Look, I know my computer isnt great, it's not the newest thing, but I used to be able to play this game without lagging down to zero frames constantly. Every time I have Drox spawn in on a map I'm playing a constant game of off screen everything or just die when all their purple bubbles spawn and my system throws a hussy fit. Please let us lower the particle effects on this damn game. Streamers with super rigs will still be playing on high settings, your game will still look good, just stop this nonsense and give us some control.
There is a really cool application of representation theory to physics which philosophically explains where mass and spin come from (in a sense at least). Let me try to explain this from the ground up to maybe incentivize more people to learn about physics -- there's some really good math in there!
To begin, in special relativity one equips space-time R^4 with a different inner product than usual: g(v, w) = v^0 w^0 - v^1 w^1 - v^2 w^2 - v^3 w^3 (the upper indices refer to the components of the vectors, as is customary in physic). To briefly see why, consider that g(v, v) = 0 if and only if (v^0)^2 = (v^1)^2 + (v^2)^2 + (v^3)^2, which if you think of this as a velocity vector means you're dealing with something that 'moves as much in time as it does in space', i.e. light (using c = 1). It's possible to push this logic further to show that all observers agree on this inner product. That is to say that the allowable changes of coordinates in R^4 are those which preserve this metric. The ones fixing the origin are automatically linear and form the Lorentz group O(1, 3), whose connected component of the identity is SO+(1,3) (the Lorentz transformations that preserve both time and space orientations). If you also allow translations of spacetime you get the Poincaré group (with connected component of the identity) R^4 |x SO+(1,3) (this is my shitty ASCII attempt at a semi-direct product sign).
Now let's bring quantum mechanics into the picture. In QM, the state of a system is described via a vector in a Hilbert space. So let's suppose we want a Hilbert space which describes the possible states of some type of elementary particle. If we want a relativistic theory, then different observers should agree on the state -- this doesn't mean they see the same state, but rather that given an element of the Poincaré group, there should be a unitary transformation of this Hilbert space that maps the state one of them sees to the state the other sees. This means our Hilbert space needs to come with a unitary representation of the Poincaré group! But actually, not quite -- in QM it makes no difference if you multiply your state vector by some unit complex number. So it should really be a representation 'up to multiplication by a unit complex number', which is called a projective representation. [A t... keep reading on reddit ➡
I’m struggling to understand why quantum computers can simulate nature better than classical computers.