md65536

This is true but I think it's the kind of statement that is easily confused. The kind that leads to teachers saying things like "if event A happened THEN event B ... an observer can SEE the events in REVERSE order" without explaining the important details of the meaning of the emphasized words, as timo did so well---simply and unambiguously. No frame of reference was mentioned in the original "A then B", and yet the example excludes causally related events. The same teacher might explain that this object really is short and that's that, implying some sort of absoluteness. It takes remembering that the object is only moving at .999c in particular reference frames to understand the truth of your statement. Or the teacher might say one thing, and the student hears another, filling in the missing details incorrectly. I imagine a scientist stating something and understanding it---not bothering to explain all of the caveats that can be expected to be understood---and a teacher explaining it essentially "right" but perhaps not realizing all of the details that should be understood, and then a student trying to make sense of it while holding on to some details that are wrong. I think that if all the details were understood and taught from the beginning, teachers and students would never get around to the idea that "relativity is weird". I guess understanding that motion is relative, and so are simultaneity and length, makes all of the thread's statements understandable. The wrong details might come from forgetting those things.

No, you wouldn't need to get into the system. If there are long messages or many messages, it gives you more data to try to figure out. Obscurity makes it harder, but that would just make it take longer to break, not make it unbreakable. Public-key systems I think involve a "one-way function", where the public key is easy to generate but the private key is difficult to extract. Eg. factoring of numbers with hundreds of digits is very hard (not unbreakable). A key like "1337" would not be hard because you can just try every number between 0 and a few thousand or millions or whatever and see what you get. If you make a system complex enough like this, and then don't allow anyone access to it, and then don't *use* it too much or send dangerous messages (eg encrypting "a", "aa", "aaa" might give someone some clues), you can probably make something that is likely to be kept secret. Cracking DVD encryption involved having access to a device: '"The nomad" allegedly found this decryption algorithm through so-called reverse engineering of a Xing DVD-player, where the [decryption] keys were more or less openly accessible.' -- http://en.wikipedia.org/wiki/DeCSS

How did you manage 13 on the left? Is there one in the center? The one I built with buckyballs wouldn't fit that. Can you easily render the intersections of pairs of spheres to show they're not overlapping? Yes, I don't see how they'll fit together as nicely as the hexagon-based ones. Anyway while searching for a ball-stacking POV script I came across a page that claims, "Mathematicians have not yet reached consensus on a proof that a Barlow packing, including the face-centered cubic (fcc) and hexagonal (hcp) is actually the densest possible, although Gauss proved the fcc’s density of approximately 0.74 optimal for a lattice (any denser arrangement would have to be more random)." -- http://grunch.net/archives/56 I'm not sure how reliable this is. Also: http://mathworld.wolfram.com/KeplerConjecture.html so it seems reliable.

Would you say that DVD encryption and other things with secret keys are unbreakable? With a key built into the system it's vulnerable. I wouldn't be able to break it but someone who knew what they were doing, who could probe the system and find clues and reverse engineer stuff could. Anyway that's "security through obscurity" and is *definitely* not what one would call "unbreakable". If you have a truly random one-time pad, then the message is unbreakable. You've taken that and crippled it by reusing the pad (each occurrence of "o" uses the same number), so you've introduced patterns. That can be fixed though. However, security through obscurity is fairly useless. You mentioned using a calculatable, pseudo-random number generator... why not just throw all of the obscurity into that, so that it's difficult (but probably not unbreakable) to figure that part out? The manipulation involving 1337 just adds a bit more obscurity, but doesn't make it perfect.

No, it's not unbreakable in similar sense to a one-time pad. In a one-time pad, the encrypted message is indistinguishable from random. Here, once you know the encryption method, your message is essentially 55, 509, 1205, 1205, 798, 319, 562, 798, 900, 1205, 29, 1329. There are 3 occurrences of 1205, and two of 798. It doesn't matter how big these random numbers are because there are only 26 + punctuation different possible numbers. Now your encryption is a simple letter substitution. On a long message, a modestly skilled person could figure out the words, just like in cryptograms. You could fix this by creating new numbers for each occurrence of a letter, necessarily reusing numbers to encode long messages. But then it is not really any different from a one-time pad, except for the extra data and math. The problem with a one-time pad is getting the same secret pad to both parties.

