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Showing content with the highest reputation on 12/26/22 in all areas

  1. When you put your hand near what you may think is steam, it is just condensed water droplets. For real steam, i.e. vapour at 100C, you would need to put your hand into the invisible stream issuing from the spout of a vigorously boiling kettle, i.e. the inch or so before it becomes visible as a cloud of "steam". If you ever do that, you will scream and need to see a doctor: the scald will be far more intense than from boiling water. Do not try it. That's because of the latent heat.
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  2. If this is occurring just after sunset, could it not be a shadow cast by that island from below your horizon. This should cut out the red end of the spectrum leaving just a blue backfill from Rayleigh scattering.
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  3. When I was growing up in the '60, living in Northern Mn., my dad was driving to work early one morning, passing through a small town, and noticed that he was feeling chilly. He checked the car heater and it was full on, and since it usually did a good job, he suspected something was wrong with it. Just then, they announced the temp in the town he was in over the radio. it was -40 degrees. He thought, "Ah, that explains it." and continued on into work. ( He worked in the iron mines, which were open pit mines, which, during the Winter, sunlight never reached the bottom of, so who knows how cold it was there.) During one recess in grade school, someone stuck their tongue to the outside of a metal door during the dead of a MN winter. (like in "A Christmas Story") However, instead of the calling the Fire Dept, and pulling him loose, a teacher simply poured warm water over the area until it heated up enough to free him.
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  4. For Earth's escape velocity the v/c parameter (the beta relativistic parameter) is about 1.4x10-11. For the other velocities involved it's much smaller. The rs/r term in Schwarzschild metric though is of order 2.4x10-9. rs being the Schwarzschild radius of the Earth, and r the actual radius of the Earth. In order to tackle these problems, you'd better not start thinking in terms of combined effects of r-dependent time dilation plus kinematical time dilation. Otherwise, you get confused, make a mess, and probably get the answer wrong. As @Markus Hanke often says, GR is highly non-linear, so it's not a matter of this effect plus that effect. I'm sure @Mordred agrees on this particular point. What you do is write the Schwarzschild metric and do all your calculations of proper times from there for different trajectories --elapsed time from different POV's, as Markus suggests. The metric really gives you everything you need for small clocks either falling or accelerating, etc. in the "background" field. You just plug in the trajectories \( r\left( t \right) \), \( \theta \left( t \right) \), and \( \phi \left( t \right) \). It's for finer approximations that things might get hairy. I've tried to do that for this case, and here's what I get: \[ d\tau^{2}=\left(1-\frac{r_{\textrm{s}}}{r}\right)dt^{2}-\frac{1}{c^{2}}\left(1-\frac{r_{\textrm{s}}}{r}\right)^{-1}dr^{2}-\frac{1}{c^{2}}r^{2}\sin^{2}\theta d\theta^{2}-\frac{1}{c^{2}}r^{2}d\phi^{2} \] You can further assume that all trajectories are equatorial, so, \[ d\tau^{2}\simeq\left[\left(1-\frac{r_{\textrm{s}}}{r}\right)-\left(1+\frac{r_{\textrm{s}}}{r}\right)\left(\frac{\dot{r}}{c}\right)^{2}-\left(\frac{r\dot{\phi}}{c}\right)^{2}\right]dt^{2} \] For small velocities \( \dot{r},r\dot{\theta},r\dot{\phi}\ll c \),and after Taylor-expanding the square roots, you get, \[ d\tau\simeq\left(1-\frac{r_{\textrm{s}}}{2r}\right)dt \] For clocks A, B, and C, we get proper times from 0 to a certain time standard assymptotic time T: \[ \tau_{A}\simeq\int_{0}^{T}dt\left(1-\frac{r_{\textrm{s}}}{2r_{A}}\right)=\left(1-\frac{r_{\textrm{s}}}{2r_{A}}\right)T \] \[ \tau_{B}\simeq\int_{0}^{T}dt\left(1-\frac{r_{\textrm{s}}}{2r_{B}}\right)=\left(1-\frac{r_{\textrm{s}}}{2r_{B}}\right)T \] \[ \tau_{C}\simeq\int_{0}^{T}dt\left(1-\frac{r_{\textrm{s}}}{2r_{C}\left(t\right)}\right) \] Remembering that, \[ r_{A}<r_{B} \] and rC monotonically goes from rB to rA, \[ r_{C}\left(0\right)=r_{B} \] \[ r_{C}\left(T\right)=r_{A} \] So that, \[ \tau_{A}<\tau_{C}<\tau_{B} \] So the proper time for observer A, who is at sea level on the Earth is shorter –proper, so from his own POV– than it appears to be from the POV of an observer at distance rA, and both shorter still than time elapsed from POV of an asymptotic observer, which is T: \[ \tau_{\infty}=\lim_{r\rightarrow\infty}\left(1-\frac{r_{\textrm{s}}}{2r}\right)T=T \] Which means that those far-away inertial observers see B slowing down, C slowing down even more, and A running the slowest of all. For clocks moving in any funny arbitrary way this would not be true. I think this approximation is good enough for our purposes, as the kinematic terms are at least a couple of orders of magnitude smaller than the r-dependent term. That's what I get from my analysis, anyway. The method I know to be correct. Please do tell me if you think I overlooked something important.
