timo

Spontaneously, I´d say they are all false: - Assuming with "doctor" you meant "physician", then I´d say a physician working in emergency medicine must know little about biology but rather have a good intuition for the current state of their patient. - I know neither biology nor chemistry, but I doubt you need much chemistry knowledge to investigate the eco system of the amazonas. - I´m sure there´s branches of chemistry that need neither QM not Thermodynamics, which is the only overlap between physics and chemistry that I can spontaneously think of. - Of course you need to be able to do some calculations in physics. But real mathematics is something slightly different. Having had too many discussions with professors about mathematical proofs or the lack thereof that ended in the statement "you just know it from physical intuition" (a statement that I don´t even necessarily reject) I´d say that "real" mathematics is usually not needed in physics. - I can remember having read revolutionary/famous texts/articles about physics that were so bone-dry that you´d throw them away after one paragraph if you didn´t know the content really is important/groundbreaking. Bottom line: All the fields you listed are adjecent, so someone working in an area of their field that leans towards the other there´s certainly some knowledge of that field that´s required for efficient working (e.g. a physician working in research might need some knowledge in chemistry and biology). But there´s also areas that have less overlap with the other field (like the physician working in emergency medicine).

Lifetime and half-life time are two different measurements of the same thing, namely how fast something decays. A decay follows [math] N(t) = N_0 \, \exp (-\kappa t) [/math], with [math]\kappa > 0 [/math]. Lifetime is [math] \tau = \frac{1}{\kappa} [/math], half-time is the time for which [math]N(t) = N_0/2[/math], i.e. the solution for t of [math] \frac{N_0}{2} = N_0 \exp (-\kappa t) [/math]. Iow, both quantities aren´t exactly the same but they both are different expressions of the same thing (kappa).

We got rid of this problem around when the forum design changed. And before someone tries to find a new solution: I like the friendly green.

For the 1st questions you just have to look at F=m*a or equivalently a = F/m, where a is the acceleration (the change in velocity), m the mass of the object and F the total force acting on it (which is zero by your conditions). In case of the 2nd question, you´ll first have to figure out the boy's mass by using the conditions for the system to be balanced.

Don´t know where to buy equipment. Just out of curiosity: Are you planning anti-gravity experiments?

@Dak: My point was that the english counting system also has a hidden affinity to 20 since the names of the number 13-19 are constructed differently than those above (nineteen vs. sixty-eight). No one really knows. In fact, there was the idea to officially allow the twenty-and-five version as correct some years ago, hoping it would ease learning of the numbers for children and avoid typical typos (writing five-and-twenty as 52 instead of 25 is a very common mistake when you don´t pay attention). As with all things where people don´t want to learn something new, reason stood no chance against lazyness, so the idea was quickly dropped.

Why do you spell 17 as "seventeen" instead of "ten-seven" ?

What he was talking about is 1 billion (eu) - 1 billion (us) = 0.999 billion (eu). More plainly: [math] 1\cdot 10^{12} - 1\cdot 10^9 = 0.999 \cdot 10^{12}[/math].

Technically, it seems easier to compensate for community costs by an appropriate tax to cigarettes (or whatever drug you want to legalize) than by taxing "driving motorcycle without wearing a helmet". So I think the "I don´t want to pay for other people's stupidity"-problem you´re raising here can principally be avoided/solved in the case of drugs.

