timo

"Logarithm", if I understand your question correctly. Same way as the result of a summation is called "sum".

He's banned.

Let's assume the increase of infant mortalitiy rate in the US (6.3) compared to Canada (4.8) is largely due to the fact that teenage mothers (share being 0.17% vs. 0.06% according to the numbers jryan linked to) have an increased probability X for infant mortality. Then, approxmately [math] \frac{(1-0.0017) + 0.0017X}{(1-0.0006)+0.0006X} = 6.3/4.8 [/math]. Feel free to do this calculation properly; I'll simplify it and claim that Canada has no pregnant children, so [math](1-0.0017) + 0.0017X = 6.3/4.8 \Rightarrow X = \frac{6.3/4.8 - 0.9983}{0.0017} \approx \frac{0.2}{0.002} = 100[/math]. According to this idea, the infant mortality rate for teenage mothers has to be more than 100 times that of adult mothers!

I doubt it.

That is not what "virtual particle" means. If you insist on the term virtual particle having a meaning other than being a factor in a Feynman diagram, then one could probably say that a virtual particle is one for which there is a mismatch between mass, energy, and momentum.

Your description is a bit scarce. Which level of education? Where is "here"? What information exactly? etc. Since you seem to have nothing right now, an interesting starting point for you might be the PISA studies. But it only measures performance which may or may not be what you are looking for.

My advice still stands: - obviously, a term h² is not going to kill you (now). It's what you were expecting, anyways. - for the rearranging, note that a*h + b*h = (a+b)*h. In other words: bring everything on the left-hand side, then sort the terms by their powers of h (i.e. terms with an h², then those with h, then those without h), then you pretty much have the form I proposed and can start with the messy part of the problem.

Do I have to publish the password to my homepage so that everyone can edit it? Or my password on arXiv, in case someone has a different opinion on my personal data that he wants to communicate to the world?

Well, I was brave enough to open the pdf: http://www.nature.com/ng/journal/v41/n12/abs/ng.478.html (you can/should probably delete the attachment now)

Several measurements are linked to in the Wikipedia article on "speed of light". With 134 references within this article (not all on measurements, of course) you should have plenty of material to browse through. Since I have good experience with the webpage (on other topics) I can also recommend the first hit (after WP) on Google: http://www.colorado.edu/physics/2000/waves_particles/lightspeed_evidence.html EDIT: Forget the above. I was somehow thinking you were looking for information how the speed of light is measured. In principle, you can of course test if it is constant by repeating the measurements under different conditions, e.g. by moving your laser source around.

As someone whose computing resources also serve as a Tier-2 node for LHC, I agree with "huge amounts" more than I do with "useful"

It's certainly debatable whether a lot of money should be spent for fundamental research with little or no obvious application. And LHC no doubt is very expensive compared to the average university's backyard experiment. In my experience, it's not someone making a lot of money there, but a lot of people making some. What exactly do you think LHC is trying to find?

Me neither, I've never really bothered about atomic models of the past. But since I encounter terms like "Bohr model" or "Rutherford model" rather often on sfn, perhaps Tom can give a very short overview here.

Your understanding is wrong. 1) The term "de Brogile wavelength" should be thought of an anachronism from the time before QM was developed. The modern name would simply be "wavelength" (the addition "de Broglie" merely emphasizes the big surprise that matter can have a wavelength, which of course everyone familiar with QM knows). More importantly, "wavelength" is something that is usually attributed to free particles, not to bound states as this one. In particular, the wavelength of an hydrogen atom would [the way people would usually understand it] be something completely different than a property of the electron circling around the proton. 2) What you are probably referring to is something like the possible wave functions for a particle in a 2D plane which is constrained to the circumference of a circle with radius R. There, the wavelength is constrained to be the circumference of the circle divided by some natural number (or formally infinite). But: 2.1) There is no R for which no solution exists. There also is no mechanism which restricts your "wavelength" (term put in quotation marks here because of 2.3). So in principle, every "wavelength" is possible. So in principle, every radius is possible. Only the combinations have to fit. 2.2) The energy eigenstates, i.e. the orbits, are not a single of such fitting combinations, but a superposition. In other words: an orbit does dictate the probability distribution for finding the electron at a certain distance from the proton. But it does not fix the distance to a unique value. 2.3) Hydrogen atoms are usually considered to exist in three spatial dimensions, not 2D. Not much of a conceptual change here (you merely need to replace the discrete wavelength with the discrete spherical harmonics), but you should probably be aware of it.

