Speaking as an engineer who knows a bit about physics, I actually prefer to not see real physical systems try to do things that are non-physical. In other words, your superconductivity induced levitation through the Meissner Effect requires really strong force fields that are not realistic over the altitudes that you mention for practical reasons (possibly as well for biological viability reasons).

If you are going with science fiction, you might as well go "all out," with unknown types of matter and/or forces which belong to the types of things real physicists discuss over a cup of coffee at Starbucks, or a good cognac at their favourite Italian Gelatto place. In other words "high-brow bovine manure" (

Yes, I've been an engineer spectator to some of those theoretical physicist types when they're drunk. College towns are great for that).

Alcohol or caffeine effects notwithstanding, some of the theories that real scientists come up when they're wearing a tinfoil hat are really interesting, and since they're a bit more removed from everyday reality, make for better speculation and science fiction while still seeming plausible.

Search for "Diametrical Drive" and "Negative Mass" on the webs...

https://en.wikipedia.org/wiki/Negative_masshttps://en.wikipedia.org/wiki/Breakthrough_Propulsion_Physics_Program#Diametricalhttps://en.wikipedia.org/wiki/Anti-gravity#General_relativity_research_in_the_1950sIt is based on a concept originally proposed by Joaquin Mazdak Luttinger, and then explained by a scientist named Hermann Bondi, in the 1950s, whereby there is such a thing as "negative mass." You can think of negative mass as being equivalently made from "negative energy", in the famous Einstein’s equation E=mc

^{2}. While the concept seems far-fetched, Bondi postulated that the existence of negative mass does not violate Einstein's concept of Gravity under his Theory of Relativity.

Einstein’s General Theory of Relativity describes gravity and the laws of motion for both positive and negative energy particles, hence negative mass, and negative mass doesn't violate anything, other than a postulate Einstein made, named the Positive Energy Condition, which doesn't affect the consistency of the equations in the theory. Meanwhile the Standard Model in Particle Physics (think particle accelerators) does not include gravity.

So there are no obstacles to the existence of negative matter as far as accepted and corroborated (by experiment) physics can say. And in fact, just recently some scientists from Washington State University in 2017, have claimed to have "reversed" the sign of mass, and observed negative mass properties in some Rubidium atoms at near absolute zero temperature...

Future Quantum Mechanics research might lead to some other conclusion though, and in fact, mathematical research by Jean-Marie Souriau in 1970 offered a different set of properties for negative matter, thus refuting Bondi's properties of negative matter, the ones I'll explain below:

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Negative mass is a bit more complicated than you might think. This is not about mass "that floats." This is not a balloon's buoyancy we're talking about. But rather this is about a strange theoretical property, in which negative mass tends to repulse all other mass (whether it's negative or positive), while positive mass always attracts other mass (positive or negative). The net effect is that negative mass can "cancel out" the Gravity of an equal amount of positive mass along the line that connects both centres of mass.

With a sharp eye, you can see the strange effect: A regular positive mass would feel a force pushing against it coming from the negative mass so it would accelerate away from the negative mass. But the negative mass on the other hand would feel a pull from the positive mass, so it would move toward the positive mass. This phenomenon is called "runaway" or "self accelerating" motion.

So if you place a positive pellet of mass (+m) on the left side, and a negative pellet of mass, (-m), on the right side, both the positive and the negative pellets of mass accelerate to the left, along the centreline between the two, with no limit, other than a relativistic speed limit!

In July 1988, Robert L. Forward presented a paper at the AIAA/ASME/SAE/ASEE 24th Joint Propulsion Conference that proposed a Bondi negative gravitational mass propulsion system.[12]

[Hermann] Bondi pointed out that a negative mass will fall toward (and not away from) "normal" matter, since although the gravitational force is repulsive, the negative mass (according to Newton's law, F=ma) responds by accelerating in the opposite of the direction of the force. Normal mass, on the other hand, will fall away from the negative matter. He noted that two identical masses, one positive and one negative, placed near each other will therefore self-accelerate in the direction of the line between them, with the negative mass chasing after the positive mass.[11] Notice that because the negative mass acquires negative kinetic energy, the total energy of the accelerating masses remains at zero. Forward pointed out that the self-acceleration effect is due to the negative inertial mass, and could be seen induced without the gravitational forces between the particles.

In 1957, following Luttinger's idea, Hermann Bondi suggested in a paper in Reviews of Modern Physics that mass might be negative as well as positive.[5] He pointed out that this does not entail a logical contradiction, as long as all three forms of mass are negative, but that the assumption of negative mass involves some counter-intuitive form of motion. For example, an object with negative inertial mass would be expected to accelerate in the opposite direction to that in which it was pushed.

