DavidAngelMX

Yes, it is a vector Space indeed. A vector space is a set of vectors associated to a group of scalars which fulfills the next conditions: a(V1+V2) = aV1 + aV2 V1*V2 = V2*V1 ; Vi vectors, a scalar Now, R3 is a Vector field, and the quation you present, which is the equation of an arbitrary plane, is a subspace of R3. In fact, it is the space of all R3 planes.

I agree about the slope, but a slight gust of wind could have helped to break the balance of the ball, leaving the rest of the job to gravity. But I think it's improbable that the gust of wind moved it by itself until it was inside the hole, because then the "slight gust of wind" wouldn't have been so slight, don't you think?

Well, not necessarily, because the alpha decay occurs even though the "potential barrier" that bounds the protons in the nuclei is greater that the energy any of the particles inside the nuclei can ever acquire. The alpha decay is a quantum effect, it doesn't mean that the emmiting nuclei has a lower potential or that the particle emmited had a higher energy that usual, it's just a consequence of Scrodinger's quation, only a probabilistic efect. So radiation emmiting atoms don't necessarily have a higher potential.

Well, let's stay on the field of mechanical waves I don't think this is right, look at it this way: When a sound has a low frecuency you identify as a lower tone(like a bass), and when it has a high frequency, as a higher tone(like a violin). So what you're saying implies that if you go to a concert with a bass player and a violinist, you would hear the violin first and then the bass, and even when you hear it from a long distance, this doesn't happen, otherwise there wouldn't be any big concert houses.

Well, I guess this thread is not interesting to anyone anymore, so, Hasta la Vista

Look, we all know that friction doesn't have to do with imperfect surfaces, but with electromagnetic interactions between the surfaces of the materials, so, if these spheres are made of matter, there should be some interaction, and as a consequence, there should be friction. So, if the friction is great enough to force the small sphere to roll and not slide, and assuming that there is no energy loss when a determined point of the surface of the small sphere is separated from the surface of the other one, then the ball should roll forever, since there is no air friction to stop it, just like the imaginary case of a ball rolling on earth without any friction except for that with the floor. Well... I don't get the idea, I don't think this is a thrilling gravitational event.

Yeah, you got it right. Just don't pay too much attention to the gray face, it's just the standard design for a parallellepiped in ms word

Okay, just lemme know.

Yeah, I agree that the events will happen simoultaneously, and what the observers would see (if the were able to) would really look cool. But still both observers would still be together in the same history.

Look, man, some of the people you´re addressing your question are science students (including me) and-or scientists, and the reason we are is because sometime, and maybe at an earlier age that you, we started making this kind of questions to ourselves and-or other persons, so you should try to be a bit more modest, that is a bliss, believe me, and no one wants a cocky genious. As for the question, my opinion is that, like everything else in physics, lines, as they are summoned in scientific work, are just an abstraction of reality. It is pretty easy for us to understand the space we live in as a three dimensional space where the dimensions are represented by three orthogonal straight lines, and it is also easy for us to think of the distance a body travels (in uniform straight movement) in a determined amount of time as a straight line mapped out by the proportionality constant ¨velocity¨. So lines do exist in our interpretation of the world, but you won´t find any dimensionless straight line anywhere.

Of course I did!!! You wanted a clear solution, there it is. I hope you believe me now and give us some opinions. Either way, it seems like the subject´s been missing for a while, but anyway.

I don't think this part is right. You would travel through time at a different rate than someone in a different inertial frame of reference, but it's not like you would travel to the future and see the future of that other person, it more likely means that, for that other person, your mevement, and your "history" would seem different, and your life would pass at a different rate than his.

Look, first I'll explain a problem like the one I posted first, then the Method of Eigenfunction Expansions and Finite Transform. I know my fingers will hurt afterwards, though. Problem.pdf Eigen.pdf

I don't know how to write any math expressions here, but if you help me out or gimme an e-mail address, you'll get a full explanation, so you can trust me.

Look again, it exists. Method f eigenfunction expansion