/sci/ - Science & Math

It's not about having to resort to something.

It's about finding a model that can explain most of the physical phenomenons that we can observe, and quantum mechanics appears to be really fitting.

The fact that electrons have a wavelength (or any particle) is just a consequence of the need we had to attach something to a concept (the wave function), and everything seems to point that electrons behave as if they were waves (which makes much more sens when you understand the interaction between light and matter).

I'd recommend "Quantum Electrodynamics" by Feynman (the title might be scary but it's not as bad as it looks). It's a small book that dumbs down some concept of quantum mechanics and uses a lot of experiences as examples.

I hope that will be a bit clearer for you.

>>5648865
>I don't get if the world actually works in probability or if everything is happening similar to classical physics
Both statements are accurate.

Every system obeys quantum mechanics... but in the limit where you start dealing with many many many-particle systems - the laws of quantum mechanics become more or less indistinguishable from the laws of classical mechanics.

>>5649370
What about the uncertainty principle? Does it mean we just can't define momentum and position with perfect precision at the same time, but the particle always has them, or the particle itself doesn't have them defined?

>>5649455
Actually the uncertainty principle says " measuring the momentum fundamentally breaks down the position finding function and vice versa"
but you can use eigeinvalues to fine the most " Pinned down" explanation of position and momentum"

CORRECT ME IF I'M WRONG

>>5649460
From what I understand, it just says that the error on momentum*error on position is equal or greater than h/4*pi.

What I don't get is, does that mean there is no way to know them, but they are actually defined at every moment, or are they just not defined?

>>5649455
Many observables in quantum mechanics are not well defined at all times, and in cases where you have what are called 'incompatible observables' the more you know about one property, the less you know about the other.

In the case of momentum and position, whose uncertainty relationship is given by the Heisenberg Uncertainty Principle:
<span class="math">\sigma_x \sigma_p \geq \hbar / 2[/spoiler]
the more you know about where a particle is at some instant, the less you know about where it's going at that moment, and vice versa.


Any individual measure of an observable will yield an eigenstate for that observable, and if you look at a very large series of measurements you get the expectation value for that observable for that system.

In general, at the macroscopic scale we no longer see an uncertainty relationship. It's still there but the uncertainty over measurements is so small relative to the scale of momentum and position of the object that we can basically say we know both with absolute precision.

>>5649516
I get the first part of your post.
What you mean though is that there is an uncertainty in the position and momentum of the object ALWAYS? Like, is the position of the object actually not defined, or is it just that WE can't define it?

>>5649537
What you have to consider is that we are humans and we have to use tools to measure the momentum or position of a particle.

Those tools will always have a fundamental precision associated with them. If you take a standard ruler, you can fairly easily measure to perhaps the nearest millimeter.

What the HUP means is that the more precisely WE AS HUMANS measure the objects position or momentum to be, the less precisely we know the other.

The particle does have a defined position in space. But we will never have equipment precise enough to measure it. That's just an unfortunate fact of nature.

[You may wish to ignore this paragraph if your confusion has been cleared up.. It only complicates things but is intreresting:]
All we can really do is attempt to measure them and get one of many possible different answers (the eigenvalue states). We can calculate the probability of getting each individual state. What you can imagine is as the probability it's in one state increases, the spread of probabilities for the other measurement will become much more varied. Much like you would have seen when you derived the HUP. The width of one peak decreases, but the other consequently increases.

Hope this helps clear things up, OP =).

>>5649873
Thanks a lot to you and everyone else that helped me in the thread. This helped clear out things quite a bit.

try this OP
http://www.youtube.com/watch?v=W9yWv5dqSKk
it's a real world analogue to how we "think" it works

>>5649537
We don't know.

The question of whether uncertainty is a consequence purely of the limitation of instrumentation or whether it's a fundamental property of reality is still a matter of some debate.

The Heisenberg and Bohr schools of thought hold that the Universe is fundamentally random and that particles don't have things like a definite position or momentum.

