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Relativists seem to devote their research in GR. I was wondering whether SR has been fully exhausted already. Probably at the physics level, but also at the mathematical level too?
On the one hand, str simply states the rules for relativistic kinematics, so in that sense there has been no mystery since 1905. But as we saw in 1907, when Minkowski introduced the notion of spacetime, a dramatic reformulation can cause a c change. A bit later the Thomas precession was discovered, which is a fundamentally important consequence of the kinematical laws. Later still, Penrose (and independently Terrell) discovered the beautiful connection between the optical experience of a relativistic observer and the Lorentz group acting by the Moebius action on the Riemann sphere. Various observations which many find surprising (sufficiently so that these observations are often called "paradoxes") have been made over the years concering relativistic kinematics, e.g. Bell's "paradox" about spaceships and string, the fact that all colliding plane waves meet "head on" in some frame, and so on. Thus, history suggests that surprises concerning relativistic kinematics are still in store.Relativists seem to devote their research in GR. I was wondering whether SR has been fully exhausted already. Probably at the physics level, but also at the mathematical level too?
Many of those problems derive from people's desire to think of the "plane of simultaneity" as some sense of reality while I believe that a "Doppler view" of reality is much more practical when it ever comes to space travel at relativistic speeds. Unfortunately, at least IMHO, to many the idea of what an observer actually measures is secondary compared to what an observer constructs as some "plane of simultaneity" reality. Hope that makes any sense.A fundamental new topic of current interest concerns relativistic navigation, and even in flat spacetime a full relativistic beacon navigation system is still a sufficiently new idea that ineresting questions remain. For example the Coll canonical chart for Minkowski spacetime (wrt some choice of four "beacons") has some perhaps surprising properties, e.g. it has four (real) null coordinate covectors but four spacelike (real) coordinate vectors, and it is clear that there is much to say about this new and fundamental concept, which obviates all the difficulties of planetary calendars/coordinates (with inevitable coordinate singularities) as well as the procedure of making laborious "relativistic corrections" to Newtonian concepts of navigation.
It does make sense, and I agree. (It sure is nice to be able to say that!) You will love the Coll chart if you haven't studied that eprint yet, since as you will see, there is a simple relationship with the Bondi k-calculus (consider one dimensional relative motion of two inertial beacons in Minkowski vacuum, and compute the transformation from the Cartesian chart to the corresponding Coll canonical chart)!Many of those problems derive from people's desire to think of the "plane of simultaneity" as some sense of reality while I believe that a "Doppler view" of reality is much more practical when it ever comes to space travel at relativistic speeds. Unfortunately, at least IMHO, to many the idea of what an observer actually measures is secondary compared to what an observer constructs as some "plane of simultaneity" reality. Hope that makes any sense.
I agree entirely; when I discuss frames, for example, I always try to stress that this concept is coordinate-free and has both a vivid geometric meaning and an immediate physical interpretation ("local Lorentz frames" of a coherent family of observers).Up to a large extent I see the same issues with explanations of GR. In my (perhaps ignorant) opinion too much emphasize is given to coordinate views and less to the intrinsic geometric properties and how they relatate to the EFE with a result that people get more confused than helped in understanding GR.
I don't think research in SR is exhausted.Relativists seem to devote their research in GR. I was wondering whether SR has been fully exhausted already. Probably at the physics level, but also at the mathematical level too?
You might like this: C.B. Giannoni, Special Relativity in Accelerated Systems, Philosophy of Science. Vol. 40, No. 3. (Sep., 1973), pp. 382-392.One outstanding problem in pedagogy is that the accelerated observer in SR has not been satisfactorily presented in textbooks yet.
You can temporarily download this paper "[URL [Broken] 1973.pdf"]here[/URL]; I intend to delete this sentence by tomorrow.C.B. Giannoni said:The Special Theory of Relativity (STR) as formulated by Einstein is applicable only to inertial systems; however, it can easily be extended to accelerated systems by a mere reformulation that does not alter its empirical content.
It matters whether one is discussing the education of future physicists or a general audience in a broad sense (e.g. electrical engineers may not require exposure to conceptual subtleties in relativistic physics). My comments here concern the problem of educating the former group.One outstanding problem in pedagogy is that the accelerated observer in SR has not been satisfactorally presented in textbooks yet.
Some graduate level textbooks do discuss relativistic thermodynamics (e.g. MTW). There is a significant literature on all these topics but I'd agree that much of this hasn't made it into the textbooks, possibly because it is not generally considered sufficiently mature/useful by most would-be textbook authors.It's not clear to me if topics like relativistic thermodynamics and relativistic (Hamiltonian and Lagrangian) mechanics have been fully worked out for SR (let alone GR)... not to mention presented in textbooks.