It would be good for using the quadratic formula. Comparing with "something * h² + otherthing * h + rest = 0" which I wrote before you'd find that something = k(-l-L)², otherthing = mg, rest=0. But I doubt that your term k(-l-L)² * h² - mg * h = 0 is correct. You should probably show the individual steps how you got from mgh = k(h-l-L)²/2 to k(-l-L)² * h² - mg * h = 0. I am sure someone will be able to point out the mistake you made there. Hint: [math] (h-l-L)^2 \neq (-l-L)^2 \cdot h^2 [/math], for example for h=1, l=0, L=0.

The starting point for the quadratic formula is "something * h² + otherthing * h + rest = 0", so rearrange your equation into this form. A rather obvious first step seems to be multiplying out the (h-l-L)² term, I think.

Proof-read it to get at least the most obvious spelling and grammar errors out. That's the very least you could do before asking other people to invest their time to help you. Apart from that: if that is really supposed to be a kind of thesis, you are possibly in for a huge load of extra work. What's the text for, exactly?

Of course. The Geodesic Equation. The mass doesn't even explicitly appear there. What does appear though is the connectivities (edit: I am not completely certain that "connectivities" is the correct English term; WP seems to call is "connection coefficients"), usually called [math]\Gamma[/math], which describe the local structure of spacetime (in the current coordinates), and can be considered something akin to the gravitational field in Newtonian Gravity.

sfn (but lately about half of the posts here are by people on my ignore list, so it's getting a bit boring) www.spiegel.de (it's news, it's free, it's pretty crappy) google c++ related question (always the same ones because I can't remember the answer from last time) downloading articles for print (and never read them) check who cited my papers (no one does) buying train tickets (instead of buying them at the train station where I don't have to provide my personal details like my phone number for a f... train ticket). I wonder how I could survive before the internet.

He did.

The keyword is gravitational redshift. I think the whole concept of gravitational time dilatation is actually rather easy to explain in your scenario (assuming 1 space dimension plus one time dimension for simplicity), so I'll give a try: You have two locations x1 and x2 and a coordinate time t, If you go some coordinate time interval dt forward, then at x1 a proper time tau1=a1*dt passes, and at x2 a proper time tau2=a2*dt passes. Proper time is the "physical time", or "ageing" (both terms are not technical terms, but probably more meaningful than "proper time"). It is the correct time to use for the description of physical processes in the sense that it is not relative. The factors a1 and a2 depend on the gravitational potential (to stay Tom's terminology). Finally, let's assume the gravitational potential does not change with coordinate time (it does of course change with location). Everything ok so far? Then let's go: Gravitational time dilatation: Assume some event happening at x1 takes a coordinate time dt (meaning that at x1 a proper time tau1=dt*a1 passed) and emits some photons. Since the gravitational well is assumed not to change over coordinate time, all of the photons take the same amount of coordinate time to travel from x1 to x2. The distance in coordinate time between the first and the last photon will be dt when they arrive at x2. So at x2, the process is seen to take a proper time tau2=dt*a2. So at x2 the process seems to take a factor tau2/tau1 = a2/a1 longer than at x1 (btw. if you want to plug in numbers for the Schwarzschild metric, a1 and a2 are the square root of the entry [math]g_{00}[/math] of the metric). Gravitational redshift: The redshift effect can be easily explained by the dilatation effect. Assume you are sending some monochromatic laser light from x1 to x2. At x1, the time for a certain number of oscillations (e.g. a single one, i.e. the inverse frequency) is tau1, which again corresponds to some coordinate interval dt. Again, this interval dt will be the same when the laser light reaches x2. Again, x2 will perceive a proper time tau2=a2*dt for this amount of oscillations. So again, tau2/tau1 = a2/a1. So the amount of proper time the oscillations take at x1 and x2 are different. And so are the frequencies f1 and f2, then: f1/f2 = a2/a1. And since the frequency of light is perceived as color, the color of the light arriving on x2 will not be the same as it was when it was sent out at x1. Note that in none of the two cases above, energy was explicitly taken into account. The commonly-known relation of converting potential energy into kinetic energy (or vice-versa) when climbing up or down a potential well is somewhat implicit here: a1 and a2 are related to potential energy, and the frequency of light is related to its kinetic energy.

