Recent content by QuarkyMeson

MIT is on a 5.0 scale, so a 4.0 would be a straight B student! That's not really the point you're trying to make, but you can differentiate between students more than just GPA and "same research area interest in application". There are also letters of recommendation which are important. The...

Go to the school where you pay the least amount of money for your degree, within reason. At my university which is a "lower ranked" state R1, we have plenty of graduates who've gone to top programs at the University of Michigan, the University of Colorado Boulder, the University of Arizona, the...

Spin is a quantum mechanical property. It's intrinsic angular momentum which isn't literally a classical rotation at all. Take an electron, it has spin but lacks any classical rotational degrees of freedom. Charge is the same, it's a quantum mechanical property. At the end of the day spin is...

Doubtful, there is just no economic reason to. All other exploration and colonization was generally tied to a solid economic thesis. If when we went to the moon in the 60's we discovered it was really a big ol ball of unobtanium and we could set up shop and send it back for a profit we would...

Also I just wanted to add, if it's possible for you to graduate you can still apply for graduate school this fall. If you get accepted into a program you like then just graduate. If you don't you could then decide to spend the extra year. It's not literally an either/or scenario here.

But brain neurons change, form new connections, die, etc in response to outside stimuli. The artificial neurons don't really change even if model weights are fuzzed somewhat and they don't change based on touch, smell, etc, with the outside environment. Contextual periods for LLM's are also...

I mean they sample from PDF's to generate their output. Even the models weights are fuzzed for models like Chatgpt depending on user settings I think. I'm assuming the objection is that the stochasticity isn't truly random? Which is true I guess. I mean, we haven't really seen anything that...

I don't think anyone will care? How long you spent in a program wasn't part of the applications. The only thing a shorter undergrad means is less time to do research and publish something and less time to explore the undergraduate catalog of courses. Grad school admissions are rough right now...

I mean, just so you know I agree with you. I don't think span preservation for quantum states is a good definition of invariance. The 0 vector isn't a quantum state. Your example shows that information has leaked out of the system into the environment, this is hardly what I would personally call...

Yeah, see Scotts post here for more information: Given a finite volume and finite amount of energy there are only a finite number of possible states.

Yes, a big caveat to all this is that the universe is truly infinite and that energy is also randomly and uniformly distributed. It appears to be so, but we will never know for sure. I called out the observable universe wrt the notion that there is only a finite number of configurations for our...

If the universe is infinite and matter is distributed randomly and uniformly, patterns have to repeat. This is because there’s a limit to how many ways you can arrange particles inside a single observable universe. Once you run out of unique arrangements, nature is forced to start repeating them.

This is a misconception. When people say it's like a particle or wave it doesn't mean it's actually either. It's just in general, sometimes it better to model quantum objects as one or the other, but it remains a quantum object described by a quantum state. In fact, when you actually learn...

I guess that makes sense. You already have engines and a fuel tank so the weight savings (if any) of adding in a parachute system instead of carrying more fuel to land probably isn't worth the extra complexity.

In QM we can look at two different update rules: $$|\psi\rangle \mapsto U|\psi\rangle$$ with ##U## unitary. This evolution of the state vector is deterministic and preserves norm: $$\|U|\psi\rangle\|=\||\psi\rangle\|$$ Alternatively, for say a measurement, each possible outcome is associated...