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  5. Yes, I am. I understand that this is what you've referred to in: I don't know. There are many inflationary models on the market. I am referring to the standard Big Bang model, LCDM, and to the expansion which we observe.
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  6. No light is coming from the black letters. Did you see my last post above? What do you think about that solution of the puzzle?
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  7. I think I got the solution. We don't see light coming from a letter, the letter is black. We see the light from background (white), the letter is where there is no light. Because of the object being out of focus, there is progressively less light coming through as we get closer to the object's edge. So, near the object's edge more light coming through from a bit farther from the object and it gets darker as we get closer. The letter appears where it is dark. The dark area moves progressively closer to the edge. Thus, the lines of the letter appear to move closer to the edge.
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  8. Wishing everyone and their loved ones happiness and a very merry Christmas. Even if you are not religious, in the words of Tiny Tim "God bless us, everyone"
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  9. A friend of mine used to bleach his towels every time he washed them. Later, he was complaining that his towels were literally falling to bits. I told him it was his habit of bleaching, and he stopped, and the towels stopped producing the holes and falling to bits. I suspect that UV would have a similar effect over time, probably not so rapidly. So it's not just pigments to worry about, it's fibres. I would say that the best tactic would be just to ensure that the damp towel is promptly hung up in such a way that it dries quickly, and not shared around once used.
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  10. I would think it is more about drying clothes? While sunlight can accelerate deactivation of viruses and some bacteria do not like sunlight much, many bugs obviously survive sunlight (otherwise much of the planet would be dead). Overall it could reduce contamination rate somewhat via a combination of radiation and drying (i.e. at very high humidity I would assume that much more fungi and bacteria will survive and potentially thrive in clothing outside).
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  11. UV will not kill microbes which are hidden in dirt, because the dirt is opaque. So you would need to start by washing things.
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  12. Also it is important to note that it does not clean, just sterilize. But even then it is difficult as the clothing would have to be irradiated inside and out and as StringJunky mentioned, would involve harmful levels of radiation. There are basically only a handful of scenarios where this would have tangible benefits, such as in hospitals perhaps. That being said, I have heard that potentially driven by the pandemic there are efforts to produce and sell household versions of such devices. But realistically they are mostly money grabs.
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  13. I anticipate I'll be banned because I called out a popular poster for trolling.
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  14. I'm focusing on the part about insulting other people's intelligence by answering nontrivial scientific questions with dictionary definitions. That's not being wrong, it's dumping on the other person's ego. Either you know you're BSing or you don't know you're BSing. Those are the choices.
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  15. There's nothing fragile about my ego, Mr. Moderator. I took three pages of abuse and logical fallacies without complaint. It's the other guy who eventually notified you. It has nothing to do with "more detail", Mr. Moderator. It's less detail. It's redirection. It's an attack on the person's reputation by ignoring an intelligent comment and treating the person like a slow-witted beginner. It's not a double standard, Mr. Moderator. It's a consistent policy of behavior. If you believe someone is a Time Waster, you'll ban them. If they follow the forum rules, you won't ban them. That's not a double standard. It's a consistent policy of behavior. If someone trolls or abuses me, my reaction to them will not be friendly. If I believe they're communicating with me in good faith, my reaction will be polite and courteous. Consistency doesn't mean guaranteeing equal outcomes. It means guaranteeing equal opportunity. Anyway, I understand that nothing I say will have any effect here, so thanks for clearing up what your real policies are, Mr. Moderator. YOU are the boss. YOU are in charge.
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