I would argue that this violates Newton's 3rd law, usually stated something like "for every action there is an equal and opposite reaction". To put it in words, there is no reaction to the action that is the second jump. On the first jump, there is a force down on the ground which displaces the ground (i.e. the planet, or whatever) by a usually very small amount; you could call this the reaction to the action of the first jump. On the second jump nothing reacts, unless you argue that some air has been kicked downward at really high speed.

Of course since the laws of physics don't apply, you could attribute the unphysical behavior to some other violations of physical laws as well, but this one seems intuitive, to me, at least.

This doesn't have a unique answer. As others have said, Newton's Second Law is a reasonable answer, but it also definitely violates conservation of momentum. It depends to some degree in which laws you take to be fundamental and which you derive as a consequence from those.

Newton's 3rd

Either you can't make the first jump or you can't make the second.

For every action there is an equal and opposite reaction. If the air was dense enough to act as a second floor then your first jump would be like jumping into a ceiling and you wouldn't make it to your second jump. If the air isn't that dense then no, you don't make the second jump.

Edit:
This is going off the assumption that:

A character jumps from a solid surface, and then is able to extend their jump by carrying out the jump action again in mid-air, starting their ballistic arc again from that position.

Refers to the case where the ballistic arc of the second jump is equal to that of the first - usually the case in games.

I'd say momentum conservation is violated. If you jump in mid-air, you accelerate the air-molecules underneath you. But as their viscosity is not high enough, they easily disperse, without taking enough mass with them. This means that not enough momentum is conserved by the acceleration of these few particles (atoms are very light...). With a higher viscosity, more atoms would be accelerated, i.e. more mass and therefore enough momentum us carried away.

With Newton's 3rd law. "for every action there is an equal and opposite reaction."

in mid air, there is not enough friction/density to give you more lift. When you are in water ,you can push yourself above.For less dense medium like air ,it makes almost impossible for human being to double jump.

Air is a medium with low density so it is very hard to push the air down to jump up as frogs can do in water. Here no physical law is violated just the medium is not suitable.

I am adding some examples. A bird flying in mid air is a similar case of jumping.because of it's low weight and muscles it can push itself up.In a similar case a frog in water can do many jumps in the medium.When bird starts the flight it can jump from the ground with legs but to jump in mid air it will need to use its wings

I think the problem with the double jump isn't so much that it contradicts physical laws. I's that it contradicts the physical fact that you create almost no force by going through the motions of a jump while airborne.

Absent this fact, I'm not sure the double jump would violate any physical law. But given that the second 'jump' generates no force, all three of Newton's laws of motion prohibit it.

• Newton's First Law states that a body in motion will maintain its motion unless a force is acting on it. And for all practical purposes, there isn't any force.




• Newton's Second law states that the sum of all forces acting on a body with a mass will accelerate according to the relation $F = m *a$. Given that $F$ is zero and the jumper's mass $m$ is not, the acceleration $a$ from the jump has to be zero.




• Newton's Third Law states that each action has an equal and opposite reaction. But the action (kicking the air down) and the reaction (kicking the body up) are both zero, given that the second kick exerts practically no force on the air.

So, to repeat, the core of the problem isn't Newton's laws. It's the false impression that a jumping motion in mid-air generates a force on one's body.

Newton's first law, i.e. "Conservation of Inertia"

Newton's first law is (boldface mine):

Every body persists in its state of being at rest or of moving uniformly straight forward, except insofar as it is compelled to change its state by force impressed.

After leaving the ledge, the body should have continued on its ballistic trajectory, affected only by the forces of gravity and air drag₍₊₎. Without another force acting on it, it should have "[persisted] in its state".

But instead the body suddenly changed velocity/inertia₍₊₊₎. In the case of a double-jump the body's velocity/inertia changes without a corresponding force acting upon it.

Hence, it is Newton's first law that is violated by the double-jump.

_{(+) in case that is modelled by the game}

_{(++) we assume the mass stays constant, hence any change of velocity comes with a corresponding change of inertia}

None as long as you have huge wing like feet which allow you to displace enough air to be lifted (and obviously you weight extremely little compared to your feet size).

However the 'laws' are such that they must be followed for an object in our universe, however they only describe how objects act. That is, a object might follow all the laws and still not be able to move in the described way in our universe due to not following the physical constraints of such.

No laws are broken, but Planck's constant is higher than in our world.

I would say that no physical laws are broken, it's just that the double jump is performed in a universe where Planck's constant has a (much) higher value.

Looking at the uncertainty principle for energy:
$$
Delta E Delta t geq frac{hbar}{2}
$$
Just like a virtual particle can break energy conservation for a short time, so can your jumper. When he jumps from the wall, he converts $Delta E $ muscle energy into $Delta E/2$ kinetic energy. And a short time later, mid-air, he converts the other $Delta E/2$ into kinetic energy. In the time period between the two jumps, energy conservation was broken, but because Planck's constant is so large, it is ok.

Another way to look at it, using the uncertainty principle for position-momentum:
$$
Delta q Delta p geq frac{hbar}{2}
$$

You say that at the second jump, he is mid-air. Are you sure? If you are very sure that he is not close to the wall, you can not be certain about his momentum, so how do you know that his momentum changed upwards?
And if you are certain that he jumped upwards, according to the uncertainty principle you don't know much about his position, so he might still be at the wall the second time...

By the way: for this to be true, Planck's constant needs to be at least $10^{34}$ times higher than it currently is. The universe would look very different.

