timo

You probably already know the xkcd comic about the topic. I don't even know what a "honor society" is; that might say a bit about the awesome international reputation of such societies - or my ignorance.

I just read another of those posts where someone said he's a layman with interest in ... and Theoretical Physics. I have a vague idea why people are interested in that and for the most part I'd advice them to rethink their interest - but that's not what I am going to ask about. Another instance I met the term and was a little puzzled was on Wikipedia where I wrote that the Einstein notation is mostly used in relativistic physics and someone "corrected" me and wrote "theoretical physics", instead. My question is What does "Theoretical Physics" mean to you? As a matter of fact, I don't really know what it is to me. Generally, I tend to think of it more as a method than a field. But for throwing some points into the discussion here's a few thoughts and possible definitions: I spoke out against the "Modern and Theoretical Physics" section of this forum on some occasions, the main reason being that apparently no one knows what the title means. The best answer I got was "it means the things written below the title", which is "Atomic structure, nuclear physics, etc.", presumably meaning to include particle physics. Well, there certainly is no reason to consider those fields the most modern ones in the sense of "new". I see no reason why those fields should be more theoretical or abstract than others, but I do think there is the tendency to assume that the more away from everyday length-scales a field of physics is, the more "theoretical" it is. I do know that some website named "Wikipedia" (often incorrectly referred to as "Wiki") exists. I do disagree with the major definition of both the English and the German Wikipedia saying: "Theoretical physics is a branch of physics which employs mathematical models and abstractions of physics in an attempt to explain natural phenomena.". That is, in my eyes, bollocks: Employing mathematical models and abstractions to explain and predict natural phenomena is a definition for all physics, irrespective of the adjective before the term. One natural definition would be that theoretical physics is what is left from physics after you take away comparing to experiment or the transfer of physics to actual applications, i.e. physics for those who don't know how to use a screwdriver. Perhaps theoretical physics is also less interested in particular experiment but more in classes of (possible) experiments, i.e. some abstraction layer over the actual work that needs to be done? In principle, I happily embrace the "perhaps one cannot fully distinguish theoretical physics from other physics"-compromise. In practice, that does not reflect reality: The term is readily used among laymen and professionals in a manner pretending it had a rather precise meaning, for example in the statement "I am interested in Theoretical Physics". Don't be shy to offer an opinion even if your actual physics education is limited to having read a popular science book - or not even that. In fact, that views on the field/technique/whatever might be the most interesting for me. But please note that since I am interested in your opinions there's little point in quoting me Wikipedia articles (unless you wrote them, of course).

In [math]\mathbb R^N[/math] multiplying with [math]v_0^t[/math] (the transpose) from the left should constitute a proof. I currently can't think of a more general solution, despite that intuitively it is clear that a matrix that kills the [math]v_0[/math] component from a vector will not have [math]v_0[/math] as a result when operated on any vector.

I think you worded your question very poorly. I might have understood your question now: The g22 term depends on only one coordinate, the g33 term depends on two coordinates. Your question is if the gXX term will always depend on at most as many variables as the gYY term for Y>X? The answer would be "no": Just switch the names of x1 and x2 which is nothing but a renaming but will also swap g22 and g33. You can also have non-zero diagonal terms in general.

The trivial fact that [math] 1^2+2^2+...+(k+1)^2 = 1^2+2^2+...+k^2+(k+1)^2 = (1^2+2^2+...+k^2)+(k+1)^2 [/math].

I don't think I hold "almost" no formal degree of school education just because I only hold one of the thousands available. Same goes with "almost no computer", "almost no job" and pretty much anything.

That would be for the kiddies in the computer gamers' corner. We can provide an old pervert giving the parental advice that young women should have sex with some older guy first () and a drunken philosopher proposing not to do what others propose () !

You could try to understand what a full solution of the hydrogen atom with all six spatial degrees of freedom looks like. I think that is better-invested time.

I just stumbled over it by accident: http://www.scienceforums.net/forum/showthread.php?t=49677. The thesis is probably not written in English .

If you want to link to some image on the web you can do that with the "insert image" button and add the URL there. [ IMG]http://www.scienceforums.net/forum/images/sfn/logo.jpg[ /IMG] (without the spaces between the brackets) gives , for example. Otherwise you might have to attach the image to the post first which is done with the "manage attachments" button under the "Additional Options" field. That will show the image as an attachment at the end of the post. In theory, that would also give you an URL that you can use for the "insert image" button, then. In practice, that usually does not work (or at least did not work in the past). EDIT: At least linking to images you've uploaded to your user galleries (My Account -> Pictures and Albums ) can be linked directly with the command shown below the image in the gallery: [ IMG]http://www.scienceforums.net/forum/picture.php?albumid=80&pictureid=887[ /IMG] =>

You do that here, too. You can solve for x^2 and then consider which of the two candidate x is the correct one. D_H just put that on the start of the statement "since the original question obviously has a positive answer, going from 'what is x^2?' to 'what is x?' is similarly unambiguous". If the equation was [math]x = -\sqrt{\dots}[/math] then you'd get the same x^2 but chose the negative candidate for x "since the original question obviously has a negative answer". Of course you should also pay attention to the range that the original term is defined over, but that problem is not unique for squaring but also appears in other operations.

a) Dark Energy and Dark Matter are two different concepts; the one resembling matter is, unsurprisingly, dark matter. b) If an object could be at two places at a time on an atomic level then you would probably measure this effect on every scale that you can measure gravity on. So the effect of "an object being at two positions at a time", assuming it exists, should already be contained in the constant of gravitation, then. In short: That shouldn't change anything. c) Please try to communicate in complete sentences with proper capitalization. The little time taken to put what looks like brainstorming into a consistent form not only increases the readability of the thread (and in effect the quality of it) but also is a sign of realizing that others spend their time trying to help you.

