md65536

https://theconversation.com/drilling-surprise-opens-door-to-volcano-powered-electricity-22515 This recent story about accidentally drilling into magma in 2009 and trying to harness the energy demonstrates that your exact idea is feasible at select unusual locations, but also hints at why it's not attempted everywhere. Maybe in the future there will be more experiments at more challenging locations, and some permanent production.

Does this mean that if an atom's position is uncertain, it will "block" atoms (from passing) over a larger space, reducing fluidity? Or does it mean that the position isn't uncertain as hypothesized, ie. the uncertainty when not in vacuum doesn't increase near absolute zero? Or simply that the "uncertainty of position" explanation doesn't make sense? Edit: If the uncertainty principle does indeed apply to position and energy, and the position of atoms in a solid can truly be constrained by neighboring particles, then the energy must be uncertain. If the average energy truly was very close to absolute zero, what would that require? The possibility of negative energy? Or that a very few atoms would have quite a high energy?

That looks okay to me. If you keep the angle the same but change the sign of velocity, the source is now moving in the opposite direction and a previous red-shift will become a blue-shift. Post #17 becomes correct for negative velocity. Whether you use a positive or negative velocity, there is still a blue shift when theta_s = 90 deg, and a red shift when theta_o = 90 deg. It's interesting/puzzling that it works out so nicely, with some symmetries.

This sounds like a classical explanation of quantum mechanical effects, or even a requirement that quantum mechanics obeys "obvious" classical reasoning. If a helium atom's position is that uncertain, can you really claim that it is in a position to block other atoms from passing, or that its behavior is the same as "normal" where atoms cannot pass through each other? Or I guess... is the obviousness of your argument based on quantum mechanics, or classical?

Those values work out for -0.8c... But I don't think you would change the sign of velocity unless you also rotated your reference frame by 180 degrees (or flipped it)? Anyway by changing the sign of v you've changed the meaning of the angle. I take it that you mean that "moving away at a negative speed" is the same as "approaching". But also I think you could say that "moving away at a positive speed at an angle greater than pi/2" is the same as "approaching". Also then, "moving away at a negative speed at an angle greater than pi/2" becomes "receding" again. If you start with a fixed velocity v and slowly increase the angle theta_s from 0 up, you'll hit the critical angle at pi/3 (or 60 deg). If you change the sign of v at pi/2, then to make the light source increasingly oriented towards the observer, the angle must now decrease from pi/2. You won't hit 2 critical angles, one at 60 deg and one at 120 deg. At -0.8c the critical angle in the source frame is 120 degrees. Having a velocity of -0.8c at an angle of 120 degrees is the same as having a velocity of 0.8c at an angle of 60 degrees, the Doppler factor will be the same (1, in this case). If this doesn't make sense or isn't a conventional explanation, hopefully someone who knows this better will correct me.

What is the truth value of a wrong sentence? What is the truth value of "This this sentence has a syntax error"?

But is the paradox an error? And if so, is there any interpretation in which the paradox wouldn't be counted as an error? This one is different than the liar's paradox, because this one is a statement about errors while the liar's paradox is a statement about validity.

If the critical angle is 60 degrees, that's the angle where the light is neither blue nor red shifted. At smaller angles, it's red-shifted. The angle is between the direction from observer to light source (when the light was emitted), and the relative direction of the movement of the light source. Or, equivalently I think, the angle between the direction from source to observer, and the relative velocity of the observer, which might be easier to think about since theta_s is measured in the source's frame. (Also these are measured at the time that the light is emitted. ???) So what that means is that with smaller angles, the light source and observer are moving more away from each other. The smaller the angle, the greater the redshift. This might make more sense in the reference frame of the observer? In that case, [math]\frac{f_o}{f_s} = \frac{1}{\gamma ( 1 + \beta \cos \theta_o )}[/math]. (http://en.wikipedia.org/wiki/Relativistic_Doppler_effect#Motion_in_an_arbitrary_direction) Then I think that [math]\theta_{o\mathrm{\ critical}}=\arccos \frac{1/\gamma - 1}{\beta} = \arccos \frac{\sqrt{1-\beta^2}-1}{\beta}[/math]. For beta = 0.8, that would be 120 degrees. Again, smaller angles are red-shifted, and light coming in at 90 degrees to the observer is red-shifted. Your experiment's over my head, but I was trying to think of one to wrap my head around these equations. Perhaps this is similar? Consider 2 observers, where one is inertial and the other is rapidly circling the other at a constant distance. In the frame of the inertial observer as a source, any light sent to the other will arrive at an angle of theta_s = 90 degrees relative to its motion around the circle. That light will then be blue-shifted, F = gamma. Meanwhile, any light from the other is emitted at theta_o = 90 degrees relative to the direction of its motion (still in the inertial observer's frame here, now as the observer of light). That light will be red-shifted, F = 1/gamma. This agrees with other calculations, where we expect to find that the traveling observer's clock is slowed by a factor of gamma relative to the inertial observer's. And it can be seen; the inertial observer will appear blue-shifted to the traveling observer, and the traveling observer will appear red-shifted (slowed) to the inertial observer. To do the same calculations in the observer's frame we'd have to account for aberration and acceleration?, I wouldn't know how...

