timo

Did you try looking at df/dn ?

In the twins' paradox the crucial point from which the presumed paradox stems is that the twins each see the other twin's time as passing slower, same as your observers A and B do. So unless you've been misunderstood the scenario you talk about is indeed part of the twins' paradox (except that there one usually goes one step further and let them meet at the same point to compare their self-measured times). Considering my statement: I doubt you'll find more about it on the net - no one sells relativity so cheap, I think. I'm also not sure if it's really helpful to you, it was also meant for the others. But let me elaborate a bit: You said now imagine you had said What's the difference? Well, one difference is that we both know that in the 2nd question, the hypothetical one, the only confusing thing is the way you expressed the question. I guess we both understand pretty well how non-relativistic velocities can depend on the reference frame - everyone has learned to understand that at some point in their childhood. The difference to your actual question is not so big from a physical or logical point of view: it's merely that not everyone (read: no one) has learned relativity in their childhood. That's in fact pretty much the only fundamental difference (that I can think of at the moment). <there is a lot that I could say here but I think I'll better cut it short to restrict the confusion I might be causing with this non-mainstream comparison>. Btw.: Considering the question whether a different passing of time is an effect of human perception: it is an effect of human perception in the very same sense as the different velocities (in your hypothetical question) are. So I'd tend to say "no, it's not". It's an effect of different frames of reference.

[math] x^{-1} = \frac {1}{x^{+1}}= \frac 1x [/math] has nothing to do with scientific notation, as far as I know. It's merely a well-known rule for calculations with exponents.

As a matter of fact it's closely related that the two observers each see the other one as moving faster. Except that no one seems to find that one paradoxical.

That is actually not the problem. The problem is that you assume that if the angle changed by A degrees over ten seconds, then in the next ten seconds it will also change by A degrees. Or in other words: you assume that the rate by which the angle changes is constant over time. If that was the case, then what you did would have been ok. But it is not the case. The velocity is constant, but the rate by which the angle changes is not. No. What I meant is that the slash usually means a derivative with respect to x. That's what makes x' particularly strange. So according to me, [math] y' = \frac{dy}{dx} = \frac{d(3x+2)}{dx} = 3[/math]. Taking a derivative with respect to <something> means that <something> is the variable in the "denominator".

From quickly looking over it: 1) You forgot the units. 2) How do you know that [math]\frac{d\Phi}{dt} = -1[/math] (in whatever units)? Hint: it's wrong. 3) What is [math]x'[/math] supposed to be? A slash usually denotes the derivative with respect to a variable called "x". You probably meant the derivative with respect to time. In principle, that would often be written as [math]\dot x[/math]. But I think you should write out [math]\frac{dx}{dt}[/math] explicitly, for now.

Perhaps for clarification: what's being called a "state" and what not is purely by convention (at least as far as I am aware of, that is). There is no physics behind it. A very similar and physically relevant term is "phase". There is a huge amount of different phases, e.g. the different structures of ice, nematic phase, superconducting phase, the ferromagnetic phase, ... . The reason that some of the phases are called "state of matter" is purely convention and based on what is practical in everyday live (since from a physical point of view different crystal structures are more distinct from another than liquid and gas are).

Guess that's hard to argue with. Dean Mullen: Perhaps it's easier to just hint you into the right direction rather than trying to explain something in own words. The keywords you should probably look for is "Conditional probability". I recommend reading the Wikipedia article, it seems to talk about something very similar in its introduction.

Bignose: I said "getting five 2s in a row when you already threw four", not "getting five additional 2s in a row". Hence the adjective "trivial".

Mini on-topic remark: note that the OP asked about "position", not about "distance". Mini off-topic remark: There is no such thing as the "Planck wavelength" (it's Planck with a "ck", btw.). What you probably meant to say was "Planck length". The correct object would have been the "Planck constant". The Planck constant is a natural constant and conceptually something entirely different than those dreaded Planck units which are essentially just a convention for units (and sound cool because they appear in the context of quantum gravity).