Neither. Both are different types of elementary particles. Contrary to quarks neutrinos do not tend to form larger structures, though.

Same as the [math]X_u[/math] except with a charm-quark instead of an up-quark.

Then it presumably means the decay of some hadron containing a b-quark to a hadron containing a u-quark and the lepton and neutrino that come from the decay of the b-quark into an up-quark. But that also is just a guess; I have little to no experience with hadrons and never read a b-physics paper myself.

I couldn't find that in the text, so I dunno. "l" probably means a charged lepton, nu probably still is a neutrino, the arrow indicates a decay. Could it be that the "B" is not a capital one and the "c" is not a subscript to the "X"? It might be the decay of a bottom-boson into a charm-boson, a lepton (i.e. electron, muon or tau), the neutrino fitting to the lepton (to preserve fermion number), and whatever crap possibly also produced but irrelevant to the discussion (some stuff X), then. But without knowing where you read that that is only a guess.

Anti-bottom-quark and Bottom-quark.

Anti-neutrinos and neutrinos, respectively. It's the Greek letter "nu", not a "v", btw.

That's not fully correct or at least not complete. I do consider the invariant mass a contribution to energy (which is probably what you mean by "form of energy"). But a contribution to energy does not necessarily have to increase with velocity - think potential energy. An increase in mass with velocity only needs to happen when you consider mass being identical (up to constants) to an energy that includes kinetic energy (e.g. kinetic energy itself or total energy). Btw: after thinking a bit about it, the idea of reading "E=mc²" as mass being equal to the total energy in every case does look even more strange to me than before: Most of us have learned that "E=mgh" is a contribution to energy. No one would start to argue stuff about mass or height of an object increasing with velocity from that. But when seeing the equation "E=mc²" that suddenly seems to sound like a great idea.

You really could have said that sooner, Swansont. I already smashed some of my Einstein statues, now.

That would be funny because speeds are different from different viewpoints/observers and hence the number of atoms in an object would depend on who is looking at it . The bottom line is that there's two ways to interpret the infamous equation [math]E=mc^2[/math]. First, you can say that it only applies when the object is not moving. Hence, the increase of kinetic energy with the increase of speed will not say anything about the mass. Alternatively, you can try to make the equation apply for all speeds. But then you should take it literal: If mass always is the same as energy (forget about the c² for a second) then mass is energy, i.e. both terms refer to the same thing. Now, if you call the mass energy, which I just argued that you could equally-well do, then you'd probably not expect new matter to appear just because the kinetic energy of an object increases. Depending on your personality you can then either consider the question answered, run away into the "but then our understanding of energy must be completely renewed, give me a few minutes to reinvent physics ..."-direction, or consider the unrestricted equality of mass and energy to be a bad idea. I consider the unrestricted equality of mass and energy to be a bad idea, btw. I also wrote a slightly more technical post about the problem of defining mass some time ago: http://www.scienceforums.net/forum/showthread.php?t=38825 .

I cannot even decipher the meaning of the first sentence.

EDIT: I figured I wrote "nuclei" instead of "protons and neutrons" in my first post so what I originally wrote in this post is redundant. Anyways: my point wasn't that all chemistry is restricted to the shell of a nucleus (although that in fact is my personal understanding of the field) but that a lot of science can be done with this "simplified" model, already (most physics doesn't concern with a sub-structure of nuclei, either).

And what is the stuff they are made up of made up of? And does this "..., now what are they made up of"-recursion ever end or is it just and infinite loop of asking for successively smaller building blocks? The answer is that to today's understanding there is an end to this loop; a smallest building block that cannot be decomposed any further. Those smallest building blocks are called "elementary particles". The quarks already are elementary particles, i.e. the answer to your question is that they are not made up of some other stuff; they just are as they are. From a slightly broader perspective that statement is probably not so complete. There is no proof -and presumably never can be- that there isn't a sub-structure to the quarks (one might only disprove it by finding one). But as there is no indication for a sub-structure, a good answer would probably be "no one (professional scientist) sees the need for quarks being made up of something else". There is another interesting feature to your question: Few people even see the need for protons and neutrons to be made up of something else. You can do very good science by assuming nuclei and electrons to be the smallest building block of matter (just not all). Chemistry, for example.

The typical jobs mentioned for theoretical physicist that also are suited for mathematicians (perhaps even better-suited) are working for insurance companies or consulting agencies. The former is probably an option with a B.Sc. Consulting agencies probably mostly buy the doctorate title and a polished CV (apart from the fact that you have to score good test results, of course) so that is not an option, then. While I cannot actually disprove it, I find Genecks idea, that companies were hiring mathematicians to do the job of a natural scientist, a bit strange.