How are you modelling these? I would try calculating locations using a pov-ray script, but it sounds like Moray is easier. Do you have to figure out where to put everything yourself, or does it automatically fit the pieces so they're touching? You should be able to run POV on even very old computers. You can render in low resolution without antialiasing to speed it up. With some basic scripting and some math I think you could replicate some of these images. If you like fitting spheres physically, you might try magnetic buckyballs https://www.google.ca/search?q=buckyballs&tbm=isch (Do they still make them? There are several other similar brands, but last I heard they stopped selling them due to swallowing hazards.) It can be frustrating when the magnets don't want to go where you want them to, but many interesting shapes can be put together. So I was thinking about this a little more, wondering why you care about the surface area of a sphere. In your construction, if you expand your spheres uniformly to take up all space, you should end up with dodecahedrons. Basically, each of the 12 points where your spheres touch should form a face. On the other hand, if you shrunk your spheres to the smallest convex polyhedron that still shares all of the same (12) contacts (Ah, it looks like this notion is a "dual" http://en.wikipedia.org/wiki/Dual_polyhedron), you would get an icosahedron, with 12 vertexes but 20 triangular faces. However it's not a regular icosahedron, because not all of the triangles are equal. Edit: I may have this wrong. Perhaps you get an icosahedron with 12 vertexes and 14 faces (6 of them rectangles). Looking at a regular icosahedron, I wonder if that is a better shape? Of course the symmetry is nice, but is the goal here to pack the spheres as densely as possible? I made one with buckyballs and it looks pretty dense. Perhaps Janus could model one??? Here's how you would do it: Have one layer of 5 balls in a ring. Fit another 5-ball ring on top of that (rotated 2pi/10). Each ring leaves a "hole" in the middle into which you fit 1 ball as a top and bottom "layer". So that's 12 balls again, in 4 layers however it looks very similar length between opposite vertexes as does your irregular icosahedron. What I don't know is: - Is this shape actually smaller? (Should be a reasonable challenge to calculate) - Do these shapes fit together as well as yours? I wonder if the best way to pack a single layer (which you have) is not necessarily the best way to pack a volume? It seems so, but perhaps shifting the balls slightly out of a flat layer might give up some space to be exploited??? Edit: The icosahedron shapes you end up with (a ring of 3, then one of 6, then one of 3) has 12 balls on the outside but it can fit another one in the middle, so I'm pretty sure it stacks balls more efficiently than the regular icosahedron can. Definitely interesting... I might try to produce a povray scene sometime if curiosity eventually beats laziness. I'm sure there are scripted ball-stacking povray scenes that can be found on the web, too.

If you had enough mass in a small enough space, you'd have a black hole. Then the effects of electromagnetism couldn't affect anything on the outside. Does that count as stronger?

"tr is 1.0742 of an sr" means that for a unit sphere the rhombic shapes have a surface area 1.0742 times that of a unit area on the sphere. The area doesn't need to be a circle. For example, a square 1 unit by 1 unit has 1 unit of area. On a unit sphere it subtends 1 sr. You may prefer your shapes to unit areas. Similarly, you might imagine cutting a unit circle into 6 equal slices, creating 6 equilateral triangles within the circle. Each triangle has a side length of 1, and its arc of the circle is slightly more. So you may say "I prefer to measure circumference using 6 special units instead of 2pi standard units," but probably no one will care. If I had to describe the shape of the wedges, the best I can think of is the "intersection of a rhombic pyramid and a smaller ball centered at the pyramid's apex". You might try to see if you can cut up a world map into these shapes. Do the continents fit nicely in them? Perhaps someone has done it before, or you could create a new map projection. One thing I notice: On the vertices shared by 4 pieces, there are basically 2 straight lines cutting across each other. You can join 3 pieces together (those that share a 3-piece vertex) and end up with a triangle shaped section of the sphere's surface. Then you'd have a sphere cut into 4 identical pieces, which you would get if you cut a ball into a spherical tetrahedron, with each wedge being roughly a tetrahedron with a rounded face. Likewise you could do the opposite and cut each of your 12 wedges into 2 equal triangular pieces, or 4 etc. Or you could take the spherical tetrahedron and cut each piece into 3 identical pieces in other ways (if you cut down the middle of an edge, you get your rhombus shapes, but if you cut from the corners you can make triangular shapes) and get other divisions of a sphere into 12 identical pieces.

