# If I move momentum from someone's body to the ground, creating thrust, am I violating the laws of thermodynamics, even though I conserve momentum?

I'm trying to create flight by mathematical adjustments that don't actually violate the laws of thermodynamics. The obvious thing to do would be to neutralize gravity, but that doesn't create directional thrust. My thought is that I could transfer momentum between the flier and "any nearby object" (usually the ground) in order to generate thrust.

I know that I'm conserving momentum with this, but is there a clause to the laws of thermodynamics that I'm unaware of that would ruin the math? In my mind, it's identical to using an exotic particle to carry the force, the same way that photons carry the electromagnetic force.

• "My thought is that I could transfer momentum between the flier and "any nearby object" (usually the ground) in order to generate thrust": Well, yes, people can jump up by pushing the ground with their feet. The total momentum of the person + earth system is conserved, person moves up, earth moves a very small tiny bit in the opposite direction. The trick is how to transfer the momentum. (And the force carriers are virtual photons, not the lovely physical photons we can see.) May 22, 2023 at 6:51

There needn't be any fundamental difference between "magical" momentum transfer and the everyday kind. Though of course, with any fictional physics, there is by definition a limit on how much detail you can go into without breaking known physics.

If you're specifying that there is some unspecified force carrier, then it's no different to a pool cue hitting a ball, or a magnet grabbing a paperclip, until you get into the detailed particle physics of this force carrier. The important thing is that if it exists, we can presume that it allows for an unbroken chain of accounting for both energy and momentum, even in distant interactions, which is the problem that "real" gauge bosons appear to solve (except for gravity).

Force carriers also solve potential problems with the second law of thermodynamics, in a similar way. Because your aircraft only directly interacts with the local force carriers, it doesn't matter what, if anything, ultimately "receives" the force. So whether the aircraft is accelerating "against" the Earth, or in an infinite void, the entropy of the system is initially only a matter of the aircraft and the force carriers. Those might interact with the Earth, increasing its entropy, or they might just spread out forever, which would constitute an increase in their own entropy.

The important principle is that if everything is always accounted for at the (sub-)micro scale, you don't end up with problems in the big picture.

• I'm going to set this as the correct answer because it discusses force carriers. That's the concept I was missing. Nov 1, 2023 at 22:24

The momentum must be transferred to some other object in a straight line (or, well, a geodesic, but that's a straight line for most practical purposes), or else you will violate conservation of angular momentum.

You will also have to expend or absorb energy appropriate to the resulting acceleration, or you will indeed violate thermodynamics through conservation of energy. Hovering place or translating at constant altitude would require no energy, but changing altitude (or more precisely, changing gravitational potential) or accelerating in any direction must require energy.

• Maybe it can be "borrowed", so long as the balance is redressed over time. May 22, 2023 at 4:18
• Good point on the angular momentum. The acceleration thing sounds right, but consider the difference between acceleration and deceleration. Both require energy going in. Why can't you recoup some of that energy like regenerative braking? The classical answer is "entropy," but entropy is a rounding error, not a law of physics. May 22, 2023 at 4:41
• Error: hovering does require energy, as the body is accelerated towards earth and earth towards the item. You need to constantly accelerate away from the planet at 1 g, which requires energy. May 22, 2023 at 6:09
• @Trish: Howering does not require energy, as illustrated by a computer sitting on a table without any consumption of energy. You are thinking about a helicopter using lots of energy to hover, but that's not required, it is just the way the pilot chose to do it. They could have built a tower and hung the helicopter with a rope, allowing it to hover without any consumption of energy; they chose to expend energy only because they wanted to hover right now and not wait for the construction of the tower. May 22, 2023 at 6:59
• with angular momentum it's not just any straight line (or geodesic) that the two objects must be joined by. The momentum must be tangent to that line May 22, 2023 at 12:41

## The obvious violation here seems to be Newton's 1st law

"An object at rest remains at rest, and an object in motion remains in motion at constant speed and in a straight line unless acted on by an unbalanced force."

In your setup, there is no unbalanced force acting on your jumper, therefore, you can not just repel yourself from the Earth without creating a new force to unbalance it. So, while shooting the Earth away from your feet conserves momentum, this requires an unbalanced force.

This is less obvious, but there is a narrow band of understanding in which this might sort of work within the laws of thermodynamics. The 2nd law states that energy must travel from a state of higher entropy to lower entropy, and not in the opposite direction unless acted on by an outside force: closely resembling Newton's first law of motion.

In layman's terms, it means that heat energy moves from a warmer area to a cooler area, but there are some substances that are quantumly synchronized so that they have zero entropy (like liquid helium) in which energy can travel in any direction it wants seemingly defying several physical laws. In liquid helium, heat can actually go flow from cold to warm just as easily as vice-versa.

Since momentum is just highly organized thermal energy, we can posit that if you could quantumly synchronize yourself and the ground around you, that you could use the thermal energy in your body to propel yourself at speeds up to the speed of sound.

This does not violate Newton's 1st law either because because you are using the heat in your body as your outside force, and are becoming colder to perform your super jump.

