md65536

So basically, if you can start cooling the edges of the cloud, more laser light penetrates further into the cloud, but the further in, the less chance the re-emitted light has of escaping the cloud? The cooling effect occurs because of absorption, but it still requires the energy being put into the cloud to escape? The initial absorption reduces heat energy, but since you can't just increase the non-thermal energy of the atoms indefinitely, it's going to have to escape the cloud or end up increasing the heat. Does this mean that the laser cooling process is effectively using light to "poke" the atoms just right so that they emit more light energy than they absorb, so that more light energy goes out of the cloud than what goes in? PS. as a spectator up till now, I appreciate the patient informative responses. Replies that focus on discouraging amateurs don't help others who are reading.

It's a bit confusing because it's not a valid sentence with all of those question marks, but if they're changed to commas, one solution is Is this the easier solution? Oh I see, just by trying some things out:

I was curious about how many answers there might be, so I wrote code. I gave up before trying to deal with parentheses, but got the following: (11 - 17) * 13 + 2 + 19 + 101 = 44 (11 - 13) * 19 - 17 - 2 + 101 = 44 (13 + 101) / 2 - 11 - 19 + 17 = 44 (11 - 13 - 17) * 2 - 19 + 101 = 44 (13 - 17 - 19) * 2 - 11 + 101 = 44 (17 - 19 - 2) * 11 - 13 + 101 = 44 (17 - 19) * 11 * 2 - 13 + 101 = 44 (13 - 11 + 19 + 101) / 2 - 17 = 44 (11 - 17 + 19 + 101) / 2 - 13 = 44 (my answer) ((17 - 19 + 101) / 11 + 13) * 2 = 44 ((13 * 17 - 19) / 101 + 2) * 11 = 44 ((19 - 11) * 17 - 13 - 101) * 2 = 44 (13 * 17 - 19) / 101 * 2 * 11 = 44 (Commander's answer, ignoring order) Sensei's answer isn't here because it's not left-to-right order of operations. I wouldn't doubt this is a small fraction of the possible answers, but neither would I bet that it is. (I also manually culled duplicates so I may have removed too many.)

I got (101+11+19-17)/2-13=44.

Okay, but I'm trying to understand a statement that you made, because it makes no sense to me and I'm trying to figure out where the misunderstanding is. You wrote, "He’s essentially using an inertial coordinate system to show that there is no acceleration - which is trivially true." That makes NO sense to me, because you can describe a particle that's accelerating, using an inertial coordinate system. The coordinate system has nothing to do with whether the particle is properly accelerating or not. Eg. Consider an inertial observer on a train bank. A train accelerates from rest at a rate of 1 m/s^2, relative to the observer. The observer's coordinate system doesn't trivially show that there is no acceleration. Am I using the term "coordinate system" incorrectly? What I don't understand is if one can refer to a particle, and its own coordinate system, as the same thing, or if you and Anamitra are talking about different things. If I have an inertial observer and a train accelerates, I don't think I can sensibly describe it as "an accelerating coordinate system". I'm trying to find out what you're saying is trivially true.

No acceleration of what? It originally mentions and later clarifies that the acceleration of "particles" is being discussed, and that's not trivially true. If you're assuming it's reference frames being accelerated, where is that stated? This topic is confusing from the start, with seemingly some explanation or details missing?? It's difficult for me to follow if I first have to guess at the same assumptions being made, even if they're reasonable. Yes, that seems to explain what is going on, thanks. I did not get that from the discussion so far. Basically is it: specify a particle that has no acceleration, conclude that it cannot be changing speed? (I'm guessing then the main flaw in reasoning is that OP starts with equations of inertial motion, but is treating them as "the equations of general motion in SR"?)

Then I still don't understand. Particles *can* accelerate, and their motion can be described in the coordinates of an inertial observer. Why do you need an accelerating observer to describe accelerating particles? It can be described in Minkowski coordinates, why suggest Rindler? Not all particles are observers; to me it looks like where OP is talking about particles, you're describing observers. "in this article we see that the particle cannot accelerate." (emphasis mine) I understand to mean that we're talking about the case of constant gamma, ie. we're limiting ourselves to particles that don't accelerate. If you two are really on the same page and understanding each other, then I apologize. (Besides all that, a particle can accelerate and maintain constant speed relative to an inertial observer, thus constant gamma in that observer's inertial frame but only changing direction, while the particle undergoes proper acceleration, so I think I disagree with both of you however your statements are understood!)

That's not what OP literally said, and you've interpreted what OP wrote as nonsense, but still I don't know what OP really meant because it could be interpreted different ways. I don't think you two are talking about the same thing, at least in some cases like this, and I don't see how the problems can possibly be resolved if you're not even talking about the same things. I think OP needs to clarify first. Eg. in this case, Anamitra were you talking about general particles, as they are measured in various inertial frames of reference? Or particles in their own rest frames, being inertial in some inertial frames of reference and accelerating in other inertial frames of reference? Or something else? I think some consider a particle being "in" a given frame to mean that the frame is its rest frame, but I take it to mean the particle "as measured in" a given frame. Eg. a train can have a positive speed in the bank's frame. The train is in all the different frames, not just its rest frame. Is that at odds with your interpretation of OP's statement?

