Random thoughts

100x100=10,000

6+7=67

no, it's 13

no its six seven

I wonder if mayonnaise is an instrument

it is

it;s not

also if 6 + 7 is 67 then

6 + 9 is 69

yea exactly

67 is 67

exactly

bruh

yes

Octopus are wet spiders

1000 eloi

elo*

If you want to accept quantum physics, you must first abandon common sense.

One of the most fundamental concepts in quantum mechanics is wave-particle duality. The double-slit experiment is a famous one that illustrates this property.

Imagine I have set up a pool of water, and a barrier with two slits in it. When I start dipping my finger in and out to generate waves, this is what we expect to see - an interference pattern. This is very characteristic of waves. In that diagram, P is the "detector" and one can see that there are points of constructive and destructive interference.

Imagine we do the same experiment, except instead of water, we use baseballs (with appropriately sized slits, of course). I'm firing baseballs in a straight line in random directions. Most of it will be blocked by the barrier, but some will go through the two slits. What do we expect to see in the detector? Two areas behind the slit where the balls will hit. There will be no interference patterns. This is the behaviour of classical particles.

Now... If we scale down the experiment so we do the same for electrons, we find that they actually interfere - just like the case with water. Electrons act like a wave! Not only do they interfere with each other, if I fire electrons one at a time, I get the same interference pattern of local maxima and minima. This suggests that the electron interferes with itself.

Warning: Prepare to abandon your common sense here.

The electron is said to travel through both slits before hitting the detector. When describing particles in quantum mechanics, we can no longer pinpoint the location of said particle - this is related to the Heisenberg uncertainty principle. The electron has some chance of going through one slit, some chance of going through the other; the matter of fact is that it actually goes through both. This is called superposition of states. The electron is said to occupy all possible "states" until it is observed. In this experiment, the "observation" is when the electron hits our detector - therefore the electron follows all possible paths to the detector before it is detected, and something called wavefunction collapse occurs - this simply means that the act of observation causes the electron to "choose" one specific state out of all its possible states.

Anyways, I've covered quite a bit here, and I've only attempted to describe one phenomenon of quantum mechanics. I hope you understood it (kinda).

tl;dr Electrons (one of many particles that exhibit quantum mechanical behaviour) are funky and can act like both a particle and a wave.

The major hurdle with quantum physics is trying to accept things we cannot see. Quantum physics arises almost purely out of mathematics, physics, and statistics - equations. Sometimes we have to take such leaps of faith and go with what makes sense mathematically, and if we're lucky it'll be correlated with an actual experiment that we can observe.

There's a few things in the universe that, take it or take it (as in, you just can't reject it), just are. Like pi, or e, or the gravitational constant, they simply just are, they're laws.

I can't explain everything in quantum physics, only bits and pieces. Let's try something like the concept of an electron. Classically (read: things we can understand no sweat), we expect electrons to orbit a nucleus because of their velocities and the acceleration toward a point charge. However, acceleration by particular laws (which are classical, so they make sense on a larger scale) that requires that the electron emit energy in the form of EMR - light. This means the electron must not be orbiting the nucleus. Take a single electron about a single proton i.e. a hydrogen atom (this is the most well understood of all atoms, because it's, point in short, simple). What makes more sense in order for an electron to not just emit all its energy in EMR and crash into the nucleus is to treat it like a standing wave - a wave that's bouncing back and forth without losing energy (so-called "particle-in-a-box"). Now in truth, these are three-dimensional waves so they're hard as hell to visualize, so comparison to a string betrays its nature, but hopefully you get the point.

Now you might be thinking, how the hell is an electron like a wave? Try asking yourself, well what makes it so damn important for it to be a particle? Why can't something just be kinda both? Just because it's fundamental doesn't mean it can't be complex. This is nature, take it or...well, you don't really have a choice. The point is the math adds up, so bear with me.

So the electron is like a wave, but how do we describe it?

Here's another leap of faith you have to take, and that's the Heisenberg Uncertainty Principle. Uncertainty is an integral part of the universe, it's just there. Just like mass, just like energy, just like gravity or life or stars, uncertainty is there, just hard to see. Effectively it doesn't just say humans can't know everything, it's more profoundly, everything doesn't really exist. The information is not complete, or rather, it is complete and we just expect to much from the universe. We can't know momentum and position to 100% certainty, that's just a fact, not just experimental error, it's fact.

Using the HUP, a man named Schrodinger derived such a function that describes an electron wave (a wave function, like how cos(kx-wt) describes some waves, this wave function describes electron waves). More specifically, his wavefunction for a proton-electron system captures the nature of this particle-in-a-box very nicely. It's a function that sort of relates how if an electron has no absolute position or velocity, then if you took all its possible positions and velocities and laid them out as a function of time, fluctuating between them (i.e. wave-like, fluctuating) then you could have this kind of standing wave. To make things simpler, we take off all the so-called "quantum" states that have a very low probability of occurring (say being very close or very far from the nucleus) and limit it to maybe the 95% occurrence (things get unreasonably unlikely approaching 100% any closer). Then, we find solutions to this equation - descriptions of location probabilities that make the function make sense - these become 3D interpretations of positions i.e. "clouds" of "probability". The solution for an electron in a proton describes a spherical shape where at a particular radius from the center the electron has a particular likelihood of being there - ultimately this resolves out as the 1s orbital (you can look that up if you haven't encountered it before).

Unfortunately there's not a lot of room to show you a nicer looking version of the Schrodinger Equation, but try something like this(that's complex looking, but take it slow). For particular values of r (radius) the probability is a maximum, whereas it drifts off at larger values of r. As with many functions, it looks much better graphed out, and when it does you get a picture like this. Look at the left side for the 1s orbital. Turns out as you add new complexities to the equation (i.e. more electrons) then another solution pops out of the Schrodinger equation that describes the 2s orbital, that says for a particular value of r the function always gives 0, that's how we physically interpreted a mathematical relationship to say, there's a region of space where the electron as 0% probability of being - it's a node (it's indicated on that picture).

tl;dr I can't explain everything, quantum physics is a very vast topic. If you can spare the time, check out an undergraduate textbook on general chemistry and check out their simplified models of quantum physics and the Schrodinger equation. Often, you will have to make compromises with your skeptical side, but that's life. If we can't trust the math when the math makes sense, we can't trust anything. Gut intuition is not what quantum physics is about, it's about rejecting what doesn't make sense and trying to accept what makes less nonsense. I hope this at least helped you approach understanding quantum physics better, which is what I meant to do.

I abandoned common sense when I joined OTF.

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i have no idea