The caveat here is that the physics that allow this sort of thing seem to only work at temperatures of about 2 Kelvin ... so probably not something that can be achieved in any practical context, even if it is theoretically doable... but it is a good starting place for techno babbling your superpower.

## You seem to violate conservation of energy

Take the normal situation: the aircraft carries a potential energy in the shape of flight height that will accelerate it down as soon as it does not exert a force $$F_u$$ upwards through its wings, that is exactly the same as the gravitational acceleration $$F_g$$. To stay at the same place, $$F_u=F_g$$. So a Net-0 Force to stay at the height. There is no upwards momentum, great... but to keep that situation you do pay with your floating system converting energy from some potential to acceleration upwards. In a normal plane that is chemical fuel that is burned into heat, which creates motion by expanding gas. In other words: we need to pay with Work $$\vec{W}=\vec{F}\times \vec{s}$$ to stay afloat by some means (other than actually moving upwards) because otherwise, the work of mass acceleration will bring the two bodies together. Typically, that work is done (like in a helicopter) by accelerating air downwards instead of you - the work performed is then the mass of air multiplied by the acceleration from the rotor and the distance the particle move, resulting in an actual work term that the machines floatation device performed. Let's call this world $$W_m$$.

To get the full picture, you need to look at the many partial energies of the item:

If you plot the (potential) Energy from height $$E_h$$ in such a way that the ground is 0 and any height is a positive value, then any height will put a positive value of potential energy on that graph, which is strictly dependent on the flight height $$E_h=mgh$$, and it is changed by the work up as well as the work by gravity $$\Delta E_h(t)=\int_0^t(W_u)dt+W_g\times t$$. The Gravity term is much simpler because on a grand scale you can assume gravity is a constant with a fixed direction (downwards), so we can simplify gravity as a negatively defined value. If the machine stays level, this should be 0, but that is not the work performed by the floatation device but the work imparted on the flying machine.

Now you also need to plot the chemical Energy of the fuel tank's contents $$E_f$$, which is dependent on the drain of the tank. These drains are the work paid to the machinery to stay up ($$W_m$$) and the work to go forward ($$W_f$$), \$E_f=E_{f0}-W_m-W_d, the energy in the tank is the starting energy minus the work for the machinery to stay up and the work for directional movement.

Finally, you need to plot the kinetic energy, which is $$E_k=\int_0^t{W_f-W_d}dt$$, the energy forward is the work forward (assuming a vacuum) minus the work induced by drag.

All the work terms from the plane drain from the fuel, so from an energy standpoint, those are paid for and conservation applies. The other two terms, $$W_g$$ is 0 if we don't drop, but $$W_d$$ is not 0 on just the plane alone. But we had a different term for staying up than work for being up: $$W_u$$ and $$W_m$$. $$W_m$$ and $$W_d$$ are results of Newton's third law, ACTIO = REACTIO: the work from the drag-force on the plane imparts the very same amount of work on the air in opposite direction and is thus net energy neutral over the full system, the gravitational pull towards earth imparts the very same amount of work on the planet as it does on the plane, so it is net-neutral on the full system and so on. In short: energy conservation applies if you include every factor, but not if you just skip on items.

## You need to pay for work

So, as pointed out, you need to pay for the work you want: staying up costs work (as the machinery to stay there is not free but moves air instead of letting you rest on a tower), and going somewhere costs work (by operating the device that provides the uplift). Even if you conserve momentum, you can not trick Newton or Thermodynamics. You will never get energy-free movement, you will always have to pay with work.

• I dont believe hovering should consume any energy, as the person flying is exerting force on the ground below them, with the ground exerting a normal force upwards. It's basically the same as if the person was simply standing on the ground, except their body is displaced upward by x distance
– M S
May 22, 2023 at 10:50
• This question doesn't have anything to do with forcing air downward.
– M S
May 22, 2023 at 11:09
• Yes, something must provide the force to balance gravity. But it does not follow that anything must move and that any work must be done. Often some work is done because that's the best compromise. But it is not necessary. A helium balloon can hover without expending energy. A magnet can hover above another magnet without expending energy. My hat hanging on a hatstand hovers without expending energy. (The last one is actually very closely related to how magnets can hover.) May 22, 2023 at 11:58
• @Trish: The nice thing about aerostats is that they have natural rest points, because the density of the air decreases with height, so that there is a height where the aerostat is, well, static. And magnets hovering absolutely can be made perfectly stable -- just provide a guiding axis. The point is, a force which does not move does not do work. It may be the case that the most convenient way to create the force which does not move involves expending energy (but not necessarily work, thermal energy is also good, for example in a hot air ballloon). May 22, 2023 at 12:14
• If you have some exotic particle allowing for force at a distance, it would require any work to hover as long as your pushing on something that doesn't move. The only reason helicopters require work to hover is that they push on something that moves away. Depending on the specifics of the exotic force, you might be able to have regenerative breaking/lowering such that the only net energy expenditure for flying around would be to cover the drag losses. This would be similar to a maglev train but allow for operating at a further distance from the "rails" where the rails are just anything.
– Rick
May 22, 2023 at 13:45