timo

PROBLEM: The deviation angle of a photon passing by a simple black hole as described by the Schwarzschild-metric is given by [math] \delta = \frac{4M}{R} [/math] where R is the minimum r-coordinate of the trajectory´s points. This equation is derived as an approximation and I doubt it´s validity for small R a bit for reasons given below. STORY: I´m currently working on a numeric simulation about black holes to visualize some effects of GR. Within this scope I decided to test my results for light deviation against the predicted values. I discovered a huge difference between my values and the prediction: At distances R>100 (M=1 in my case, btw) the values look fine and the relative error <5% is absolutely acceptable. But for smaller R the relative error climbs up to >40%. What makes me especially surprised it that the relative error is a nice 1/R - type plot. Hence, the cause of this difference is almost certainly systematically. My first guess of course was that the cause of this error is my integration routine or the fact that I can´t start the ray at infinite deistance for obvious reasons. But neither reducing the stepsize in my integration by a factor 0.01 nor increasing the original distance by a factor of 10 (1000->10000) made any noticeable difference. Insertion: If anyone here has experience with Python: Do the timesteps I give to the "odeint"-routine have any impact on the result or was the reduction of the stepsize useless because the routine does not care about them when integrating? While slowly running out of easily verificable options where the problem with my code lies I came up with the idea that maybe above approximation which is said to have been verified at a relative error <1% on the sun according to one of my books is completely wrong for small R. My thoughts about that: - Due to the radius of the sun these measurement have been made at R>10^5 so there is no contradition between these experiments and my numeric results. - Above equation is derived by an expansion in 1/r which is cut off (approximation, as I allready said). It seems only reasonable the the higher powers uf 1/r cause a significant difference for small R. - From pure intuition I miss a pi in the equation. I tested 2pi/R which in fact gave good results for small distances but -of course- completely failed for bigger ones. QUESTION: I wrote quite some text for a simple question: Does someone here have experience with GR and can either verify my assumption that 4M/R gives wrong results for small R (preferrably with a better formula + derivation) or convince me that 4M/R must be correct for all R ? Well, I might be able to figure out the question myself within the next week but it´s late in the night and I can´t get some sleep so I can also post my question here as well. Maybe someone is interested in this or has a usefull answer for me. EDIT: A simple test with [math] \delta = \frac{4}{R} + \frac{8}{R^{2}} + \frac{16}{R^{3}} + \frac{32}{R^{4}} [/math] gave great results and pushed the errors way below 1% except for extremely small R (close to the limit of my integration routine). This seems to back up my assumption. Yet, an internet resource containing a better approximation than 4M/R would be still interesting for me.

hmmm... seems to be episode 15 not 10. Nevertheless, the joke about "The engines don´t move the ship at all. The ship stays where it is and the engines move the universe around it." is ... well .... when I´m sitting in my car/spaceship I don´t move but the road/universe moves around me (<- c´mon disbelievers, jump on me allready with your "would take infinite energy" stuff). Sorry, I´m not very serious but I hope this thread wasn´t, too. You seem to have quite a range of interests which leads me to a quote from Terry Pratchett, "The 5th elephant" (this time translating from german to english): "The genius of a whole civilisation seemed to concentrate in this single brain which thus experienced a continuous intellectual flight. God knows what fate had awaited humanity if Leonard had been able to concentrate on one thing for more than an hour."

Admit it: The idea is from the same Futurama episode as the quote in your signature: S2E10: "A clone of my own"

Funny statement for someone with that nick

had to browse through a 23-page thread in another forum to dig it out but maybe it´ll save you some time: http://www.talkorigins.org/ especially http://www.talkorigins.org/indexcc/index.html

^^ agreed @ that. I never realized the links before but now I´ve visited one of the pages the origin of some very obscure threads and posts (especially all those "I don´t understand relativity but I can prove it wrong" ones) here seem clear. PS: Scientist are a conspirative elitist group that that is mainly interested in fooling people to believe their oviously wrong theories because ..... well, they certainly have a reason to do so. EDIT: @swanson: flipacoin.jpg will certainly be an attachment in my next E-Mail I send to a physicist . Also, your counter is broke, i think.

uh, oh ... equation for time?!? Equation for gravity ??? Where did you read that stuff (and in which context?). energy/matter divided by volume is energy/matter density, btw.

