# Decelerating: laser vs gun vs rocket

In our pa­per on ex­plor­ing the uni­verse, some of our probes re­quired huge quan­tities of re­ac­tion mass in or­der to de­cel­er­ate on ar­rival.

This is due to the tyranny of the rocket equa­tion: to de­cel­er­ate our fi­nal mass by , we need an ini­tial mass so that:

• , where is the ex­haust ve­loc­ity.

Given this equa­tion, the ini­tial mass needed grows as ex­po­nen­tial in the re­quired de­cel­er­a­tion .

The rel­a­tivis­tic rocket equa­tion is similar but even worse, with an ex­tra term in it.

So the most effec­tive way of al­low­ing high speed ex­plo­ra­tion of the uni­verse is to some­how get around the rocket equa­tion. I was vaguely think­ing about ways of us­ing the tar­get galaxy or so­lar sys­tem to do that—maybe the probe could scoop up in­ter­stel­lar dust or use grav­ity sling­shots. But I re­al­ised that we can get around the rocket equa­tion more di­rectly.

# De­cel­er­at­ing with guns

Sup­pose you are shoot­ing through space, and you want to de­cel­er­ate by point­ing a gun in the di­rec­tion of travel. Be­cause of rel­a­tivity, we can con­sider that you are at rest, and that you are ac­cel­er­at­ing by shoot­ing a gun in an op­po­site di­rec­tion.

You have two bul­lets, and you can shoot the bul­lets se­quen­tially or si­mul­ta­neously; imag­ine that you had two guns strapped to­gether. If you shoot the bul­lets one af­ter an­other, the first will start mov­ing at ve­loc­ity of while you re­coil at some . Then when you shoot the sec­ond bul­let, it will start mov­ing at (if we stay in the clas­si­cal model for the mo­ment). So the to­tal back­wards mo­men­tum is , where is the mass of a bul­let.

If you fire the bul­lets si­mul­ta­neously, the to­tal back­wards mo­men­tum is , how­ever, and . By con­ser­va­tion of mo­men­tum, you will there­fore be re­coiling faster than if you shot the bul­lets se­quen­tially.

What’s hap­pened? When you shot the bul­lets se­quen­tially, part of re­coil of the first bul­let went into mov­ing the sec­ond bul­let at the same speed as you, which you ac­tu­ally didn’t want. When you shot both bul­lets to­gether, the re­coil of both went purely to mov­ing you. There­fore si­mul­ta­neous fire is more effec­tive at ac­cel­er­at­ing/​de­cel­er­at­ing. The real tyranny of the rocket equa­tion comes from the fact that the early fuel needs to move the later fuel that needs to move the even later fuel. And most of that mo­men­tum gain is com­pletely wasted: we don’t ac­tu­ally care that ex­haust fuel has gained mo­men­tum through the pro­cess. We’d like that ex­tra mo­men­tum to be ap­plied to the pay­load or probe, not to the fuel.

# In prac­tice: laser and so­lar sail

So there’s a the­o­ret­i­cal way around the rocket equa­tion; can we do this in prac­tice? Ex­pend­ing all fuel si­mul­ta­neously would help (the equiv­a­lent of shoot­ing all your bul­lets at once), but that ex­treme discharge might tear the probe and the rocket to pieces.

In space, there’s no differ­ence be­tween the gun and the bul­let—they’re both just pieces of mass that fly off in op­po­site di­rec­tions due to an ex­plo­sion. So now imag­ine that there are ten thou­sand guns, float­ing in­de­pen­dently in space, point­ing at you. Every­thing is at rest with each other, and all the guns will fire in some se­quence, and you will catch all the bul­lets (com­pletely in­elas­tic col­li­sion). As­sume each gun, of mass , will re­coil with ve­loc­ity . Then the guns will have a to­tal mo­men­tum of , and, by con­ser­va­tion of mo­men­tum, you and the bul­lets will have the same mo­men­tum in the op­po­site di­rec­tion. If the mass of the bul­lets (and you) is small com­pared to , this will be an effec­tive way of ac­cel­er­at­ing you. And note that your to­tal fi­nal mo­men­tum de­pends on your mass, the mass of the bul­lets, the num­ber of guns, , and . So it does not de­pend on the guns be­ing fired at the same time, or any de­tails of when they were fired. As long as you can catch ev­ery bul­let, your fi­nal ac­cel­er­a­tion/​de­cel­er­a­tion will be the same. So you don’t need to burn all your en­ergy at once.

