Johnny5

I already had one in mind Tom, or Thomas. (x-2)(x-2)=x^2-2x-2x+4=x^2-4x+4 Start with: x^2 - 4x +4 = 0 The degree is 2. By the meaning of two, there are two roots. The only root is 2. So there is only one root. Thus contradicting the hypothesis that there are two roots. QED Did you see this coming? Regards PS: by the way i didn't use all that logical power to find a counterexample.

Well lets see, here is your answer to part e: Let V® = -ke/r. Now compute the gradient of V®. Ñ V® = ¶V /¶r r = ¶(-ke/r) /¶r r = -ke¶(1/r) /¶r r = -ke(-r-2) r = ke/r2r Since E = -Ñ v It follows that: E = - ke/r2r Which is the electric field of an electron, at the origin of a reference frame. The force on a positively charged test charge, with charge Q, is given by QE, hence we have: F = - kQe/r2r The negative sign implies the force is attractive, since Q, and e are positive. Ok so we have the potential of an electron, as a function of r, namely: V® = -ke/r Now, suppose we add the constant ke/r0 to V®, to obtain: V® = -ke/r + ke/r0 When we take the partial with respect to r, we get the same gradient function as before, hence the same electric field. But clearly, when r=r0 the potential is zero, that is: If V® = -ke/r + ke/r0 then V(r0)=0 So r0 is a point in the field where the potential is zero, as you can see. It cannot be the origin, because that is division by zero error, unless the charge unit e, is zero inside the electron.

See this is the kind of answer i want to read. By saying that there are frames that aren't rotating, you are saying that rotation is absolute. The formulation of the statement, is as if that is the case. Yes, rotation is absolute. There is a mathematical relativeness to it, but when you are talking reality, it is as you say. I just don't want to be in the minority here, and don't bail on me. For quite some time, I've been trying to develop the logic necessary to discuss rotation as an absolute. There has to be some element which is beyond the mathematical treatment of it.

It's not necessary to start the thread off with a massive amount of mathematics. I was hoping to slowly move from simple things about rotating frames of reference, to the math. Hopefully we can both avoid headaches, although matrices are not that complicated, but certainly if you aren't familiar with linear algebra, you dont have a chance at understanding rotation explained in terms of matrices. However, and this would be my point, I think anyone can develop an intuitive understanding of rotation, without knowing matrix algebra, which is the reason I started off this paragraph by saying, "it's not necessary..." So don't worry about matrices for now.

Here is hyperphysics on parallel axis theorem

Here is an article at Wolfram about rotation. In the article you will see mention of a rotation matrix. I'd like to discuss this particular article, with a view in mind to answer the question, "is rotation absolute or relative." This is going to help me in my ongoing analysis of precession, and things like Foucalt's pendulum. I am hoping to learn something new, and resolve a hundred or so unanswered questions of mine. The article starts off with what is a very important statement, as regards the mathematical analysis of rotating frames of reference. The article begins: I do not see them as conventions. Something deeper, which involves the very meaning of "inertial reference frame" is going on. There may be some kind of mathematical equivalence between rotating objects in stationary coordinate systems, and stationary objects in rotating coordinate systems, but there is a physical difference. My point is this, I don't think the mathematical treatment brings out the physics of rotation. If you read down into the Wolfram article, which is extremely well written, you will notice the following: Somewhere in the Euler rotation theorem lies a connection to the aerospace concepts of: yaw, pitch, and roll.

Dr. Swanson, is there any standard terminology for what I was referring to? "Proper time" doesn't seem quite adequate, since I am referring to a property of clocks, not a property of time. If I am being unclear, I know how to remedy that.

That's not what I thought it was' date=' maybe I was thinking of something else. Let me see if i can find what i was thinking of. Here is what i was thinking of, i got universal turing machine confused with universal truth machine. When you said Godel that threw me off. Godel's universal truth machine There is an error in the reasoning Godel used. At any rate that doesn't appear to be what you were talking about. Also, if you have a link to what you read at Stephen Wolfram's site, I'd like to have a look at it. I went to the link you posted, and saw mention of three kinds of "Universal Turning Machines" Regards

If I may, i think i know what might be constructive. According to history, the mathematician Gauss proved that every integral rational equation of degree n, has exactly n roots. Apparently, so the history books say, one of his proofs was his dissertation for his doctorate. He gave three others. Now, I have never even seen one of these supposed proofs. So i challenge anyone, to produce a proof of that which is italicized above. If such a proof is successful, it must be the case that: x^2+1=0 has exactly two roots, and they will be +i, and -i. So if the proof doesn't contain any errors, then imaginary numbers will be justified. I suspect though, that there is a logical error in all four of Gauss' proofs.

That's right.

This question arose in post 17 of http://www.scienceforums.net/forums/showthread.php?t=11414from It was off topic so I'm moving it here. At the center of universe the gravitational potential should be at maximum' date=' the sum of gravity forces is zero.[/quote'] All I really meant was that if you put something at the center of the universe, the net gravitational force on it should be zero, and thus it will remain at rest there. I believe it was Sir Isaac Newton who proved this. In order to prove that at the center of the universe the gravitational potential should be a maximum, you have to use gravitational field theory. If and when Latex is working, perhaps I will check what you say by doing that. First you have define gravitational potential, analagous to electrical potential, and go from there. Mathematically speaking, its really easy. You even come up with the idea of objects which gravitationally repel each other. Mach's idea. Just postulate negative inertial mass.