- You accidentally wrote 2x2x2x2x2 instead of 3x3x3x3x3 - It is not common to say "the odds are five". One says the odds "are one in five" (though probably less common except for "one in a million"), "one fifth", or "one to four". - Realizing that the odds of an event happening can change when the conditions have changed is cool. But you'll hardly impress anyone with this finding. Obviously, the odds of someone knocking on the door of my flat in the next five minutes are lower in the middle of the night than just after someone rang the bell downstairs. In a similar (but even more trivial) way the odds of getting five 2s in a row are higher when you already threw four. EDIT FOR CLARIFICATION: by "the odds getting five 2s when you already threw four" I mean the probability to throw 2 in the fifth trial after four 2s have already been already-thrown, which would then make it five 2s in total (i.e. the presumably paradoxical scenario that this thread is about).

- Proper capitalization kicks ass! - What variable is the term a function of? - What is "am-gm" and "am-qm" supposed to mean? - "Also pf for mean of k nos will be preferable than for 3 stated above" ... In short: Try being at least remotely comprehensible - especially with a question about math. Precise statements are the essence of this science.

After writing the text below I now see that you asked for frequency, not wavelength: the statement is the same except that "wavelength" then is "frequency" and "length" is "time interval". You can indeed not sensibly define lengths -in this case a wavelength- with a measure by which all lengths are zero. The wavelength of a photon is measured in the frame of the lab/observer, where lengths are properly defined. Note that this implies that the same photon will usually have different wavelengths for different frames of reference.

I have no idea. I am not an engineer. My daily work is not even remotely related to real-world applications. But to throw in some spontaneous idea: judging from the long name of the stuff and the terms "parallel" and "normal": are you possibly talking about a long polymer in the form/phase in which the polymers are semi-randomly distributed but arranged roughly in parallel, i.e. something like liquid crystal (not necessarily with liquid-like positions)? In that case, the two values might be the expansions in the direction parallel to the orientation of the polymer chain and the two spacial directions perpendicular to this orientation axis. Just a guess, but maybe you can judge if it's helpful to you or not.

Oh, and I made a little typo. It's [math] \frac{d f_i}{dT} = \frac{\partial f_i}{\partial T} + \sum_j \frac{\partial f_i}{\partial x_j} \frac{d x_j}{d T}[/math], not [math] \frac{d f_i}{dT} = \frac{\partial f_i}{\partial T} + \sum_j \frac{\partial f_i}{\partial x_j} \frac{\partial x_j}{\partial T}[/math] (i.e. a total derivative in the last term, not a partial one). But I hope that typo was obvious when comparing to the image you linked (or at least insignificant).

From a quick look: I've not seen the notation before, but if [math]\vec f(T, \vec x)[/math] is a vector-valued function with components [math]f_i[/math] depending on the real-valued variable T and the vector-valued [math]\vec x[/math] which has components [math]x_j[/math], then [math] \frac{d f_i}{dT} = \frac{\partial f_i}{\partial T} + \sum_j \frac{\partial f_i}{\partial x_j} \frac{\partial x_j}{\partial T}[/math] for all i. I'd guess that's what the equation means (note that the terms [math]\frac{\partial f_i}{\partial x_j}[/math] can be considered forming a matrix with indices i and j).

I think the jump from "I do not understand basic relativity texts" to "based on this I can explain to you the true nature of light" is a bit radical.

I am saying that when a moving object emits light, the light moves with the speed of light. Seen from the perspective of the moving object, the light also moves with the speed of light. That is in one of the assumptions (possibly the assumption) in relativity. This assumptions is completely counterintuitive, because intuitively velocities should add up. But the constant speed of light seems to actually be the case. In nature, velocities do not add up [in this simple manner]. That is, as I said, completely counterintuitive. That's probably why the texts you read on it are so hard to understand. It does not "make sense", it's just a fact. I'm not sure where you read equations in which the variables are not properly defined. But when the problem is only understanding what the variables in an equation mean, you might have rather good chances to get an explanation if you ask in this forum.

What's the derivative of an equation supposed to be, anyhow?