Catch­ing bul­lets is hard, and we want to min­imise their mass. So it’s even bet­ter if we do this with lasers! Un­furl a so­lar sail around your­self, and have ten thou­sand free-float­ing lasers shoot at you in some se­quence. This will gain you all the mo­men­tum of the lasers, in­de­pen­dently of the se­quence of firing.

The only real prac­ti­cal con­sid­er­a­tion is that you can cool down fast enough that each laser can fire be­fore your sail moves out of their fo­cus range; but a big­ger sail can make both cool­ing and long dis­tance firing eas­ier.

## Ex­tra, the­o­ret­i­cal, efficiency

What if your sail doesn’t perfectly ab­sorb all the laser light, but re­flects some of it back? That’s even bet­ter! In terms of bul­lets, that’s the equiv­a­lent of elas­tic col­li­sions, and you’ll ac­cel­er­ate/​de­cel­er­ate even faster, los­ing less en­ergy. Think in terms of con­ser­va­tion of mo­men­tum again: some light is now mov­ing back­wards, away from you. This can only hap­pen if you’ve your­self gained some for­ward mo­men­tum.

In fact, the perfectly effi­cient way of de­cel­er­at­ing would be for you to de­ploy a gi­ant mir­ror, and for a sin­gle gi­ant laser to do the same, then for the laser to blast you. The laser beam would bounce back be­tween your mir­ror and the laser’s mir­ror, grad­u­ally get­ting red­shifted as you and the laser move faster and faster apart. This setup pre­serves both mo­men­tum and en­ergy, and is the most perfectly effi­cient way of de­cel­er­at­ing—and it doesn’t de­pend on how fast the laser fires, a slow burn reaches the same con­clu­sion as a swift burst. Why? Be­cause con­serv­ing en­ergy and mo­men­tum dic­tates the speeds at which you and the laser will end up.

Of course, in prac­tice, the mir­rors would not be perfectly re­flec­tive, the beam would lose fo­cus, there would be some cos­mic dust, and so on. Still, it’s in­ter­est­ing to note that, in the­ory, we can com­pletely do away with the rocket equa­tion and ac­cel­er­ate/​de­cel­er­ate in the most effi­cient way pos­si­ble, while us­ing up en­ergy ar­bi­trar­ily slowly to do so. This hints that there may be prac­ti­cal meth­ods that could get very effi­cient as well.

• The qual­i­ta­tive ex­pla­na­tion of the rocket equa­tion here is very clear!

• Thanks!

• Avoid­ing car­ry­ing fuel with you is cer­tainly tempt­ing, so­lar sail and var­i­ous beam-pow­ered types of propul­sion are some of the bet­ter known ones. Var­i­ous types of the so­lar wind sail would give much more thrust if one could figure out how to effi­ciently stop or deflect the so­lar wind par­ti­cles (mostly pro­tons), and var­i­ous ver­sions of a ram­jet when in in­ter­stel­lar space. https://​​en.wikipe­dia.org/​​wiki/​​Mag­netic_sail#In­ter­stel­lar_travel is a de­cent sum­mary. My bet is on that kind of tech­nol­ogy, un­less some­one rev­olu­tionizes space travel by figur­ing out how to bend space­time more effi­ciently than with sheer mass, and makes some­thing like the Alcu­bierre drive fea­si­ble.

• >un­less some­one rev­olu­tionizes space travel by figur­ing out how to bend space­time more effi­ciently than with sheer mass, and makes some­thing like the Alcu­bierre drive fea­si­ble.

The big­ger prob­lem here is just that gen­uine nega­tive in­er­tial mass (which you need for warp drives) is con­sid­ered to be prob­a­bly im­pos­si­ble for good rea­son, since it lets you both vi­o­late causal­ity and cre­ate per­pet­ual mo­tion ma­chines.

