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Being a high-school physics teacher, I always am searching for compelling and different approaches to the subject. In the case of (special) relativity a frequent curiosity arises while discussing what a speeding observer would see in front of him. I'd love if the community could point me to some reference text/book/paper which deals in a mathematically rigorous way with this problem.

EDIT: for clarity's sake, as my question coud be misinterpreted, I'd like to study in (mathematical) detail the problem of human vision in relativity, so the reference I'm looking for should not be intended for high school students but for a person with a more rigorous mathematical background (university level).

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Before answering, please see our policy on resource recommendation questions. Please write substantial answers that detail the style, content, and prerequisites of the book, paper or other resource. Explain the nature of the resource so that readers can decide which one is best suited for them rather than relying on the opinions of others. Answers containing only a reference to a book or paper will be removed!

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    $\begingroup$ Why spend days digging trough math, when you can go relativistic yourself: gamelab.mit.edu/games/a-slower-speed-of-light :-) $\endgroup$ – CuriousOne Jan 13 '16 at 18:48
  • $\begingroup$ :) because 1) my computer is (ironically) too slow for the game to run smoothly and 2) I want to understand it! $\endgroup$ – marco trevi Jan 13 '16 at 18:55
  • $\begingroup$ I've played this game 4 times through. Although it's definitely not 100% accurate, it at least says which relativistic effects they're trying to exemplify. testtubegames.com/velocityraptor.html $\endgroup$ – Arturo don Juan Jan 13 '16 at 19:10
  • $\begingroup$ Sorry about your computer... runs fine at 2560x1440 and "fantastic" mode on my Mac. As for the search for papers... what would you tell a kid in school who didn't do a literature search before asking... insufficient effort? That's what I would do as a teacher. OK, kids in university never liked me, either. $\endgroup$ – CuriousOne Jan 13 '16 at 19:17
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    $\begingroup$ Don't get me wrong either, but if I happen to know an expert in a certain field I'd ask him for a worthy reference instead of digging through the vast and often overestimated internet with google. This is what I think a reference request question is about, or did I get it wrong? $\endgroup$ – marco trevi Jan 13 '16 at 19:47
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The topic of relativistic imaging is strongly related to the Terrell-Penrose effect, a.k.a. Terrell rotation, see this Wikipedia page and references therein. The Terrel effect concerns the visual appearance of a relativistically moving object as seen by a human observer or point-like camera, due to the fact that light rays leaving different points of an object at the same time (in the camera frame) reach the recording sensor at different times. Here are other helpful resources for getting acquainted with it:

J. Terrell, "Invisibility of the Lorentz Contraction" (Phys.Rev.1959) : the seminal paper that (re)started it all, from the observation that "if the apparent directions of objects are plotted as points on a sphere surrounding the observer, the Lorentz transformation corresponds to a conformal transformation on the surface of this sphere." Robert Penrose also discovered the effect at about the same time, but both Terrell and Penrose have been predated by Anton Lampa who described the same effect in 1925.

V. F. Weisskopf, "The Visual Appearance of Rapidly Moving Objects", (Physics Today 1960): another often cited paper on the topic, explaining in simple terms of geometry and special relativity Terrell's observation on the appearance of moving objects.

Sec.7.6.2 What the Observer Actually Observes, from David Tong's notes on Special Relativity. Provides a discussion of the celestial sphere as seen by different observers, including stereographic projections, Hopf maps, and Moebius transformations.

R.J. Deissler, "The appearance, apparent speed, and removal of optical effects for relativistically moving objects": a paper on recovering length contraction in images of relativistic objects despite all those optical effects; it also explains why relativistic objects may appear to move much faster than light in optical recordings.

R.T.Rau, D.Weiskopf, H.Ruder, "Special Relativity in Virtual Reality": a paper on special relativistic rendering and the geometry involved.

• MIT's game A Slower Speed of Light, as already mentioned in the comments.

Through Einstein's Eyes: a very nice site from Craig Savage's group at the Australian National University, dedicated specifically to introductory relativistic visualizations and geared to high school and undergrad students. In fact you may want to pay close attention to the "Relativistic visualization" section of their Bibliography page, which I think answers your question by itself with a list of about 25 articles on the subject.

Real Time Relativity: companion simulation software for Through Einstein's Eyes, the source of all movies shown on the site. This program actually predated the Slower Speed Of Light by a few good years, is very easy to master, is not resource intensive, and so works great even on slightly older computers (Windows and Mac versions available). It allows free exploration of several environments with a few customizable options, and if you are familiar with the Unity engine, you may even attempt to modify/ add your own setting. A description of RTR and its philosophy can be found in "Real Time Relativity: exploration learning of special relativity".

Spacetime Travel: a German site by Ute Kraus and Corvin Zahn from Institut für Physik, Universität Hildesheim, also dedicated to visualizations of relativity. Many nice simulations, including the Terrell-Penrose effect and even a realistic wormhole between Tübingen and a beach in France, detailed explanations of what is going on, and even cut-out paper models. No stand alone software though. Described in U.Kraus, "First-person visualizations of the special and general theory of relativity".

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