http://en.wikipedia.org/wiki/Banach%E2%80%93Tarski_paradox The BanachTarski paradox as I've heard it basically says that you can "disassemble an orange and then reassemble it into 2 oranges identical to the first." You can do this mathematically on a set of points but you can't do it with a real orange because it requires taking it apart into uncountably infinite points, I think, and you can't take apart quanta of matter like that. I'm wondering if reasoning in the opposite direction is useful. Outline: 1. Assume that matter isn't quantized, and any piece can be split into several smaller pieces. 2. Find a way to partition a sphere according to the B-T paradox without changing the density of the matter. 3. Create 2 spheres, thus mass is not conserved. Step 2 is the speculative part, I'm not sure it could be meaningfully done since we start by assuming something unreal. But perhaps there might be no meaningful mathematical way to have matter that isn't quantized yet can't be partitioned like that??? (Whether that's true or not is beyond my ability to figure out.) One problem is that the result of splitting up a piece of matter might always result in a countable number of pieces. Anyway I wondered further if it might be possible to apply the idea to anything that follows a conservation law, requiring that thing to be quantized.

A 12-sided polyhedron is a dodecahedron. This would be a "rhombic dodecahedron." As a sphere it is a spherical rhombic dodecahedron. http://en.wikipedia.org/wiki/File:Rhombic_dodecahedron_spherical.png

You can get something similar just by adding sine waves with different wavelengths. https://www.wolframalpha.com/input/?i=sin(x)+%2B+sin(x*30)%2F10 You can generate such a wave in sound editing program. In Audacity, generate a low frequency, high amplitude tone, and generate a higher frequency, lower amplitude tone. Then merge the tracks (select both, "mix and render"). Just by adding two waves, you get a wave on top of another wave. However you can see that the graph doesn't quite look like what you drew. It looks like your high-frequency wave might be partly rotated along the curvature of the low-frequency wave? Is that what you want?

Well I'm in over my head and not reasoning sensibly. I guess it doesn't matter if you can extract energy at the detector, because you can end up converting between potential and kinetic energy. What really matters is that the source loses energy due to radiation of gravitational energy (independently of other forms of radiation). Any info I've found leads back to swansont's answer in post #2: A supernova will radiate gravitational waves unless it is (spherically?) symmetrical. The book, Gravitation (Misner, Thorne and Wheeler) seems to answer all the questions in the thread. Sec 35.5 explains the transverse nature of the wave: Sec. 36.1 explains the quadrupole (or higher) nature of gravitational waves, and why a spherically symmetric source is impossible. This is the only thing that made sense to me: (p 978) I think that one problem with my own reasoning in this thread is that I'm imagining gravitational waves as unrealistically simple. Perturbations on a rubber sheet can be described with a scalar (ie. the height at a point on the sheet). Longitudinal waves can be described with a vector. So reasoning with these analogies will get us stuck??? I don't think a loss of mass eg. by conversion to energy would itself produce gravitational waves, because wouldn't that be spherically symmetrical?

I'm mostly interested in hearing what your answer is to Bignose's question. Sorry I was looking at the code posted in #49. As for the code at your previously linked site, I don't think the program is simple, as I don't know what these values or the variables represent or what is being calculated and charted. Why is the tooltip on the 100 line? If it's put on the 1500 line the result is not as good. Why must d0 and d1 be less than 1800? If I use 100 and 700 the lines are closer together, so how is the point at Dist 5500 still significant? I think it's more important to answer Bignose's question about what makes the point at 5500 so important in the first place.

Sorry, I must do the opposite. I haven't analyzed a lot of your code but my impression of what I've seen is that it has "magic number" constants that are behind some of the "interesting" results, that and calling a desired value "significant" without quantifying why, as Bignose has stated. I think that if the code was simpler it would generate a sin curve or bell curve or whatever, but that this would have a conventional geometric explanation. I agree with Bignose, except that I don't think anyone should go easy on you about this, especially yourself. I think you must prove to yourself quantitatively that your results are significant. I think that you've been tricking yourself, and rather than facing challenges, your confidence despite the challenges suggests to me delusion. This isn't just something speculative scientists must do, this is something every scientist must do, especially theoretical scientists who are coming up with predictions far before the experimental evidence backs it up. Just today I heard an example of exactly the attitude I wish you had: "I always leave with this feeling, 'what if I'm tricked?' What if I believe into this just because it is beautiful?" -- Professor Andrei Linde, who probably has a good chance at a Nobel prize now for work on cosmic inflation. I have no interest in your work or in backing you up, until you are actually working toward answering Bignose's challenge, or dropping those claims. But by the way, I have quite a bit of experience in tricking myself, but I know it and always suspect it, and the feeling of understanding that comes with fitting an idea into existing physics has so far always outweighed the disappointment of realizing that a "discovery" is wrong or unimportant --- or it might simply be not what you thought it was. Fitting an idea into existing physics has always improved it, in my experience. I wish you could feel that feeling, but you seem to resist it, waving away the challenges instead of wondering "what if I'm tricked?", and building up the case to prove (to yourself and everyone) that you're not. I think that the problems in your claims far outweigh the importance of the claims themselves, and you should be focusing on whether the results are significant, and not yet so much on what they mean.

