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petsfed
Jan 19, 2007, 6:19 AM
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rrradam wrote: Even light, think 'line of sight', is believed to be straight, but as evidenced by Einstien Halos and/or the light bent by a star, light does not propogate in entirely straight lines... Instead they follow geodesics, which are the 'quickest'/straightest lines through space time. Let me explain...
No Adam. The definition of a straight line in physical space between two points is the path light would take between those two points in a vacuum. Gravitational lensing is a much more pronounced effect that refraction due to media change. If we plotted a course to a galaxy whose light is gravitationally lensed to us, the straightest path would not be the fastest path because we would not be following the contours of space time. Just like great circle routes on the earth seem curved when in the geometry they refer to, they ARE straight lines.
Again, localized, this phenomena is not apparent at all. But its the nature of the universe. In any curved geometry, a straight line is a curve that follows exactly the curvature of the system, even in hyperbolic space where what is a "straight line" is clearly not, by our euclidean definition. Thus light, which follows the curvature of space, is our definition of a straight line. Despite the fact that it is obviously not, according to euclidean geometry. You are confusing the premise that a light ray follows a straight line which is not quite accurate with the premise that a light ray is a straight line, which is more accurate.
/physics and astronomy student near graduation
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arrettinator
Jan 19, 2007, 3:31 PM
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petsfed wrote: /physics and astronomy student near graduation
I have a 6" f/5 parabolic primary. Think of a folded newtonian, but instead of a flat secondary I want to use a spherical secondary. I'm having trouble figuring out what fl secondary to use. I'm thinking it's going to be a 2" spherical w/ a smaller flat diagonal, as well. This is just me brainstorming. I've got the newtonian design already for this primary, but am bored with it already. I am losing illumination w/ the bigger secondary, but I can't afford a bigger primary. I'll probably get at least an 8" primary, or 10" some day, but for now this is what I'm working with. Any suggestions.
(drawing not to scale, obviously)
(This post was edited by arrettinator on Jan 19, 2007, 3:32 PM)
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petsfed
Jan 19, 2007, 10:46 PM
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arrettinator wrote: petsfed wrote: /physics and astronomy student near graduation Totally off topic but, I'm thinking of building a style of Gregorian/Folded Newtonian telescope. I have a 6" f/5 parabolic primary. Think of a folded newtonian, but instead of a flat secondary I want to use a spherical secondary. I'm having trouble figuring out what fl secondary to use. I'm thinking it's going to be a 2" spherical w/ a smaller flat diagonal, as well. This is just me brainstorming. I've got the newtonian design already for this primary, but am bored with it already. I am losing illumination w/ the bigger secondary, but I can't afford a bigger primary. I'll probably get at least an 8" primary, or 10" some day, but for now this is what I'm working with. Any suggestions. (drawing not to scale, obviously)
Man, I wish I was in an instrumentation focussed department. Dunno what to tell you. I mean, obviously you're gonna lose precision the smaller a secondary mirror you go, but you can't have too big of a secondary or else your light gathering ability is lost. And for a mirror as small as an 8 or a 10, that's pretty significant. I don't doubt you're familiar with spherical aberration so I won't bore you with that, but I'm curious how much additional aberration you're introducing by using one as the secondary (as opposed to a not-necessarily-spherical ellipsoid mirror). As I recall aberration between mirrors is multiplicative, so you could run the equations between aberration of your mirror combinations and total light lost due to a larger secondary and find out what the best combo would be.
That is, I'd plot the product of the expected resolution (or percent abberation, if available, but it should be proportionate to the inverse of the expected resolution) of your mirror system (y-axis) vs. secondary mirror diameter (x-axis), then plot light arriving on the primary (y-axis) vs. secondary mirror diameter (x-axis), then compare the two plots. Where aberration is the lowest while still having a maximum area of the primary not obscured, that's the way to go.
Good luck man. I don't really do too much telescope building in my field.
