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Some background

As most of us know, accelerating to relativistic speeds requires truly astronomical amounts of energy. I have internalized that a ship carrying enough energy/fuel to accelerate to near-lightspeed by its nature also carries enough energy to destroy a planet several times over, even ignoring the fact that the near-C ship could just ram a planet to explode it rather effectively. The trick, though, is carrying enough stored energy onboard the ship to accelerate to those preposterous speeds, and then decelerate again at some point. Fuel has mass, and mass requires more fuel to accelerate it at the same rate as less mass, and so there is no way, in my understanding, to store enough energy aboard a ship to reach speeds like 0.5C, let alone 0.99C as is popular in these types of discussions. The answer to this problem is to not store the energy on the ship at all, but to beam it into the ship remotely. This is called beam propulsion, and is stupidly easy if you have something like a Dyson Sphere. I'm sure many of you are already familiar with this, but for those who are not, basically, a ship is built with large sail-like structures (think solar sails) that are targeted and fired on by intense and focused beams of energy that have access to astronomical amounts of energy, pushing the ship at a constant and high rate of acceleration for prolonged periods.

In-universe context; and main question

In the sci-fi universe I am building, Dyson Spheres, or stellar engines or whatever you want to call them, are common, albeit very expensive installations, and human civilization overall is very adept at beam propulsion, aided in no small part by their prodigious energy budget. Ships are sent between star systems at speeds often exceeding half of lightspeed (0.5C), and civilized space is formed into a network of these beam-powered routes that many of you might know as a concept called an Interstellar Laser Highway system. This works fine for traveling between systems with established infrastructure to speed you up at one end and then slow you down again at the other, but what about traveling to uninhabited systems where no infrastructure has been built yet?

Technologies and limitations

In the setting, I have decided that energy can be stored as photons within chambers lined completely with a perfectly reflective substance, trapping photons indefinitely. This method of power storage would be extremely energy dense, and I have read that light confined in this way, at a certain point of energy density, will start behaving something like a gas, and exert pressure, establishing an upper limit to how much energy can be stored in these chambers. So, say we have a starship en route to an uninhabited system. It was propelled to about 0.5C by a stellar laser back in a nearby frontier system, and has been traveling for a few centuries now. I have been trying to figure out a way for this ship to decelerate at its destination, and have tried to avoid having it use the energy it has stored onboard, for fear that it will not be anywhere near enough, but I can think of no other way that does not involve magic or cartoon physics.

The question, expounded

This question has multiple facets:

  1. Exactly how much energy is needed to decelerate a ship from (or for that matter accelerate it to) 0.5C ? I am badly under-informed in all kinds of mathematics, and energy is among my weakest areas in math, so I hope someone smarter than me will see the way.
  2. Exactly how much energy could be stored in one of those photon-imprisonment chambers of a given internal volume, according to current understanding, ignoring the issue of how to get the photons in and out of the chamber? Would the energy stored in one of these chambers of a reasonable size be enough to decelerate a craft from 0.5C?
  3. I've heard that photons have mass, and so would the mass of the light trapped aboard the ship amount to anything that could alter the ship's delta-V? I am also assuming in this setting that they have futuristic engines that can essentially convert electrical energy directly into velocity, among the setting's only clarketechs. Would the photon-imprisonment chambers be superior propulsion to the magical momentum drives if you broke them open? If so, what level of acceleration could they provide?
  4. What sources or courses can I consult to try to learn how to work out these math problems for myself? where should I go to actually understand things like the standard Rocket Equation or Specific Impulse?
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  • $\begingroup$ similar? worldbuilding.stackexchange.com/questions/23683/… $\endgroup$
    – Willk
    Jul 5 at 19:36
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    $\begingroup$ "I am also assuming in this setting that they have futuristic engines that can essentially convert electrical energy directly into velocity, among the setting's only clarketechs." ...this is huge. This means you have reactionless drives. I feel obliged to point you towards Burnside's Advice: scifi.stackexchange.com/questions/170017/… $\endgroup$
    – Qami
    Jul 5 at 19:49
  • $\begingroup$ With a really good mass fraction (>0.8 or so, if I did this right...), you may not strictly need a clarketech photon-storage device to get half a c of velocity; a good old antimatter beam core rocket should do the trick. This is how Valkyrie was designed, after all. And a civilization with Dyson swarms could pony up the antimatter pretty easily. $\endgroup$
    – parasoup
    Jul 5 at 20:03
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    $\begingroup$ Since the mass of the spacecraft is unspecified, no specific answer is possible. Therefore, regarding subquestion 1, refer to the kinetic energy formula for relativistic bodies, e.g. courses.lumenlearning.com/physics/chapter/… , although given that you're staying below 0.5c, the classical E=0.5*mv² probably works well enough. For subquestion 2+3,Einstein's good old E=mc² for mass-energy conversion applies here when rearranged to m = E/c². $\endgroup$ Jul 5 at 20:32
  • $\begingroup$ Humanity is only just starting to understand photons. From our understanding today, photons have no mass, only energy. This is important because, relativistically, any mass at all accelerated to the speed of light will increase in its relativistic mass to infinity. Could our math be wrong? Of course. We don't yet have a perfect understanding, but today, photons have no mass. $\endgroup$ Jul 5 at 20:41
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Your photon cage already gives you the most efficient thruster possible: a photon rocket.