The edit time has been changed to six hours. After you make your post' date=' it is editable for only six hours. As for your last posts, the main thing I see is that the idea of a hypersphere goes against so much classical physics, as to be the source of endless problems in the conceptualization of relative motion. The sheer number of problems caused, suffices to indicate that the universe is not hyperspherical. The motion of the ship has to take place in some frame. If there is no frame of reference that this can happen in, its over for the idea. If an object travels in a straight line, then the direction of its motion cannot change, and if its speed is constant, it will not return to where it was, [i']intuitively[/i]. If it does manage to return to its starting point, the rational conclusion is that its direction changed, hence it was accelerating. So therefore, the one who defines a hyperspherical universe, needs to state whether or not the direction of motion changes, in this example problem. That is, they must explain the frame in which the motion is to be analyzed in. They will undoubtedly find that their definition is riddled with contradictions.

I haven't had the chance to read the whole article, but I read enough to know that the author intends to be taken seriously. In the part I read through carefully, he is discussing braking radiation, and comparing light emitted by electrons, when they are accelerated, and comparing inertial accelerations, to gravitational accelerations. I've been aware of a problem there for a very very long time. I'm not sure if he is mathematically saying something I already know, but the very fact that he is thinking about the issue, shows that he understands the location of a problem with the EEP. There is something to his article. Regards

Hold your horses. What is meant by "universe can run on a universal Turing machine"? That's one question I have. I read about this awhile back, and figured out how I would approach the problem. (Godel sentence, and rules of how a UTM works. As I recall, the Universal Turing/truth machine, spits out true sentences when you ask it a question, but there is some kind of sentence which confuses the machine.) The second question I have is this... How do you connect the first question, together with the meaning of 'determinism" to loop quantum gravity? So those are my two questions. Regards

Actually, the dot product method must be correct. But I'm not sure why the other approach didn't work yet. Im gonna figure it out and fix it tomorrow.

I don't fully comprehend his explanation either. I don't think he does either, so that makes three of us. I would start of questioning his first sentence "Quantum mechanics works." There are different interpretations of QM. I think that's a source of confusion. A question I would ask him though, is what is meant by 'determinism.'

I am going to try your suggestion and see what happens. Here is the formula for the dot product of two vectors: U*V = |U||V| cos(U,V) If U is perpendicular to V, then the angle between them is 90. Cosine of 90 degrees is zero. Now, here is what you wrote for his part a: Ok, I drew a picture to help me understand what you wrote up there. Pretty much the same formula I used. I have R(t), for position vector, you have C(t), for location of a point. In your formula there, i take it that is vector B minus vector A, times t. So they appear to be the same formula. Now, we need to find a vector from the origin O, to a point P on the line, such that vector OP is perpendicular to the infinite straight line through AB. Your idea is to use the dot product to do this. Let me pretend I already know the answer. So here is the answer: OP = Xi + Yj + Zk Now, here is the vector, which lies entirely on the line, through the points A,B: AB= <10-1,10-(-5),5-(-7)> = <9,15,12> = 9i + 15j + 12 k (I got that from post #2 in this thread) So these two vectors will be perpendicular iff their dot product is zero. They are perpendicular, hence: 0 = <X,Y,Z>*<9,15,12> Therefore: 0 = 9X+15Y+12Z Now, here is the formula (again) for arbitrary position vectors to points on the line: R(t) = <9t+1,15t-5,12t-7> (I took that from post #11 in this thread) So we have: X(t) = 9t+1 Y(t) = 15t-5 Z(t) = 12t-7 Hence: 9X(t) = 9(9t+1) 15Y(t) = 15(15t-5) 12Z(t) = 12(12t-7) So that we must have: 0 = 9(9t+1) + 15(15t-5) + 12(12t-7) As a constraint on parameter t. So therefore: 0 = 81t+9 + 225t-75 + 144t-84 So therefore: 0 = (81+225+144)t+9 -75 -84 So therefore: 0=450t-150 So 150=450t 15=45t 3=9t 1=3t hence t=1/3 hmm ok somewhere there is an error.

Do it in your head, Dave does.

Its ok. I don't fully understand the German. Or have I went not kapiert? Also, do you want the other questions answered? Question b is really quite interesting. You want the vector with the minimum length that runs from the origin of the frame, to the straight line in question. There is a unique answer to this question, for any randomly chosen line. O is the origin of the frame, and has coordinates (0,0,0) P is a point on the given line. Here is a formula for all vectors which extend from the origin to points on the line: R = <9t+1,15t-5,12t-7> = <x(t),y(t),z(t)> The above is a position vector, which means that its tail is at the origin of the reference frame, and the tip lies on the line in question. Using the pythagorean theorem the magnitude of R is given by: |R| = [ (9t+1)2 + (15t-5)2 + (12t-7)2 ]1/2 Which implies that: |R|2 = [ (9t+1)2 + (15t-5)2 + (12t-7)2 ] Differentiating both sides with respect to t yields: 2|R| d R/dt = 2(9t+1)(9) + 2(15t-5)(15) + 2(12t-7)(12) Minima at dR/dt=0 0=(18t+2)(9) + (30t-10)(15) + (24t-14)(12) 0=(162t+18) + (450t-150) + (288t-168) 0= (162+450+288)t +18-150-268 0= 900t +18-150-268 0= 900t -400 400= 900t 4=9t t=4/9 R(t) = <9t+1,15t-5,12t-7> R(4/9) = <9(4/9)+1,15(4/9)-5,12(4/9)-7> R(4/9) = <5, 5/3, -5/3> Here is the answer for part b: 5i + 5/3j - 5/3k Regards