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I'm doing some thought experiments towards a computer game that simulates space combat, and I want my engagements to be interesting to players but still be relatively hard-science. Yes, I know this is a challenge.

So, the aim is to make as few modifications to the laws of physics as possible to allow:

  1. Easy travel between "interesting" locations
  2. Travel in a timely manner
  3. Combat makes sense in visual range or near-visual range

In order to achieve this, my solution is a jump drive. This allows spacecraft to instantaneously warp to various locations, and it can be used to avoid the whole "lasers at light-seconds range" issue and bring the spacecraft to a railgun/short-range-laser/missile sort of range.

What issues are there with a jump drive that "just" moves matter from one point in space to another?

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  • $\begingroup$ For long range combat its the railguns that take the cake. If you want lasers to remain effective at the ligtminute range you need focussing arrays that are miles across. Compared to that shooting a railgun or a missile is a far superior option. Especially missiles can be helpful as they can steer themselves and without an explosive payload their kinetic energy will be the threat, so shooting it with lasers or explosives would only create a cloud of expanding shrapnel with still the same kinetic energy that will hit you. $\endgroup$ – Demigan Aug 10 '19 at 11:58
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    $\begingroup$ Huh, I would have thought that the lower velocity of railgus/lasers combined with electronic warfare would tip the balance in favor of lasers. I guess I need to read more projectrho..... $\endgroup$ – sdfgeoff Aug 10 '19 at 12:04
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    $\begingroup$ Is it perhaps better to switch the tag from "hard science" to "science based"? You are purposefully breaking the laws of physics and I wouldnt know how to explain the creation of negative matter, and since we arent even sure if it can be created at all neither do the experts and I would hate to have to solve that and put it in my answer below as that is going to take me a few eons... $\endgroup$ – Demigan Aug 10 '19 at 13:17
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    $\begingroup$ Good point @Demigan I had forgotten about the science-based tag $\endgroup$ – sdfgeoff Aug 10 '19 at 17:32
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    $\begingroup$ How long would it take for your jump-drive to jump again? If you can jump only every few minutes, jumping in-fight must be tactically timed. If you can jump every few seconds, fighting would become a complicated mess, or even impossible. $\endgroup$ – DarthDonut Aug 12 '19 at 9:55
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In order to stay physically "accurate", a jump drive cannot create or destroy energy or momentum. This means the drive has the following limitations:

Momentum conservation

To comply with momentum conservation, your velocity and direction before a jump is the same as what you'll have afterwards. If you are in orbit on one planet, you better go to the right place in the orbit of another planet otherwise you won't be in orbit for long. This means you can either use normal rockets for maneuvering, or if you have the time (and jump-drive energy budget) then you can jump into a gravity well, let it accelerate you, and jump out again.

Energy Conservation

You have to consider gravitational potential energy before jumping. This means maneuvers in orbit can be performed cheaply (aka jumping in/out of combat), and but jumps to other planets are extremely expensive

I wrote a calculator to estimate jump energies. For the energy estimates I'll be assuming a 10 tonne spaceship, and that the gravitational potential energy difference comes from the jump drive (and thus has to be generated by a reactor on board the craft):

  • To jump from LEO to lunar orbit takes 460GJ (150 tonnes of TNT, vaporize 292 tonnes of water). If it has a 1MW reactor, it'll take 127 hours to generate the 460GJ of energy.
  • Jumping from Geostationary still takes 78GJ (18 tonnes TNT, vaporize 35 tonnes of water). A 1MW reactor would take 22 hours to charge for this jump

Why only a 1MW reactor? You still require hundreds of meters of radiators for a 1MW reactor! Batteries? A lithium ion chemistry battery is about a megajoule per kilogram. So you're looking at thousands of kilograms of batteries.

There's a nice map of gravity wells on XKCD:

Given that it takes hours for our reactor to jump a super lightweight spacecraft a couple pixels vertically, we can assume that a jump drive can travel approximately horizontally on this image. This means that a jump drive from the earth or moon can only take you to an orbit around Jupiter, into the middle of Saturn, or half-way to Venus.