Photons carry momentum (that's how lightsails work) so you simply open a hole in the photon cage and the outflow of photons creates thrust in the opposite direction. Specific efficiency depends on the mass of your photon cages and energy of the photons stored but if you want to do the math, see https://en.wikipedia.org/wiki/Nuclear_photonic_rocket for an explanation. The article cites a theoretical max efficiency of 300 megawatts per newton of thrust, which sounds like a lot of energy to store in day to day terms but possessing a means of directly storing photons (effectively 100% efficiency in photon generation relative to fuel stored) is maximally efficient compared to converting fuel to photons as in the nuclear photonic rocket or even an anti-matter powered equivalent.

[EDIT] So, here's some basic math to help you get started on your calculations.

  • Energy to get up to 0.5c. That isn't near a relativistic speed so we should be able to use the classical formula to calculate the kinetic energy: K.E.=0.5*mv². Plugging in the numbers says that for every metric ton of mass (1000 kg) in the ship requires ~11,234,439,734,210 megajoules of energy to accelerate it to 0.5c. Each megajoule is about equivalent to 1 stick of TNT so, in total, that's the energy of about 2685 megatons of TNT. Or, to incorporate quarage's suggestion from a comment, a megawatt is one megajoule per second so for a normal 500 MW nuclear power plant, that's 712.5 years of output (or equivalently the output of 712.5 500 MW power plants for one year). If the ship weighs a million metric tons, multiply the above number by one million. Also remember that that much is needed again to decelerate the ship back to a stop at the end of the journey.

  • How much does that much energy weigh when you put it into a photon cage? Well, we know that mass and energy are equivalent through Einstein's famous equation, E=mc². Rearranging that, we get m=E/c². If we plug in the above number, we get almost exactly 125 kilograms, which is amazingly small for the energies involved. So, for each metric ton of mass in the ship, at least 125 kilograms of it has to be stored photons to either fully decelerate it (or fully accelerate it) to 0.5c, assuming perfect conversion of energy to thrust. (For convenience, we ignore the fact that the ship gets lighter as the photons are expended for thrust.) And remember, this is close maximally efficient in terms of fuel to mass ratio for a photon rocket since it's already in the form of raw photons. We don't know how much photon cages weigh per megajoule held so we cannot say any further how efficient the overall system is relative to anything else.

