Recent content by jk_er_gamma

I have currently applied to 4 schools. There are at least 2 more in the plans. I will update with how it turns out.

The idea that experiment is a valid form of testing truth is a specific kind of philosophy, worked out in the ages when competing philosophies were rationalism and empiricism. Maybe the scientific method is something we take in through the science community, but it has philosophical underpinnings.

Not trying to argue with the practicality of curtailing discussions where people end up changing their definitions or do not believe in a standard of logic in the beginning, but I would just like to say that science is a subfield of philosophy, in its origin and its mission. What is theoretical...

It's basically the same as one of the questions I was asking, and I think the main source of confusion. I think PeroK was saying that it should be zero for a free particle, since there is no gain or loss of kinetic energy. At certain steps in the process of examining functions of x and v...

doesn't need to be official, but saying that got the desired response.

Interesting. So that's what is meant by taking position and velocity as independent variables for this process.

edit: on closer examination, it is ranked, but not by quality. For most focused ~600/700 (no surprise, it was a small program) and for highest paid ~300/540. The math major is ranked for quality, at ~270/475.

I'm imagining that you start with the assumption that there is an equation of motion (1-dimensional) x(t). Then, at every point on the graph of that function should be a derivative, the velocity, which you can graph as well. Since x(t) and v(t) have a common parameter of t, you can graph v...

If I understand this correctly, you're saying that for a free particle, there is no change in T (and thus no change in dx/dt). But what about the problem indicates that it was a free particle? Was it that the Lagrangian included (dx/dt)^2?

I don't think it is significantly ranked, probably not Top 50. Is there an official system of rankings? Yeah, I think I could do better, but I have already waited until after graduation to take it, so waiting another year might be a bit iffy.

There is another problem as well. There are things we would like to express in language that are not expressed well in normal math, such as possibility and causality. Because of the "Law of the Excluded Middle" in Math (Not False=True), some math statements work counterintuitively. For example...

Thanks for clearing that up. However, you can have a particle modeled by a Lagrangian which differs in velocity along the positions of the motion, correct?

Thanks. It's hard to explain why I haven't yet. When I thought I should join was when I was reading threads and kept wanting to respond.

What about giving calculus a day to save?

Looks like derivatives are assumed to commute: d(dx/dt)/dx=d(dx/dx)/dt. However, if position is a function of time, it does seem meaningful to ask how the velocity is changing from one position to the next. To take it as saying velocity is not changing with position is problematic, since...