January 2018

Quantum Mechanics since its inception has been one of the most philosophically controversial concepts in all of physics. But what really is so confusing about quantum mechanics? The answer lies in two fundamental principles: locality and realism.

Locality – locality asserts that all information and matter in the universe is limited by the speed of light. No experiment has ever contradicted this principle thus far. One may bring up the idea of quantum entanglement with EPR pairs but if you refer to my post on Quantum Teleportation, I discuss how, even in this case, no information can actually be sent faster than the speed of light preserving locality. An interesting visualization of this is the following with light cones.

Light cone.png

Continue reading Philosophy of Quantum Mechanics

It has admittedly been quite a while since my last post over a year ago. I thought I would restart the posts by revisiting one of the first topics I discussed on the website: quaternions. My previous post, upon review, seems to be quite uninformative on what the nature and use of them are which I will attempt to show in this post.

Formalism

Quaternions are a generalization of complex numbers ( $\mathbb{C}$ ) or hypercomplex numbers and they are denoted with $\mathbb{H}$ . Below I write both in their general form.

$\displaystyle \mathbb{C}: a+bi$

$\displaystyle \mathbb{H}: a+bi+cj+dk$
where $\displaystyle ijk=i^2=j^2=k^2=-1$

Now, there are 3 “imaginary” components and they are defined by that relation at the bottom. This is super interesting! What does this even mean though? A real number with some sort of 3-dimensional imaginary component?
quaternions

Continue reading Quaternions Revisited