# Making 4D Radiators Good Enough for Stealth, Unremarkable for Power

I am trying to find a solution for a specific subset of the Stealth in Space Problem: dealing with waste heat without tipping off properly positioned observers. This question is scoped specifically this one way of tackling the problem, not to the problem's other aspects (such as trapping said waste heat). I'm open to bending the laws of nature, but I would rather do this in a knowing and consistent way, and understand the possible unintended consequences, and at least the orders of magnitude of things like efficiency and energy levels involved, thus the tag.

My goal is to come up with a paradigm-shifting radiator/heatsink-like technology that is good enough to deal with the waste heat a spaceship may produce as a result of her activities (preferably good enough to deal with a reactor running strongly enough for life support and other typical on-board equipment), but that cannot be used in a way that completely invalidates other power plants (e.g. running a Stirling engine on waste heat of life activities alone).

Here is my starting point, which is open to adjustments:

Let's postulate a technology that allows building radiators that radiate into a direction that is perpendicular to all three of our spatial dimensions - a 4D radiator. For every X³ of volume of the device, it can radiate as well as a normal modern radiator with an X² surface; the device has a density of approximately 1/5 of a kg per litre; cost is yet undecided. The background temperature of the fourth-dimensional void is close to 3K. For now, assume there are no ways for other ships to remotely perceive what's going on the fourth dimension near the stealthy ships, and thus no way to trace that irradiated heat.

Is the above setup already good enough for my goals? Or would it require some adjustments (e.g. scale radiative capability to a different power of X, perhaps)? Or is my request such that satisfying the stealth usage requirement will under all circumstances result in 4D Stirlings so good that they replace all other engines?

• If you civilization has access to a 4th space dimensions, it feels like they could do more awesome things with it then just dumping excess heat in there. So if the heat dump is the only mention of 4D this looks odd to me. Commented Jan 23, 2020 at 10:38
• @StarfishPrime and [at]LDutch On deeper thought, fair enough. Downgrading the tag. Commented Jan 23, 2020 at 10:49
• For a 4-D radiator it "surface" is actually its volume X³. But than rises a question: what it's 4-D volume? How our 3D ship, radiator, universe looks like in that 4D space? For example if it folded titghtly - you would create a lot of heat sources around you in 3D space, wich may or a may not be the opposite of heat stealth. Commented Jan 23, 2020 at 10:52
• @ksbes This is is why I pointed out that there are no ways to spot those 4th-D heat emissions by other ships. Should I also add that without the special technology, no heat is being exchanged in the fourth axis, to avoid tangents in answers? Commented Jan 23, 2020 at 10:54
• @ksbes it seems reasonable to assume that 4D radiators, like 3D radiators, will be placed in such a way that they radiate heat away. There's no need to nitpick that. Commented Jan 23, 2020 at 11:45

For every X³ of volume of the device, it can radiate as well as a normal modern radiator with an X² surface

So a cubic metre of radiator material weighs 200kg, and has the same radiating ability as a square metre of regular radiator. That makes it somewhat heavier, by radiating capacity, than even simple 3D heat-pipe radiators. Possibly this is a deliberate choice for balance reasons, but it does mean that a decent 4D heatsink array is going to be very big and heavy.

cannot be used in a way that completely invalidates other power plants (e.g. running a Stirling engine on waste heat of life activities alone

Well, you're already out of luck. You've declared the cold-end of your 4D radiator to be at 3K, so practically anything will generate a heat gradient relative to that. Does it really matter, though? You can already stick a heat engine between a heat source and regular 3D radiators, but mostly you don't because it ends up needing bigger and heavier heatsink arrays, and if bigger 4D heatsinks impair your rocket performance then no-one will bother.

If your 4D heatsinks are effectively inertialess then all bets are off. Don't allow arbitrary heatsink sizes to be strapped to spacecraft. That way lies madness.

