Wikipedia SR page, but perhaps someone has the time? —Preceding unsigned comment added by 87.110.137.116 (talk • contribs)

Archived
I redistributed the archived discussions in the 4 archive pages found in this version of this talk page into 14 archives because their size was very big (not suitable for slow connections). The new pages are: Archive 1, Archive 2, Archive 3, Archive 4, Archive 5, Archive 6, Archive 7, Archive 8, Archive 9, Archive 10, Archive 11, Archive 12, Archive 13 and Archive 14 --Meno25 07:08, 11 December 2006 (UTC)

GA Re-Review and In-line citations
Members of the WikiProject Good articles are in the process of doing a re-review of current Good Article listings to ensure compliance with the standards of the Good Article Criteria. (Discussion of the changes and re-review can be found here). A significant change to the GA criteria is the mandatory use of some sort of in-line citation (In accordance to WP:CITE) to be used in order for an article to pass the verification and reference criteria. Currently this article does not include in-line citations. It is recommended that the article's editors take a look at the inclusion of in-line citations as well as how the article stacks up against the rest of the Good Article criteria. GA reviewers will give you at least a week's time from the date of this notice to work on the in-line citations before doing a full re-review and deciding if the article still merits being considered a Good Article or would need to be de-listed. If you have any questions, please don't hesitate to contact us on the Good Article project talk page or you may contact me personally. On behalf of the Good Articles Project, I want to thank you for all the time and effort that you have put into working on this article and improving the overall quality of the Wikipedia project.


 * I draw your attention to the fact that the Mathematics and Physics projects are using Scientific citation guidelines and also that this article already has three in-line citations. If you think that there is a specific point that requires more references, please point it out. JRSpriggs 05:14, 14 December 2006 (UTC)