timo

The few numbers you gave clearly do not define a unique pattern. My guess is an irrational number ~1.62, but that's with guessing a particular pattern and not showing it to actually being the limit (only a fix-point), only.

Yes. Not only do I agree, but that's a widely spread argument against faster than light phenomena, meaning the idea is not really mine. Because I screwed up that statement. Not completely sure if I understand; I wonder where you left length contraction. Anyways, to get some common point. Assume the ship exists during some time interval [math][0,\tau][/math] (where the zero could as well be -infinity, but I want to get a rectangle in the spacetime diagram to make life possibly easier) in a space interval [0,L] (meaning it has a length of L). So in its frame, the edges of the rectangle it forms in spacetime-coordinates (x,t) are (0,0), (0,L), [math](\tau,L), (\tau, 0)[/math]. After a boost to another frame, these coordinates of the edges are (0,0), [math](\beta \gamma L, \gamma L), (\gamma \tau + \beta \gamma L, \beta \gamma \tau + \gamma L), (\gamma \tau, \beta \gamma \tau)[/math]. You could get the length at any time t' from that as I did, but I already wondered which information that should carry. The real question (if I got your original post correctly) is: From which point within this quad to which other point do you want to send a signal? An interesting idea would be sending along or faster than the upper line , the one where parts of the ship disappear (meaning a vanishing part would communicate something to a not-vanished part). This line obeys the equation [math](\gamma \tau, \gamma \beta \tau) + \alpha (\gamma \beta, \gamma)[/math] (with alpha just being the line parameter) and now this gradient is faster than lightspeed (because beta <1). As a sidenote why the vanishing speed might not suffice: The speed with which one of the sides disappears is not equal to the vanishing speed, but equal to the vanishing speed plus the speed with which the ship is already moving itself. Iow, to get the speed with which the "place of vanishing" moves away, you'd have to add another v/c to my equation about the vanishing speed, leaving you with c²/v, which then is indeed >1. General remark: In case you didn't do it already, drawing a spacetime diagram x vs. ct (so that the speed of light is a line with a slope of 1) is often, and imho in this case, very helpful. I personally see little to nothing from the numbers alone.

So what's the answer?

That reply was neither representative for the majority of the people in science, nor for the majority of the people in this forum. The last two sentences provided some funny irony, though.

Ok, a few notes about what I understood so far. I might or might not elaborate later, depending on mood/time/ability to understand what you said/... . At first glance, your example looks like the causality problem (that's not the official name, but "causality" itself is). The idea is pretty much the same as the one you (if I understood you correctly) tried to sketch: You run into paradoxa with time ordering as soon as you allow FTL. The idea boils down to this: Under orthochronous Lorentz transformations (i.e. excluding tricks like t -> -t), the time order of two events is preserved if their connection line is time-like or light-like. So if you have a cause at spacetime point A which ... err ... causes an effect at B, the order of cause and effect will always be the same if cause and effect have time-like or light-like relations (e.g. by being mediated via a particle travelling with v<c or v=c). As soon as you allow them to have space-like relations (which would then require a messenger particle with v>c), the order of cause and effect is not preserved under changes of coordinate systems. That is believed to be paradoxical. I'd have to do some calculations to understand what you did, where you got your numbers from and where a potential error might lie. EDIT: If I define "the speed of the wave" the change in length (as soon as part of the ship started to disappear) with time (i.e. dL/dt), then I get [math]\frac{dL}{dt} = \left(\frac{1}{\beta} - \beta \right) c > c[/math], i.e. always a "vanishing speed" greater than the speed of light. I either misunderstood what you meant with "speed of the wave", or you got some numbers or the calculation wrong. You should possibly present your calculation if you don't find the error. I am pretty convinced that there is no QM necessary in this thread at all (and also almost convinced that someone will mention it to complicate things a bit, though).

That has nothing to do with what I said for two reasons: 1) I was talking about schoolbooks, not what you recall from your classes. If Farsight had said "as I recall/think/imagine ..." rather than "schoolroom textbooks tell you ..." I'd have had no problem with the statement. 2) I was saying that a sample schoolbook does not define work via energy. This then breaks up the circular reasoning Farsight sees. Whether energy is then defined via work (I assume by "perform an action" you meant "do work" - action also exists as a physical term but has a different meaning) or not does not matter anymore.

Are you sure of that (meaning: Did you actually check any schoolbooks to verify that claim)? Only schoolbook I have on my shelf is Resnick, Halliday, Krane "Physics", which sais (emphasizing copied from the book, not done by me).