The De Broglie school of thought (as I recall) holds that its purely a limitation of what we as humans are capable of observing.

>>5649907
Wow, that video is incredibly interesting. /sci/ is really helpful.

Just a side note, introductory quantum mechanics texts aren't very math heavy at all. Just some basic knowledge of differential equations and a bunch of linear algebra. If you want, I'm sure you could read an intro QM text without much trouble.

>>5649930
Despite its reputation, /sci/ can be really quite genuinely informative and helpful when it's not being spammed with homework and troll science threads.

>>5649945
Define 'introductory quantum mechanics texts'

Are we talking high school or undergrad?

>>5649455
That is a really good question. Reading through the post I can see this has already been partially answered. If you want a different approach, perhaps a slightly philosophical one, here's what a kantianistic view on it. Whether the uncertainty principle is due to our instruments affecting the position or momentum (or other incompatibles) or due to the fact that the particle doesn't have a well-defined position/momentum in its nature is an irrelevant question (forgive me for my poor English skills, the question is very interesting and fundamental indeed), because the fact is that we will never be able to know the difference. Say, for example, there exists a pure world free from assumptions where everything is deterministic (the "ding an sich"). Us humans are ultimately limitted by the way we were built to measure and interpret the world (for example, it is impossible for us to imagine what a 4th spacial dimension looks like). The world we live in which we are able to interpret ("ding für uns") is the only thing we will ever measure. Asking whether the uncertainty principle is really the true nature of particles or only due to our limitted interpretation of the world is irrelevant since we will never be able to comprehend the pure and real world. Bohr was kantianist and this was his view on Quantum Mechanics which has now become the Copenhagen Interpretation.

>>5650279
This is not unlike the conclusions of the Michelson-Morely experiment - whether there is no 'luminiferous aether' or whether there is one and it merely acts ways which is not observable is irrelevant as there is no fundamental difference between a thing not being observable under any conditions and a thing not existing.

>>5649537
Well that's the real mind-blower... we aren't completely sure.

Wave-particle duality, you mean?

Basically, particles like you're familiar with aren't quite particles; a commonly-used term is wavicle. A wavicle is more like a cloud than a single point; within a certain area, it's everywhere at once.

The confusion comes from a quirk of the universe: wavicles, when measured, look like particles. The particle manifests in a certain spot within the cloud-like wavicle; exactly where is decided randomly.

So, basically, particles are clouds; they only look like finite dots when they're measured.

>>5650416
>wavicles
>particles are clouds
>they look like dots

>>5649920
If you have ever heard the Einstein quote, "God doesn't play dice with the world." He is referring to this debate, and arguing that the particle does exist in a certain place, but we are limited by our tools to the precision with which we can mesure it.
We do not know the answer to that question, so instead of thinking of it like a theorist think of the equations like a experimentalist. You have some limited precision with which you can mesure a certain thing, so you have to make do and use a probability to calculate where the thing is.

Surely you must of done probability density functions? It is the same concept as that. Imagine that you throw a ball up in the air with and have a very good amount of knowledge about the how much drag it will create, how much it weights, and with how much force you threw it up, but because of the wind, which you can't mesure as precisely, the ball will not fall directly where you measured it to fall. Yet because you know the lack of precision of your measurement you can create a probability density function to get a general idea of where it is going to fall. If you were to draw an outline around the region on the pavement where there is a 90% chance of the ball falling, then you would of drawn something similar to an electron orbital.

>>5650533
He's not exactly arguing that the particle exists in a certain place, he's just arguing that there's some deterministic process at work.

Location is somewhat ill-defined for waves, and may be as well for particles.

You can't understand the physics without understanding the math.

>>5650573
You can... just not well.

A person can understand the basic idea that, say, you can't know a particle's position and momentum exactly at the same time without understanding how to derive the uncertainty for a given quantum system.

>>5651463
If you don't understand the math, you don't understand shit. Understanding basic concepts is fine if you're a fucking grade school student but not if you're a grown man.