What is the theory behind the Arduino UNO being able to create AM waves at 800 kHz I am doing a school project and saw someone use an Arduino and a piece of wire as an antenna here: https://forum.arduino.cc/index.php?topic=88422.0

I've tested this experiment and it works, but I have searched the internet for some time now for some background knowledge or theory on why this works, and how does it?

If anyone knows anything about the arduino creating simple AM waves, could you please let me know about it or redirect me to another source.

For some context, in this school project I've got to explain the theory behind creating basic AM waves and amplitude modulation in general, then prove the theory by conducting this experiment which I prove it correct.
Strictly speaking it's not AM, it's OOK (On-Off Keying) which just turns a carrier frequency (800kHz PWM, 50% duty cycle) on and off.

Many cheap 443MHz (eBay) modules do the same thing - turn the carrier frequency on and off.

The presence of the carrier frequency is seen as a logic 1 and the absence as a logic 0.

The fact that it's using PWM to generate a square wave means that the "cleanliness" of the signal will be incredibly horrible. You really want to get the carrier frequency as close to a pure sine wave as possible. A square wave has lots of harmonics at 3x, 5x, 7x, 9x etc the frequency. So your 800kHz signal will also have a 2.4MHz signal, a 4MHz signal, a 5.6MHz signal and so on, each at a lower level. That causes interference in other signals.

To understand more about why it works you first have to understand radio transmission theory, and that's not something we can cover on an Arduino site (it's an entire college course all by itself).