This is actually a common misconception about how jet engines work. The engine is not pushing against the surrounding medium (the air), it is operating purely due to the conservation of momentum of throwing combustion byproducts at a high velocity in the opposite direction. This is the same principle upon which a rocket engine operates, the difference being that the jet only needs to bring along fuel for the combustion reaction, thereby massively increasing the efficiency of the engine by making use of ambient atmospheric oxygen.

In fact, a jet engine could in theory (ignoring things like heat rejection) operate just fine in space if you brought along a massive bag of air and hooked it up to the intake duct. But then you've basically just designed the world's worst rocket engine :)

Well put. For anyone interested in the similarities of jet engines and rocket engines, read up on the SABRE engine that the UK company Reaction Engines is working on for the proposed Skylon spaceplane. SABRE is a hybrid that's designed to work like a jet engine straight from its horizontal take-off up to about Mach 5.5+ and 25Km in altitude. Higher/faster than that, it switches from using atmospheric oxygen to oxygen stored in its fuel tanks and works like a rocket engine. (Of course the technical details are far more complex than that, but that's the TL;DR.)

Using atmospheric oxygen for the early phase of flight is a massive weight savings. If/when SABRE works, the Skylon spaceplane could be a practical reusable SSTO. It could carry a very respectable payload mass (the aim is 11-17 metric tonnes) to LEO, and it could do so quite cheaply if the designers' claims pan out.

Fun fact for Kerbal fans: the RAPIER engine in the game is inspired by SABRE.

This is just a complicated way of saying the same thing. Of course a jet engine is not just a really fast propeller. And if you hooked a "bag of air" to a propeller, that would also work in space.

Either way, an LED is not generating any meaningful thrust, and pointing that thrust at a sail adds no benefit.

No, it's not.

A propeller makes thrust like a paddle, by pushing off of something. A jet/rocket engine makes thrust by recoil, using conservation of momentum.

Almost all modern jet engines have (ducted) fans. In planes that never go supersonic, e.g., all current commercial airliners, the fan provides most, but not all, the propulsion. And the only difference between a fan an a propeller is how many blades it has. (The presence of a duct around the fan does not change anything basic.)

But even if they did not have fans, there is no fundamental difference between using a propeller or fan to speed up the flow of air and heating the air inside a chamber to speed up the flow of air. (The fan is used because at subsonic speeds it can be made more efficient.)

In other words, all 3 means of propulsion work by conservation of momentum.

So you are saying if I put the car in a vacuum chamber and mounted a CO2 cartridge instead, it wouldn't work?

The basic physics at work here is conservation of momentum. Rockets work because they are sending mass in the opposite direction of the main vessel. If you draw a box around the whole system (rocket + spent fuel), you have net zero momentum.

There is a whole separate device called an EM Drive, which claims to basically violate conservation of momentum. It is highly controversial, and unlikely to be anything other than a measurement mistake.

Of course it would, but what wouldn't work is bouncing that CO2 off of some sail.

I would think a sail, or rudder, could redirect the force from the CO2 canister.

It could, but it would be significantly more efficient to just point the CO2 canister in a different direction.