Johnny5

What are you saying?

I think they do both, what do you think?

Severian, if I may, i would like to ask you an intelligent question, which is related to the original poster's question. Why does [math] \sqrt -1 [/math] show up in Schrodinger's formulation? I seem to recall it has something to do with making the velocity of the wave be equivalent to the velocity of the object. In other words, do you know how the square root of negative one ended up in the wave equation? Thank you

That is the Born interpretation right?

I have to go, unfortunately. Yes, I have heard of gravitational waves. Do photons mediate the gravitational force? I will pick this up tomorrow.

slowly, because i know things... Listen to me... Forget about volume being a frame dependent quantity. Focus on the mass. That which has units of kilograms. Why is it called "mass-energy" density, why not just density, or mass density, energy has units of time, we don't want that. Time makes everything complicated. And here is an important question... You said that volume is a frame dependent quantity, is that because of SR?

Do photons mediate the gravitational force?

[math] (p+\rho)U^{\alpha}U^{\alpha}+g^{\alpha\beta}p [/math] [math] \rho+p_x+p_y+p_z [/math] You can hook this up to quantum mechanics if the inertia waves. Rho is the "mass-energy" distribution. Units? Other three are pressures. Pressure how, where?

Here it is. what are the terms called from left to right? i recognize [math]g^{\alpha\beta}[/math] as the metric tensor. I am interested in the momentum flux you just mentioned. Is there a momentum wave? And if so, what is the speed? Does inertial mass wave? [math]U^{\alpha}[/math] What is the letter p, what is the letter rho? What do they denote? I am going to do my linear algebra review concurrently. I will learn faster that way. Keep going. I'm not afraid to make mistakes, mistakes are easily corrected.

cool... this is very cool right or wrong it's still cool, I am going to learn this very fast. I will pay close attention. In the trace above, what are the four terms called from left to right?

Wait a moment here.... Are you saying that in a region of vacuum, the trace of the stress energy tensor is zero, but that if I have a billiard ball in my hand, then within the boundaries of the billiar ball the stress energy tensor is nonzero?

Trace of the stress energy tensor. [math] \rho+p_x+p_y+p_z [/math] Trace of a matrix is the sum of the components along the main diagonal. The first term corresponds to the entry which is related to the time coordinate, the next three are related to the space coordinates.

I took advanced calc' date=' there was a picture for this one... Don't worry about it... Here I found it. Mean Value Theorem Ok that is easy to remember. Tangent is parallel to secant, at at least one point c.

Thanks Let me ask you this, how do you remember that? Let f denote a function that maps the closed interval [a,b] onto the reals. If the function f is differentiable on the open interval (a,b), and continuous on the closed interval [a,b] then there is at least one point c, in the open interval (a,b) such that the derivative at c is equal to f(b)-f(a)/(b-a)

Can you state the mean value theorem please?

Dave... B was just the codomain. (x,y) is an ordered pair. And i have decided to use [math] \exists! [/math] whenever I want to say "there is exactly one," they have the notation, and its rarely used. It minimizes the mental effort required to interpret what is being looked at. Translation: f is a function that maps A into B if and only if For any x an element of A, there is one and only one element y of B, such that the ordered pair (x,y) is an element of f. Dave, I need something using first order logic please. You win. Ok I read this here Mathworld definition of Relation Luckily I know what a Cartesian product is. So let me ask you if you can define 'relation' using first order logical symbols please? I can have a try at is i guess... [math] A \times B = \mathcal{f}(x,y) | x \in A \ \& \y \in B \mathcal{g} [/math] Translation: The cartesian product of two sets A,B, is the set of all ordered pairs (x,y) such that x comes from set A, and y is an element of set B. It is the set of all points in the XY plane. A binary relation from A to B, is a subset of A X B, and A relation on A, is a subset of AXA.

Dave too much all at once. Can you simplify the definition? Forget about relation right now. I don't think you need to define 'function' using 'relation.' I want a string of first order logical symbols' date=' which communicates the idea of function rapidly. Something like this: Presume your student is comfortable with using coordinates to represent points in three dimensional space. ASSUME THAT, but little else. And you want to teach them what a function is, so that they never forget. Now, start out with the special case of XY plane. Now, do me a favor, and criticize my definition here: [b']Definition:[/b] f is a function from A into B if and only if [math] \forall x \in A \exists! y \in B [(x,y) \in f] [/math]

No, I know what it is guys, but WHAT IS IT? What in nature is complex valued?

Oh sorry, i didnt say what i mean... In trying to understand "linear transformation" i got pushed backwards to understanding the meaning of "function." In trying to understand the meaning of "function" i realized I need to express "exactly one." In other words, the final goal is to understand linear transformation fully and competently, but i kept having to go backwards unfortunately. Hoffman Kunze were the authors of the book I was reading. Obviously, I started off reading the chapter on Linear Transformations, and saw what you have basically. I want to never forget this again.