timo

Do you homework, get good grades in math and natural sciences. Go to university and study physics or chemistry. Apart from that, just follow your interests.

Absolutely possible:

As a matter of fact by "1000 times the mass of gas" I mean a typical fluid. Of course looking up the density or approximately knowig it is more accurate than my guess. I like the argument for chosing water as a specific fluid.

Assume a thousand times the density of a gas (NA atoms in 23 litres, if I remember correctly) and scale it down to the volume of a human cell. Should give a rough estimate.

I don't really see a proof, yet. First of all: Don't worry if the question is a problem for you. Such "proof that ..." questions are, in my opinion, all about experience and perhaps a bit of endurance. They have little to do with physics skill. To your question: What you want to show is [math]HP | \phi \rangle = a P | \phi \rangle[/math] knowing that [math] H | \phi \rangle = a | \phi \rangle[/math] and HP=PH. Perhaps an extra hint: Numbers commute with operators. Finally, as you may have noted already this forum is not exactly about getting answers very quickly. Members here live on different continents and many, especially those who can answer questions about operators, have jobs: I've been sleeping for the last eight hours and now go to my office for the next twelve.

That one's actually so straightforward that it's hard to give a hint without telling you the solution. How about this: There is not so much you can do with HP=PH and the definition of an eigenvector f of H. Try the few things you can do. Maybe you'll see something.

Perhaps you are right with your statement when seen from a global perspective. But as a somewhat experienced c++ programmer now mostly working on Java projects, I run into conceptual differences on almost a daily basis. Java's lack of nested namespaced, reference-only policy, lack of friend declarations, the differences between generics and templates, lack of destructors and most importantly Java's lack of const-correctness regularly make me bang my head on the keyboard. And that is after already having accepted the more-widely known differences like Java philosophy rejecting the concepts of operator overloading or multiple inheritance. And before you get me wrong: There are advantages of Java over c++, too. In fact, most Java programmers I meet actually consider the differences I listed as advantages. But there are also issues like "portability" that even I consider an advantage.

It is indeed unlikely that two equations not containing the letters "a" or "b" at all result in "a=..." or "b=..." after combining them. Unless further information is given that you missed out in your post. Chances are, "a" and "b" are defined somewhere else in the text you are reading. EDIT: Or, as ajb mentions, this is supposed to be the definition of a and b, not a result of a calculation.

<nevermind>

... and according to the theory of evolution, photons that moved slower than the speed of light became extinct.

In some sense, yes. But inertia is not really a prominent concept in quantum physics. Inertia does not slow down objects.

To cut it short, two comments: 1) My guess would be that an archeologist's hypothesis saying "I found traces of blood on this altar-like pile of stones, therefore the culture having built it probably offered sacrifices to its gods" does not involve heavy math. 2) Since those "does science depends on math" questions/claims often tend to actually refer to physics or at least natural sciences rather than "science": Physics can be understood as an attempt to describe nature's behavior by means of numbers and rules connecting these numbers (see also Bignose's post). That's probably what an average person would call "math".

That's a rather interesting proposition in the sense that in common notation 9!! = 1*3*5*7*9 < 9!. I don't think I've ever seen more than two exclamation marks, but in a logical continuation you'd probably end up with 9!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! = 1.

I wonder whether your question misses a verb or not.

To make a long story short: The length scale l you are looking for is roughly given by the quotient of the Planck constant h times speed of light c and the energy E per proton (a few TeV, look it up): l=(h*c)/E. The concept behind this number is that you can resolve structures in the order of size of the wavelength of your projectile. One can argue to what this extend this concept sensibly applies to collider physics or yields sensible information. But I am pretty sure it is the number that you are looking for in this thread, give or take a few Pi. Elementary particles have size zero by standard definition, btw.

27000 in circumference. But I have the faint feeling this is not what you are actually asking about.

Call me a grammar Nazi. But I believe that we should have forum rules that require posts, especially opening posts, to at least have any punctuation.

I almost thought that was a single sentence, but then I spotted the litte exclamation mark hidden in your wall of text. The main importance of the Higgs Boson is that its possible (and in retrospect successful) discovery is the only solid argument for getting funding for the LHC. What most people mean by "it gives mass to things" is "I heard somewhere that it gives mass to things, so I repeat that here". What particle physicists mean by that if you assume a background field (the Higgs field) of constant value (which is believed to be a sensible approximation for many scenarios), then the mathematical expressions for the interaction of known elementary particles with this constant background field look like the mathematical expressions commonly called "mass terms". More importantly, they not only look like that but can actually have the same effects (provided some freely chosen parameters are chosen suitably ...). Ironically, the Higgs Boson represents some fluctuations around this constant background, i.e. it is the part of the story that is not responsible for mass-like mathematical expressions. But explaining this doesn't fit into a single headline, where, depending on font size, only "Higgs Boson causes mass" may fit. No offense meant by being cynical.

The zero vector 0 is -in some sense- an Eigenvector to every matrix A and every eigenvalue n, since A0 = 0 = n0. From the little you said (in detail) about how you try to determine the eigenvector, I have the gut feeling you don't really know what you are doing. Take the eigenvalue 1: When looking to an eigenvector to this eigenvalue, what you are looking for are all possible solutions [math]\vec x[/math] to the system of equations [math]A\vec x = 1 \vec x[/math].

Just don't equate "IQ" with "intelligence", then. As you say, the latter is usually a vague hand-waving term (which language has many of), the former is a pretty well-defined measure that anyone not taking it seriously is free to ignore as "just a number". My take: I don't equate "intelligence" with "IQ", per se. But as far as I understand (without actually knowing much about the topic), there are well-established correlations between IQ and traits like "job performance" so I do tend to consider "IQ" a relevant (statistical) property, not just a number.

The electron-proton system contains a kinetic energy term that I expect to be non-zero ("the electron orbits the core"). Hence, I do not think that |E|=|V| is correct.

There are several things in your statement that could be considered wrong. Most importantly, you didn't express yourself clearly and unambiguously: What system are you talking about? What process? What are V and E, respectively? Is it possible to formulate your pseudo-equation in proper sentences?

The energy term in the Hydrogen atom is usually expressed as the sum of the kinetic energy of center-of-mass motion (which can pretty much be attributed to the proton), the remaining kinetic energy (which can be attributed to the electron, as Swansont sais), and the potential energy. The latter is a collective property of the Proton-Electron system, and cannot be sensibly attributed to either of the individual components, in my opinion. Note that the center-of-mass motion if often ommitted, because it's solutions and the process how they combine into the total solution are assumed to be well-known to the reader (which in my experience usually isn't the case).

Just leave the paper out of your publication list, if you don't consider it a proper scientific publication. You're not required to have a scientific publication until you finished your PhD. Hope you enjoyed the conference, at least.

For those whose idol is Sheldon Cooper (poor souls): Being really pedantic one could argue that the mere concept of "a photon's energy" doesn't make sense in the first place in "4 dimensional space-time". The answer to the original question would probably still qualify as "no", though.