Making a problem that already is over your head more complicated does not necessarily prove your point or help understanding. I think from a scientific viewpoint my answer to the original question, an explicit example how we could notice a difference in the passing of time, is more than Paranoia could have hoped for on sfn. I don't want to spend time explaining to you (Michel) why the transfer process is irrelevant in this case.

No. That's not the standard point of view. Also, the term "time" is slightly ambiguous, anyways. The closest you get to "physical substance" is possibly the concept of ageing, which is called "proper time" in the context of relativity. It is a real physical property in some sense (in particular in the sense that it is not "relative"), but not a substance. That's cool as long as you don't run around claiming you knew better than the professionals because of that. And that your ideas are actually the sages' stone, and all those idiots disagreeing with you merely lack the creativity/intelligence/karma to realize that. Believe it or not: not only do such people exist, they are in fact rather common on the Internet. About what I wrote? Yes, except for grammar and some words (e.g. "attic") that I had to look up in an online-translator. Yes. Unless you want to get philosophical, because ultimately light has to do with taking a shower, of course. Anyways: I already had my doubts that my post could be a bit hard to understand when I wrote it. The problem is that this fixation of people on the action of visually seeing things is so strong that question like the one in this thread are "would we see X" rather than "would X happen". That makes it hard to give answers because what actually happens is relatively easy to describe but not what was actually asked for. And answering what is literally asked for ("what we see") is possibly not helpful, since it distracts from the crucial point. I tried to answer both. But seeing that it did seem to cause confusion, I've rewritten it.

Absolutely. You'd think twice whether to store your potatoes in the cellar or below the rooftop. The whole issue has nothing to do with light at all (except that light is the most common method for observing things). It only matters where you store your potatoes, not whether you leave the light on or not. You can think about what you visually see, but that's merely an additional level of complication, and not what is meant by time passing differently. It may be somewhat surprising that light has nothing to do with relativity considering that the "speed of light", the maximum speed possible (with some restrictions), seems to play such a prominent role. The reason is historic, I believe. Light was known to travel with this speed before it was realized to be the maximum speed. So it was called "speed of light". Had that not been known by the time it was discovered to be the maximum speed, it would probably be called "maximum speed" today - which is probably a more appropriate name. Ignoring the process of bringing the potatoes into or out of the cellar/attic, which takes very little time, anyways: Yes, you'd see the potatoes rot with at a different rate. And in some weird color, too. EDIT (new version, hopefully less confuing): The potatoes do rot with a different rate in the sense that if you leave some lying around in the attic and some in the cellar for some time and then bring both bags into the kitchen, you'll find that the potatoes in the two bags will have aged differently. There is no light or "seeing" involved (imagine measuring the water content and giving it out via a speaker if you want to be really anal about the "no seeing involved" - it's not going to change the fact). Now, of course you could insist on watching your potatoes through your glass floor/ceiling while they rot in the cellar/attic. In this case, the striked-out sentence above would apply, i.e. you would observe them rot at a different rate. The effect why you see them rot at a different rate is not due to the transmission of light, though. That merely adds an additional layer of complication. To re-emphasize this point: Light has as much to do with time dilatation due to gravity as it has with the mechanical stability of the house you live in.