Johnny5

he was joshing you

Actually swansont, De Broglie and Born were totally different minds. It was De Broglie who postulated that matter has wave properties. He didn't say in what sense. Schrodinger thought the energy density was waving, and Born said probability is waving. But it was De Broglie who started it all, with the following postulate: [math] p = \frac{\hbar}{\lambda} [/math] So how do you go from what De Broglie thought, to what Born thought?

Oh boy, someone right next to the object, locally to it in both regions.

Yes zeo, that was one of several ways to realize you cant travel into the past. You throw a rock back in time, just a little bit, and you have new matter appear from out of nowhere, because that rock is there already, just a wee bit younger. So this is violation of conservation of matter.

All of them?

What do you mean it's unlikely to be Euclidean, or Lorentzian?

Something is waving though. I am hoping it's the inertia.

What is an absolute reference frame?

Ok suppose that some region of space is severely curved. And some other region is almost perfectly flat. And I have a yardstick, which is straight when its in the region of flat space. Now, I bring that yardstick to the region of space which is severely curved. What is the shape of the yardstick now?

What kind of clocks?

Thanks What is quantum clock synchronization?

Well then, let there be two kinds of frames to be defined. One kind has axes which cannot expand or contract, the other which can. Therefore, I need a definition of rigid. And I already know what that means, now I just have to say it logically. Yes swansont, they measure distance. The Pythagorean theorem is true. By choosing a unit of distance, that means that you have selected a real physical ruler. A meterstick. So the distance between any two units on one of the axes, is the length of the meterstick. And that fact has to remain constant in time, in the case of rigid axes. Suppose you have a real sphere, which can expand and contract, due to heat. Let it be a billiard ball. Thus, its volume can change in time. And we can talk all we want about the volume of it, using a frame with rigid axes. If its radius decreases by .05 millimeters, then there was a rigid frame, used to determine that fact. In other words, a ruler was used to make the measurment. The diameter of the sphere was compared to the ruler at one moment in time, and then later compared again, and either the ruler expanded, or the billiard ball contracted. So how would you know which of the statements is true? If you are certain your ruler cannot expand or contract, then you know that the billiardball contracted. (this is the reason I want my axes rigid) One way to figure out that the sphere contracted, and not the ruler, would be to check the temperature of the sphere, at both moments in time when the length measurement is made. If the temperature of the ruler was constant, but the temperature of the sphere wasn't this indicates that the sphere contracted (or expanded), not the ruler. The lines of a frame aren't physical objects, they cannot contract. But I realize this goes against the whole space expansion model of the universe. I have to define rigid axes. If they were straight lines without coordinates, there would be no way, but a frame has coordinate axes. What I can do, is set up the logic to lead to a contradiction, if the axes are allowed to expand or contract. Some definitions are needed. F is a rigid frame if and only if F is a frame and I need to think about the coordinates of various points in a rigid frame. The Pythagorean theorem is true in the frame.

Why do you have to go and complicate things. I don't want the axes to be able to expand and contract though, because there was a unit of distance chosen. I want the axes rigid. Let matter expand and contract, not the axes.

I think the first thing to do, is define equality, on the set of all frames. In other words, I need an equivalence relation on the set of frames. Frames are going to be permitted to move relative to one another, so it could be the case that two frames which are different, eventually have their axes coincide, at which point they are equivalent in some sense. Now it could be the case that the axes of the frame overlap, but the x axis of one is the y axis of the other. So I have to decide if the unit vectors of the x,y,z axis also have to be the same as well, in order to say two frames are really one frame. This is spatiotemporal logic. Let F1 denote a frame, and let F2 denote a frame. F1=F2 if and only if

This comment struck me as excellent.

I worked very hard yesterday, and I realized this morning that my analysis wasn't thorough enough. Specifically, the axes of frame F2 could be spinning in such a manner, as the eightball at rest in frame F1 would not be in orbit about the origin of F2. I ignored many other possibilities. And I do now realize why they got ignored. I wasn't mathematical enough, about those possibilities. If you read pack to post #45, then you will see that I introduce angular speed, and I say that it follows that the eightball is in orbit around the origin of F2, and therefore F2 would be non-inertial. Now that is right, but there are many other ways for F2 to be non-inertial. For example, suppose that one of the axes of F2 passes through the center of inertia of the eightball, and the other two axes are spinning in frame F1, with the axis of rotation being the axis that runs through the CM of the eightball. In this case, the eightball would be at rest in frame F2, and there are no external forces acting upon it, yet F2 is still non inertial, because there are other objects in the universe, which also have no net force acting on them, and some of them would appear to be accelerating, without an action/reaction pair. Now, I have studied the TNB frame, but I don't remember all the formulas anymore. And I am reminded that 5614 said you cannot re-do everything. There's no reason really. But whatever book that discussion was in, the author wasn't logical enough, or I'd have still remembered it. Or maybe not... it doesn't matter. What does matter is I don't have what I want, right now. I want the right mathematics for this job. In another thread, I called what I want, "frame theorems." But not a single person responded. Most likely because they don't understand what I asked for. The vector space of linear algebra. But perhaps with a modification here and there. So that's what I'm going to work on today... my frame theorems. And all that work yesterday was not for nothing... something good did come from it. In trying to get 5614 to define "absolute reference frame" using first order logic, I was forced to formulate a definition of 'frame'. A frame is three mutually orthogonal infinite straight lines, with coordinates on them, and a unit of distance chosen. What everyone refers to as a rectangular coordinate system. For two infinite straight lines to be mutually orthogonal, they have to meet at a point. So what a frame is should be quite clear to anyone who can reason spatially. One of the logical aspects of geometry, is that the statements made there do not have a truth value which can vary in time. From a logical point of view this makes them very interesting. Once we throw time into the mix, things become complicated very fast, as swansont keeps pointing out. But the truth of geometrical relationships is independent of time. And from a practical standpoint, what that means is that it will be easier to mentally manipulate geometrical statements, then statements involving relative motion. I know this is so from experience. The thing about frames, is that they can translate, and rotate. That means that the truth value of certain statements can vary in time. So... What I need are axioms, and definitions, and theorems. If I reproduce something already done, that won't matter.

Is there one I could read?

It was only two pages long, and the argument was perfect. The reason why not, is because they get a thousand of them per year. No one even read it. You know, it's very difficult to get published.

Well maybe I should expand on why it's not ok with me, but right now I have my hands full in the other thread.

It didn't get published. They told me to try a pedagogical journal like the American journal.

Probability of what?

Haha.