joigus

I see. Thanks.

OK. I've got a little bit to digest for the time being. I do believe you can get away with the rs/r term in 1st order and ignore kinematical corrections. Reason being that rs/r is of order \( 2.4\times10^{-9} \), while \( v/c \) is of order \( 1.4\times10^{-11} \). First corrections to "kinematic" terms are square of the latter, so order \( 2\times10^{-22} \) while first corrections for the r-dependent term are just of order (1st order in rs/r for sqrt of g00 and grr) as said before. Mmmm. @Mordred. I think I understand your main argument on rotation/acceleration, but... I wouldn't invoke Cartesian coordinates either. It's all more transparent in spherical coordinates. I'm confused by isotropic dust in the discussion too... What are you deploying on me man? I did make a rough estimation for rotating A and B clocks and didn't find that much of a difference if speeds are safely orders below c, but I could be wrong. I picked circular paths with fixed radii and used a 3rd-Kepler kind of approximation. GR corrections to Kepler's law don't seem to change scenario significantly, I think. They differ only by a sqrt(g00)... I'll keep an eye on this for further comments. I always try to keep as pedestrian as humanly possible. So far I stand by my estimation. Maybe later...

I see how you would think that. It sounds very common-sensical. But that's not how it works. Keep in mind that any exact solution of Einstein's field equations already has any possible kinematical effects included. It's a package deal. Most of these solutions have a structure, \[ f\left(r\right)dt^{2}-\frac{1}{f\left(r\right)}dr^{2}-r^{2}d\Omega^{2} \] The \( f\left( r \right) \) and \( 1/f\left( r \right) \) play the role of "local contraction and dilation gamma factors" so to speak. Because GR is obtained from --among other things-- a demand that it satisfies SR locally, it is guaranteed to take care of that. \( \left(1-\frac{r_{\textrm{s}}}{r}\right)^{-1} \) plays the role of a gamma factor of sorts, while \( \left(1-\frac{r_{\textrm{s}}}{2r}\right) \) plays the role of an inverse gamma factor of sorts, if you will. It's true that the SR metric is different, but GR is under no obligation to follow SR's intuitions so closely. The equation that you wrote is off by a square in the differentials, so it should be, \[ d\tau^{2}\simeq\left(1-\frac{r_{\textrm{s}}}{r}\right)dt^{2} \] Which, after taking the square root becomes, \[ d\tau\simeq\left(1-\frac{r_{\textrm{s}}}{r}\right)^{1/2}dt \] And, only after Taylor expanding and keeping first-order terms, \[ d\tau\simeq\left(1-\frac{r_{\textrm{s}}}{2r}\right)dt \] which is the approximation I used.

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.

Quarks don't want to get pulled apart...

That physical intuition makes sense to me. Something like that is to be expected. But a proton is uud only on the average. I don't think it would be anything as simple as a dielectric.

Same distance, same "force," meaning same Feynman diagram to all levels in QED (except for sign) if you assume the proton to be point-like. If you ramp-up the collision energy though you would eventually find EM form factors in the proton, but no form factors in the electron, so... You must not assume, as a matter of course, a question to have the most possible conceivable context, I think. You must narrow down the possibilities by assuming a natural context. This could be said of any question.

Well, yes. But if I'm allowed to play with distances, then any force can be made stronger, or weaker, as any other. I'm assuming same distance.

No. The measure of such strenght is the fine-structure constant, which in turn is basically the square of the fundamental unit of free electric charge. You can find it in many a good scientific calculator. So no.

Yes, it's probably combined effects of refraction and diffraction. In the case of refraction, light would appear to bend away from the border if the refraction index has the necessary gradient near the surface of the obstacle. The main point being: Light doesn't have to go in a straight line. I can't contribute anything much now. I'll try to follow, and then maybe comment further.