So while jump drives may allow the type of space combat you're looking for, you also need to hand-wave a power source and heat-sink if you want to actually go anywhere.

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    $\begingroup$ In general relativity there is no coordinate-independent way of saying what it means for two objects at different locations in curved spacetime to have the "same" energy/momentum vector, due to the way that parallel transport of vectors between two points is path-dependent in curved spacetime. So in general, energy is not conserved in a global sense in GR, not in a coordinate-independent way anyway, though it is conserved locally. $\endgroup$ – Hypnosifl Aug 10 '19 at 18:38
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    $\begingroup$ BTW, if the OP wants a version of a "jump drive" that is theoretically compatible with GR, they can just use a traversable wormhole. In this case the local momentum when exiting the wormhole would depend on the motion of the wormhole mouth itself. According to comment #7 by pervect in this thread, there is a type of momentum conservation with wormholes if you assume they're in an asymptotically flat spacetime. $\endgroup$ – Hypnosifl Aug 10 '19 at 18:43
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I would go for the Alcubierre drive.

https://en.m.wikipedia.org/wiki/Alcubierre_drive

The alcubierre drive circumvents many problems of FTL travel. The ship can be virtually at a standstill and experience no time dilation or other relative effects while the ship rides a sort of wave of gravity/space to its destination, and this wave does move faster than light as it pushes the ship along.

The problems:

  • you need negative matter to travel. Its unsure if it can be created and would cost a ton of energy. This could also be a good thing as it explains why there are few alcubierre-based weapons. For the energy you could have dyson swarms, kugelblitz's and black hole generators create the necessary energy for negative matter production.

  • you can only really travel as fast as you can throw the negative matter in front of the torus's around your ship. This limits your velocity to below the speed of light... unless you cheat here a little. Quantum tunneling (https://en.m.wikipedia.org/wiki/Quantum_tunnelling) allows things on the tiny quantum scale to avoid traveling through a portion of space. This is in fact the only reason our sun can even start fusion as particles tunnel into each other to start the reaction. If you say your ships have a way to actively control the tunneling and send enough negative matter particles to their location for the effect you could theoretically reach beyond lightspeed.

  • the ships require two or more torus shaped objects around them to travel. Damage to these torus's would basically make the ship dead as it cant escape and cant continue effective attacks. You could perhaps say that the ship carries spare torus's or have the ability to retract them into the ship in short notice after use to protect them.

  • the alcubierre drive is a seperate engine. For things like maneuvering into a planetary orbit you need seperate thrusters and fuel.

There's probably more problems but I dont know that much about the exact formula's and such of the alcubierre drive.

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    $\begingroup$ According to the known laws of quantum field theory it's impossible to use quantum tunneling or any other quantum effect to control the behavior of distant matter/energy in a way that involves information moving faster than light, see here and here. But the "Physics" section of the wiki on Alcubierre drive does say "a similar result could be achieved without tachyons by placing in advance some devices along the travel path and programming them to come into operation at preassigned moments" $\endgroup$ – Hypnosifl Aug 10 '19 at 18:50
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    $\begingroup$ @Demigan - if you can push a button at one location and have it determine whether negative matter reaches another location at a point in spacetime outside the future light cone of the person pushing the button, then that's a transfer of information faster than light, since a person who knows the setup and is at the location the negative matter arrives will be able to infer something about the switch being pushed at a point outside their past light cone. In general, it's prohibited for a person to be able to causally influence whether or not some event happens outside their future light cone. $\endgroup$ – Hypnosifl Aug 10 '19 at 21:56
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    $\begingroup$ According to the article here no individual particle is ever measured to get from one location to another faster than light in tunneling experiments. Besides, physicists have already analyzed the problem of an Alcubierre drive without any external machinery and believe it would require genuine tachyonic motion for the exotic matter; is it really plausible your idea about using tunneling could be a workable solution that eluded all those physicists? $\endgroup$ – Hypnosifl Aug 11 '19 at 1:33
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    $\begingroup$ If you continue to read that article he says of the electron experiment, 'It isn't as though at one instant you can say "this particle is over there" and then, some tiny amount of time later, you can say "this particle is now located here instead" with that change-in-distance divided by the change-in-time exceeding the speed of light.' He isn't talking about the issue you bring up of whether the particle "moved" between measurements, he's saying these experiments don't involve two local measurements such that separation divided by time between the two measurements is larger than c. $\endgroup$ – Hypnosifl Aug 11 '19 at 6:21
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    $\begingroup$ Also see the video here, especially the discussion of the experiment with a tunneling barrier along one possible path for photons, and then the part about 8 minutes in that although photons arrive at the detector earlier on average with the barrier present, there's already uncertainty in when they arrive when there's no barrier and hence no tunneling, and the ones that tunnel don't arrive any earlier than the earliest-arriving ones with no barrier, the barrier just screens out the part of the wave function corresponding to later-arriving photons. $\endgroup$ – Hypnosifl Aug 11 '19 at 6:39
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You can have a jump drive by accessing additional spatial dimensions.