(This post was edited by petsfed on Jan 19, 2007, 10:47 PM)
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rrrADAM
Jan 20, 2007, 1:13 AM
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philbox wrote: Adam, you might explain in laymans terms why speed trumps time in light. Why could it not be possible for time to be the constant rather than speed of light in the equation E=mc2
Time dilation brutha:
Space and time are NOT 2 seperate things, they are inseperable parts of one thing: SPACETIME.
Just as front-back is a part of 3D space as much as left-right and up-down, time cannot be seperated from it, nor can it be compressed anymore than one dimension of space can (relative to us within the universe... some theorize that viewed from outside the universe cosmic expansion would be seen to have the effect of elongating time), as it is just another dimension of spacetime... And remember, light travels "through" space, so it has to traverse the distance and cannot take a shortcut skipping some space or time, so the observable effect is that time and space are constant locally... It is only when space (distance) and/or time are compared to different frames of reference in regards to motion or gravity that there is a measured effect, and this is relativity.
Now... Think of 'spacetime' in 2 dimensions instead of 4 (3 space / 1 time), with space on the horizontal (x) axis, time on the vertical (t) axis and your motion plotted out through spacetime with the gamma(this is a Minkowski Diagram)...
If you're standing still (i.e. are not moving through space (horizontally)), you will trace out a line vertically (time) through time, but as you move through space you effect the rate at which you move through time... Now imagine you are going as fast as you can (c), this would be represented in this 2D space as only moving horizontally, thus time now stands still (no vertical movement). Some theorize that if you were able to accelerate past this threashold, the line would now tip down, so you would be in effect moving backwards in time (on the minus side of the vertical line).
You can subsitute North-South with time (t), and East West with space (x), and your motion being in a car driving 55 MPH (instead of c) on the gamma... You will see that if you travel East (analogous to space) at all, you will effect the rate at which you move North (analogous to time), and that if you move East at exactly 55MPH, you will NOT move North at all (same as no motion through time).
Does this make sense ???
There is some really good info here:
http://en.wikipedia.org/wiki/Time_dilation
They even have some good graphics, and lots of experimental confirmation of this.
petsfed... I used refraction (Snell's Law) as a conceptual analogy only for ease of explanation, but it is an acurate analogy, as the curvature of space (Einstien's Field Equations) can be viewed as denser space in the analogy.
According to QED, light quantum mechanically does not always follow the straightest possible path, but instead takes all possible paths, and it is only the sum of all possibilities, with those that are the quickest, seen reinforcing each other and becomming emergent locally, whereas those that are not gennerally cancel each other out. Thus, quantum mechanically, photons of light can travel in a straight line through a curvature (among an infinate number of paths), but that particular photon will not be seen locally, as it is not the quickest due to having to traverse through the curvature (where spacetime is curved/denser)... Hence my initial analogy. 
Also, I for one believe that space is granular and discrete, thus it IS an un-understood medium, but this line of thinking is 'taboo', as it smaks of the ether. It is accepted that space behaves as if it were a something and this is consistant with experiment and observation, but it is also accepted to be a nothing despite this, and that is a contradiction.... But that is another topic for discussion all together. 
petsfed wrote: The definition of a straight line in physical space between two points is the path light would take between those two points in a vacuum.
http://en.wikipedia.org/wiki/Geodesicwikipedia.org wrote: In mathematics, a geodesic is a generalization of the notion of a "straight line" to "curved spaces". In presence of a metric, geodesics are defined to be (locally) the shortest path between points on the space.
Also... Try to imagine a true 'vacuum' in space, as space is filled with light of spectra of all going every which way, so try to imagine a small cube, even 1" squared, that does not contain a pion, mumeson, netrino, photon, etc... If gravitons are particles (I do NOT believe they are), then add those too... So, a true vacuum is also not a physical reality. As spacetime itself may be granular, descrete and quantizable... At least according to many of the current leading theoretical physicists of today. Meaning space is filled with "space".
Being an astronomer, you should know that quantum mechanically the photon you detect here on Earth is NOT the same photon that was emmitted by the source... If not, then you need to read up on Quantum Electrodynamics (QED), as just the atoms in the lens alone absorbs the photons, moves an electron to a higher shell in each atom for each photon, then emmits another photon when the electron returns to its proiper shell.