It happens because of diffraction of light. When light goes past a sharp edge, the trajectory of light rays differs significantly from that of a straight line. The effect generally depends on the light frequency and the typical sizes of the objects involved, as well as the refraction index of the medium that carries the waves. If the source light is bluer, the effect should be less noticeable for objects of the same size, while if the source light is redder, the result should be more noticeable. Diffraction has many similar or related effects associated to it. A nice analogy to understand this qualitatively is provided by sound. As sound has much much longer wavelenghts than typical light --say, visible light--, it can turn corners, so you can hear someone speak even though there are obstacles standing in the way. Diffraction of sound also explains that in Greek theaters you could hear the actors declaiming as if they were next to you, even though they may be many metres away. Analysing diffraction properly is a complicated problem mathematically. In this case, it seems that, instead of seeing the image behind the finger, what happens is the opposite. The take-home message is: Waves can do funny things around corners.

As Swansont points out... DNA by itself is useless. You need a suite of proteins to read regulatory sequences, beside the protein-coding sequences. Don't forget the former constitute up to 95% of its length or thereabouts. You need proteins to tell DNA when to shut up, and when to start "talking." Otherwise, it's like sending a book to Mars, where there are no potential readers, and with the book saying both "do this" and "don't do this" to those non-existent readers. When to do this or that is key to DNA's function. The "readers" are proteins and RNA. Sending organisms --with their ribosomes and proteins-- is more like it. First I would choose a planet with magnetosphere. Then I would send archaea/bacteria that produce the desired metabolic waste --hello, oxygen. Easier said than done though.

Hell, I wish I knew a little bit more about Asian languages. I tried my best, but failed. This question about vagueness gets me thinking about language every other day. I think it becomes a real challenge when the language you're trying to learn uses different words for different concepts that your native language assigns the same word to. Somehow your brain shifts from one concept to another without ever realising it's actually a different concept. A particularly nice example I've found between English and Spanish is the word "time" vs the word "tiempo" in Spanish. There is polysemy in both words, in English and Spanish as well. But the problem is both polysemies are impossible to coordinate. So, English: time (uncountable), as in "time goes by" vs time (countable) as in "how many times have I told you..." Spanish: tiempo (uncountable) as in "el tiempo pasa" = "times goes by" vs tiempo = "weather" as in "hace buen tiempo hoy" = "we have good weather today." For countable "time" we have "vez" or "veces" (pl.) While for "tiempo" English-speaking people have "weather." That's why I always say, if you want to really learn another language, you must in a way become a child again, and learn it from scratch, by as direct association as possible. Yes, there's context, and also cultural entendres. In ASL, "pasteurized milk" is represented by having the sign for "milk" go past your eyes. Thereby: "past your eyes milk." How a coding that's understandable only if[?] you have an idea of the sounds makes its way to a sign language is a total mystery to me. So I would say: You don't need to explain too much if the other person is aware of enough context. And you don't need to explain the connection to the particular symbols if everybody knows those symbols are what the convention has established. I think it was Ferdinand de Saussure who first pointed out that symbols are quite arbitrary. What's amazing to me is that this arbitrariness can be extended to all kinds of languages --even SL's-- even when the original connection was sound-based. Also amazing that most people can so quickly catch on to this... And even more amazing, that this correspondence can be extended to idioms and other combinations of words.

I suppose it depends on where you put the top. Also, I haven't heard the particular fairy tales we're talking about. Usually, fairy tales put me to sleep, something I'm in sore need of lately.

What is religion without people?

If that's a statement, "Computer science is technology-related." I agree. If that's a question, "Is computer science technology-related?" Sure, it is. Obviously.

I'd invert your logic, for better effect: Every religion should respect everybody.

I don't think it would. What I'm assuming here is that this notion of self must be acquired based on recursive references in the experience. If nothing repeats so as to form patterns, no construct of self would be possible to build. Arguably, and furthermore, no construct of any other notion or concept would be possible to build. Yet, we can picture this individual as having a stream of experiences. This individual would be a temporal "congruence" of flashes of colour, sound, and other sensorial imput with no cohesion, no correlations, so it would be incapable of forming a construct for itself. Does that make sense?