So doesn't that make the statement (eg. "There are 2 errors in this this sentence.") true? Is there any way to make the statement not true? Now I must flipflop... I think you may be right. I looked it up and all I could find was that if a formula is valid, it's negation must be inconsistent (incapable of being true). Since "There are not 2 errors in this this sentence," can be true, then the original must not be valid. HOWEVER I must flipflop again. Since the sentence is self-referencial, its meaning changes in a way that negating it does not make it a logical negation of the original. So I think it might require interpretation of the meaning of the sentence, and the rules of logic can't be applied naively. Edit: The logical negation should be "There are not 2 errors in the original sentence." Is there an interpretation of the original sentence that is not true? Is there an interpretation where there are not 2 errors in the sentence? All I can think of is that the mix-up of the count of errors is not itself an error if the count turns out to be right, and that any paradox that that creates is not an error either. Personally I don't think that's an acceptable interpretation.

I hope you plan to cover the difference between error-free and valid (true). A grammatical error does not necessarily change the logic of a statement. So we're dealing with at least 3 types of error here: grammatical/syntax errors, falseness of a statement, and inconsistency of an argument. Be careful not to mix different types of errors into one thing.

Fix your errors before trying to educate people. You've switched from [math]f_o[/math] to [math]f_0[/math], I no longer know what you're talking about. Post #17 doesn't make sense. Please correct it before quizzing me, thanks. ---- Trying to get this thread back on track... The angle between the direction to the source and the direction of movement of the source is different in the source frame and the observer frame, due to abberation of light. When the angle according to the source, [math]\theta_s[/math], is 90 degrees, that light will be observed as blueshifted. When the angle according to the observer, [math]\theta_o[/math], is 90 degrees, that light will be observed as redshifted. See http://en.wikipedia.org/wiki/Relativistic_Doppler_effect#Motion_in_an_arbitrary_direction The equations of post #17 are according to the source frame, I'm guessing with a mistaken attempt to apply them to the observer's frame, messing up the math.

theta_s is the angle in the source frame. Your error is here: How can redshift occur for smaller values of f_o, but greater values of theta_s? Try increasing theta_s. f_o increases. Do you understand what that means? The formula you solved is for theta_s, not theta_o.

Check again, have you copied the wrong formula? f_o increases as theta increases. Higher angles means increasingly blue-shifted. Using the formulas in this thread, an angle of pi means the light source is directly approaching, and is blue-shifted. The angle theta equals theta_s in your formula. At angle pi/2, the light is blueshifted, not redshifted.

That should be all [math]\theta_s < \theta_{s\mathrm{\ critical}}=\arccos \frac{1-\sqrt{1-\beta^2}}{\beta}[/math]. Your theta_s is the angle in the source frame. At 90 degrees light will be blueshifted. The angle in the observer's frame (theta_o, using http://en.wikipedia.org/wiki/Relativistic_aberration_formula) will be greater, due to aberration... it seems the critical theta_o will always be greater than 90 degrees (light coming from the side is red-shifted).