I'm not following this. An accelerometer that is measuring proper acceleration can be described in the coordinates of an inertial observer. My reading of what you replied to, is "An inertial observer remains inertial as measured in any other inertial reference frame, but a particle can (properly) accelerate as measured in an inertial reference frame." It only mentions particles being able to accelerate. What are you referring to when you say "there is no proper acceleration"?

I just quoted the wiki page. I can't explain other than with another quote from the page: "But because the principle is so vague, many distinct statements can be (and have been) made that would qualify as a Mach principle, and some of these are false." Definitely Mach's principle doesn't answer the questions here. I see it more as philosophical in that it provides questions that can't be answered, or at least aren't settled by science. I disagree that there's evidence of what would be observed if all matter was taken away, as far as I know no one has performed such an experiment! The evidence is based on extrapolation from what we currently observe. Does the Higgs mechanism depend on other fundamental constants or measurements? I think to settle this, and to answer OP's questions about a massless universe etc, you'd first have to know if and how the fundamental constants etc. would change in such a case. You'd have to settle Mach's principle in general. I think Mach7 is not true based on current evidence, best current theoretical models, and the assumption that some specific aspects of Mach's principle are not true.

This is a variation of a variation of Mach's Principle https://en.wikipedia.org/wiki/Mach's_principle "Mach7: If you take away all matter, there is no more space." I think that if time and distance are emergent properties of the universe then nothing requires spacetime, because everything could be described in terms of whatever they're emergent from. Eg. maybe causal connections could be described using topology without geometry. In that case, c is a property of the relationship between distance and time, something describing how things are connected in the underlying universe and emerging as a speed in our possibly emergent observations and measurements of that universe. As an example or analogy, consider the emergent 3d space depicted by a 2d hologram. The observable depths and distances of that 3d space are not needed to describe the hologram completely.

The thread's question needs interpretation, and I might be interpreting it differently than others. I think that what you're asking is how much mass you would need to make everything in the universe gravitationally bound to it, despite the current rate of expansion. If I'm thinking about it right, any constant rate of expansion will result in a constant-size cosmic horizon, beyond which it is impossible for matter to be gravitationally bound across that distance. The reason is that the matter would have to be falling in faster than the speed of light, to overcome the expansion of space between it and the mass. The horizon is determined by expansion alone, so making a more massive BH won't help... except... If you had matter right on the cosmic horizon, you'd need to basically have it falling in at a speed of c to overcome expansion. That would imply a BH with an event horizon at the same radius as the cosmic horizon??? (assuming Schwarzschild BH) But then, if you had a BH even close to that size, matter on the cosmic horizon would be a lot closer to it than if it were a point mass, so wouldn't it fall in anyway? Or does it work out that the gravitational influence of a BH is still the same as if it were a point mass? This seems really weird, because even if we completely ignore expansion for a moment, wouldn't this mean that the gravitational influence of a BH is roughly proportional to 1/r^2, while the mass is proportional to 1/r, no matter how big it is? That seems to imply that if you could have a BH of unlimited mass, you could make it so that the Schwarzschild radius is so large that an object outside it is so extremely far away from the center of the BH that the gravitational acceleration is small, even if it is near the horizon. Am I thinking about this correctly? How would an infalling observer describe the BH? It seems that the event horizon (a lightlike surface) would still pass by it at the speed of light, despite minimal acceleration. Meanwhile it seems like another observer, hovering farther away, outside the horizon, could easily avoid falling in, and see that same event horizon as stationary. Where's the error in my thinking? Back to expansion, would it even make sense to talk about a constant rate of expansion of spacetime, in a volume that is entirely occupied by a massive BH? The BH curves the spacetime so extremely that the volume inside the horizon is not a part of the same spacetime outside??? Does curved spacetime expand the same as flat spacetime? Would a volume containing a large BH expand the same as a volume of empty space?

It's still curved pieces projected onto a flat image. It is a projection. You can see distortion closer to the edges of the pieces. There is less distortion of size compared to the usual Mercator maps. It can be improved. If you look at the Dymaxion map that Acme posted, you'll see that the surface gets "split" along water. Yours handles Australia really well but cuts up many land masses, making it a poor map along those cuts. You could move where the cuts are, and you can also join the cut pieces differently. For example, instead of joining the main South America piece on a corner over water, if you join it to the rest of the continent then it reduces the extreme distortion of distances between the two pieces. That's an easy fix. Perhaps harder is something that Fuller solved, is getting optimal cuts or whatever. A lot of your pieces are part land, part water. Is it possible to get more pieces that are all water, and others that more closely fit the land, as Fuller's does? This might require more effort than you're willing to spend though. Also it assumes that a land map is what's important, and that distortion and breaks over the ocean are acceptable. A tool would make this easier. Perhaps a wire polyhedron that could be rotated over a physical globe. There are also downloadable polyhedrons that can be added to Google Earth. I'm sure it would be possible to create one for a rhombic dodecahedron, and to have it fixed in space so that you could rotate the globe underneath and try out different mappings. While trying to find something like that, I came across this related info: http://www.progonos.com/furuti/MapProj/Normal/ProjPoly/projPoly.html