I'm wondering how you would detect it? Would there be a gravitational gradient, detectable using two observers along the line of sight? And, can you extract energy from it, that is lost from the source? A gravitational wave source radiates energy in the form of those waves. Does such an energy transfer occur here? From what I've read, it certainly sounds like "gravitational waves" are more than just "change in gravitational field strength." I'm in way over my head, but I'm going to guess that an approaching mass like that of an asymmetrical super nova does not constitute a gravitational wave, but instead might involve movement of the entire gravitational field as if it were static. Or equivalently, the observer is moving through the field. Modelling the supernova as two (or more) masses with static fields that move along with the masses, there would be no need to propagate changes through the field??? Not unless there is a change in acceleration. Anyway, I think that gravitational waves have a specific definition (they're quadrupole radiation and transverse, as you said, and they require not just acceleration but a change in acceleration). I don't think the longitudinal example is gravitational radiation, nor a gravitational wave. As an analogy, suppose you have an inertial moving static electric charge, and as it approaches the observer, the measured field strength changes. Does that involve radiation? Would it require photons? I think it doesn't, and that it would be silly to say that the change involves "light waves". There is a detectable change there, but it is not an EM wave, which is something that has a specific definition and describes more than just a field strength gradient.

No worries MigL, your example was clear enough but I completely misread it and got lost in my own reasoning. I'll stick to citable references here... This isn't true, neither for gravity nor for EM. http://math.ucr.edu/home/baez/physics/Relativity/GR/grav_speed.html : ... the gory mathematical details of which can be found in the reference: Aberration and the Speed of Gravity -- http://arxiv.org/abs/gr-qc/9909087 EM case: GR case, and explanation of how the lack of a "god-frame" doesn't matter:

Also what happens when you consider aberration of light? Suppose the two observers are traveling the length of an infinity long football field, crossing some number of transverse lines, and they send out such a particle at every line. The field lines will appear warped toward the forward direction. Since the two objects initially share an inertial frame, they should appear to not be moving, so no relativistic effects. They should appear directly to each other's side. The pull of the particle should be directly to the side, so not slowing nor speeding up the mass in the forward direction, relative to their rest frame. But this is a backward pull in the football field's frame. But what does it mean that gravitational effects appear in the direction that the mass is "now"? If the objects are massive, and one mass crosses a given line, it sees the line aberrated and the other mass not yet appearing to have reached that line, due to delay of light. But "now" the two synchronized masses are both crossing the line at the same time. Does that mean that the pull of gravity is along the aberrated line? This would make sense, because in the football field's frame, the pull of either mass is directly perpendicular, meaning that they would neither speed up nor slow down??? Definitely puzzling. It seems that gravitational effects shouldn't change the speed of the masses, yet charged particles should slow them down relative to the football field. Since the masses are not accelerating with respect to their direction of travel, there is no need for a graviton to be transmitted; there's no need for a delay of gravitational effect? Another puzzling aspect is that if one of the masses were to suddenly stop well before the line, such that the other would cross the line before seeing the other stop, then the other would "feel" the gravitational pull in the direction of the line as it was crossing. It would not be pulled toward where the other mass "is now" until it is able to know where the mass actually should be now. Edit: On second thought... why would one mass feel a slightly forward pull from the other mass, if the other is essentially at rest directly off to the side? Why would the existence of another massless moving frame of reference make any difference (it mustn't). When we say "where something is now" we must be referring to the observer's rest frame? I think so far I've only made myself more confused. My current feeble understanding is that the masses would slow relative to the football field, whether due to gravitational attraction or reception of opposite charged particles, but that this is consistent with the difference between photons and gravitons. I think you would need relative motion of the gravitational mass before detecting any difference in the direction of light and gravity, so I don't think this thought experiment is explanatory. Okay, but they're moving relative to what? In that other frame, yes the particles seem to come from behind, but the two masses seem twisted due to relativistic effects, so the particles don't seem to hit the backs of the masses. The particles hit the sides. Consistent with that, in the frames of the masses, the other mass doesn't have relative motion. The direction of the particles, and of gravitational attraction, is the same. The particles hit the sides. These two frames must be consistent. From the "other frame's" perspective, the particles come from behind and hit the twisted object on its side. Meanwhile if gravitational attraction is directly to the side then it affects the object as if it isn't twisted at all. So, just like the direction of light and gravity are different, the relativistic effects on the shape of the mass are different (it would be twisted by measure of light, but not twisted by measure of gravitational attraction). [This still doesn't make sense because it seems to imply that the particles would slow the masses in the "other" frame, while gravitation wouldn't, even though the acceleration is in the same direction in the masses' frame, so I must be missing something important. :S Perhaps "frame dragging" provides a solution.]