• This is not di­rectly re­lated to the post, but while read­ing the pa­per a thought struck me and I wanted to get it down:

• We ap­ply the medi­ocrity as­sump­tion to the Earth among planets; we should also ap­ply it to in­tel­li­gence among pro­cesses.

• The only in­tel­li­gence we know of cur­rently runs on chem­i­cal pro­cesses.

• All chem­i­cal pro­cesses I know of nat­u­rally ter­mi­nate.

• The medi­ocrity as­sump­tion there­fore says an in­tel­li­gence pro­cess will also nat­u­rally ter­mi­nate.

• I there­fore sus­pect a late filter.

• Note: the Filter might not ex­ist. In a nut­shell, the Fermi para­dox can be dis­solved by re­al­iz­ing that “av­er­age num­ber of civ­i­liza­tions per galaxy” is less im­por­tant than “prob­a­bil­ity of galaxy con­tain­ing sin­gle civ­i­liza­tion”. (Note: de­pend­ing on your an­throp­ics, this may or may not ac­tu­ally dis­solve the para­dox.)

• Yes, I should amend that to “I sus­pect a late filter, if one ex­ists.”

• Wait. You don’t know enough chem­i­cal pro­cesses if you think they all (or even most) ter­mi­nate nat­u­rally, ex­cept when their en­ergy source runs out. I find it easy to be­lieve that chem­i­cal pro­cesses much like the ones I com­prise will be func­tion­ing many eons in the fu­ture. What part of “self-repli­cat­ing DNA-like or­ga­ni­za­tion of chem­i­cal com­pounds” do you claim has a nat­u­ral ter­mi­na­tion point?

• ex­cept when their en­ergy source runs out

There aren’t any chem­i­cal pro­cesses for which this is not a prob­lem. For com­plex ones like DNA, it is more of a prob­lem rather than less be­cause the ab­sence of any one of the mul­ti­ple re­quired in­puts will do it. A pro­cess needs a sys­tem, and all the sys­tems with which we are ex­pe­rienced have limits. We also have sev­eral known can­di­dates for catas­trophic dis­rup­tion to DNA-like pro­cesses, in the form of X-risk.

The prob­lem boils down to whether we can keep jump­ing up to a larger sys­tem level be­fore we de­plete or dis­rupt the one we cur­rently oc­cupy; I see no rea­son to as­sume this will always suc­ceed, even if the prob­a­bil­ity turns in our fa­vor.

• One way for the de­cel­er­a­tion is a black hole close flyby where it’s grav­i­ta­tion and pow­er­ful mag­netic field could be used by the probe’s mag­netic sail. But from prac­ti­cal point of view, it un­likely to work, as the probe will be dam­aged by in­tense ra­di­a­tion.

How­ever, my fa­vorit method is to send mul­ti­ple probes with slightly differ­ent speeds by a nanoprobe’s ac­cel­er­a­tor. The first probe have v-nx speed, the next probe has v-(n-1)x speed and the last probe has the speed v. The differ­ence x is so small that all the probes will reach each other near the tar­get and clump in one large ob­ject. All this mass gain is used to built an ac­cel­er­a­tor-gun which send a nanoprobe with the speed -v, that is back, and this probe will have the near zero speed at the rest frame.

• Hum, what does this gain over send­ing out all the probes in one clump from the start?

• The size and price of the ac­cel­er­a­tor. For ex­am­ple, aliens have an ac­cel­er­a­tor which could send 1mg probe ev­ery sec­ond, and the ac­cel­er­a­tor’s weight is 1000 tons. Thus, it will send its own mass in 20 000 years. All these probes clump (us­ing some in­ter­nal nav­i­ga­tion and small differ­ence in ini­tial speed) with each other af­ter a few mil­lion years, and us­ing some nan­otech, they build an­other ac­cel­er­a­tor, which send just one probe in the back di­rec­tion, which is the de­cel­er­a­tion, as its speed will be zero.

To send all the probes si­mul­ta­neously, one need to build a trillion of such ac­cel­er­a­tors. How­ever, this seems to be achiev­able even with one Dyson sphere. So clump­ing make sense only if there are some limits on the size of the ac­cel­er­a­tors.