Oops, I blame myself for an earlier suggestion along those lines. I should have realized something was wrong. If you take a regular tetrahedron, you can successively divide each triangle into 4 equilateral triangles, recursively. Then you have a bunch of equal-sized triangles. If however the tetrahedron is inscribed in a sphere, and you extend all the interior triangle vertices out to the surface of the sphere, the points will not all be translated the same distance. So the triangles on the sphere would not all be equal. I should have realized that equal size on a such a polyhedron wouldn't mean equal size on a sphere, but I didn't until told.

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.

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.

"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.

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

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 agree with Bignose, who presented a very clear and immediate problem. It's not a matter of opinion, it's a matter of science. I think you either have to show significance or drop the claim. You said you're not interested in fooling yourself but I think you're doing just that. One way is, assuming that your understanding is great enough that a challenge to it is just an "opinion", no more important than your own, and so a refusal to even accept the validity of challenges. Another way is, avoiding facing a major problem that is brought up, brushing it aside and being content to have it "opted out" of discussion. Do you understand the problem Bignose has identified, and its importance? Do you understand how if you can't explain the significance of the values you're using, not even to yourself while being critical, you're tricking yourself?

What do you make of this? http://en.wikipedia.org/wiki/Buffon's_needle There are known relationships between randomly oriented lines, and pi. They have geometrical explanations. Is this similar enough to your idea that you would say that the results of Buffon's experiment is due to the physical nature of matter, and not just mathematical concepts that also work abstractly? Can you rule out a geometrical explanation of your results? Eg. if reality were *not* made up of your model's lines, would you expect to get different results for electron mass or whatever? It sounds to me like your evidence is only your claim that your model works and corresponds with reality. Is there a simpler explanation of why you get your results, other than that they directly model physical reality? (I still think the answer to that last question is "yes", and that by putting constants like 1822.8885 in your code and then doing some random things, you're arriving at some meaningful-looking results but tricking yourself about how they came about.) If yes, then I don't see how anyone else would accept it as actually representative of reality. If you use your model to predict a new, experimentally verifiable result, then people will be more interested.

The brain is built or trained to get 3D visual clues from 2D images, which is why it's possible to create illusions in which 2d geometrical shapes appear 3D. Is there a difference that you notice between what you're describing, and 3d illusions? For example, adding shadows can give an appearance of depth. The image could be seen as paint splatters, with apparent depth to them. Can you describe the extra dimension that you see? Is it like paint-like surface texture, or is it extreme differences in depth? If the latter, does it feel puzzling trying to resolve a lack of parallax in the image as seen with both eyes, or does the 3d nature of it feel consistent and "right"?

You're welcome. It wasn't a burden!

Well it's all part of communicating the idea. If the code's ugly but does what you say and the data are interesting, it doesn't matter that much. I don't think it's helpful to try to get me interested. Tailoring this for me is a dead end. It's just a slight curiosity (but not a huge curiosity because the program's bugs hide any interesting behavior), but I don't know anything about the topic---I'm not even a scientist---and I'm not seeing the point that you're seeing in all this. Even if I saw what you're seeing, I can't see what I would do with it. There are others who would be able to see pages of grandiose but vague claims, equations and numbers, and descriptions of simulations... and put it all together in their head much better than I can. But I don't expect you'll find that. I would suspect that there's a lack of interest in discussing your ideas because you start so big that there's nothing to respond to eg. "The Bohr model falls out of QSA" would need to be researched maybe for hours before someone could comment on it! For me the specifics also get lost in a sea of explanations and data. Anyway, if you want my advice anyway as a non-scientist I'd suggest working on an abstract (I think http://www.lightbluetouchpaper.org/2007/03/14/how-not-to-write-an-abstract/ gives good advice about it). My non-professional opinion is that you should describe in one paragraph: - What it is that you're simulating (I mean your methods, not what you think it represents), - What your results are, - Why you think that's important. Something simple, not "all of QM..." unless you're showing that literally every detail of QM really does correspond (either covering every detail or show how your stuff precisely accommodates it as a whole or explain why the details that you don't know about don't matter). - Perhaps address what I see as a problem: show that the results happen naturally rather than that the program has been molded and tweaked to arrive at the results you want. I know a lot of that has been mentioned but for me it's too scattered and impossible for me to synthesize. I think your goal should be getting the interest of others, by writing something that's simple enough for experts in the field to say "Here's what is wrong or missing: ..." I'm using gcc-4.6 on Ubuntu. How about you?