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  • $\begingroup$ Focusing more on the photon cages as thrusters in and of themselves, would you be able to control the thrusting power of a breached photon cage by changing the size of the aperture, or would all that light just come pouring out in one cataclysmic deluge? Controlling the rate at which light leaves the chamber, and therefore the level of acceleration experience by the craft, would be necessary to make the maneuver safe for humans, or even just safe for the ship itself. What size of aperture would be needed for a steady 1G of acceleration, and how would I work this out? Thank you for your reply. $\endgroup$ Jul 5 at 23:21
  • $\begingroup$ @EldritchEntity Given that how the photon cage works is unspecified, I can't answer that question. Presumably whatever mechanism allowed the photon cage to power systems on the ship without instantaneously dumping all its energy can be used to modulate its output. (There has to be one otherwise when one tried to charge it, the photon cage would back-feed all its energy out into the charging system, likely destroying it.) As for aperture size, try using the formulas I provided in my comment on the original question; you haven't told us the mass of your ship. $\endgroup$ Jul 5 at 23:42
  • $\begingroup$ @EldritchEntity Alternatively, if a photon cage can only be dumped all at once, you can use the shock absorbing system from en.wikipedia.org/wiki/Nuclear_pulse_propulsion to keep the acceleration manageable and subdivide the photon cages so that the impulse from each one of them is equal to the max impulse the shock absorbers can handle. $\endgroup$ Jul 6 at 0:01
  • $\begingroup$ Looking at this en.wikipedia.org/wiki/Kardashev_scale article lets you convert your energy usage from megatons of TNT to proportions of the total energy output of the sun and compare with humanities current total energy usage. $\endgroup$
    – quarague
    Jul 6 at 13:03
  • $\begingroup$ This answer introduces a very interesting concept - instead of laser highways, one can have the laser-equivalent of gas stations at the edge of the know system for refueling those photon cages. That could be the start of a delicious take on the Space Trucker idea. $\endgroup$
    – T.Sar
    Jul 6 at 19:13
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If there's no laser at the target you have decelerate on your launch beam. This can be done if you can manipulate things precisely enough--when it's time to stop you cut a ring off your sail, it goes on ahead and you flip your spacecraft. Note that the discarded ring must be the majority of the mass of your spacecraft as well as the majority of your sail!

Some of the incoming energy hits the sail you have left and pushes you, but the majority goes on by, hits the ring and is bounced back into your sail. You must decelerate fast enough that you're slowed to insystem velocity before the ring gets too far away.

Also, given that you are describing a system with many inhabited systems you could decelerate on beams from other stars that are able to bear on your sail. Better get the coordination right!

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    $\begingroup$ Can you back this up with anything? A beam of light strong enough to push an object is reflected off of something connected to that object in an effort to slow the object? No mirror is perfect and we're talking about a humongous amount of energy. It's a cool idea, but it would help a lot if there was a citation somewhere showing the plausibility of the physics (I'm choking on that mirror-attached-to-the-object-slowing-down). Also, note that your third paragraph requires the undiscovered planet to be within a sphere of discovered planets. That seriously limits exploration. $\endgroup$ Jul 5 at 20:59
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    $\begingroup$ Check out Robert L Forward's novel Rocheworld. It's about a laser-pumped lightsail voyage and subsequent planetary exploration and gives some of the numbers. (And when he gave numbers, figure they work.) And note that it is not connected! The ring flies free in space and accelerates once the laser fires. $\endgroup$ Jul 6 at 0:09
  • $\begingroup$ As for using other worlds to decelerate, I do agree that isn't always an option. I was saying that sometimes it would be. More interesting stars will get investigated before less interesting ones--many exploration voyages will be to systems not on the edge. $\endgroup$ Jul 6 at 0:10
  • $\begingroup$ That's cool, but it needs to be in your answer. $\endgroup$ Jul 6 at 1:00
  • $\begingroup$ The discarded ring does NOT have to be the majority of the mass of the spacecraft. All that is necessary is that E_reflect > E_direct, i.e., the energy reflected off the released ring back at the ship has to exceed the energy hitting the ship directly from the beam from Earth. $\endgroup$ Jul 6 at 14:06
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Use the laser highway system to both accelerate and decelerate your spacecraft

lightsail config

The yellow arrows represent the laser light coming from the origin star system (the one with the laser infrastructure). The red arrows represent the laser light bounced back off the blue detached light sail, onto the pink light sail attached aft of your spacecraft.