Also, any in­ter­galac­tic probe will ex­pe­rience “nat­u­ral” de­cel­er­a­tion be­cause of ex­pand­ing uni­verse, similar to red shift, so the back-ac­cel­er­a­tor may be small than the send­ing ac­cel­er­a­tor.

• What is a “mag­netic sail”? That sounds in­ter­est­ing. Is it just a large elec­tro­mag­net?

I don’t un­der­stand your sec­ond method ei­ther. What is a nanoprobe? What is an ac­cel­er­a­tor? You’re say­ing there’s a small thing in space which can push things? Then you send many probes (which may or may not also be nanoprobes) to the same point. Then some­thing hap­pens in­volv­ing an “ac­cel­er­a­tor gun”, and now a (new?) nanoprobe is trav­el­ing back­wards at the same speed at which the origi­nal probes were trav­el­ing for­ward? And it has “near zero speed at the rest frame”—the rest frame of what? Its own rest frame? But ev­ery­thing is at rest in its rest frame! And what’s the mo­ti­va­tion? If you can launch things for­ward at speed v, can’t you just launch things back­ward at that same speed? How do we benefit from this setup?

• Copied form the com­ment above: aliens have an ac­cel­er­a­tor which could send 1mg probe ev­ery sec­ond, and the ac­cel­er­a­tor’s weight is 1000 tons. Thus, it will send its own mass in 20 000 years. All these probes clump (us­ing some in­ter­nal nav­i­ga­tion and small differ­ence in ini­tial speed) with each other af­ter a few mil­lion years, and us­ing some nan­otech, they build an­other ac­cel­er­a­tor, which send just one probe in the back di­rec­tion, which is the de­cel­er­a­tion, as its speed will be zero.

Nanoprobe is a small star­ship send by an ac­cel­er­a­tor, which is similar to elec­tric rail­gun or hadron col­lider.

All nanoprobes are send in the same di­rec­tion.

They are send with the differ­ent speeds, in such a way, that later nanoprobes are quicker and will catch up the first ones is some mo­ment in time. They cou­ple each over at that mo­ment. This re­sults in “clump­ing”.

Re­sult­ing large clump of mat­ter which it­self is trav­el­ing with near с speed re­or­ganise it­self in a large star­ship us­ing nan­otech.

This star­ship builds an­other ac­cel­er­a­tor which sends one nanoprobe in the back di­rec­tion with speed near c.

Rest frame is the frame of the first ac­cel­er­a­tor here, that is, of the alien civil­i­sa­tion.

The new nanoprobe has 0 speed rel­a­tive to alien civil­i­sa­tion, but is now lo­cated mil­lions light years from it, so the task of de­cel­er­a­tion is solved.

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Typ­i­cal mag­netic sail uses mag­netiс field gen­er­ated by the space­craft to cap­ture stel­lar wind. https://​​en.wikipe­dia.org/​​wiki/​​Mag­netic_sail

This could be also used for de­cel­er­a­tion by in­ter­ac­tion with in­ter­stel­lar plasma.

But I thought about differ­ent thing: to use the mag­netic field of the black hole for de­cel­er­a­tion. In this case, the space craft gen­er­ates its small mag­netic field which in­ter­acts with gi­ant mag­netic field of the black hole.

• Thanks for ex­plain­ing. I see what you mean now. But I still don’t get how this is use­ful. Why not sim­ply send the larger ship in the first place, in­stead of send­ing the build­ing ma­te­ri­als?

Per­haps it’s eas­ier to ac­cel­er­ate smaller things? You can give the nanoprobe all the nec­es­sary mo­men­tum in the so­lar sys­tem—it doesn’t have to carry any fuel—whereas you can’t fea­si­bly ac­cel­er­ate an en­tire ship to near-c within the so­lar sys­tem.

• Yes, it is about price: this scheme will be a trillion times cheaper, as I dis­cuss in a com­ment above. A su­per-in­tel­li­gent alien AI may not worry about prices, but if it has some re­source limi­ta­tions, it would use more eco­nom­i­cal solu­tions.