This question has good stuff on the concept. Could you have more than one building in the same spot by "stacking" them in 4th dimensional space?

Consider your motion as a vector. You can calculate the energy needed for any given motion. In 3d space we have X, Y, Z vectors for our 3 dimensions. If you could move through a fourth spatial dimension you could in your ship access other three dimensional spaces "neighboring" our own and re-emerge in our 3d space at a great distance from your original location. The classic example uses a Flatlander in 2d space with only x and y coordinates. If its paper 2d plane could be folded end to end thru 3d space the Flatlander could jump from one edge of the paper to the other thru z (the third spatial dimension) while actually moving very little.

So too your jump drive. It may be that space is not arbitrarily folded according to your whim, but has a fixed topological shape in many (infinitely many?) dimensions. You can move through higher and higher dimensional spaces to re-emerge in your own space where you want to be. You need a map to figure out how to get there, or known locations in our own plane at which the curvature of our plane in 4d allows easy access to other parts of our plane.

It is still just vectors and you can calculate energies the same way. You get additional vectors as you increase spatial dimensions.

Danger: just as you can stack infinitely many 2d planes in a 3d cube, within any 4d space there are infinitely many 3d spaces into which you might emerge. Within any 5d space there are infinitely many 4d spaces. It gets big. Your jump drive pilot might need some cognitive assistance wrapping his head around the geometry of your course.

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    $\begingroup$ If 4-space is simply another perpendicular axis, it makes no change to the energy requirements: the radius vector now contains x, y, z and w coordinates. Folded dimensions may or may not influence it as I guess any difference in energy between the two locations would be needed to cross the fold? So if there's a gravity potential difference, there would be a very strong suction/repulsion at the position of the "fold". I wonder what light would do? Would looking from one side allow light to pass and from the other block it? Fun stuff! $\endgroup$ – sdfgeoff Aug 12 '19 at 19:29
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I am going with the model used by the author Jack Campbell in his series "The Lost Fleet" and its spinoffs.

Here the FTL-method of choice is a jumpdrive which accesses another dimension wich allows the travel between star systems in days and weeks. The ramifications for the use of said drive are limited range (only about 2 weeks of travel time are considered save) and fixed entry and exit points that are given with the gravitational fields of a star system.

Now consider this:
If you do the hard science approach, do you use superluminal sensors? No? Good! Because now you have to close in for combat, or else your data is so unprecise that you won't hit anything! Now for a little math!
Consider an enemy ship only a lightsecond away. That are about 30,000 kilometers! You, as the captain are giving the fatefull order "FIRE!" and your ship(s) are activating their Cannons of Doom(tm).
The shots will travel with a velocity smaller or equal to light speed, depending on the type of weapon (projectile or laser/maser/phaser whatever). This means that they will take atleast a second to reach their target.

To recap: your data is a second old, and your shots need atleast a second => two seconds time for your enemy to move his ship. Typical speeds in space today are multiple kilometers per second (Pioneer 10: about 12 km/s). I do not know how big these ships are, but they only have to move about their own size out of the way to avoid getting hit. And with typical speeds involved in space, that is easy.

Tl;dr: Effectively, it does not exclusively hang on the drive, but also on the sensors. You need to get near so that your targeting calculations don't have to guess "where will he be" when firing.

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