I say again your teacher is in error calculating the result. I know this sounds rather incredible but this conclusion is based on results from multiple calculations. At least one of the places where you say "sequence is important" is suspicious. I think that for example your teacher is counting "First blue peg in slot A, second blue peg in slot B, red in C, yellow in D" and "Second blue peg in slot A, first blue peg in slot B, red in C, yellow in D" as two separate possibilities. When I counted such things separately, I got 2160. I think 2160 might be what you get if there were two numbered pegs of each color (and you made sure to always select a color's peg-1 before peg-2). This sort of thing has cropped up before and it has always been due to human error.

There is OP's caveat that a "specific colour can't be repeated more than 2 times", which if I understand means that the (4,0,0,0) and (3,1,0,0) arrangements aren't valid.

Hrm, yes. Most of the examples here involve damage due to different parts of the body accelerating differently from other parts. This is typical of human experience, where we are accelerated via an external force that pushes on the edge of the body, but doesn't directly push on the insides. What about if all parts are accelerated directly, like if you could switch on a uniform gravitational field while the body is in free fall (no other forces pushing on part of the body)? Assuming Born rigid acceleration, where no part of the body is displaced from another due to acceleration, I suspect that there might be no limit to safe acceleration??? Assuming you're accelerated by some method that has no other effect other than acceleration, you would still be able to detect the acceleration, but I'm not sure what it would feel like if no part of you moves relative to any other. There would be temporal distortions. And if we're not assuming approximately Born rigid acceleration, you could always cause damage at some point just by having different parts tear away from each other, I think even if you had fairly low acceleration and enough time.

The teacher's answer doesn't make sense to me. If there are no restrictions on duplication, you should have a maximum of 6^4 = 1296 possible choices of pins. I get 2160 if I add: 360 the number of possibilities with 4 unique colors 1440 the number of possibilities with 2 ordered pins of the same color, with 2 others of unique color 360 the number of possibilities with 2 ordered pins of the same color, with the other 2 pins also an ordered pair. Is that what the teacher's equation represents? I think this is an error mainly because 2160 is greater than 1296. ! I think maybe the error is that the order of the 2 same-colored pins doesn't matter, so the teacher is counting a lot of cases twice. The answer I get is 1170 doing it 2 different ways: 1296 Total arrangements with no restrictions of duplicates -6 arrangements of 4 pins all the same color -120 arrangements of 3 pins of the same color. Or... something like what the teacher did except ignoring order, I won't write it out because I think I did it a convoluted way.

I don't think c+/-v is a meaningful closing speed of anything from the viewpoint of an observer on the ring. If so, what does v refer to? I think that from this perspective, c+v would be a coordinate speed of light as measured by a single observer on the ring using only its own clock. As discussed in other threads, coordinate speed is not the same as speed. The calculations work out the same (since the different observer viewpoints are consistent)... but I think it would be counter productive to consider it a speed. I think it is "the average rate of light's propagation when measured using a single clock that is out of sync with other clocks along the light's path (and thus can differ from the locally measured speed of light along that path)." The clocks on the ring can't be synchronized (to the full definition) by any method. I don't know what simultaneity convention you might use either, but whatever you use, the simultaneity of two specific events will generally depend on the choice of observer frame of reference on the ring. Setting the ring's clocks to be the same in the lab frame is useful conceptually, because then every location on the ring can be treated symmetrically, simplifying some ideas. To me, the lack of synchronization, ie. the relativity of simultaneity on the ring, is the explanation of why the average(?) coordinate speed of light can differ from c. According to your link: http://www.physicsinsights.org/sagnac_1.html "Note that You Can't Synchronize the Clocks in a Rotating Frame [...] This is, in fact, the essence of the Sagnac effect. The clocks on the rotating disk can't be properly synchronized: any attempt to do so leads to a discontinuity somewhere on the disk. Any signal which goes all the way around the disk crosses the discontinuity." So I don't know if it's possible to figure out the Sagnac effect from a ring perspective before considering relativity of simultaneity. Unfortunately, I'm content with vague ideas of why it works, without the maths that show how.

