Johnny5

Who, invented the mathematical idea of cross product, and in what year? Why did they invent it, and how did they do it? Thank you

I meant a real experiment, not a "thought experiment." Keep in mind, that in order to invalidate the Galilean transformations, you do not have to prove that the Lorentz transformations are correct, it would suffice to show that the Galilean transformations lead to a contradiction. At any rate I will have a look at that link in a little while. But, in the meantime, I would ask you only one thing, if time must dilate according to the formula found in the link, must length contract according to the Lorentz contraction formula?

What experiment proves they are inadequate for anything besides low-speed phenomena? And when I say prove, I mean prove. That means there can be no error in the interpretation of the experimental results. I am setting aside Maxwell's wave theory for now.

I didn't take it from Zeno, but it is similiar to Zeno's paradox of the runner, shown in this article, also called the dichotomy paradox here. I am also familiar with the mathematical analysis of the race between Achilles and the Tortoise, and his arrow paradox. Which of Zeno's paradoxes are you thinking of?

How did you draw the conclusion that the Galilean transformations do not work?

What exactly is a "non-accelerating frame"? I guess here is what I want to know. Is an inertial reference frame one in which Newton's first law is true, or one in which all three of his laws are true. Which do you say it is?

That's a good objection, if it's correct. What is wrong with the transformations then?

Ok let S denote an inertial reference frame. Now, let a photon be traveling along the x axis of S, in the direction of increasing x coordinates. Now, let S` denote a reference frame in which the photon is at rest. Let the origin of S` be the location of the photon. Let S and S` be in standard configuration. That means the positive x rays of both systems are parallel and point in the same direction, and the positive y rays are parallel and point in the same direction, and the positive z rays are parallel and point in the same direction. Let the origins of both frames coincide when t=t`=0. Here are the Galilean transforms: x`= x-ct y`=y z`=z t`=t So the axes of S` aren't spinning in S. From which it follows that S` is also an inertial reference frame. Kind regards PS: If this is insufficient, tell me what your objection is.

Well if you understood that proof, tell it to me. I am also checking google right now. Well I found this: The italicized part indicates the reasoning. The reasoning is wrong.

The appropriate category for this is classical electrodynamics, but there is no category here for that. But since relativity comes out of EM, I figured I would put it here. My question is quite simple. I want to know if this propulsion system will work or not. Construct a solenoid. Wrap a wire around a cylinder N times. Now place an iron ring around the solenoid, and then connect the leads to a battery. There will be an induced EMF in the iron ring, and the ring will be launched into the air. Jumping ring demonstration. So something is pushing that ring up, in the rest frame of the solenoid. Ignoring action/reaction for the moment... Suppose you connect the ring to the cylinder using a dielectric, and then turn on the current. Now, the force is transmitted to the solenoid, not just to the iron ring. If that force exceeds the weight of the ring, solenoid, and battery, the whole system can rise into the air. The formula for the magnetic field of a solenoid is, to a good approximation: B= m N I Where mu is the permeability of free space (which is a constant of nature) N is the number of times we wrapped a wire around a cylinder I is the electric current in the wire We can easily control B since we can easily control N, and I. The current would have to be huge in order to do this, but perhaps in the future, a superconductive wire will be found, which can sustain huge electric currents. So can a superconductive solenoid propel us through the vacuum?

Are quarks really particles, or is something else going on?

c is not the only constant in the universe.

If I understand you, the answer is yes. You don't want to use the Pythagorean theorem to prove the Pythagorean theorem, that's circular reasoning which is a no no. I made reference to trig relations, but they are just definitions, and they have nothing whatsoever to do with the pythagorean theorem, but definitions aren't necessary, they are for convenience. Sin B = length of side opposite angle B/hypotenuse Cos B = length of side adjacent to angle B/hypotenuse So you could use them if they help you, but you don't need to have them memorized. What was needed in that proof, was the notion of similiar triangles, which doesn't have anything to do with the pythagorean theorem, and in fact proved it, as you saw. The only previous theorem that you would need, is one which taught you how to construct the altitude, and that is covered in Book I of Euclid, long before Euclid proves the Pythagorean theorem. Here it is: Euclid's twelfth proposition

Review dipole for me if you don't mind. Griffith's EM book discussed them for atoms. Basically just a + somwhere and a - somewhere else. Di-pole... two poles. Here It still doesn't tell me what a B field is, just the field lines, due to the existence of a dipole. You say that it's just another magnetic dipole. I'm looking at this now. Neutron electric dipole moment and this Neutron magnetic dipole moment

Yes I know this one, but you have a 'neutron' particle's dipole moment acting with a 'field.' Thats strange, certainly non-classical. What is the B field composed of?

Do you know why I chose three non-collinear points?

Why don't you break up your question into two parts. Part I: How can you measure the position of a particle? Part II: How can you measure the momentum of a particle? Swanson gave an answer to part I clearly. You fire a photon at the particle, it rebounds, and comes back to you. If you know the speed of the photon, and its travel time, you can compute the distance away that the particle WAS. That is information about the past, not the present of course.

Well that explains that... i suppose. i mean it does explain quark theory at least. But I'm bothered by something. We don't know what a magnetic field is. I don't know what is being done to those little neutrons. Are they being bombarded by magnetic particles? The quick answer is no, because magnetic monopoles do not exist, since the divergence of a magnetic field is zero. But if magnetic monopoles do not exist, then what is a magnetic field. It can't be nothing.

Neutron interferometry? How can a magnetic field rotate a neutrally charged object? magnetic force = Q(vXB) v = neutron speed B= external magnetic field. Both are nonzero so everything looks good but q=0 for a neutron hence F=0 So where is my mistake? I know you are going to say... force on magnetic moment. But a magnetic moment can only arise from a current loop, so now what?

Who on earth actually understands what a magnetic field is? There has got to be some kind of interaction of something external with the electron. Right off the bat, the magnetic force formula is totally strange, because its a cross product. What force in classical mechanics is like this? F = q(v X B)