*snip*

Runaway motion

Although no particles are known to have negative mass, physicists (primarily Hermann Bondi in 1957,[5] William B. Bonnor in 1989,[11] then Robert L. Forward[12]) have been able to describe some of the anticipated properties such particles may have. Assuming that all three concepts of mass are equivalent the gravitational interactions between masses of arbitrary sign can be explored, based on the Einstein field equations:

1. Positive mass attracts both other positive masses and negative masses.

2. Negative mass repels both other negative masses and positive masses.

Sounds ridiculous and impossible, and this is of course is refuted by Bondi, the same physicist who came up with negative mass and the explanation of how negative mass would behave, because he sees it as a purely mathematical construct allowed by the equations in Einstein's General Theory of Relativity and not a real phenomenon. Remember Jean-Marie Souriau mentioned above? She seems to show that reversing the energy of matter (hence it's mass) is actually equivalent to reversing the arrow of time in matter. In other words, negative matter, she argued, is matter that is moving backward in time. Souriau explained through some high level maths that the mathematical properties in General Theory of Relativity, actually precluded negative matter from being able to do the "runaway motion" trick - so no perpetual machine.

But the fact is, that as incredible as this sounds - basically a perpetual motion machine- Bondi's "laws" don't violate conservation of energy and momentum on the following grounds, AND provided you look at the system of two pellets as a unit, and assume an initial velocity for each mass to be the same as the other, and the mass of both pellets is exactly the same:

1. The net Mass of the system is zero.

2. The net Momentum of the system is zero (even though it may be moving!!!)

3. The net Kinetic Energy of the system is also zero.

Hence the system is not violating any physics outside of itself. The keyword here is ZERO, if you think about it. That cancellation effect of mass.

One other interesting property follows:

1. When negative mass and regular mass come in contact they annihilate each other like matter and antimatter, EXCEPT that when the negative mass particles and positive mass particles come together they don't explode releasing energy, but instead the collision releases zero energy. In other words, they simply cancel out.

Of course, Bondi's negative mass element "Unobtanium" is nowhere to be found.

Or is it?

The closest we have come is the experiment where Rubidium atoms were "converted" in 2017 by Prof. Peter Engels and a team of his colleagues at Washington State University... Speculate as you will

Prof. Peter Engels and a team of colleagues at Washington State University claim to have observed negative mass on the 10th April 2017 when they created new negative effective mass by reducing the temperature of rubidium atoms to near absolute zero, generating a Bose-Einstein condensate. By using a laser-trap, the team were able to reverse the spin of some of the rubidium atoms in this state, and observed that once released from the trap, the atoms expanded and displayed properties of negative mass, in particular accelerating towards a pushing force instead of away from it.[22][23] This kind of negative effective mass is analogous to the well-known apparent negative effective mass of electrons in the upper part of the dispersion bands in solids[24]

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Now. What can you do with Bondi's negative mass? Plenty I'd say, because remember, the mass (hence the weight) of the system is zero, Your limitation is how much volume do you need to carry an equal mass to your ship? And of course, the system will be stable as long as you keep the negative mass sealed in a magnetic bottle and and within it a perfect vacuum, to avoid "disappearing mass."

For a small "negative mass balloon" you can make an hourglass container or a dumbbell shape where one side of the dumbbell contains positive mass and the other negative mass. The negative mass, located above the cabin for stability, like in a balloon envelope, and if it was like metallic solid liquid or gas, could be contained safely in a magnetic field. The other side of the dumbbell is the entire mass of the ship plus passengers plus the propulsion and weapon systems, as your hourglass/dumbbell will have near zero mass such that you can offset that non-zero weight by more conventional means (propellers. rotors).

I don't see why you could not make shapes other than a balloon. You could treat your ship as a neutrally buoyant airship and use aerodynamic body lift by pushing yourself with propellers. Or forget about aerodynamics and make the propulsion systems do all the work. You would determine the ultimate payload of the ship as being equal to the negative weight of the "excess negative matter" which means you’d need to carry some disposable mass (e.g. water) in your system to push you down when your ship is empty. When you're ready to take a payload, you will have to dump in water the same mass your bringing up the ship - which the sailors will unceremoniously refer to as "whale piss"

When you get to port and unload the ship you will have to refill your water tanks.

Now imagine battle damage. This could be serious. Because if the negative mass container is breached, the positive mass will "cancel out" an equal amount of positive mass in the vicinity. Not only would the ship fall to it's doom, but any sailors (or their body parts), plus anything else on the ship in the vicinity of a leak, would also be "erased" from existence upon contact with the mysterious Unobtanium.

So my guess is that flying ships would have to be very well armoured, or have various systems with "chambers" of negative mass, similar to sealable bulkheads.

Perhaps you should be looking at the Steam/Dieselpunk-ish Anime Series "Last Exile." While they don't refer to negative mass, they keep talking about a mysterious blue liquid named "Claudia," which is circulated through pipes coming out of a mysterious contraption...

Concept images and screenshots from Last Exile

Just an idea...

*Sitting comfortably on a large leather chair, wearing a kepi and a smoking jacket, Wilhelm blows soap bubbles out the smoking pipe*

J. Wilhelm....