Johnny5

Can someone express for me the relationship between the two. I want to do some review. Also, I don't know what latex symbol can be used to represent the Laplace transform, so I'd like to see that. And also the symbol for a Fourier transform as well. Thanks PS: I used to use the Gamma function all the time, but I forget it now. I could google it, but I'd rather discuss it here.

If you want to discuss Fourier transforms with me, I'm up for it. But it's that picture which was used in the derivation that I'm most concerned about, because I never understood how they arrived at the uncertainty principle from the picture.

That's not what I mean. There was a picture in the book, I think of beats, and then some kind of reasoning, using k, and w.

You know, this was one of the first things I thought about this morning. I was running through your construction again. I was also thinking about how to prove (in the Euclidean spirit), that the perpendicular line which you finally drew is tangent to the circle at the given point. You have a given circle and a given point on it. You draw a radius, from the center of the circle to the given point. Now, all you have to do, is construct a line which is perpendicular to the radius, and you're done, you have the tangent. But how would Euclid have concluded that the line you finally constructed is a tangent. That's what I was thinking about this morning. I know he would label everything, but exactly how he would draw the conclusion i don't know. So now, I'm going to see where in Euclid, such a construction is given, and put a link here. It just seems appropriate. Here it is, book three, proposition 17. Euclid's Elements, Book III, Proposition 17 In the proposition above, the given point was outside the given circle, which wasn't this problem, and I don't see this exact problem in Book three.

I want to learn differential geometry as well, because someone mentioned that it would help me do something which I am trying to do. What is it? Regards

Can you explain your question more please?

I don't understand your questions. Do you know what an inertial frame is? If you do, please explain it to me.

Originally Posted by Johnny5 Ok then a followup question. Does classical EM predict this? Alright then lets go slowly, because I have a chance to learn something apparently. Firstly, can you provide a proof for me, that classical EM predicts this. And secondly, I read that certain problems in classical EM exhibit a breakdown of Newton's third law. I would like to see such an example. I remember reading about the Larmor formula, and in my book, there was a comment about something reacting before a force was exerted. I think that alone would demonstrate a third law violation. If you don't have the time to answer, then you needn't. It's just that I really would like to finally understand this. Thank you

It would go like this. Let S denote an arbitrary statement. Let |S| denote the truth value of S. If I am uncertain as to the truth value of S then U ( |S| ) = 1' date=' and conversely. If I am not uncertain as to the truth value of S then U ( |S| ) = 0 Ok so... Let U (X or not X) denote my certainty of the statement (X or not X). I know binary logic, so I know this is the law of the excluded middle for any specific statement X, so that I know that its true, for any statement X, so U(X or not X) = 0 So thats going to hold for me, no matter what statement is used as X. But let X denote a statement about the future, like this one: X = Tomorrow I win the lottery. Well i didn't buy a ticket for it, and I don't plan to, so I don't expect to win the lottery, but I may go out and buy one tomorrow, and really win in the evening. So I don't currently know the truth value of the statement, "tomorrow I win the lottery." I also don't currently know the truth value of the statement, "tomorrow I don't win the lottery" So... U(X) = 1 U(not X) = 1 So it is [i']not [/i] a theorem of the logic I am using that: 2=U(X) + U(not X) = U(X or not X)=0 It can't be a theorem of it. Regards

I am certain of this much though: Either the world will still exist tomorrow or not. You can be uncertain about both things... You can be uncertain about the truth of the statement, "The world will still be here tomorrow" You can also be uncertain about the truth value of the statement, "the world will not still be here tomorrow" There is nothing strange about this, because these statements are about the future. But, you cannot add up your uncertainties of each of the parts, and expect the values to equal your certainty of the whole. Maybe I can say that better later, when I think about it some more.

Ok then a followup question. Does classical EM predict this?

Yeah I figured as much. Sometimes rigor is good, sometimes not. Depends. Let me ask you this, do you personally know how to derive the uncertainty principle from wave analysis? It was in a book of mine, but I confess I didn't follow the argument.

The thing is I don't reify space, so I don't get the whole 'expansion' model of the universe. I can imagine galaxies moving away from each other, but I don't see why you have to suggest that the space is expanding. If you think of space as a vacuum, something that offers no impedance to foward motion, then space cannot expand. Certainly, if a true vacuum were filled with microscopic particles, and formed a fluid, that motion through the FLUID would impede foward motion, but in between two microscopic particles, there would just be vacuum. I think the thing which gives me a sense of relief, is that even experts in the field, who know the formulas, and have used computers to simulate black holes, aren't convinced about the true structure of 'space.' I guess I don't know what space that can stretch is being conceived as. If its a fluid, i can imagine the particles changing position, I just cannot imagine a vacuum stretching. No it's not that I can't imagine it, it's that it is some kind of contradiction. PS re·i·fy (rē'ə-fī', rā'-) tr.v., -fied, -fy·ing, -fies. To regard or treat (an abstraction) as if it had concrete or material existence

Delta X is uncertainty in position, and p is momentum. The thing is there are two relationships for momentum, the classical one p=mv, and the quantum mechanical one p = h/ 2 p l .

How did you get lambda outside of the Uncertainty opertator.

In another thread, I asked how would you locate the center of a given circle, using only a compass and straightedge, and I got absolutely wonderful answers. During that thread, many solutions involved already knowing how to construct a tangent line to one of the points on the circumference of the given circle. I must confess, I don't know how to do it. So here is a related question. Using only a compass, and a straightedge, how do you construct a line which is tangent to a given circle, at a given point on the circumference? Regards

Well in the case where we replace p by Planck's constant divided by wavelength, we get: [math] \Delta x \Delta \frac{\hbar}{\lambda} \ \underline{>} \ \frac{\hbar}{2} [/math] Now the uncertainty is defined using probability theory we have for example: [math] \Delta P = <P^2> - <P>^2 [/math] Realizing that they are integrals, we can just pull out planck's constant and then divide both sides of the inequality by it to obtain: [math] \Delta x \Delta \frac{1}{\lambda} \ \underline{>} \ \frac{1}{2} [/math] You say that if I put in wavelength, I basically get an identity. We have an inequality here not an identity, so you didn't say what you meant. But I am not sure how to interpret the inequality above, nor do I remember how to derive it.