@Genecks: Hmmmm. I didn't write "be sure you understood the paper" because I thought it's too obvious. As for the form of presentation, CharonY is probably right: no one gives really good first talks. Just be sure to learn something, and be it only that you are not capable of something, e.g. giving the talk without looking at your slides all the time. I usually try out something new in every talk (e.g. last time I tested how well I do without having practiced the talk - went surprisingly well). While it seems you learned that you need to understand a paper better before you really understand it (well, the guys spent a year of research into it, it's perhaps not that surprising that the topic isn't trivial on closer look), it's probably nothing to worry too much about for further talks. Giving a talk about someone else's work is a very artificial situation. You usually talk about your own work (and if you don't really understand that, then you've got bigger problems than not being a good speaker). @everyone: I'm kind of surprised that I seem to be the only one who thinks it is the teacher's responsibility to help a student on such an assignment. In regular lectures, tutorial sessions are held, and the tutors are supposed to answer the students' questions, even when they go beyond the actual homework questions (one of the reason why I do not like the concept of undergrads tutoring other undergrads). Students are also welcome to ask outside of the the meetings (but usually no one does). That's at least the system that I am used to. I am talking about absolute mainstream lectures here, i.e. the answers are usually found in every textbook. For such a form of lecturing, reading research papers, I would expect a similar supervision. I don't expect the lecturer to offer formal office hours for it so that he can answer questions himself. But at least some poor subordinate should be appointed as a contact person for the students to turn to when questions arise (and I can think of a heap of very appropriate questions there - and be it only "how do I get access to the restricted reference [2]?"). I consider not actively offering a contact to the students as unprofessional. I am not saying that students should have the paper explained to them by a professional. And in particular, offering a contact does not exclude that the contact sends the student home with the message that he should read the paper more carefully rather than wasting his time with stupid questions that are clearly answered in the article or a standard textbook. I don't want to comment on the particular case of Genecks (I only know one side's statement, and it's presented in a not-very-objective way). But with the general "you have to do it all by yourself"-attitude I do not agree. Since someone mentioned asking on forums rather than asking the professor: I fully disagree. It is not the idea of a university education that people learn their profession in the Internet and only pay their fees to attend the exams and get a piece of paper with a stamp on it, afterwards. It is certainly ok to ask for advices on the Internet, especially on "soft skills" like giving a good talk, using TeX, ..., where perfection is not required and "somehow works" suffices. Or possibly even on science that is not strictly within your own field of study. But just look at the sfn speculations forum to see what kind of great minds getting "hard skills" from the Internet produces.

My assumption that the Hydrogen is stable is indeed partly intuitive. In particular: I cannot think of any lower-energetic system. I'm not fully sure what you mean with being clear from the Schrödinger eq. Today's mainstream physics (the SM) and a proper mathematical treatment of QM do not cooperate very well, as far as I know. - The energy levels of the standard Hamiltonian (the one always being asked for in diploma exams) have a minimum, which is the ground state. I faintly remember that the solutions for a relativistic electron (i.e. based on the Dirac equation of motion) can't be written down that easy anymore and must be approximated graphically/numerically, but still preserve the structure of discrete levels with a minimum. I don't know enough QM to say something about a full-fledged QED Hydrogen or even an SM hydrogen. - If you're assuming BSM physics in which the proton decays, say P -> e+ pi+, then the hydrogen can decay rather trivially (from the perspective of a physicist who just ignores the presence of the electron for the decay of the nucleus). - In SM physics, it boils down to the fact that I cannot think of a lower-energetic state. The first idea would indeed be moving the electron's charge to the proton. But the resulting neutron+neutrino state is higher in energy. For the proton, there is not that much you can do with it, either. All Feynman vertices I can think of at the moment conserve the total number of quarks. So your final state would in some way have to have a total charge of zero, three net quarks, and one net lepton. From the physicists perspective, you could just go through all combinations of known particles that satisfy this criterion (I have to admit didn't do that). That of course heavily relies on the (somewhat reasonable) assumption that the particles in the sought-for final state are already known. For a rigorous treatment I think you're already stuck because of not being able to handle QCD bound states.

