Johnny5

Do you remember the thread title of the other one?

Yes I see it here:

yes i can use radians. Even steradians You say that the photons from the sun have a negligible effect on an orbital path, and of course my question is whether perhaps it is those photons which are responsible for that path somehow. Immediately, you started talking about photon mass, and how it's so miniscule that a photon cannot be responsible for gravitational force. I know radiation pressure is slight. When I turn on the lights in my house, it is not the case that the expanding sphere of light pushes my head backwards. Yes radiation pressure is slight, but nonzero. As I read that, the principle of equivalence came to mind. There is the weak equivalence principle, and the strong equivalence principle, I don't remember them usually. But of course I am trying to learn something which I don't yet know, so i have been reading up on GR lately. Here is where I remember reading about them last: Wikipedia article on equivalence principle (by the way, the article has changed since the last time I read it) It's the strong equivalence principle I'm thinking of. Wikipedia has it in words. I believe it means the same thing as SEP: Gravitational mass = Inertial mass So Martin here is my question... If the principle of equivalence is false, might it be the case that photons emitted by the sun are responsible for curving the path of the earth around it? Now I will try and answer your question. [math] R_0 = \frac {GM}{c^2} [/math] Let me check the units first G has units mmm/Kgss M has units Kg c has units mm/ss GM has units mmmKg/Kgss = mmm/ss GM/c^2 has units (mmm/ss)(ss/mm) = m Ok yes units of distance, meters. So R0 is a length. You say that the angle it will be bent is 4R0/R. Hmm. Well assuming that this angle formula thing is right, the answer is: [math] G = 6.672 \times 10^{-11} \frac{m^3}{Kg s^2} [/math] [math] M_{sun} = 1.988 \times 10^{30} Kg [/math] [math] c = 299792458 \frac{m}{s} [/math] Therefore: [math] \frac{GM}{c^2} = \frac{(6.672 \times 10^{-11})(1.988 \times 10^{30})}{(299792458)^2} = 1475.8 [/math] So the units are meters, R0 for our sun, is 1475 meters. You give the radius of the sun as 700,000 Km. You give the perpendicular distance at which photons from the Plieades passed by our sun as 800,000 Km. So in that angle formula thing, which you stated without proof, the value of R would be umm, R is the distance from the center of our sun so... R = 800,000 Km, = 800,000 X 1000 meters [math] 4R_0 = 4(1475) = 5900 [/math] [math] \frac{4R_0}{R} = \frac{5900 }{800,000 X 1000 } = \frac{5.9 }{800,000 } = 7.375 \times 10^{-6}[/math] That is the answer I get to your question Martin.

That makes no sense. Here is the formula for the one, in terms of the other: [math] C = 2 \pi R [/math] If the circumference C increases, then the radius R increases, since the value of pi is constant in time. If the circumference C decreases, then the radius R decreases, since the value of pi is constant in time. The equation has to always be a true statement. If either C,R varied, but the other didn't, a false statement would be true. Regards

I want to make sure I'm reading this right... f is a function which maps the inverval from negative pi to pi, onto the reals?? Also, does it matter whether or not n goes from 1 to infinity, shouldn't that be minus infinity to infinity. When I took PDE's I derived that formula which you posted including the constant term a0/2, which is outside of the series. I'd like to do it again. There were some integral formulas, sine's weighted by sines and cosines, I don't remember them anymore. As I recall, the derivation did make sense after I verified four true statements about integrals of sine times cosine, and so on... I don't know how anyone figured it out, but I did verify the four integrals first, and then the rest just followed... as I recall.

The radiation pressure yes I've seen it. Perhaps the photons carry with them two effects?

Thank you very much for this answer Meir... Perhaps you can answer me this... Would the circumference of the closed polygon be decreasing, as the rotational speed is increased? GR or SR...

I have, I wanted to know what your mind thinks. Regards My answer's are these: 1. Don't know. 2. Don't Know. 3. Don't know, probably discrete. 4. Quantized.

Zeo... You cannot travel to the past, because it is logically impossible, and that which is logically impossible, is impossible. Regards

I want to refresh my memory of fourier series. Can anyone explain what a Fourer series is for me? Thank you

I want to know if the photons which the sun emits, are responsible for the path of earth's orbit around it. The sun is for certain emitting photons, and they must leave the sun at a speed 299792458 meters per second relative to the sun. They are emitted in many directions, roughly in a spherical shape. So the region of space surrounding our massive sun, is filled with the photons which the sun is sending out. So could these photons be solely responsible for the orbital path's of the planets? Thank you PS: If the answer is yes, then the speed of gravity is c.