As for more on geodesics, especially timelike geodesics and its relevance to the propogation of light in the presence of matter, please refer to 'Geodesic (General Relativity)':
http://en.wikipedia.org/...(general_relativity)
wikipedia.org wrote: As the Einstein Field Equations determine the geometry of spacetime, it should be possible to determine the geodesics of the spacetime as well.
Or from 'Spacetime':
http://en.wikipedia.org/wiki/Spacetimeagain, wikipedia.org wrote: Certain types of worldlines (called geodesics of the space-time), are the shortest paths between any two events, with distance being defined in terms of space-time intervals. The concept of geodesics becomes critical in general relativity, since geodesic motion may be thought of as "pure motion" (inertial motion) in space-time, that is, free from any external influences.
Do you disagree that if one were to be able to see a light ray from outside the universe it would be seen to curve, but that seen from within the universe of, it is straight ???
To see examples of light behaving oddly requiring quantum mechanical explanations, think difraction and even better, Poisson's Spot. (click that link if you are unfamiliar with that phenomenon)
As far as:petsfed wrote: /physics and astronomy student near graduation
You got me there brutha, I'm just a:
/highschool drop out
BTW... I think we are actually saying the same thing, as we both ackowledge that light follows the curvature of space, but we cannot see this as we are local. If we draw a straight line in the universe from within the universe, and view it from outside, it will appear curved... If we draw a straight line in the universe as viewed from outside it, it will appear curved from within it. My argument is that cosmologically speaking, there is no physical reality to a "straight line" within the universe.
(This post was edited by rrradam on Jan 20, 2007, 6:46 AM)
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thegreytradster
Jan 20, 2007, 3:50 AM
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Arretinator,
Get your hands on Mil hdbk 141 Everything you want to know is in there.
Google!
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petsfed
Jan 20, 2007, 6:17 AM
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Upon further reflection, pun fully intended, you can figure out the approximate aberration based simply on mirror diameter. And I'm still running the equations to figure it out. So be patient.
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petsfed
Jan 20, 2007, 6:32 AM
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rrradam wrote: Also, I for one believe that space is granular and discrete, thus it IS an un-understood medium, but this line of thinking is 'taboo', as it smaks of the ether. It is accepted that space behaves as if it were a something and this is consistant with experiment and observation, but it is also accepted to be a nothing despite this, and that is a contradiction.... But that is another topic for discussion all together. As far as: petsfed wrote: /physics and astronomy student near graduation You got me there brutha, I'm just a: /highschool drop out BTW... I think we are actually saying the same thing, as we both ackowledge that light follows the curvature of space, but we cannot see this as we are local. If we draw a straight line in the universe from within the universe, and view it from outside, it will appear curved... If we draw a straight line in the universe as viewed from outside it, it will appear curved from within it. My argument is that cosmologically speaking, there is no physical reality to a "straight line" within the universe.
First, I don't buy into the granular principle of space-time simply because I tend to reject the "I don't get it, lets blame it on a particle" school of physics. Fails Occam's razor, but that's another discussion.
Second, no worries on level of education. This stuff's too much fun to pollute it up with equations (which is all the college degree does).
Third, I think we're mostly in agreement, although I dispute the non-reality of straight lines from a cosmological perspective, because like I said, within each geometry is the premise of a straight line as defined by the intrinsic shape of that geometry. And in the case of a single photon, classically it must follow a single path, and that path is a straight line in terms of the geometry of the universe.
To be certain, the "all possible paths" idea of the path of light is technically true, but its a case of the facts obscuring the truth. But again, a discussion for another time.
The fact remains that the unique geometry of the universe, a non-constant geometry though it may be, still has an intrinsic definition of a straight line, and that is most easily seen by the path light takes. As you pointed out, that path is the shortest distance between two points in space time. Its bizarre to think that a straight-line could be curved, but in certain regions (at the event horizon of a black hole, for instance), a straight line is in fact a ring, which is to say that there are certain regions of space-time that are untraversable. Bizarre, eh?
