Can Heat Differential Generate Thrust?

[cosmonium]

This is an experiment I have wanted to do for a few years now but don't have the necessary equipment. GR tells us if you have identical objects with the same weight exactly when they are at the same temperature, then when one object is heated, it will weigh more. This is because the gravitational force depends on the stress energy tensor in general relativity. The stress energy tensor 00 component is the total energy of the body, which includes the rest mass plus the kinetic energy of the object. Temperature differences mean that there is a different amount of kinetic energy in the motion of the atoms of the two bodies.

Therefore, if you were to use a motor to spin a massive disk at high speeds while applying heat energy on one side of the fixture (by laser or friction) and remove heat on the other (by laser cooling or some sort of radiator if possible), would this create a force in the perpendicular direction to where the heat is applied since it would effectively be creating an inertia differential which would cause higher acceleration reaction force on the hot side compared to the cold and be equal to the force of the motor required to counter this and keep the disk at a constant speed?

Obviously this force if any would be extremely small and difficult to measure but, if it could be scaled up, would be a method of electric propulsion. I can’t find any record of anyone attempting this experiment but it seems like if you had access to laser cooling and extremely sensitive force measurements it would be worth a try.

 

[PeterDonis]

if you were to us a motor to spin a massive disk at high speeds while applying heat energy on one side of the fixture (by laser or friction) and remove heat on the other (by laser cooling or some sort of radiator if possible), would this create a force in the perpendicular direction to where the heat is applied

Try thinking of it without the fixture or any other external object: just a massive spinning disk in free space, which starts out at the same temperature throughout. Your question would then be: can we exert thrust on this disk by heating one side and cooling the other? We assume that we can ignore any radiation pressure or other effects from the heating/cooling, the only effect those have is to create a temperature differential in the disk.

When you ask the question that way, the answer should be obvious: no, because of conservation of momentum. Think of how an ordinary rocket works: it ejects some exhaust out the back and as a result it accelerates forward, because of conservation of momentum: the exhaust gains momentum in one direction, the rocket gains momentum in the other. But in your scenario, there is no exhaust; there is no way the disk can change its momentum because it remains self-contained and doesn't exchange momentum with anything else.

By the way, even the heating/cooling in this problem is really a red herring. You mentioned the stress-energy tensor; stress is also part of that tensor, and a spinning disk will have varying stresses in it even if it is all at the same temperature. So if it were possible for differences in the stress-energy tensor in different parts of the disk to create thrust, which is basically what you're hypothesizing, any spinning disk would be able to create thrust within itself. But again, that obviously violates conservation of momentum.

 

[cosmonium]

But in your scenario, there is no exhaust; there is no way the disk can change its momentum because it remains self-contained and doesn't exchange momentum with anything else.

Unless you consider the heat energy as the exchange. Heat energy is radiated in exchange for the force. Or a more off the wall theory would be that it is not exchanging momentum but redirecting it. But honestly i don't expect the experiment to work, i just think it is worth trying.

By the way, even the heating/cooling in this problem is really a red herring. You mentioned the stress-energy tensor; stress is also part of that tensor, and a spinning disk will have varying stresses in it even if it is all at the same temperature. So if it were possible for differences in the stress-energy tensor in different parts of the disk to create thrust, which is basically what you're hypothesizing, any spinning disk would be able to create thrust within itself. But again, that obviously violates conservation of momentum.

Right but in a uniform temperature disk (or even a disk of non-uniform temperature but is not activly having heat added and removed at fixed points relative to the whole fixture) those stresses are symetric across the disk which would cancel out the effect.

 

[PeterDonis]

Unless you consider the heat energy as the exchange.

Energy is not momentum. If the heat exchange involves a differential in momentum, then that can create thrust--but then it isn't the difference in energy or temperature that's creating the thrust, it's the fact that you have momentum exchange taking place; the fact that the momentum exchange happens to come along with heat exchange is irrelevant. And in this case the first thing an engineer would do anyway is to try to minimize the heat exchange required for a given momentum exchange, to minimize the thermal stress on the disk.

a more off the wall theory would be that it is not exchanging momentum but redirecting it.

Please read the PF guidelines regarding personal theories. If your idea violates conservation of momentum (which is what "not exchanging but redirecting" looks like to me--momentum has a direction so "redirecting" means "changing in a way that is not conserved"), it is out of bounds for discussion here.

 

[cosmonium]

Energy is not momentum. If the heat exchange involves a differential in momentum, then that can create thrust--but then it isn't the difference in energy or temperature that's creating the thrust, it's the fact that you have momentum exchange taking place; the fact that the momentum exchange happens to come along with heat exchange is irrelevant. And in this case the first thing an engineer would do anyway is to try to minimize the heat exchange required for a given momentum exchange, to minimize the thermal stress on the disk.

But just the fact that heat energy can be transferred from one object to another thru radiation (which we know) and that the energy transferred in that exchange effects the weight of both objects (which is theorized in GR) means that it would violate conservation of momentum NOT to consider it a valid method of momentum exchange when calculating momentum

Please read the PF guidelines regarding personal theories. If your idea violates conservation of momentum (which is what "not exchanging but redirecting" looks like to me--momentum has a direction so "redirecting" means "changing in a way that is not conserved"), it is out of bounds for discussion here.

That is not my personal theory; it is just one possible explanation as I am a fan of Clarke's first law. But if we are sticking to only published theories then i believe this experiment is still valid as stated above.

 

[Dale]

Differential temperature can certainly cause thrust, but it is much simpler than you have written and doesn't have anything to do with GR. The hot side radiates more than the cold side, so there is net radiation thrust in the direction of the cold side. This is believed to be the explanation for the famous Pioneer anomaly.

 

[cosmonium]

Differential temperature can certainly cause thrust, but it is much simpler than you have written and doesn't have anything to do with GR. The hot side radiates more than the cold side, so there is net radiation thrust in the direction of the cold side. This is believed to be the explanation for the famous Pioneer anomaly.

I am unfamiliar with the Pioneer anomaly but i will certainly look into it. But if that is true would this system therefore not violate the law of conservation of momentum since in the end radiation is released? But i suppose if that ends up being the only cause of a net force then it wouldn’t matter if the disk was spinning or not as the path would be irrelevant.

 

[Dale]

But if that is true would this system therefore not violate the law of conservation of momentum since in the end radiation is released?

The radiation carries momentum, just like rocket exhaust. So conservation of momentum is not violated.

i suppose if that ends up being the only cause of a net force then it wouldn’t matter if the disk was spinning or not as the path would be irrelevant.

Yes, I agree.

 

[PeterDonis]

just the fact that heat energy can be transferred from one object to another thru radiation (which we know) and that the energy transferred in that exchange effects the weight of both objects (which is theorized in GR) means that it would violate conservation of momentum NOT to consider it a valid method of momentum exchange when calculating momentum

In other words, radiation carries momentum as well as energy. Yes, it does, as Dale has pointed out.

As far as "affecting the weight" goes, "weight" is not what GR says changes. The object's stress-energy changes. But it is perfectly possible for the "energy" component of stress-energy to change without the "momentum" components changing. If both change, it is because whatever is adding the energy is also adding momentum--as with the radiation carrying momentum, as above.

That is not my personal theory; it is just one possible explanation

No, it isn't a possible explanation because it violates conservation of momentum. Momentum can't be "redirected".