Suppose that I have a 'loop' with spokes, attached to a motor. Let the ring be a regular N sided polygon. Therefore N>3. Might as well analyze the simplest case. Let N=3. So the polygon is an equilateral triangle. There are three spokes, and they meet at the center of inertia of the triangular loop. Let the perimeter of the equilateral triangle be one meter. Therefore, the length of any side is 1/3 of a meter. (incidentally you can tessalate a plane with equilateral triangles) Ok so this object is going to start spinning. Suppose that the Lorentz contraction formula is a true statement. Here is my question. What is the radius of the equilateral triangle, as a function of its rotational speed w ? Thank you PS: You can assume that the wire which this contraption is made out of has a uniform density r , when it isn't spinning. Now, you cannot assume that the wire is a rigid body, because that contradicts the LCF, which this question has you assuming is true. So you will have to deal with that some other way.

Martin, there is a purple picture at the very beginning of Rovelli's online book, what is that? Does it have any relationship to LQG?

1. What is an electric field? 2. What is a magnetic field? 3. If |E| denotes the magnitude of an electric field, is |E| a continuous quantity? 4. IF |B| denotes the magnitude of a magnetic field, is |B| a continuous quantity, or a discrete one?

I want to derive the formula for the inverse Fourier transform. Does anyone know how to do this? Thank you PS: I was looking at this site here , and they talk about convolutions. I don't know if convolutions would help or not. I remember using the convolution theorem, but it's been awhile.

In this post, I'm going to attempt to understand the derivation in that link you gave, thanks. OK I am starting with the: Bromwich Inversion Formula The derivation begins by stating the definition of the Laplace transform of a function of t: Definition (Laplace Transform): [math] \mathcal{L} [ f(t) ] \equiv \int_{t=0}^{t= \infty} f(t) e^{-St} dt[/math] Now, in the attached derivation, the author uses the letter p, instead of the letter S, but because I used the letter S earlier in this thread, I am going to stick with S. In the attachment, the author states that p is a real variable. A real variable, is a symbol which when instantiated, must be instantiated with a real number. In other words, a real variable is a symbol which denotes a real number, but that symbol is to be considered a variable quantity, and not a constant. Apparently, the crucial step in deriving a formula for the inverse of the Laplace transform, is to allow S (or p in the attachment), to range over the complex numbers. Recall that the real numbers are considered to be a subset of the complex numbers. We can write this as follows: [math] \mathbb{R} \subset \mathbb{C} [/math] So the assumption which this entire derivation appears to be founded on, is the following: [math] S \in \mathbb{C} [/math] That is read, "S is an element of the complex numbers" Recall that a complex number is usually expressed in the following form: [math] a + bi [/math] Where a,b are elements of the real number system, and i denotes the square root of negative one. The chief difference between the complex number system, and the real number system, is that the real number system is ordered, and the complex number system is not. In other words suppose that x,y are elements of the real numbers. The the following statement must be true: (x<y XOR x=y XOR x>y). But now suppose that x,y are arbitrary complex numbers... it is not necessarily true that (x<y XOR x=y XOR x>y). It must be true if the two numbers chosen happened to be real numbers, but it probably isn't true if the two numbers both have nonzero imaginary components, and are not equivalent. You wont be able to say the one number is less than the other. This fact stems from a contradiction that arises when one assumes that i is a number, but I won't go into it right now. Let me continue trying to follow this man's derivation of the formula for the inverse of the Laplace transform... He continues by saying this... "By assuming that p (in our case S) is complex, we can use the known formula for the inverse of the Fourier transform." My question would be, "known to whom?" Apparently, he has pushed the derivation of the one, onto the derivation of the other.

Swansont... Is the wave something physical? What is doing the waving, in the case of light?

Yes, the center of mass of earth+inhabitants will continue in its roughly elliptical path, as if they had never jumped. The earth will buck slightly one way, but for all intent and purpose, the earth can be considered infinitely massive compared to the mass of the people, and they can jump up and down all they want, there will be no effect which is measurable.