recoilless propulsion

[freker]

Suppose you have two objects in a perfect vacuum (where there is no friction) attached to each other with a wire.
Object 1 can instill a force on object 2 (for instance by shoving it away), because of Newton's 3rd law both objects will move away from each other, keeping the center of the total system in the same place.
now suppose object 2 has a system inside containing a certain amount of antimatter and an equal amount of matter, the matter and antimatter will be brought together and conversed into energy, which will be contained inside object 2. this will happen before the wire connecting the objects reaches its maximum extension.
now the mass, and thus the kinetic energy of object 2 has changed, so when the wire is fully extended the negative force from object 2 on the wire must be lower than the positive force of object 1, resulting in a net force on the system causing the center of the system to move.

Is this feasible or am I missing something with the conversion of matter to energy?

I could not find a similar topic, so if there is one could you please redirect me to it?

[Wyrm]

now the mass, and thus the kinetic energy of object 2 has changed, so when the wire is fully extended the negative force from object 2 on the wire must be lower than the positive force of object 1, resulting in a net force on the system causing the center of the system to move.

The energy of the matter/antimatter annihilation is considerable and has significant inertia of its own — it cannot be ignored. Indeed, it has exactly the same inertia as the matter and antimatter used to create it. Object 2's mass is therefore unchanged, and thus the physics of the scenario are unchanged from the one where object 2 does nothing. The center of mass of the two objects remains stubbornly the same place.

If object 2 were to expell the energy created in the reaction, then while the center of mass of object 1 and 2 would move in some direction, considering the center of mass of object 1, object 2, and the radiation object 2 expelled also remains unchanged.

[Kuroneko]

The operation will not change the amount of force neeeded to accelerate the object. To expand on the above, Newton's second law states that force is the rate of change of momentum, but relativistic momentum has a Lorentz factor: p = γmv. The mass-energy relationship is E = γmc². Hence force is the rate of change of (E/c²)v, rather than the Newtonian mv.

One interesting consequence of this heating an object increases its internal energy, which leads to a higher necessary force for acceleration. By a very small amount, but there nonetheless.

Strictly speaking there is no such thing as conversion to energy. People frequently say that, and what's meant is conversion to some form that has no rest mass, which is usually the electromagnetic field. But the field has energy rather than 'being' energy. Historically, that a charged particle's electromagnetic field would resist acceleration and hence contributes to the inertial mass of the charge, along with E = mc² (in the rest frame of the object, where γ = 1), was derived several years before Einstein's theory of relativity.