Trying to understand conservation of momentum [Split from another topic]

[Clamp-o-Tron]

5 minutes ago, SOXBLOX said:

Fact of life: all physical processes are less than 100% efficient.

Yes. Even black holes, and, as I’ve seen theorized, the expansion of the universe itself (no idea if that guy knew what he was talking about)

[kerbiloid]

12 minutes ago, Clamp-o-Tron said:

the expansion of the universe itself (no idea if that guy knew what he was talking about)

Does any guy know why it's theoretically expanding?

[Codraroll]

3 hours ago, SOXBLOX said:

 

13 hours ago, Arugela said:

Yes you can. If current design is 80% of max potential from a physics standpoint you can design it to 85%...

So you can increase the efficiency. Great. But the efficiency can't go over 100%. That would mean that you were getting more work out of the system than you put in.

Interestingly, there are examples where the maximum efficiency is far lower than 100. Take Betz's Law, for instance. It states that you can't design a wind turbine more efficient than ~59.3 %. 16/27 is the hard limit, no matter how much you engineer. A turbine extracting more energy from the wind than that would effectively slow down the airstream - meaning it wouldn't extract more energy from the wind after all. 

That being said, there's some nugget of sense in Arugela's comment here. Modern wind turbines achieve around 80 % of the Betz Limit. Theoretically, we could probably get that up to 85. But the overall efficiency of the turbine still would never exceed those magical 59.3 %.

Edited October 27, 2020 by Codraroll

[Entropian]

Has nobody mentioned laws for Carnot cycle engines?  They have maximum efficiencies.

EDIT: Found it: n_I = W/Q_h = 1-(T_c/T_H)

Edited October 27, 2020 by Entropian

[K^2]

This isn't about efficiency, really, while I do understand how that discussion started. It's just not a philosophical discussion. It's a lot cleaner than this.

∇_μT^μν = 0

Divergence of stress-energy tensor is zero. Always. This is mathematically precise. It's not a question of approximations or not accounting for losses. There are no exceptions, there are no violations, because this is a consequence of symmetries in space-time. It's like if I glue two ends of a tape together, the number of twists is a fixed number now. You can move them around, you can try to stretch or flatten them, but you cannot change the number of these twists, because the topology of the tape has been fixed. This is exactly the same concept. This is embedded into the fabric of space-time.

Now we can interpret it. Take a ship floating in space. Draw a boundary around it. Take center of mass of everything in the boundary and chose coordinate system where that center of mass is momentarily at rest. By Gauss' Theorem and using the conservation law above, change in net momentum inside the boundary is dependent on the flow of energy across boundary. In human terms, the object will remain on the same trajectory (moving in straight line with constant speed in open space or remaining in the same orbit if it's orbiting a star/planet) unless some non-zero amount of energy is flowing across the boundary.

No propulsion without exhaust. It's mathematically precise. And we aren't talking about forces balancing out between particles and looking for losses. No, this accounts for absolutely all manner of energy flowing across the boundary, and in fact any boundary we may chose around our ship. It can be exhaust gasses, light, theoretical particles we haven't discovered, angry spirits of dead physicists - whatever you want, so long as it has energy. And if you aren't moving through some sort of medium, the only way to satisfy this condition is to produce exhaust. You have to expel energy to move, and that means you are using reaction mass.

There are no loopholes, no losses to account for. This isn't a 99.9% situation. The equality from which this is derived is strict and fundamental to living in this particular cosmos.