Recent content by Alephu5

Given the relationships: \lambda = \frac{h}{p} = \frac{h}{mv} and E = hf for wavelike non-relativistic matter, and v = \lambda f for a general wave, one can obtain the result: E = \frac{h^2}{m \lambda^2}. Whilst for particulate matter, we have E = \frac{1}{2}mv^2, which when combined with the...

@D_Tr: Thank you for the elegant demonstration of this fact. I knew I could demonstrate it by thinking about the vectors that lie along the lines between the heads of \mathbf{u} and \mathbf{w}; and \mathbf{v} and \mathbf{w}. Explicitly these are \mathbf{w} + r\mathbf{(u-w)} and \mathbf{w} +...

Homework Statement Suppose \mathbf{u,v,w} \in {\rm I\!R}^2 are noncollinear points, and let \mathbf{x} \in {\rm I\!R}^2. Show that we can write \mathbf{x} uniquely in the form \mathbf{x} = r\mathbf{u} + s\mathbf{v} + t\mathbf{w}, where r + s + t = 1. Homework Equations Suppose \mathbf{a,b}...

From what I gather, the multiplication is due to an attempt to divide a fraction by another fraction: \frac{1}{8}\div\frac{1}{16}=\frac{1}{8}\times\frac{16}{1} This would cancel out the 16 on the RHS and leave you with: 2=\frac{1}{2}^\frac{t}{H} Also from what I understand, the last part...

Homework Statement Firstly, I'd just like to point out that this is not actually a course related question. I have been trying to teach myself mathematics, and have been grappling with this for a couple of days. The book has no answer at the back for this particular question. Variables...

This is similar to a philosophical perspective called "Model-dependant realism" put forward in a book called "The Grand Design" by Stephen Hawking and Leonard Mlodinow. It does not talk about hierarchies of subsystems within supersystems, but rather that there is a common scientific...

I think there is unanimous agreement that as humans, we all experience something which can be called "time" in English, which describes a one-directional increase in entropy of the universe at a constant rate. In this sense it is perfectly reasonable to assume that it exists. The real challenge...

I cannot visualise looking at an nD shape, but if you want to imagine being in a hyperdimensional universe it's pretty simple. Basically just extrapolate from the experience of repeatedly turning through 90° in a 3D universe; on the fourth turn you see the same view as when you started turning...

I am writing a theorem to do with a fractional factorial design for an experiment. I have had minimal formal training in mathematics, and this is my first theorem. I am fairly happy with most of the statement, but the last part does not feel right. Basically I want to say "If S is a subset...

I know that theorists have explored the idea of the universe being cyclic, but found it to be implausible due to the nature of entropy. Each reborn universe would start off more disordered than the previous one, until universes are coming into existence with infinite entropy. In my opinion...

For a simplistic understanding of electricity, you can imagine it as water running through pipes. The voltage is the result of an imbalance in the circuit; the negative end of a cell has an excess of electrons, whilst the positive end does not have enough to be electrically stable. This is...