If we assume the atmosphere is air with the same properties as in real life and if we assume we have an intuitive sense of the force the character is exerting when performing a second jump, then there would be an apparent violation of momentum conservation. This is because to have a vertical jump mid-air, the air needs to experience an equal amount of momentum downwards. But because air is in the gaseous phase and has low density, when we kick downwards very little momentum is transferred directly below us. Helicopters get away with this because they not only have very big wings to beat more air downwards, but also spin very fast to increase both the velocity and mass flow rate of air going down. We can expect the momentum from a midair jump is in great excess of what the conservation of momentum would suggest from a human foot kicking air down.

In the real world, and assuming you're not flapping madly to exert sufficient force on the air to instigate a second "jump", then you're breaking:

• Conservation of Energy,


• Conservation of Momentum,


• All of Newton's Laws,


• Probably most of the laws of Thermodynamics


• and likely a few more that are all derived from the first two.

Dealing with the question itself though - which game dynamics would have to be suspended - the answer is strictly "None". Games allow you to arbitrarily change the velocities on objects without explaining it to the dynamics systems.

No law is broken

• Imagine that the planet has a magnetic field. Also imagine that the double-jumper's feet are strapped to a lightweight board with a high-temperate superconducting material. The jumper jumps off the board (fixed by contact with the ground), pulls it up with her feet, cools the superconductor below the critical threshold, jumps again off the board (fixed by electromagnetic repulsion, also transferring the momentum to the ground), heats it back up above the threshold and pulls it with her feet.


• Imagine that the double-jumper's shoes have extending lightweight poles on the bottom. The jumper jumps off the ground, extends the poles, and jumps again off the ground.


• Imagine that the double-jumper's shoes fire a massive invisible bouncy ball each, then catch it again. The balls would hit the ground and bounce back really quickly, transferring half the momentum and then half again to make the full momentum transferred between the ground and the double-jumper.

There are many ways of doing this. That's just the first three I thought of. Other magic like I've listed here could be substituted.

It's a law of Nature that all elementary particles (be it an electron or a quark) have an associated fixed rest mass. The values of these masses can't change. That is to say, at low temperatures; at the very high temperature of about $10^{15}(K)$, the Higgs field, which allegedly gives particles like electrons and quarks mass, evaporates and electrons and quarks become massless, but that is obviously not the case here, because in that case, our man will cease to exist. Now, if at the moment the computer figure (who in the real world is made up out of electrons and quarks) tries to jump for the second time these values lower drastically (in such a way that his mass becomes much less than the mass off the air he occupies), he should be able to jump. By pushing himself against the air upwards, by the buoyant force of the air (in which case he doesn't have to do any effort), or by a combination of both. Right after his second launch, the rest masses of the electrons and quarks resume their original values.

So it's the law of the constancy of the rest mass of elementary particles that is broken (or the conservation of mass/energy).

Some people are attributing this to conservation of energy or momentum. But really those are derived principles, aside from energy which was partially set up/defined such that it would be conserved. Ultimately this is an issue about forces and what sort of forces are allowed to exist.

Basically there are 4 fundamental forces (that I am aware of)

The strong nuclear force

The weak nuclear force

Gravity

Electromagnetic forces

If we assume that nothing pushes the player upwards (and since some games allow for jumping in space) and that this works even in a vacuum then the violation isn't energy or conservation of momentum directly. The real violation here is that there must be a fifth type of force that acts on the player for the instant they jump. The reason is that the forces given are already well defined in physics. Therefore if one claimed to have done such an experiment in a vacuum (and no flaw was found in the experiment itself) and concluded that it wasn't electromagnetic or nuclear in nature (or involving physical fracturing or expulsion of mass/energy) then it would mean that for conservation of energy to be preserved (which is a bedrock principle and should be left intact at all costs) there has to be something else exhibiting a force on the object. Therefore my assumption here would be that another elementary particle or type of force needs to exist in this system. Of course, whether that system has conservation of energy can be further debated and studied but the experiment itself should not lead to immediate contradiction. I would say that the law here being contradicted is the law of completeness (which is a name I just made up). What that means is that our current model is assumed to be "complete". While we do not know everything in the universe and how it works entirely we assume that we have all of the pieces. Gluons, protons, etc. We have rules saying how all of them work and interact. None of those rules or laws are violated if another particle is added. The interactions between those particles still all continue in the same way. It's just that there's another thing that causes unexpected results such as double jumping. That's my take on this.

Of course in a more realistic scenario my presumption is that the player is somehow giving off a repulsive electrical charge or something involving dark matter/negative mass. However, the latter I only know by name and is probably not going to give the desired result.

The fundamental problem with this question however is that if any rule is specifically contradicted then because physics (as a system rather than an ongoing experimental study) is a logically consistent system and because of the principle of explosion (that any contradiction leads to all facts being simultaneously true and false), the contradiction or law violation can be set up to be anything without specifically drawing upon the presence of a contradiction. Therefore while of course one could try to pin down "obvious" candidates for a violation of physical laws one could probably easier than I am imagining set up a formal proof by contradiction to this being possible in the current defined system of physics where the contradiction is found by showing that in such a scenario $0 = 1$. Of course that isn't obvious but under such a scenario of assuming that is possible in a vacuum without charge being involved and with no other particles being newly defined one could show that $0 = 1$ and state that therefore the assumption leading to that must be contradictory to the system as a whole.

On another side however which goes back to my first thoughts physics is not a system of formal proofs. One never proves anything except that data is not being lied about or improperly collected. I would say however that you aren't asking about that as you speak of what it would contradict, which means you are asking about a model of physics and the mathematical rules used to construct rather than the actual ideal physics which may already contain such contradictions that we just haven't yet found and therefore we cannot claim that your scenario is impossible outside of reasonable doubt (unless you specify the question very very narrowly such that undiscovered physics is barred in which case see the previous paragraph).

Has no one mentioned non-Newtonian fluids? Double jump would (to some extent) work in a corn starch solution, so all that is “broken” is that air is treated as a strongly non-Newtonian liquid.