(This post was edited by petsfed on Jan 20, 2007, 6:35 AM)
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rrrADAM
Jan 20, 2007, 6:40 AM
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Dammit !!! I never get it right the forst time, and you replied before I was done editing... Please read for changes/additions. 
My fault... I'm retarded bro... So retarded, I was working on that posts off and on for hours.
And yes... Physical reality is very bizzare. But it is that fact that makes it so interesting. In fact, many times reality "fails Occam's Razor" as well. (simple reflection according to QED as just one example, and most of all quantum mechanics))
Another example:petsfed wrote: And in the case of a single photon, classically it must follow a single path, and that path is a straight line in terms of the geometry of the universe.
Note... QED is the most accurately measured and confirmed theory in history, and has been confirmed on an order of 10^-43 I believe, and that was in Feynman's time, and he described its accuracy as measuring the distance from LA to NY with an accuracy of the width of a human hair.
(This post was edited by rrradam on Jan 20, 2007, 7:13 AM)
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petsfed
Jan 20, 2007, 8:22 AM
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rrradam wrote: Another example: petsfed wrote: And in the case of a single photon, classically it must follow a single path, and that path is a straight line in terms of the geometry of the universe. Actually, a single photon can take any of an infinate number of paths, and even the double slit experiment shows this. What we see "classically" is the emergent result of many photon taking the same path, reiforcing eachother, and the other ones canceling each other out...
Once more, you're missing my point, but that's primarily because you don't have to actually work with this stuff on a regular basis.
We cling to classical explanations of things because they work. To be strictly accurate, we have to throw in relativistic and/or quantum mechanical corrections to our classical calculations. However on a local scale, relativity doesn't apply (in most cases the change to the results is less than the precision of our instruments, and occasionally less than a planck quantity of the unit measured), and on large scales, quantum mechanics has zero net effect. Quantum effects are typically limited to within a few atomic radii.
Thermodynamics, for instance, has its explanation firmly grounded in quantum mechanical interactions between particles, but to calculate heat transmission via an Avogadro's number of linked differential equations is pointless when we can just point to the psuedo-classical equations set out by the laws of thermodynamics. Its a case of facts obscuring the truth.
Likewise, always dealing with the path of light as all possible paths until measured is to make our life way too hard. Treating a photon as a semi-classical particle allows us to build telescopes (and indeed, use Snell's law) or operate lasers.
I will concede that light takes a path that is largely dependent on its end interactions, but I feel this discussion is getting too close to asking how many angels can dance on the head of a pin, or the equivalent quantum mechanical debate.
Also, QED I presume stands for Quantum Electro Dynamics, and its not quite accurate to say that its the most well confirmed theory in history. That honor belongs to classical electrodynamics (Maxwell's equations) and it is indicative of the accuracy of that theory that it translated easily into the quantum realm. Maxwell's equations, by the way, are the only set of equations describing physical phenomena that are said to be complete (in the sense that no other equations are necessary to describe interactions between charged particles).
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rrrADAM
Jan 20, 2007, 10:04 AM
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petsfed wrote: Also, QED I presume stands for Quantum Electro Dynamics, and its not quite accurate to say that its the most well confirmed theory in history. That honor belongs to classical electrodynamics (Maxwell's equations) and it is indicative of the accuracy of that theory that it translated easily into the quantum realm. Maxwell's equations, by the way, are the only set of equations describing physical phenomena that are said to be complete (in the sense that no other equations are necessary to describe interactions between charged particles). RP Feynman in QED wrote: ]Because the theory of quantum mechanics could explain all of chemistry and the various properties of substances, it was a tremendous success. But still there was the problem of light and matter. That is, Maxwell's theory of electricity and magnetism had to be changed to be in accord with the new prinicples of quantum mechanics that had been developed. So a new theory, the quantum theory of the interaction of light and matter, which is called by the horrible name "quantum electrodynamics", was finally developed by a number of physicists in 1929.
Also...
again, Feynman in QED wrote: Things [with regards to QED] have been checked at distance scales that range from 100 x the size of the earth down to 1/100 the size of an atomic nucleus.