Agreed. With constant radial velocity and radial symmetry, at any time any observer on the ring should see the same thing as any other ring observer at any other time. The ring clocks couldn't tick at different rates without diverging, contradicting what the lab observer sees. It makes sense to me that the + and - values would end up the same. Consider some n clocks spaced evenly around the ring. Suppose that all of the ring clocks are set to the same time in the lab frame. The situation is the same at any of the clocks, as any of the others. Then relative to any given individual clock, if the previous clock is ahead by t seconds, then the next will be behind by the same value t. Do you agree? If you make your way around the ring in one direction, each next clock is ahead by the same value t, making a sync error of t*n all around the ring. In the opposite direction the sync error is -t*n. Edit: I think your link explains this in a slightly different way. However, if you fix the observer viewpoint at one clock, you'll find something like, the previous clock is ahead by t, and the one before that is ahead of it by a different amount, and about a quarter around the ring subsequent clocks start being behind the previous. A graph of the sync error relative to the single observer would look something like a sin wave, rather than a linearly increasing sync error. The fact that this observer disagrees with eg. an observer on the other side of the ring, about which of a given pair of clocks is ahead of the other, shows that the ring clocks can't be synchronized. Edit: Sorry I keep switching 'ahead/behind' when I think I got it backwards. It doesn't change the reasoning tho.

It looks like the anomaly is relative to the 36-year(???) average of the values in the second graph you linked. I think it means that since we don't have a "nominal" temperature that the Earth should be, we base the anomaly off of average. That way we can look at trends in the change in temperature, without needing to (or being able to) say whether the temperature is higher or lower than where it "should" be. If I'm reading this right it shows how sloppy the self-proclaimed "Lord" Monckton is, because he left the anomaly based on the 36-year average instead of computing a new average. So in this cherry-picked data set, the temperature is still about .24 degrees above the average of the full data set, showing that even though Monckton picked a section where there is no upward trend, that data still shows an average excess warmth over the chosen period that is above the average of the full data set. In short, I think anomaly is usually with respect to average across the period, and Monckton's anomaly is a revealing error.

I'm trying to think my way through your post, and perhaps making progress that might be useful to discuss? To figure out what's going on, it might be useful to place imaginary measuring devices all over the place. So imagine you have detectors placed all around the ring, and they have clocks and can indicate when the beam passes in either direction. One thing to consider is the synchronization of the clocks. Considering from the lab (center of ring) frame, it must be that all of the ring clocks tick at the same (slowed) rate. Imagine a lab clock controlling the clocks on the ring, by sending out a sync pulse from the center of the ring. Then from the lab frame only, the ring's clocks are all set the same. From the perspective of a ring observer, the clocks on the ring cannot be synchronized. A single pulse from the center will reach different clocks at different times. Yet the ring clocks must all tick at the same rate, so there must be a "shift" in simultaneity, where --- I think --- the clocks in front of an observer (with respect to the ring's rotation in the lab frame) are behind ahead in time, and ones behind are ahead behind in time. (Is this right??? My grasp on the reasoning is feeble and I think I got it backwards first attempt. ... and second, dammit!!) At some point near halfway around the ring, one of the clocks can be in sync with the observer's. So immediately you have a problem now of how you're going to measure the speed of light as the beam goes around the ring. You can use each local clock and the local speed will equal c. But you can't use only the one clock at the observer location, because as you make your way around the ring there will be a shift in simultaneity. If you do this while ignoring relative simultaneity, then you should get the "c+/-v" values that don't match the locally measured speed, but you're not properly measuring speed this way. That's as far as I got but can this line of reasoning be carried further?