# How fast does an antimatter bullet need to move to pierce rather than explode?

The environment is set in (ideal) space with no air for the bullet to interact with. It should encounter nothing until it reaches its target. The bullet is assumed to be a perfect sphere with a diameter of 7mm (what I believe is common for sniper rifles) and is made of antimatter. All variables should be assumed to be "ideal" like in common physics homework.

From what I know, antimatter tends to explode when it comes into contact with regular matter. However, I'd like to see an antimatter bullet go so fast that it pierces without exploding.

The AM bullet doesn't necessarily explode (as explained by @Tim B II) but does react a lot with the target. Whether it's a bunch of explosions or just some fission, I'm not entirely sure. I just want to see some part of the bullet come out.

What would be the minimum speed at which the bullet needs to move in order to pierce through 1 meter of material and exit without entirely blowing up? (Just having a portion of the bullet material removed is OK. I just want to see the bullet exit as a bullet.)

• This question may be harder than you suspect to answer. The real question is how many particles of antimatter actually annihilate with the bullet, and how many are simply pushed away: physics.stackexchange.com/questions/213878/… – SurpriseDog Dec 23 '19 at 4:40
• I think there is some minimal probability that a single atom of the bullet makes it through. I don't think that's going to quite meet your needs of "exit as a bullet" thought. – Cort Ammon Dec 23 '19 at 8:29
• If you can load the bullet into the gun, it means you have a very effective containment method for antimatter. So let that container be fired together with the bullet: let the bullet itself be the container, designed to fail when the bullet hits (or has traveled far enough). They use a similar strategy in the game UFO:AI, but with plasma instead of antimatter. – vsz Dec 23 '19 at 13:19
• I just want to point out that even a normal-matter lead bullet of that size could not penetrate 1 meter of average structural material and "exit as a bullet" without a lot of help (like from a teflon-coated steel jacket) because the impact will liquefy the lead almost instantly. – RBarryYoung Dec 23 '19 at 16:56
• Sniper bullets are quite long, not spherical, so that's about 3x more volume. As for "going trough": a common 12.7mm sniper bullet can go through 1m of awful lot of things. Using nothing but current tech. What you're describing is basically fulfilled by an anti-materiel rifle; those start at 12mm where sniper's stop and go to 20mm. Keep in mind that armor and weapons scale together - if something is big enough to carry 1m thick steel armor, it will be engaged by a platform with weapon of comparable size. If a single solder could take down a battleship, battleships would get insta scrapped. – Agent_L Dec 24 '19 at 19:35

There's a very simple bit of math that tells you how far an antimatter projectile can penetrate something, assuming that the massive amounts of energy released aren't involved in that penetration.

As the bullet passes through the target, it will annihilate itself with the matter in the target at a 1:1 ratio. Meaning that the bullet can make contact with no more than it's own mass of target matter before being converted entirely into energy. (Lots, and lots, and lots of energy).

A 7mm sphere has a volume of ~0.18 cm3. Since you're making solid bullets out of this, let's assume you've somehow managed to produce, contain, and fire anti-lead. The density of lead is 11.34 g/cm3, so you have 2 grams of the stuff. So your bullet will be completely consumed by 2 grams worth of matter.

You're asking how fast the projectile can be fired in order to penetrate, but there's a problem with that. You need to fire the bullet fast enough that the annihilation reaction at its point of impact doesn't deflect the bulk of the bullet off the surface of the target (sort of like a droplet of water skittering off a hot surface). However, above a certain velocity (basically the speed of sound in the material), the matter in the target physically cannot move out of the way of the bullet, meaning that the bullet will at least make contact with the cylinder (or more like the cone) of matter in it's path; it can't "wedge" a crack open in the material and penetrate that way.

So basically what this boils down to is this: if there's more than 2 grams of matter in its direct path, then it can't penetrate no matter how fast it's moving. A 7mm by 1m cylinder is ~38.5 cm3. 2g/38.5 cm3 is 0.053 g/cm3, which is less dense than styrofoam.