Have you read QED ??? Are you familiar with it ??? Theoretical physics is a vastly different field from Astronomy and basic physics, as I am sure you know. Even Cosmology and Astrophysics are only briefly covered in a general physics degree, unless you are working toward a graduate degree in those areas. Would you not agree ???
Its kinda like being able to detect and describe the properties and formation of a nuetron star... But not understanding the actual detailed quantum physical process of changing atoms containing protons, nuetrons, and electrons into only nuetrons, meaning describing how a proton and electron actually become a nuetron, and thus form the nuetron star... This takes quantum mechanics to do, as now were talking about taking a proton (3 quarks) and an electron (1 lepton), over comming the resistance of the atom to compress due to electromagnetic force carrying bosons (photons), then over comming the strong nuclear force carrying bosons of the nucleus (gluons), and making a nuetron out of it (3 quarks).
Not questioning your education, as you are clearly more educated than I am, but we are talking about several different apsects of physics, and some of them combine like oil and water. I do appreciate the discussion though, too bad we couldn't do it over coffee with paper and pencil... I really type like shit.
(This post was edited by rrradam on Jan 20, 2007, 10:13 AM)
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petsfed
Jan 20, 2007, 7:58 PM
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rrradam wrote: Have you read QED ??? Are you familiar with it ??? Theoretical physics is a vastly different field from Astronomy and basic physics, as I am sure you know. Even Cosmology and Astrophysics are only briefly covered in a general physics degree, unless you are working toward a graduate degree in those areas. Would you not agree ???
I'm in a physics heavy astro-department. And most simply put, most of the research I do in astrophysics is described by QED, but we don't use that formulation because its unwieldy.
Also, you misunderstand the progression of sciences. Maxwell's equations showed that light travels at the same speed regardless of the observer's velocity relative to the light source. This caused Einstein to formulate a theory of relativity that allowed for a constant speed of light from any "rest" frame. Concurrently, he worked on explaining the photo-electric effect (and also Brownian motion), which led (eventually) to quantum mechanics, which led (eventually) to Feynman and others reformulating classical electro- and magneto-dynamics to fit the quantum world view. However, what remains is a melding of relativity and QED (and later a quantum-relativistic theory of gravitation) into the grand unified field theory.
However, to claim that astronomy and theoretical physics are different fields is an error of confusing the methods for the explanation. Like I said, over macroscopic distances, QED doesn't really apply, and for low masses and low velocities, relativity doesn't really apply, so we go back to the classical equations, which are themselves still very complex.
For instance, I've done some work with semi-hot plasma clouds that radiate in the visible because of energy released via gravitational compression. They radiate in a way that we can't reproduce in a laboratory, but is still predicted by QM. The reason for this phenomenon is that the density of the gas clouds in question is lower than the best lab vacuum available. Its only in that situation that special "forbidden" energy transitions can happen.
Another example is the preliminary finding that time is not quantatized because that would have a measurable effect on the appearance of very distant quasars. That it doesn't have that effect implies that time itself is not quantatized like distance seems to be.
Finally, the cosmic microwave background radiation has its explanations firmly rooted in quantum processes. Its effect on the large scale structure of the universe (a research interest of mine) is obvious, but obscured by complexity all the same.
Something you have to realize is that while Feynman is a brilliant teacher, he is only one source. I suggest looking into Weinberg as well, and maybe some of Hawking's work, although the latter should be taken with a grain of salt. Anybody locked in their own mind as long as Hawking can be characterised as at least a little bit crazy.
I have not had the opportunity to read much of Feynman's work (Six Easy Pieces is all that I've read, a book you should read as well) because I've been a bit too wrapped up in my course work. However, it should say something that my courses these last 2 years have been Electro- & Magneto-dynamics, Quantum Mechanics, Mathematical and Computational Physics, and Thermodynamics & Statistical Mechanics. By the time I graduate, I'll have taken 2 astronomy courses.
(This post was edited by petsfed on Jan 20, 2007, 8:02 PM)
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rrrADAM
Jan 20, 2007, 8:59 PM
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Great points, and agreed.