The pink sail receives light from both behind and in front, however, the blue sail is focusing more light down onto the pink sail's front, so the net effect is deceleration.

The blue sail, after detaching, will continue accelerating out into space. No way you're getting that back.

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  • $\begingroup$ I was considering something like that, but can these beams really be effective at interstellar distances? Is it really possible to create a laser that can retain such high levels of concentration over such vast reaches of space and time? I was imagining the ship being in-system while being pushed up to speed over the course of a few months to a year, and those distances are manageable for the beam tech they have in this setting, but interstellar distances are mindbogglingly vast, and make solar systems look microscopic. I don't buy it, but then again, I know hardly anything about lasers. $\endgroup$ Jul 5 at 21:40
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    $\begingroup$ @EldritchEntity for interstellar travel, the laser would need to be tremendously powerful and the sail tremendously enormous. If you have the power and focus the light properly, it can be done. Using Robert L. Forward's lightsail from his novel Roche World... A 1,500 Terawatt laser at Sol shone through an "acceleration lens" 100 km in diameter. In the acceleration phase the laser propelled the spacecraft, rigged on a 1000 km diameter aluminum sail, at 0.01g for 20 years, sending it 2 ly distant at 0.2c. (cont.) $\endgroup$
    – BMF
    Jul 5 at 23:19
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    $\begingroup$ A 300 km deceleration lens was swapped out and the 1000 km sail was ejected to focus the laser light down onto a 300 km sail, decelerating for 20 more years and covering 4 more ly. I may not have all the information I need to backup Forward's numbers, but he writes mostly hard-scifi and I trust his conclusion that his lightsail system works. I imagine it could be scaled up quite a bit to higher accelerations and shorter transit times, potentially looking at lenses and sails tens of thousands of km in diameter. But that's miniscule when your people build Dyson swarms. $\endgroup$
    – BMF
    Jul 5 at 23:22
  • $\begingroup$ I've seen this many times, but the ring sail is simply propellant. The specific velocity is limited by how well the beam can be focused. It seems like it would be more efficient to capture the light energy and use it to work an ion drive. $\endgroup$ Jul 6 at 0:47
  • $\begingroup$ @MikeSerfas Yeah, that makes sense. The beam can bounce back between the two sails multiple times, but in the end, what you're essentially doing is pushing off the big lightsail. Ion engines are about the most efficient way to push off of stuff. $\endgroup$
    – BMF
    Jul 6 at 0:55
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You don't have to have a photon cage at all.

So, say we have a starship en route to an uninhabited system. It was propelled to about 0.5C by a stellar laser back in a nearby frontier system, and has been traveling for a few centuries now. I have been trying to figure out a way for this ship to decelerate at its destination, and have tried to avoid having it use the energy it has stored onboard, for fear that it will not be anywhere near enough, but I can think of no other way that does not involve magic or cartoon physics.

Because the question about the photon cage's efficiency is motivated by this, I'm going to contest the premise entirely and open up the possibilities a little. Good news: someone did already think of one. It was called Valkyrie, and it centered on an antimatter beam-core rocket.

This kind of rocket carries big tanks of hydrogen and antihydrogen, and annihilates them to produce charged pions (and a lot of waste as neutrinos and gamma radiation). These pions are then ejected backwards; their change in momentum is opposite that of the ship, so the whole thing accelerates. While the acceleration is very low, you'll have years and years to slow down and eventually enter a parking orbit around your target star.

The biggest drawback of this design is that antimatter is expensive, but a civilization with multiple Dyson swarms for power should be able to create enough of it fairly readily through pair production. There are undoubtedly also engineering problems, such as how antimatter waste products will gradually transmute surrounding material. However, a one-way acceleration of 0.5c is tame compared to what Valkyrie or the multi-stage Frisbee designs propose for this kind of antimatter propulsion. It also violates no laws of physics, as your proposed electricity-to-velocity drive would, and requires no photon-trapping chamber at all.