What it does mean is that any immobile object can be attached to a 4D radiator of stupendous size. That means it can actively cool its own structure to ward off the heating effect of long-range energy weapons, and can operate gigantic lasers of incredible range and fire them indefinitely.

With the ability to run unreasonably powerful systems, you open the possibility of space stations detecting your stealth ships via active sensors...

Is the above setup already good enough for my goals?

Probably. Is it good enough to avoid unintended consequences for your setting? Maybe not.

• Thanks. 1. Note the scaling is one of the things open to rewriting if necessary. 2. I know some heat engine will be possible. I'm concerned about such heat engines being so good that they remove the need to ever have any real power plants (effectively ending the era of ICE, power cells, reactors etc.). I'm not sure from your answer whether that's the case with current numbers. Commented Jan 23, 2020 at 11:59
• @vicky_molokh it won't remove the use-case for batteries, and for combustion engines it can only make them more efficient but not replace them entirely... a 270K temperature difference to ambient might mean that 4D-heatsink-sterlings replace most small motors and batteries, but more powerful engines and power plants have higher temperature differences than that. If nothing else, you can just handwave in cost overheads and the problem will go away. Commented Jan 23, 2020 at 12:04
• It's not just a matter of temperature in colder system, it's also a matter of how fast you can transfer heat there. You can stick hand into liquid nitrogen or fire for very short lengths of time because heat transfer isn't low enough to cause damage. Just because 4D radiator emits to somewhere with ambient T=3K doesn't mean it can transfer heat fast enough to itself reach anything close to 3K or cool Stirling's working fluid to such temperatures, severely limiting practical efficiencies. Commented Jan 23, 2020 at 12:39
• @Miech it has to transfer heat fast enough to support science-fictionally "interesting" spacecraft engines, I'm assuming. That's an absolutely punishing requirement, and it demands decent thermal conductivity. Of course, I could be wrong, and the OP's stealth-ships might all be using complex minimal-delta-V multi-year trajectories on their missions... Commented Jan 23, 2020 at 12:41

Essentially you are really creating a "basement universe" which can be thought of as a balloon where you are dumping waste heat orthogonal to the other three dimensions of our universe.

However, the implications of that are pretty mind blowing. Computational limits, the Carnot limit for heat engines and most other thermodynamic limitations created by the Second Law of Thermodynamics go right out the window. Perpetual motion and "free" energy suddenly become possible...in fact virtually every sort of limitation that exist in the physical universe become irrelevant. Think about the implications of that for a moment.

So now that you have effectively created a universe of magic, mundane things like waste heat no longer bother you. Indeed, lots of things might not be a problem. Need some time to think about problem? Blow a bubble, create a pocket universe, do your stuff and then come back into our universe. IF time isn't synchronized between the universes, you might have spent years "outside" the universe in subjective time, while in "objective" time, I just saw you flicker for a moment. On the other hand, if you make a mistake with the time dimension....

What takes this outside the realm of hard (or any) science is the idea of wormholes, basement universes and other manipulations of Space-Time really depend on starting assumptions which have not been proven, or technologies and concepts like negative matter which have not been demonstrated to exist in the real universe. The implications are pretty huge, so if this is in any way possible, then (assuming other beings exist in the Universe), sometime in the past 13 billion years someone will have been hard at work to attempt this, and there should be pretty unmistakable evidence of this, since standard physics will have been grossly violated in the region(s) where this is taking place.

While not really helpful for your story, it should cause you to rethink things, and perhaps generate new ideas.

• This answer seems to assume that the basement's door is a two-way street that anything other than raw emissions (in this specific example, one-way radiative heat) can walk. It is not, and I apologise if my question mislead you to think it is. Now, free energy from plugging heat engines between a warm environment and the cold 'hypervoid' are exactly the implication I've been aware of and trying to evaluate in how bad it is (some back-of-the-envelope estimates elsewhere indicate it's less cost-efficient than even solar power), but second opinions are very welcome. Commented Jan 24, 2020 at 7:41