Ok, so if I understood correctly, the equation you are trying to solve is [math] x = \left[(x+3)^3 - (x+1)^3 + (x+8)^3 \right]^{1/3}. [/math] As said, take this to its third power, leading to [math] x^3 = (x+3)^3 - (x+1)^3 + (x+8)^3. [/math] Multiply that out. As yourdadonapogos said, the x³-terms will cancel, leading to an equation of the type ax²+bx+c=0 which then can be solved using the pq-equation.

The first question is a pretty strange one when coming from a moderator of a science forum. Checking it out takes about 5 minutes and yields the results: - Strongly disagree all, strongly disagree on the astro question: 0/-4.36 - Strongly disagree all, strongly agree on the astro question: 0/-3.9 - Strongly agree all, strongly disagree on the astro question: 0/3.9 - Strongly agree all, strongly agree on the astro question: 0/4.36 2nd part was covered (ok, "touched" is probably a better term) in the part of the FAQ Dak gave.

That pretty much matches also my impression of the field. However, be aware that "not too difficult" still is a decent level above school-level.

you mean [math]x = 3 \sqrt{(x+3)^3} - (x+1)^3 + (x+8)^3 [/math]? I'm not even convinced that it can be analytically solved at all.

I actually found it quite disturbing that I could (possibly 'can', but I think most of the related problems now got banned, too) barely read any thread because a significant share of posts came from people on my ignore list. Pretty nice feature, btw.

What is a time operator and how does the hamiltonian fit into this description?

1) "get closer", "remain at a fixed distance" and "get further apart" means (or at least can be understood) how their distance changes over time. 2) That already sounds like velocity, and indeed velocity of the drops is the key. 3) Now, which relations should the velocities of two drops fullfill for a, b and c, respectively? 4) What is (or what do you assume is) the relation of the velocities? 5) If you did follow to this point, then you get your reasoning from the reasoning in 4). @MrMongoose: I think she meant the distance between two subsequent drops during falling.

a) He doesn't name it dark because of that but because that's the name of it (although in the case of dark energy it might be true that it's got that name because we don't know much about it - I dunno). b) He's talking about "dark energy" and one of the first things he sais is that it shouldn't be confused with dark matter. c) I just spent 10 minutes (and some additional minutes rewatching the parts where he could have said what you claimed he did) watching someone giving a pop-science talk about standard cosmology in the early universe, just to find out a) and b). Please don't post random might-be-related videos claiming someone said X, without properly quoting it.

That is not the usually given reason for giving it that adjective.

Hooray for susy-breaking!

The following rules might help you: log(a/b) = log(a) - log(b), e^(a+b) = e^a * e^b, e^(a*b) = (e^a)^b = (e^b)^a. Other than that (and for future forum usage): Please don't simply state your homework questions and hope someone will give you the answer. Do at least give your ideas of how you think it could be done or why you think that all ways you can think of will probably not work. Ideally, you'd also show your previous attempts to solve the problem.

Not to mention that getting the blood stains out of your clothes can become really annoying, especially if you have to do it regularly. I would have believed that without experimental results. Absolutely. That observable is highly dependent on the frame of reference. Imho it clearly does not. And I find it pretty shocking that you think it did.

By "numbers with decimals" you mean non-natural numbers? A greatest common factor is usually used for naturals only.

I don't know what you call a "mathematical application", but if you're going for Python then the packages "NumPy" and "SciPy" (http://numpy.scipy.org/ and http://www.scipy.org/) might be worth a look.

Off-topic: Which, cosindering the idea supposedly solves some of the biggest problems the human race currently has, imho is a completely ridiculous/inacceptable attitude. On-topic: Can't be too hard googling for some numbers. Very first google hit for the nuclear power plant near from where I live gave a power output of ~1200 MW (per reactor) and a pressure of ~50 bar at the steam turbine.

Huh? Having written an article or two for the german WP and just this morning having deleted some (and not even all) very stupid statements in the article "photon" (i.e. not some super-exotic topic but a relatively basic one) that comes as a big surprise. Would be interesting to find out which 50 articles were chosen - seems unlikely that there were physics articles in it . EDIT: Found it, so in case someone bothers: Six of the articles were from the resort science: * Gravitation * Stem cells * ISS * Polar Bear * Wind Power Plants * MP3 Further six were from medical sciences (so should probably also count as science by sfn definitions).

It can probably be seen as an effect of the SR transformations, yes. Considering an electron is an elementary particle and that an electron with an energy of 1 MeV does not move at [math]v = \sqrt{2E/m} = \sqrt{2c^2 \text{ MeV}/ 0.5 \text{ MeV}} = 2 c[/math] but at ~c, I would say "pretty arbitrarily small for SR".

I'm quite sure I'm not the only one who doesn't understand the question. You should probably elaborate why you think so, what you mean by that, etc.