So recently my uncle gave me a Deore M5100 11 speed RD, but my current setup uses an Alivio shifter with a LTWOO A5 elite RD and an 11-46T cassette. While yes the LTWOO RD is designed to handle a 46T 9 speed cassette, im wondering if a Deore M5100 can handle not only the 9 speed shifter, but also the 46T cassette. Based on my minimal research, an RD doesnt particularly know what "speed" it is, rather the shifter dictates how much it moves. Thats why im thinking that the M5100 is fine even if im using a 9 speed shifter and cassette. Of course, a longer chain would be needed in that case. I am aware that you should always match drivetrain components, but in a hypothetical scenario will it work? What do you guys think?
You're correct in your reasoning: the shifter defines in which speed the derailleur will be. The points that you miss are the notions of cable pull (the movement of the cable when you change a speed, in mm) and pull ratio: which is the ratio between the cable pull and the lateral movement of the derailleur (dimension-less number).
A 9-speed shifter has cable pull of 2.5mm and an 11-speed MTB derailleur has a pull ratio of 1.1, which means that the derailleur will move 2.75mm per level when you actuate your shifter. But the distance between the sprockets for a 9-speed cassette is 4.35mm, so your derailleur won't move enough to reach another sprocket.
For reference: 9-speed systems have cable pull of 2.5mm and pull ratios of 1.7. 11-speed systems have cable pulls of 3.6mm but pull ratios of 1.1.
There are adapters that allow to use derailleurs and shifters that don't match (like the Wofltooth Tanpan), but as far as I know, they are mostly used to allow using road shifters with MTB derailleurs (or the other way around).
it's an old discussion but worth a response in case someone is looking for it... 11 speed shimano are compatibile with 9 speed cassette with a 9 speed SRAM (it's important) shifter. Also 12 speed sram and shimano and 11 speed sram derailleur should work for it. Reason is, pull ratio is the same or very close, 1.1 , for sram x-actuation, and shimano 11-12 MTB derailleur. Shimano 10 speed derailleur are close but not the same, it can sort of work. With 11 speed derailleur is possibile also to use 9 speed chain, with 12 speed it will likely rub. So yes, you can use 11-46 9 speed cassette with sram 9 speed shifter and shimano 11 derailleurs, or 11-50 (and 11-46) 9 speed cassette with sram shifter and deore rd-m5100 derailleur, that is what i personally suggest - great bang for the buck. A couple of note 1) the only long range derailleur that i'm aware of that is compatible with 9 speed shimano shifter (and 8 speed as well) is the sunrace rdm900. 2) it seems that also microshift advent 9 speed system is compatibile with 1.1 pull ratio, but i've not enough data to confirm this. Source of all of this: i've been using only 9 speed systems since 15 years, and experimented on my bikes almost all possibile ways to have a cluched 9 speed derailleur...