Forces only exist as something real if you restrict the allowed coordinate systems to certain classes. If you have a movement following the equation of motion [math] x(t) = ct^2 [/math] with c being any constant (or constant vector of R³ if you prefer), then you have the acceleration [math] a = \ddot x = \frac{d^2x}{dt^2} = 2c [/math] and by [math]F=ma[/math] can state that a force of [math] F=2mc [/math] was working. If you describe the motion of the same object with coordinates [math]x'[/math] which transform from old coordinate system by [math]x' = x - ct^2[/math], then obviously [math] x'(t) = 0 \Rightarrow a' = 0 \Rightarrow F'=0 [/math], where [math] a' [/math] and [math] F' [/math] mean acceleration and force in the new system, respectively. So the question whether a force is working on the object or not becomes a matter of perspective. A common example fitting to that calculation is someone in free-fall in an elevator. For a person inside the elevator, there is no measurable force since he/she is floating weightless inside the cabin. For someone standing outside on the surface of earth, the whole system seems to be accelerating due to gravity, with a potentially unpleasant outcome for the person inside the elevator. The argument about forces being dependent on perspective is not restricted to gravitational attraction, though. Above calculation only assumed a constant force in some coordinate system which was canceled by chosing an appropriate other coordinate system. Whether the force was a gravitational or an electric one doesn´t matter for this example. For different geometries, different coordinate systems are practical. In GR, gravity is described by giving spacetime some dynamic properties (which play an analogous role as the "field" I mentioned here). Adding a mass to spacetime alters these properties, which can lead to your old coordinate system not anymore having the nice properties for which you have chosen it previously. As a result you can now have a force acting where no force was acting before. So in some sense the warping of spacetime induces a force. But you can in principle again do a coordinate transformation to a new coordinate system where the force vanishes. Sidenote: Note that the term "force" is sometimes used synonymiously for "interaction" and not in its closer sense.

I naturally don´t know how to interpret your coursework, either. So just a few suggestions what one could investigate about sequences: - What is the value of the n´th number (e.g. the 10051th)? What is the value of the n'th difference between numbers (e.g. the 6252th)? - Is there a biggest and/or a smallest number in the series? If so, which? Otherwise, why not? - Is there a "greater than" or "lesser than" relation between subsequent numbers?

I find those four questions pretty interesting and I think that there´s potentially a lot of insight to be gained by trying to give coherent answers to them - not primarily to justify the actions of your goverment but for finding your personal standpoint by a rather rational method, less prone to propaganda influences from whatever side. For example "Al Qeada and their ilk" seems like a pretty weak/nonsaying answer to me. Besides making Al Qaeda sound like a club where you´re formally a member or not, the addition "and their ilk" is so vague that you could as well have said "the bad guys" instead. Answering "how will you ..." by "with difficulty" seems even more senseless to me. Your answers to #3 and #4 seem more sensible but I´d hope that given some more thought there´s better answers to come up with (but that´sjust what I´d hope, it doesn´t necessarily have to be the case just because I want that). I think I had tried answering #1 by starting with something like "people who harm innocent civilians" and then going on by analyzing what the terms "harm", "innocent" and "civilian" mean and then adjusting the sentence and the definitions I found for the three terms until I got a satisfactionary answer for myself.

That is probably true but I am not sure if it correctly reflects what modern chemistry is about; sounds too much like the chemistry you learn in school. I´d think that almost all modern chemistry uses QM methods or results to a lesser (spectroscopy) or greater (density functional theory) degree. Speaking for physics and staying with your example: I spontaneously wouldn´t personally know (from what I know or guess about their work) any physicist who uses Newtonian mechanics on a daily basis while all I know use relativistic calculations to various extends (ranging roughly from solid state physicists who analyze their probes with X-ray over people doing optics to nuclear and particle physicists). EDIT: @next post: That does indeed seem interesting. I´ve already thought about asking a mod to move this thread to some chemistry section hoping to get some information by people more familiar with chemistry, there. So pls tell us what he said about it (or convince him to join sfn and post it here ).

QM will not and does not replace (modern) chemistry. Chemistry and QM are not mutually exclusive and in fact QM is an essential part of some (many?) branches of chemistry, notably physical chemistry. As for the question how long that´s been the case already: Not being a chemicist I have little clue, but the 50 years mentioned by Meir Achuz seem reasonable.

*pokes admins* ... so what?

And the new feature of the year is that the link in the top bar is finally fixed

Now this sparks my interest. However, I have no idea how this is supposed to work. Classically, we derive physics from the principle of extremal action so you could start interpreting the local action as a probability and might get a probability distribution that, on sufficiently large scales, peaks sharply for the classical solution. Is it somehow related to that or am I completely on the wrong track? Can you give some additional information or maybe links to work on that subject?

What about not restricting it to books and not restricting it to pre-scientific level? What about recommendations for someone with a scientific degree in a related area (e.g. an introductionary text about GR which is readable for physicists who didn´t take the GR course during their studies)? I see the additional advantage that on this level, a good recommendation can be really helpful while for stuff like "linear algebra for engineers" it´s mostly just a matter of taste who prefers which book.