I´ve once seen the numbers that a buch of demonstrants against transports of nuclear waste (there are almost always some, at least in germany) emmit a lot more radiation than the actual container

it makes you posting here instead of going to bed ...

Yes. Staying in your picture which comes quite close to reality it would be "no kinetic energy" <=> "T=0K" While Helium is right you have to use more sophisticated methods to obtain low temperatures. See the website I´ll propose below. Don´t know where you heard that and also don´t know what that means. Nevertheless the state equation for ideal gases "pV = NkT" (p:Pressure, V:Volume, N: Number of particles, k: Constant, T: Temp) might help you figuring it out. Proposed reading: I held a small speech about cooling and bose-einstein condensates for 1st semesters about one year ago. While preparing for the speech I stumbled across a very nice webpage that should be easy to understand for non-scientists while it still is accurate: http://www.colorado.edu/physics/2000/bec/temperature.html

To answer thermodynamical questions it is nessecary to know the properties of the system and the properties of the process you´re talking about. In this case, I think this might help you: - An isolated system with variable volume V in an external pressure will expand/compress until the internal pressure equals the external pressure. - Reducing the volume V of a system with a pressure of p by dV increases it´s internal energy E by: dE = p*dV - For an ideal gas (that most common gases can be treatened as) the relation between energy and temperature is: E = 1.5*N*k*T, where N is the number of particles and k is a constant (Boltzmann-constant). EDIT: I think for most "real" gases like O2 you simply have to adjust the 1.5. Proposed process: Increasing external pressure => Reducing volume of the system with positive internal pressure => increase in energy => increase in temperature. Note: - internal pressure does not nessecarily remain constant over the process. - your question lacked a lot (almost all) of nessecary details to be answered correctly. Above is just what I thought that might help you. EDIT2: Oh, I just saw I allready met one of your posts before. Well, this was slightly better but not really good. Try to stick to the [Title: question in short form; 1st paragraph: Introduction what you´re trying to do/find out; Next paragraph(s): What you allready know or think to know about the problem, Last paragraph: Your question] scheme. I know it´s not so easy to formulate questions/answers/texts in a way they´re easily understandable for others. Had to learn it the hard way myself . And I´m still on it which is one of the main reasons I post in forums such as this.

Ever considered that other people don´t know what you think when you´re posting? What is "we usually apply the two techniques"? Does the title of your thread have any meaning? Ok, this is not meant as a flamepost -though I´m very annoyed of people who want to be helped but don´t even take the time to formulate a proper post- so from the little I understood -the little being "he talks about lenses"- you might want to look up "real images" and "virtual images". Real images can be presented on the screen while "virtual images" can only be seen with the human eye because it´s tricked by the lens.

The correct formula would be E = g*m*c², where g = (1-v²/c²)^-0.5. In this formula m is allways constant for a particle since it´s a property of it. If you do a Tayolor Expansion of this formula it leads you to E = m*c² + 0.5*m*v² + X, where X is small for nonrelativistic velocities. Thats the normal Ekin= 0.5*m*v² you might know from basic Newtonian Physics. However: For some reasons some people still use E=m'*c², where m'=g*m. I don´t really know why people use that notation because it doesn´t make much sense for reasons I don´t want to discuss on this board. One reason might be that "E=mc²" is easier to remember. Another might be that this is the one that you allways read in the press. Maybe you can even find some shortcuts for certain conditions with using m'. In this picture m' increases as velocity increases (of course: g increases) so the people using m' say that the mass of a particle increases. To avoid confusion with these two notations one usually calls m the "rest mass" and m' the "relativistic mass" To come back to what your teacher said: If work is done on the particle then, in this case, it´s energy increases => E increases => g increases (all other factors are constant) => m' increases.