Feynman is my favorite, by a long shot, and I've read many of his books, and watched a few of his lectures, but QED is easily his best book, and its a transcript of the Dirac Memorial Lectures on QED I believe... You really should read it--its a quick read of just a day... Short and sweet.
As for other sources, I prefer Smolin, Susskind, Penrose, Kip Thorne, Robert Laughlin, and even Neil Tyson... Hawking's was OK, but highly over-rated...
You may be suprised that I do apply much of this in my job, albeit in a non-cosmological way:
In Ultrasonic angle beam inspection, I need to use Snell's Law to calc out my actual refracted angle within the parts I am inspecting, as sound has different velocities in the lucite wedge on my transducer and the part. Quantum and classical mechanics also plays a part in the sound's attenuation.
In Radiography, I need to understand and apply the priniples of difraction, geometry (penumbral shadows, enlargment, etc...), and even higher energy interactions... Co-60 peaks at two energies, both of which are high enough to create Compton Scatter/Pair production, and other photo-electric effetcs. We even use Lin-Acs (Linear Accelerators) to punch through feet of steel. Again, QM and CM describe its attenuation.
Maxwell's equations, among others, are used when I use Magnetic Testing to calc out field strengths, flux leakage, and such.
I've even been an instructor in the above disiplines, so a much deeper understanding of the theories behind the aplications is required to teach it well... Not to mention, I now work inspecting operating nuclear power plants, so while not required, an understanding of what exactly is happening at the nuke is a plus: from the nuclear reactions in the reactor, to the thermodynamics of the energy transfer, to the mechanical principles of the machinery. And I also find it interesting to the point of being enthrawled with it at times.
I've spent WAY too much money on books in the last 2 years, and I list seems grows evertime I refer to the footnotes and citations within the books. I am fortunate to have a friend that has a PhD in Math, and a Masters on Theoretical Physics that I bounce questions and ideas off of on a regular basis.
As for my particular interest, Cosmology and Quantum Gravity... As far as QG goes, there's not even a light at the end of the tunnel. For those that think that String Theory is the light, they're gonna get hit by the train comming at them, as ST is crap, but unfortunately almost 85% of the PhD students in Theoretical Pysics are working on ST, as its career suicide to think 'outside your Research Advisor's box'.
petsfed wrote: Finally, the cosmic microwave background radiation has its explanations firmly rooted in quantum processes. Its effect on the large scale structure of the universe (a research interest of mine) is obvious, but obscured by complexity all the same.
At the moment of decoupling (~300,000 years after BB), when the hot dense plasma of electrons bound to nuclii and formed atoms (H, He, Li), the universe became transparent, and what we see today as the CMB is the light from that moment... But lessor known is that at that moment, that light was in the UV spectrum, and it is only through the subsequent expansion of the universe that that wavelength of light has lengthened to that of the Microwave spectrum... Meaning that the 'cosmic background' has gone through UV, violet, blue, indigo, green, yellow, orange, red, Infrared, and now to Microwave, and it will keep stretching down to radio.... It may be billions of years from now, but it will make radioastronomy a little harder. 
(This post was edited by rrradam on Jan 20, 2007, 10:23 PM)
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mowz
Jan 20, 2007, 10:05 PM
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quadfire wrote: I prefer my lines to be skew
I prefer my lines to be white, fine and made from fish scale.
N.B.: for those that don't know, fish scale is slang for an ultra-pure form of cocaine.
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thegreytradster
Jan 21, 2007, 3:31 AM
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What about Carver Mead? Collective Electrodynamics
He seems to do a pretty good job of dispensing with Maxwell.
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petsfed
Jan 22, 2007, 9:03 AM
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rrradam wrote: At the moment of decoupling (~300,000 years after BB), when the hot dense plasma of electrons bound to nuclii and formed atoms (H, He, Li), the universe became transparent, and what we see today as the CMB is the light from that moment... But lessor known is that at that moment, that light was in the UV spectrum, and it is only through the subsequent expansion of the universe that that wavelength of light has lengthened to that of the Microwave spectrum... Meaning that the 'cosmic background' has gone through UV, violet, blue, indigo, green, yellow, orange, red, Infrared, and now to Microwave, and it will keep stretching down to radio.... It may be billions of years from now, but it will make radioastronomy a little harder.