Andrew Liddle: "An Introduction to Modern Cosmology".

Sry Foodchain but I don´t understand anything of what you wrote, not even the grammatical structure of your sentences. Can you rephrase your question?

dL/dt looks more basic to me.

It might be helpful if you start with what you think/know to have a basis. I like the introductionary sentence from Wikipedia which is: "In physics, torque (or often called a moment) can informally be thought of as "rotational force" or "angular force" which causes a change in rotational motion".

Yes. In fact in the simplemost models (not sure about more sophisticated models), galaxies are not assumed to move at all. They stay in their positions but distances between them increase due to the changing geometry. The common example is a balloon on which you mark two points. When you blow up the balloon, the two points stay in place but the distance between them increases because the geometry of the balloon changes (the radius increases). In SR you´d have the points on a piece of paper. I meant changing over time hoping that no one examines the statement too closely. The statement "dynamic spacetime" in that sense does of course have a catch if taken too seriously: If time is already part of spacetime in whatever sense, who can it change with time? I cannot answer the question right now, I assume that saying spacetime was dynamic in the sense of "it changes with time" is simply not correct. You might be able use "dynamic" in the sense of "changes with respect to particle content". In the case of cosmology, however, there is something similar to saying "spacetime changes over time". In the coordiante system used in cosmology you can tell space from time. There, you can tell how space changes with time. In above analogon: You can tell how the radius of the balloon changes with time.

Let me also add a reply here since it neatly continues what I said earlier today (http://www.scienceforums.net/forum/showpost.php?p=330894&postcount=12). The field equations for gravity, i.e. the dependency of the spacetime geometry of the sources and the dynamics of spacetime geometry (e.g. gravitational waves), are not part of SR. The calculations about the shape/structure of the universe are nothing but calculations of spacetime geometry as a function of the particle content using some rather broad (symmetry) assumptions - the Friedman equations are already the simplified results that incorporate the symmetry assumptions and boundary conditions and only take some scalar inputs describing the sources. The calculations are GR calculations, hence there´s no need for GR corrections to the calculations. As Swansont said, SR assumes a special static form of spacetime and a special form of coordinates to describe this spacetime. The term "local" in physics refers to a sufficiently small area around a point of interest - the size of that area generally depends on situation and tolerable error (similar to an "epsilon-delta enviroment", in case you ever heard that term in maths). In the GR case, for a sufficiently small area of spacetime (generally, "area" also refers to a sufficiently small time interval, not only spacial distances) you can often assume a flat gemometry and use the common SR coordinates. This not only rules out any curvature effects, but also any effects due to dynamics of spacetime (due to the limited time interval). A classical example of how a geometry can locally be approximated with a seemingly completely different geometry is earth. Assuming it was a sphere, you still can (and usually do) approximate it as being flat locally, like on a city map. Distant galaxies moving away with speeds (note that I explicitely did not use the term "velocity") so large that a light-ray could never reach them are an effect of spacetime dynamics (the expansion) and therefore not covered by SR - they are also very far away so you wouldn´t necessarily expect the locality assumption to be valid anyways.

Let´s say it is a better lie than saying mass was the source of gravity. The source of gravity (in the sense that it takes the position mass had in Newtonian Gravity) is the energy-stress tensor (http://en.wikipedia.org/wiki/Stress-energy_tensor). For your confusion about energy being the source of gravity, it is probably important to clearify what the "source" means. In the equation telling you how a particle moves (the equation of movement, the geodesic equation ), there is no term that is dependent on the particle´s mass or energy; it is solely dependent on the geometry (~= curvature) of space. But a theory of an interaction consists of more than the question how a particular field (the gravitational field, i.e. the geometry of spacetime) affects the particles in it. The theory must also contain a part telling you what the field looks like and how it behaves. This part is the field equation (in the case of GR the Einstein equation). It´s the field equation where energy comes in as the source that shapes the geometry. I think the reason why the "only dependent on the geometry and not on mass/energy"-part is sometimes stressed is that it is in contrast to eletromagnetism. There, electric charge not only creates the electromagnetic field, but the movement of particles within an electromagnetic field is also dependent on their charge while in GR no such charge term comes in.