Sweet /sci/

Heisenberg's uncertainty principle

>>8878530
Looks like an uncertainty relation.

>using chi for position
>using rho for momentum
Jesus Christ, do people actually do this?

>>8878579
Chi rho?
Jesus joke?

>>8878530
this is actually pretty fucking simple to learn, maybe not understand tho.

if you know a lot about where something is, then you know a little about it's momentum, vice versa

>>8878530

A trivial result from Fourier analysis.

>>8878530
A general result born from two operators which don't commute.

>triangle cross triangle circle
Back to >>>/v/ you playstarded.

>>8878702
In what world does [math] \rho [/math] look like [math] \circ [/math]?

>>8878530
why do math dudes use frat symbols for math shit? cant they get their own symbols?

>>8878530
>tfw they teach this formula in 12th grade
>good goy just learn this formula we'll only tell you a vague idea of what it's about just fill the variables to get the answer shhhhh don't ask anymore questions
STEM education is garbage.

>>8878622

You missed the cross with the virgin kneeling behind it.

>>8878530
the cauchy schwarz inequality on function spaces

>>8878579
They could just be conjugate operators (commutator is just i) totally unrelated to position or momentum brainlet.

>>8878579
i think its just a stylized x and p.

i blame OP for using a retarded font

>>8878530

It's not so much a quantum physics thing as it is a wave thing. The same applies to sound.

It's possible to express any periodic function as an infinite sum of sine waves where each has a period that's the period of the function divided by an integer. If you have a function that's not periodic, you can do the same by integrating across an infinite number of sine waves.

In a lot of systems, such as sound and quantum physics, decomposing something into sine waves makes it easier to understand. It's nice to be able to analyze sound by looking at the pitches of the sine waves that make it up.

But you often want to know what pitch a note makes and when the note happens. That doesn't really work as well. It turns out that if you have a short, precise sound, you'll need to add together a lot of slightly different sine waves that mostly cancel each other out but compound on that one place, so there will be a large variation in the pitches that make it up. If you have a note largely composed of one sine wave, then it's going to actually look like a big piece of that sine wave. You can't have a 10 Hz note play for a hundredth of a second.

The end result is that the uncertainty in the time of the note times the uncertainty in the pitch must be greater than some constant.

>>8879954
The same applies to particles in quantum physics. Particles are not discrete balls of "stuff". Rather, they are like waves of "stuff" that cannot be broken down and behave according to some very specific equations. It moves in a way most analogous to how temperature spreads out in an object. This means that it doesn't mean anything to talk about "where" a particle is or "how fast" it is moving. Just imagine small wave of water, can you tell me where it is? No, because it's spread out. Can you tell me how fast the heat in a room is spreading? No, because it moves at different speeds at different places.

We can imagine that this "wave" is distributed somehow in space, and then look at the standard deviation of this distribution, Sx. The bigger the standard deviation, the more spread out the particle is. The smaller the standard deviation, the less spread out it is and more it looks like a ball of "stuff". But the particle will be moving at different speeds, some speeds will be more preferred than others, so we can imagine that all these speeds have their own distribution. We can then look at the standard deviation of this distribution too, Sp. The larger the standard deviation, the more it is moving like a wave. The smaller the standard deviation, the more it is moving in a uniform way, like a ball does. If Sx is small then it "looks" like a discrete particle. If Sp is small then it "moves like" a discrete particle.

The Uncertainty Principle says that the product (Sx)(Sp) cannot get too small. This means that we can't have Sx and Sy be small simultaneously. In other words, it can either look like a discrete particle or move like a discrete particle, never both. This is just a consequence of the fact that particles are these weird wave-things and are not discrete particles.

The Uncertainty Principle is not restricted to Quantum Mechanics, it's actually just an idea from probability and statistics that is used in quantum mechanics.

>>8879957
the reduced planck's constant definitely suggests this is something quantum. I can't think of any other situation where that would pop up.