No, the liar still always lies and the truth-teller is always honest. That still doesn't require that they give you good information. The liar may just say "The sky is yellow" while the truth-teller says "The sky is blue." The bad assumptions are that both guards will act in the best interest of resolving the puzzle, ie. helping the player. Usually with logic puzzles you want to do the exact opposite, and imagine that the puzzle is run by a demon who can manipulate things in order to produce the worst outcome possible that is still consistent with the rules and the information. This way you can be sure that if a solution is based on logic, there's no opportunity that a favorable outcome may also be arrived at by chance. Here's another puzzle to show what I mean: There are two wooden boxes with engraved messages on the top. The first says "Only one of these boxes' messages is true." The other says "The gold is in the other box." Where is the gold? Or, which box do you open? I think it's equivalent to "This statement is false," and asking if it's true or false. However, if you ask how many errors there are in the statement "This statement is false", you might reasonably say 1, counting the logical inconsistency as an error. So I think that by playing with semantics there's room to count 2 errors in the original sentence. One is "the the", and the other is that the count of errors (while true!) is logically inconsistent. Or, "the paradox is an error." This treats differently whether a sentence is true, and whether or not it is in error. A true statement may have errors. This is probably subject to interpretation.

Janus explained this. Observers R and A each see the other blue-shifted (clocks appearing to tick faster) but for different amounts of time. R sees it for a longer duration, because the effect that it sees immediately is delayed by the travel time of light before A sees it. Thus both can agree that observer A is seen to tick away more time overall. You can work it out considering only durations of constant motion, but those durations won't appear to be the same for the different observers.

Suppose you ask the correct question and a guard replies, "The white of the egg is yellow!" Is the question still a correct one? The puzzle doesn't require the guard to reply at all. Well okay the intention of the puzzle (that a guard would answer) is obvious, but surely it's a stretch to assume that the liar will answer a question as helpfully as possible. It's not even certain that the guards even know which door is which! Since they're guarding the door, I might presume that neither wants you to go through to freedom. The honest guard could answer "Definitely one or the other." As it's worded here, there are too many assumptions required and the logic kinda falls apart. I think usually it's worded such that a chosen guard will answer one question with yes or no, which takes out most of the possibility of ambiguity.

Why is it a common assumption that if you "travel" to a different place and time, you'll still also be in another place and time? I guess you're figuring that things persist through time in such a way that "time" dictates what exists and where. When and where become properties of time, rather than properties of the object (ie. its worldline). I don't think this idea has any basis in reality. I think it's only based on a common-sense interpretation of our experience of time. Consider this alternative puzzle: A traveler travels exactly three meters north of where he is standing. When he arrives, he sees himself three meters away, but he does not see himself traveling to where he is now. How is this possible? Is this really any different from the original puzzle, and can it be reasoned through? Both describe a physically impossible jump or movement through spacetime (this one involving faster-than-light travel, and the original involving negative time or some arbitrary control of a time coordinate or whatever), and I don't think that anything meaningful can come from it unless it is reasoned in terms of a real physical process or a theoretical one. (For example if you consider something like wormholes as a way to make it possible, then the description of what is seen should come from what wormhole theory predicts. And still I doubt that anything physically meaningful would come from such reasoning.)

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"?

And the surface area of a sphere is proportional to r squared, so I'm guessing that the simple geometric explanation is that the total number of flux lines is constant through spheres at any distance from a gravitational mass, just that the concentration is lower farther out as the flux lines are spread out over a larger spherical area? Yes, but it is consistent with measurements; so is a flat universe. New measurements that agree with flatness just put constraints on how big the universe must be or how little curvature it may have, but so far haven't ruled out a closed universe. As you mentioned with your ant analogy, sufficiently small and imprecise measurements of our curved Earth are also consistent with a flat Earth. We could measure an anthill-sized area and say "measurements are consistent with a flat Earth", or we could measure a continent-sized area on a flat surface and say the same thing, or we could measure a continent-sized area on the surface of VY Canis Majoris and say the same thing. How do we know how the observable universe compares in size to the whole universe? I don't know if this is a problem for anyone, but just to be sure: This isn't a question of whether there is spacetime curvature or not, just (I think) whether or not there is on the largest of scales. As an analogy, you can ask "Is the Earth curved or flat?" and "Is the surface smooth or are there mountains?" as separate questions. In the analogy we know there are mountains (spacetime curvature corresponding with gravitational mass), but that's not inconsistent with a flat universe.

