timo

By definition the WF contains all information about the particle; that does indeed include probabilities for finding it at certain locations The probability for any event to happen within the next 20 minutes is larger or equal to the probability for the same event to happen within the next 10 minutes. That has nothing to do with quantum mechanics and wave functions, though. The probability for location of an object is to be understood as an instantaneous one, not an integrated one. Not sure what you mean there. Certainly, the characteristic behavior of cheese on the time scales of minutes (lay around, do nothing) qualitatively differs from that on the time scale of years (rot). No. Yes. Dunno, I didn't understand your argument. I think it means that your line of reasoning, which I cannot really follow, is flawed. The wave function is (often) given as a function f(x,t). That does include time. I don't quite see how the statement "the chance to roll two equal numbers with two dice is 1/6" would require the element of time, though.

It is possible that object A with an energy of E orbits the sun while another object B with the same energy E crashes into the sun. In other words: the energy level does not (exclusively) determine whether a stellar object crashes into the sun, orbits it, or is slightly bent in its curve but leaves the solar system (like I guess some comets do). The statement "electrons follow their orbits because of their energy level" is slightly problematic, as it can be understood to imply that having a certain energy is the cause for some orbit. It is probably better to think of it the other way round (a certain energy being the effect of being in an orbit - whatever an electron orbit may be): Electrons follow orbits, orbits have an energy associated to them. Therefore, an electron following an orbit has some (specific) energy. Notice that there is a subtle difference, e.g. that in the latter picture two different orbits can in principle have the same energy - similarly as the planet orbiting the sun and the planet crashing into the sun can have the same energy.

A potential future in the field is more likely to be based on your work than on the department's label.

The force that I spoke about (notice the singular!) is the centripetal force of gravity.

They have a velocity that tries to move them further apart from the central body (say the sun) but at the same time are attracted towards it. The two effects roughly compensate. Note that in principle it may well happen that the moon crashes into earth - and that it merely takes a lot of time to happen. No.

I would think it's more a historical thing: If a university had an Astronomy department for ages, then it still may have. If they hadn't, then they may be more likely to install an Astrophysics chair in the physics department. That's just a guess of an outsider who cares little about the Astro hype, though.

I don't know the exact working of the "grad school" system in the US, but as soon as you start to conduct research my advice would be: Read a paper a week which is from your field, even though it may not be directly necessary at the very moment. Read them properly but casually (e.g. in the bus or train - perhaps not during lunch with your group ). Don't worry if you do not understand everything (during the first year or so). Don't get excited and try to read ten a week to be a better student (unless there is actual reason to do it, like that you cite them - which for most people is not necessarily a reason to read them, anyways ). Just keep doing it - it will accumulate to quite a bit of reading over 3+ years.

Create a class "Polynomial" that represents functions of the type [math]f(x) = a_0 + a_1 x^2 + a_2 x^2[/math] (hint: constructor) Create a method of that class that prints out pairs of x and f(x) over a specified range and with a specified distance between subsequent x. An output of this would look like x f(x) -1 0.5 -0.8 0.4 -0.6 0.3 -0.4 0.2 (hints: method, std::cout) Do the same but write to a text file rather than the screen (hint: std::ofstream) Not directly C++ related by arguably even more important for a scientist: Plot these data with a program of your choice to visualize the function. Use the program's built-in function parser to verify that the data you were writing out is correct. (hint: gnuplot) Extend the class to handle functions of the type [math]f(x) = a_0 + a_1 x^2 + a_2 x^2 + \dots[/math] (hint: std::vector) Implement an algebra over these objects, i.e. overload operators such than you can add two of these objects ([math] f^{(1)}(x) + f^{(2)}(x) = (a_0^{(1)} + a_0^{(2)}) + (a_1^{(1)} + a_1^{(2)}) x + \dots [/math]) and allows to multiply them with a real ( d * f(x) = d*a0 + d*a1*x + ...) (the term is "operator overloading"). Implement a method that finds the maximum f(x) over a given range [x0; x1] (no hint: there's several ways and the purpose of this task already is to spark your ambition to try out things for yourself). This program should be appropriate for a ambitious beginner, teach some basics of c++, and keep you occupied for some time (so don't worry if you are not finished with all those points after a day).

I'm not sure if there is a "many worlds interpretation theory" at all. I think "interpretation" already is the classification of the "many worlds" idea, not part of the name. I have heard about the "many worlds interpretation", which I have understood to be an interpretation of quantum mechanics (an attempt to make QM intuitive), not a theory. I've not heard about a "many worlds theory". So to answer your question: I think that by default an interpretation cannot be proven, but only become mainstream or not (e.g. because of proving to be useful). The notion of a lot of parallel universes has not become the mainstream interpretation of probability theory. Even though one could expect more interactions between the parallel universes in QM, I still don't expect it to suddenly show much more useful, there. Btw.: While some physicists may actually be thinking about the "many worlds interpretation", the only occasion I ever encountered it is presented by non-physicists on the Internet. That does not invalidate speaking about it, of course. But maybe take it as a warning sign that is may not be the hot topic in physics that some people seem to conceive it as. After all, "maybe when you make a decision the universe splits into two branches" alone is a thought on the intellectual level of a kid learning that actions have consequences (there may be more to the "many world" thing, though).

Allowing for particles to react into particles with different names is not what is usually considered the defining property of a "unifying force".