I´m not very good at genetics so I can´t judge about your examples. But if I get you right your point was: Homosexuality is evolution. Is that correct?

Well...

Of course homosexuals are abnormal: They´re a minority. What´s your point?

>> Almost all physicists think that gravitational force acts on object and makes it >> have weight and free fall. Almost all physicists know General Relativity which basically sais that there is no gravitational force. Didn´t read the rest of your post but judging from your references I´d guess you were also saying that. If you were saying more than this basic principle of GR then please sum that up in a short abstract (or call me an idiot being too lazy to read your whole post and let it be).

Simpleton, I quickly parsed through your text and ... I don´t have the slightest clue what you wanted to say with your post. Maybe you can sum that up in a few words? I´d guess I´m not the only one who doesn´t want to read through a lot of half-sentences without even knowing where it´s going to lead.

wow, so many replies and noone knew an answer and just randomly quoted some things one reads into newspapers, sci-fi pages and popular scientific books. I don´t know the answer myself -in fact I never even read one page of a scientific paper of theories using more than four dimensions- but I´d guess you introduce new dimension to imbed your 4D-curved space into a flat one like you can imbed your 2D surface of the earth into 3D by maping it on a sphere. Just a rough guess, like I said. ´

Well, maybe you could tell us what you want to say with this post? - Do you want to know if your calculation is correct? Well, black holes only appear in general relativity as a coordinate singularity. As I allready said in another post there is no forces due to gravity in GR. Calculating celestial problems with Newtonian Physics (forces) is ok as long as gravitational fields are not too strong. But the Schwarzschild-radius you picked is one of the points where Newtonian Mechanics ultiamtely fails. That´s why it became so popular. - Did you want to show something with that calculation? For example what is the greatest force due to gravity that can exist? The term "strongest possible force" is almost certainly incorrect. You could locate two charges at any distance you want exceeding any force if the distance is small enough. Also "strongest gravitational force" would not be correct because in your picture nothing would prevent you to add further black holes in a way that the two forces add up to a bigger force (triangle). - One thing I didn´t understand but what would really interest me. Given two equal black holes at a distance of twice their Schwarzschild-Radius: What makes you think they´ll merge into one at this point? Why not at smaller or greater distances? Why at all? -> Is that what you intuitively think? Yes, it would be intuitively clear. But things like the Schwarzschild-radius are not intuitively understandable anyways. -> Did you read that somewhere in the internet? If yes, what did the original poster say about that? -> Do you have a scientific proof for that? I really don´t know if someone did a relativistic calculation of such a system, but I´d be very interested if there´s one. On the one hand there is no known general solution of the Einstein-equations but on the other hand there are many symmetries that can be used so there might be one.

I´d rather wonder where you use forces in modern/theoretical physics. Only part that uses forces that´d come to my mind right now would be Newtonian Physics which is a bit outdated (about 100 years). About calculatong the force without knowing the mass: Yes, you could construct problems like "I know the momentum p(t) of my particle for all times t. What is the force working on it?" => F = d/dt p. I wrote a paragraph about "F=ma is an axion in Newtonian Physics so it´s allways true while in this scope". But then I decided to look it up in my very good handbook of physics and it said: 2. Newtonian axiom: F = d/dt p (allready used that in the previous paragraph). If the mass is constant, then: F = d(mv)/dt = m * dv/dt = ma.

yes, but it´s also what all measurements say (the michelson-interferometer was the 1st experimental setup that led to this assumption, in case you want to look it up).

the scientist i know the most is my ex-girlfriend

my ex for obvious reasons

Define "travel faster than light speed globally"! The answer is probably quite obvious, then.