The evidence of dark matter does not depend on having a single coherent image of the universe. You can find evidence in fragments of images, or in looking at different things (it's not just imaged positions of things). Besides, there is a coherent model of the universe that comes from piecing all the different observations together appropriately. It's not the perfect NOW image of everything that you might want, but it does the job. Science looks at evidence and draws conclusions from that, based on chosen models. It makes sense to a lot of people. Unfortunately, I don't think it's a priority that it makes sense to you, ie. that anyone would doubt the evidence in search of something that you prefer. I'm sure that if you really looked deeply into what observations have been made, and how the models are put together, it will become more coherent for you.

So which experiments or results fail to take this into account, and how much of an error is it (how "off" are the results?), and what different results are obtained when this is factored in? It's not about changing equations, but whether they fit with newer observations. Einstein's equations fit observations of the solar system. They do not fit observations of the galaxy, and larger scale. It wasn't a case of "the equations were good enough back then", it was a case of "as soon as observations of the galaxy's behavior with respect to gravity were made, they did not fit the models (including equations like GR and Newtonian gravity, as well as up-to-date models of the amount of matter in the galaxy)." As usual your thread has quickly gone from asking questions about a topic to "I'm sure everybody has it wrong." I think anyone reading this forum should expect that the scientists dealing with astronomical observations know the issues and know how to deal with them, better than the average amateur, so I don't think you'll convince anyone that all of the scientists are missing or ignoring an obvious problem. You'd be more effective by writing a paper about this, instead of proclaiming on a forum, but to do that you'd have to cite specific observations or results, and quantitatively explain the error. Why not find out how scientists deal with this "problem", before being so sure that they're doing it wrong? Do they not realize that light takes time to arrive here? Do they ignore the problem and pretend it doesn't matter? Or does it not make a significant difference (quantitatively, not just "I guess")? Or does it simply not factor at all into the results? Perhaps certain assumptions are made, like about how things change over time on a large scale, that you could look deeper into. But do it quantitatively... for example you mention 100,000 years... so how much could a structure that large change over that period of time, and what conclusions could be invalidated by such a possible change? ...And before wasting too much time researching (one can always dream!) or repeating, have you considered that the results are consistent with many different observations, not just one galaxy and it's exact positions of stars in a single image, including galaxies that are viewed "from the top", so that light from different ends of it arrive roughly from the same time, and that the existence of dark matter agrees with generally all of the observations. So how would you explain that "forgotten" delays of light, missed by all of science, could change all of these observations so much that dark matter no longer "makes sense"?

Of course we don't have all the information possible, or all that we'd like, and the science isn't yet settled. Is there any specific evidence that you think has been wrongly used, that you can show via your ideas that the conclusions of some scientists might be wrong? It is easy to assume that the scientists don't know what they're doing, but harder to pick apart what they're actually doing and to find fault with that. What specific evidence have they got wrong?

We never noticed it because it doesn't interact electromagnetically, so it can't be seen. We never noticed it when looking at the solar system because matter alone could account for the known effects of gravity here, to the extent of our understanding of it and ability to measure its effects. It is only when looking at the galactic scale and larger that normal matter no longer suffices... and that's how we noticed it*. Now enough is known about it for scientists to be able to make predictions, and distinguish between noticeable effects of dark matter vs matter here in the solar system. The 80% dark matter "rule" applies to galaxies and the universe as a whole, but not to the solar system. Dark matter around a galaxy is expected to be much larger and more diffuse than the galaxy itself. So within the solar system, normal matter exists in much higher concentration, and dominates the gravitational behavior of stuff within the system. * That alone isn't conclusive evidence of dark matter. Other explanations have been proposed, and dark matter is only the current best explanation that best fits the multiple lines of evidence. For example, it fits better than MOND: http://scienceblogs.com/startswithabang/2013/01/18/why-the-universe-needs-dark-matter-and-not-mond-in-one-graph/ This might explain the multiple lines of evidence that fit with dark matter: http://scienceblogs.com/startswithabang/2012/04/19/the-whole-story-on-dark-matter/

This is true but is attributed to the changing delay of light, not to time. The original signals were delayed 10 years so B's clock appeared to be 10 years behind, and on arrival it appears not delayed at all. If by "see" you're talking about appearance, then it's true. If you're talking about measurements, ie. the "correct time" at B when accounting for the delay of light, then it's not true. Even taking into consideration relativistic Doppler effect, B's clock will appear to tick faster as you approach it, due to the decreasing delay of light which overwhelms the time dilation effect at speeds less than c.