Maybe because of those particular tenses being less specific? French is strange though. Their verbs are person-specific, and yet they use the pronoun all the time. Je suis, tu es, elle est,... Je google, donc je sais

In Latin: So both referring to 'I'. I don't know why it is always cited as just 'cogito, ergo sum'. Missing the 'I', resp 'ego' in it. Just a note about language. In English pronoun+tense give you all the information you need, but you need the pronoun to remove ambiguity. In Latin you kind of have the pronoun incorporated in the verb: Cogito (I think), cogitas (you think), cogitat (he/she thinks), cogitant (they think), cogitamus (we think), cogitant (they think). It's very much like Italian and Spanish. You can use the pronoun, but it sounds emphatic. In the nominative case the pronouns usually don't appear. It's therefore not natural to say "ego cogito, ergo ego sum." I might be missing finer points. It's been a while since I last talked to an ancient Roman.

The question seems far from being settled. I've just found this interesting article: https://www.smithsonianmag.com/science-nature/why-did-humans-evolve-lose-fur-180970980/ Some of the hypotheses seem a bit far-fetched to me. Let go of you fur because you are better able to notice other people blushing? It seems a tad extreme. A protein seems to be involved that apparently acts as an inhibitor to selectively suppress hair growth in certain areas. In most mammals --according to the article-- the difference manifests itself in the plantar skin in some exceptional mammals --polar bears and some rabbits. Maybe for humans there are intensifiers at the level of regulatory sequences or the like? But there must be a strong evolutionary pressure behind it. Another interesting piece of information providing likely timeline: https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3002236/ The main argument is about when clothing probably appeared based on evolutionary divergence of head/clothing lice.

I do remember other people being under neg-rep attack, and reporting accordingly. I know I've been protected when I was under fire for no other reason than disagreeing with someone. I like communities that are self-correcting to some extent. A judicious combination of refereeing and community awareness.

What's very interesting is that hair loss is universal in all human families, irrespective of environment. It could have been a spandrel that got carried along because humans started using animal pelts, so there was no adaptive pressure on having more and thicker hair. If you go to the tundra you still got mammoth! If it further affords you the possibility of turning them into a sensory device for ticks, that would be very welcome. Some further thoughts... I'm acting like a sounding board to people that know much more about this. But I love the discussion.

You must get a few of them (neg-reps). It's a rite of passage. It's bound to happen if you clash with some nut here or there. I'd be concerned if I didn't get any. Have you gotten yours?

I disagree. A cat is a cat, and a jellyfish is a jellyfish. Why do I know that? By virtue of examples of catness and jellyfishness being available to me. That way, I can look at a tree and say "that is no cat, nor is it a jellyfish." "It possesses no catness, nor does it possess any jellyfishness." I've never seen, felt, or even been able to surmise, a non-self. You know, "in the world of selfness, this is no self." As a matter of fact, I've never seen a self either. A self cannot be re-instanciated, or multiply instanciated, it cannot be gradually deprived of its qualities by removing aspects of it, even mentally --like a jellyfish can. It cannot be compared to another "self" in any meaningful way that I can think of. It cannot be presented to my conscience as a distinct, clear-cut --or any other way cut-- thing. I cannot even start to fathom whether you have a self, the same way that I feel I do, anymore than I can fathom whether there is some other space and time outside of this space and time. I can only use the --learnt, inferred, constructed-- notions of time and space to say things like: "Before I was born, there was no catness, no jellyfishness, no quality or example of anything." That's all I can say, but even that is unredeemably contaminated by my experience. How can I be sure that time makes sense outside of my experience? In that sense, I'm with @Sensei in that, if a machine engaged me in a conversation about its self, it might be able to convince me that it has one. How would I know it doesn't? The self is a construct. Very powerful, very intimately-attached to survival for us humans, and therefore very convincing*, but a construct. * How could it be otherwise for animals for whom an essential tool for their survival is guessing each other's minds?