No it won't. The hard part about measuring the CMB, as it turned out, was picking what was "real" and what was normal microwave emission (from normal stars and the galactic core, for instance). So in a couple billion years, when its turned into longwave radio background, it'll be even easier to account for, since we already know what to look for. Also, while it seems like a huge span for us, the visual band is actually an incredibly narrow span, both in terms of frequency and wavelength. Both the ultraviolet and the infrared cover larger spans of wavelengths (on the infrared side) and frequency (on the ultraviolet side).
In other news:
"Facts are meaningless! They can be used to prove anything!"
-- H. J. Simpson
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coloredchalker
Jan 22, 2007, 1:37 PM
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In reply to: Let me try and translate: Blondgecko and RRRadam were at the bar getting smashed, when RRRadam started arguing nonsensical philosophy about mixing fire with water, crossing parallel lines, tree's falling in the forest, hovering cat/toast combinations, and perpetual motion machines. is that about right?
Thats the picture in my mind 
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quadfire
Jan 22, 2007, 7:31 PM
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j_ung wrote: rrradam wrote: They will ALWAYS cross... Draw them on the earth (a sphere) and they will cross, just as the longitudinal lines cross at the poles. Since space IS curved, they will cross in space also. Doesn't that kinda depend on how long the lines are? I just drew two parallel lines on a sheet of paper, and I'm pretty sure they do not intersect. 
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j_ung
Jan 22, 2007, 7:33 PM
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Hence the little laughy face.
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wideguy
Jan 22, 2007, 7:59 PM
Post #45 of 72
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Registered: Jan 9, 2003
Posts: 15045
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quadfire wrote: j_ung wrote: Doesn't that kinda depend on how long the lines are? I just drew two parallel lines on a sheet of paper, and I'm pretty sure they do not intersect. Actually what you drew were line segments, lines never end
Segments shmegments.... I never heard someone at a party go into a back room to do some "Segments"
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bizarrodrinker
Jan 22, 2007, 8:29 PM
Post #46 of 72
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Registered: Dec 20, 2005
Posts: 2316
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wideguy wrote: quadfire wrote: j_ung wrote: Doesn't that kinda depend on how long the lines are? I just drew two parallel lines on a sheet of paper, and I'm pretty sure they do not intersect. Actually what you drew were line segments, lines never end Segments shmegments.... I never heard someone at a party go into a back room to do some "Segments"
What a party that would be if the lines, er, segments were never ending!
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quadfire
Jan 22, 2007, 9:21 PM
Post #47 of 72
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Registered: Sep 13, 2006
Posts: 203
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bizarrodrinker wrote: wideguy wrote: quadfire wrote: j_ung wrote: Doesn't that kinda depend on how long the lines are? I just drew two parallel lines on a sheet of paper, and I'm pretty sure they do not intersect. Actually what you drew were line segments, lines never end Segments shmegments.... I never heard someone at a party go into a back room to do some "Segments" What a party that would be if the lines, er, segments were never ending!
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hrtmnstrfr
Jan 23, 2007, 3:07 PM
Post #48 of 72
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Registered: Aug 27, 2006
Posts: 71
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The longitudinal lines on a sphere are not parallel, the latitudal ones are though...
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petsfed
Jan 23, 2007, 11:42 PM
Post #49 of 72
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Registered: Sep 25, 2002
Posts: 8599
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hrtmnstrfr wrote: The longitudinal lines on a sphere are not parallel, the latitudal ones are though...
Actually, they are, in a spherical geometry. Its just that in a spherical geometry, parallel lines do cross, and also the sum of the interior angles of a triangle are less than 180 degrees.
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hrtmnstrfr
Jan 24, 2007, 2:06 AM
Post #50 of 72
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Registered: Aug 27, 2006
Posts: 71
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I always thought there was no such thing as a true parallel line is spherical coordinate systems. The closest thing would be equidistant lines, which are called parallels of latitude.
I finished my BS in physics in '04, nice to see other physicists on here.
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