I see. I though you were referring to the original question. Ajb's statement was a bit weird - while it's true that in principle excited states can contain enough energy to undergo a transition that wouldn't be available to the ground state, this doesn't apply to the example given, where a few hundred keV would be needed and only up to 13.6 eV are available from excited states. In particle physics, lifetime usually refers to a scenario where the object is at rest and not influenced from the outside. That includes no thermal fluctuations, i.e. a constant-energy and not a temperature-based scenario. Incidently, that's pretty much what the OP was asking for. Since energy is conserved and no kinetic energy is available, this directly means that anything can only decay into decay products that have the same or less mass - the decay product may have momentum, so a energy difference in mass (E=mc²) can be compensated by kinetic energy of the final-state products. This directly means that objects for which no final state with a lower (summed up) mass than the current one exists cannot decay into anything and are stable. Such a case is the Hydrogen atom. The question to what extent that scenario is realistic is indeed a different question. In principle, the question about anything having an infinite lifetime has a very simple answer once you allow for interference from the outside: anything can be destroyed if you kick it hard enough. That's not a very useful statement in practice. What you presumably are very used to is thermal equilibrium situations. In principle, you can get arbitrary energy kicks there, too (except for T=0). Thermal equilibrium is a very important and powerful concept (as a matter of fact I recently published a paper where I propose that structures expected in living systems can be understood from the static equilibrium case). It is, however, not always appropriate. Particularly in physics, you often have processes that happen on entirely different time scales (from chemistry you might know the Born-Oppenheimer approximation). In such a case, thermal equilibrium might not be the correct concept for at least part of the process. Take for instance a bit of Uranium. The motion of the atoms is nicely equilibrated with the surrounding - average kinetic energy is constant. However, the ratio of radioactive (A) and already-decayed (D) Uranium atoms is not equilibrated with the surroundings. Instead of maintaining a constant number of As, you have a constantly-decreasing number of them. With respect to the A/D ratio, the system is far from thermal equilibrium and instead relaxing towards it. On a time-scale that a Chemist would most likely call "very slowly", to say the least. To close the circle of my statement: this system of decaying Uranium is an example where the particle physicist's understanding of lifetime seems like a more appropriate concept to use than thermal equilibrium. The decay of the Uranium is (afaik) largely unaffected by putting it in a fridge or in some solvent - on human timescales, that is. In short: Thanks for clarification. While equilibrium is a powerful concept, it's not what was asked for.

The watch would show less time being passed. No. The watch merely doesn't show local time. Depends how you count earth rotations and which direction the plane traveled. Non-relativistically: If I travel around the earth four times in 24 hours in a direction anti-parallel to the direction of earth rotation, how many earth rotations do I count in your opinion? Try to use more than one sentence for that statement/question. If I understand you right, then the answer is "no". Relativity foots on the speed of light (which you cannot travel at, but you could replace your example with sending a message at the speed of light, if I understood it correctly) being constant. For everyone. Getting a different results means that either a calculation error occurred. Or that calculations weren't performed at all, and that some concept was mis-applied.

Perhaps you should try some of the Youtube tutorials on Python under Windows. They might show you where to click when.

I think there is no formal need for structure (except for the existence of an abstract which you usually write last, anyways). If your structure is as non-saying as "intro, middle part, conclusion" you can as well write without a structure. "Problem statement -> very brief summary of previous attempts -> general idea -> introduction of the terminology -> calculation or description of experiments/simulations -> results -> explaining the relevance of the results, how they relate to the idea or problem, mention possible remaining issues/questions" might be a good rough guideline. The abstract is best written last. For format, just have a look at physics papers, e.g. any random ones on www.arxiv.org - better even some from the category your work is supposed to be in. Format is not a real problem, anyways. You can still re-type the whole thing with a professional program to make it look cooler, once you've finished writing. I'd like to emphasize the absolute need for what I named points A) and B) in my previous post. "I think maybe the big bang wasn't a singularity but a quantum fluctuation from a previous universe. It makes sense!" is not a piece of scientific work.