At least for a magnetic (mono-) north-pole . In case of the magnetic field the lines only tell you which way a compass would point at the given location (with the arrow in your diagram above pointing towards the south-half of the needle).

You misunderstand it. The lines are merely visualizations of the magnetic field.

I don't think I have ever seen anything but "e" being raised to some power of "i" (but in case you wanted to do that for some exotic reason, ajb already provided a possible definition). The standard definition of the exponential function (in physics) is [math] e^x = \exp (x) := \sum_{n=0}^\infty \frac{x^n}{n!} [/math]. As you hopefully see, this definition does allow for complex-valued arguments "x". Sidenote: It is also common to define terms [math]e^M[/math] with matrices "M" this way.

I do not think the statement about "ground state" energy means much more than to highlight an unexpected effect - that the energy of the ground states of the classical and the respective QM system (given the same Hamiltonian) differ. You can -to my knowledge- not measure absolute energy levels - only energy differences. And you also cannot pull a switch to transform a non-QM system into a QM system. To me, ground state energy seems like one of the more overrated and misunderstood concepts in quantum mechanics. That's rather interesting considering that I just claimed you couldn't measure absolute energies. Are you sure they didn't measure the different distributions of energy levels above the ground state, instead? I also don't really see how you want to make "quantum fluctuations" (what exactly is that supposed to be, anyways?) fit into the picture of a system being in its ground state. The standard examples of "basic quantum mechanics" have a ground state in which the probability density is constant as a function of time (which in fact directly follows for all systems with a unique ground state and a time-independent Hamiltonian). (btw.: no offense meant by being disruptive; most of the physics related posts in here are even below the level of even bothering to reply) edit: on 2nd tough, you do not even need a unique ground state

I guess I could indeed have read your OP a bit more carefully. Two comments, still: 1) By an undergrad being too inexperienced to perform research on his or her own I pretty much meant any academic level below a PhD. 2) My point about doing work in a research group indeed was not the "group" aspect but the professional supervision. So if you were working for a professor who has a project for you that he thinks may be publishable (e.g. you get a publication out of your thesis), then that is totally fine, too. Disclaimer: Note also that I am in a different academic field (physics) and country (Germany). Things may be a bit different in computer science and whatever country you are currently living in.

I can't imagine hat "having a paper published" is supposed to mean that you should sit down for yourself, write and publish one. That would be a rather ridiculous assumption and would not exactly speak for whoever told you about your chances being improved if you had a publication. An undergrad does not have the necessary overview over current research to know what has been done before and what is interesting. What it supposedly means is that you should do some research supervised by a professional (as part of a groups research project or as an individual project within the frame of some research group) and show off that you did this "internship" successfully by coming out of it with a publication with your name on it. The group leader will take care about questions like "how to write it" and "which journal should we submit to". Or as the short mainstream answer: Submit to one of the journals that you read regularly. If there is no such journal, submit to none. I am afraid I cannot help you with the question about a PhD program. One thing that was not clear and that you may want to clarify, though: Does "with funding" mean that you have funding or that you need funding?

Note also that despite what the name may suggest, "fast" is not really the point of a particle accelerator. The point is to give the objects (protons in this case) a high (kinetic) energy; the increase in velocity close to that of the speed of light is in some sense merely a side effect of increasing the kinetic energy.

Sure: Declaration of Human Rights, articles 2 and 5.

According to Wikipedia, an A-level refers to "advanced" courses in school grade 12 and 13. That does not sound like being a real career decision (my "Leistungskurse", which I believe may be the German equivalent of an A-level, where relatively unrelated to what I went for in university - which I consider as a plus). Unless I am wrong about "not a career decision", I recommend choosing based on talent, current interest, teacher, timetable, nice and (if of opposite sex) good-looking fellow students, ... (possibly even in that order).

Your method is correct but tedious and unnecessarily complicated to justify (as demonstrated by the fact that you are not even sure if it is the correct way). A simpler explanation is to consequently use the definition of g(x): For [math]1\leq x < 2[/math], [math]g(x) = \int_0^x \! f(x) \, dx = \int_0^1 \! f(x) \, dx + \int_1^x \! f(x) \, dx = \dots [/math].

What you are doing wrong (I assume the green hooks and red crosses are supposed to indicate the parts you did correct and wrong, respectively) is that you are giving an antiderivative of f(x) for the respective x. What is asked for, however, is g(x). If you look careful at the definition of g(x) you will realize that g(x) is an arbitrary antiderivative of f(x) (or in fact should in this context not be thought of as the antiderivative at all) EDIT: In an earlier version of this post I said that g(x) is not the antiderivative of f(x). That was wrong (it is an antiderivative, but a very specific one) and has been corrected now.

You probably don't speak German, but by visual inspection you may realize that the way Einstein introduced relativity in his original publication is surprisingly similar to the way it is introduced in some modern physics textbooks. As a matter of fact, the abstract says (and "yes", such terribly long sentences are the default style choice in this work of Einstein )

It's pretty clear what you meant so take this as nitpicking: There's strong experimental evidence that the temperature of the sun is actually quite sufficient for a self-sustained fusion, at least at the parts of the sun where self-sustained fusion happens .

Unless you really want an "X vs. Y" thread, I think you should also state what these webpages (that I both do not know) are supposed to be for. I have the feeling that my reply would be "I use Google Scholar", but that is just from blindly assuming you speak about finding publications and citations.

But with already 530 posts on sfn you should know well enough that you shouldn't expect one