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    $\begingroup$ A thoughtful reply, but I think you are missing the essence of the question, particularly parts 1 and 2. I am wondering how much energy could be stored in a photon cage of a given volume, and if this would be enough energy to decelerate a craft from 0.5C using a form of propulsion not requiring reaction mass (assuming that light is massless) over any period of time. Is it enough energy, mathematically speaking? How large a photon cage would be needed and how would I go about figuring this out? $\endgroup$ Jul 5 at 23:10
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in the science fiction book "The Mote in God's Eye" aliens used a laser to accelerate, then when they reached their target system, built up an electric charge on the hull of their ship. This caused the ship to precess around the galaxy's magnetic field. When the ship velocity had rotated by 180 degrees the aliens then fired another laser pulse to stop the speed all-together.

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  • $\begingroup$ Must've been some other book: The Mote in God's Eye used a laser array for the initial boost, yes, but braking was (for plot-relevant reasons) done using a simple solar sail. $\endgroup$
    – Mark
    Jul 6 at 23:46
  • $\begingroup$ The civilians in the system that was visited by the Moties were confused because the "eye of god" solar system turned red for a while. That was the deceleration laser. Also Crazy Eddie showed up from the opposite direction. $\endgroup$ Jul 7 at 11:32
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For something perhaps less reliant on undiscovered physics than a photon chamber, try the Bussard Ramjet: you generate a miles-wide magnetic field ahead of the ship that funnels and compresses interstellar hydrogen into your spacecraft. Due to the speed at which the hydrogen is compressed, it undergoes nuclear fusion, propelling the spacecraft forward. To decelerate you can use the magnetic field as a magnetic sail, and shape it so that it no longer causes fusion.

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You send a decelerator up ahead.

The energy you have stored is probably not enough to slow down the entire ship. So you have modules that you shoot up ahead that slow down and begin shooting you with those same lasers that brought you up to speed in the first place.

Then you have that decelerator make more lasers and eventually you have set up a new branch of the laser highway on the go. This does mean you will need the ship to be specialised to include these decelerators. But you could also just have a highway building ship be sent up ahead of the main passenger ship.

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  • $\begingroup$ I entertained an idea like that for a time, but if the decelerator can carry enough energy to decelerate a ship from 0.5C, whose to say that the ship can't also carry hat much energy? If you are suggesting that the decelerator harvest the energy locally, how is it able to harness anywhere near enough? This decelerator craft is presumably traveling at a speed comparable to that of the ship, and so it doesn't seem like it would have any way of, say, stoping to build anything like solar collectors, it's just going to crash through the star in a glorious demise, or fly past it and be lost forever. $\endgroup$ Jul 14 at 4:10
  • $\begingroup$ @EldritchEntity The idea was basically small decelerators which can slow down with solar sails and harness that energy to beam it forwards. So then you send one decelerator which goes straight into the star, but on its way it manages to beam more energy into the next decelerator down the line which slows down more, but still probably crashes into the star, but it slows down the next one a bit more,... You end up crashing a bunch of ships into the star, but eventually one slows down enough to be stationary and act as an endpoint on the laser highway. $\endgroup$
    – TineO
    Jul 14 at 6:58
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Just make the light bend back on itself.

Did I drink from the wrong bottle? Maybe I woke up in the wrong universe? Or did Science print that somebody re-solved Maxwell's equations, yeah, those Maxwell's equations, and show that you can send out a beam of light that bends around 180 degrees in free space? I don't know, you be the judge!

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    $\begingroup$ Link-only answers get deleted. Can you quote the relevant portions? $\endgroup$
    – rek
    Jul 6 at 1:55
  • $\begingroup$ I believe I summarized that source: somebody re-solved Maxwell's equations to make light bend back on itself, according to Science. It should be worthwhile to sacrifice an occasional answer to an ultimatum so as to illustrate that deletionism has consequences. $\endgroup$ Jul 7 at 1:06
  • $\begingroup$ Perhaps you could summarise a bit more of the linked article. At the moment, it is still a borderline link-only answer that is at risk of deletion. $\endgroup$
    – Monty Wild
    Jul 10 at 9:38

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