On the other hand, the annihilation of 2g of antimatter with 2g of matter is going to release a smidge under 86 kilotons of energy, so your target is almost certainly just going to be vaporized, at which point the question of "penetrating" it becomes rather moot.

• Which brings up the follow-up question: Just how far away would the shooter have to be from the impact to avoid being vaporized themselves? I'd imagine it would be quite some distance - this weapon would be suicidally foolish to use at close range. – Darrel Hoffman Dec 23 '19 at 15:25
• @DarrelHoffman, nukes in space (which this AM bullet most definitely is) are a bit non-intuitive for those of us used to living in an atmosphere. Most of the pushing and burning energy from a nuke comes from the X-rays interacting with air, heating it up in a very short time. If you're in the "fireball" radius that Seth linked to, your ship might lose a bit of paint and a few mm of its skin, but it won't be blasted away since there's no shockwave. You WILL have a lethal dose of gamma radiation, though. – Ghedipunk Dec 23 '19 at 16:47
• Of course, space warfare is typically conducted at thousands or millions of kilometers distance, so if you're within 5km of your target, something has gone horribly wrong already. – Ghedipunk Dec 23 '19 at 16:48
• @Ghedipunk Typical by whose standard? I mean, space warfare isn't really even a thing yet in reality. And honestly, even shooting from 5km away is going to require some pretty precise aim. From thousands or millions of km, aiming reliably might be impossible, given that the target could move unpredictably in the amount of time it would take a projectile to travel that distance, and it wouldn't take much movement to dodge a bullet. Now if the bullet was somehow guided, it might be another story, but that's more of a missile than a bullet at that point. – Darrel Hoffman Dec 23 '19 at 17:53
• @DarrelHoffman, take some time to browse through Atomic Rockets (I linked to the Nukes in Space section above). It's maintained by one of the more prolific sci-fi game designers, and contributed to by quite a few established sci-fi authors and current (actual) rocket scientists. The reason why space combat is going to happen at vast distances is: It's incredibly hard to change the direction that your spacecraft is moving, so you can't dodge bullets, lasers, or rockets. There is also no such thing as stealth in space. – Ghedipunk Dec 23 '19 at 17:58

First of all, I think we need to clear up the science a little bit.

Anti-matter doesn't 'explode' when it comes in contact with matter - it mutually annihilates both itself and the matter that it comes into contact with in equal quantities of mass, becoming pure energy.

This means that in essence, the anti-matter bullet is far more efficient at creating energy than a fission reactor, and probably just as lethal given that most of that energy would probably be released as gamma radiation (this is based on current theory - we have little practical experience with creating anti-matter explosions).

The formula E=mc2 tells us that for every gram of antimatter in the bullet, we multiply that by twice the speed of light squared (because the antimatter is only half the mass annihilated) to get an energy release value.

This is also in line with how thermonuclear explosions work in that a nuclear bomb doesn't really 'explode' as it does release a massive amount of energy in the form of heat. Fission is effectively just breaking large complex molecules atoms up into smaller ones, resulting in a minor decrease in overall mass, the remainder of the mass becoming heat energy to be released in the process. What makes the blast waves and 'explosion' is that heat increases the atmospheric pressure and this form of sudden and uncontrolled release of heat results in a massive and sudden increase in the atmospheric pressure, not to mention the creation of plasma out of existing mass around the blast - all in all it's a bad outcome.

In the case of your antimatter bullet however, the bullet won't just create fission - molecules of it literally cease to exist when reacting with a normal matter counterpart. The ENTIRE AM molecule, and the molecule it reacts with, become pure energy. With fission, no actual protons, electrons or neutrons go missing as such, but they are reconfigured in a lower energy state as the complex molecules become multiple simpler ones. in the case of antimatter the effect would be far more devastating because mass is literally being converted to energy.

As such, the AM bullet is not a kinetic weapon per se; in other words, you can't just sharpen it and fire it with a really high velocity (even relativistic speeds) to make it bypass some of the armour and annihilate mass behind it. Antimatter just doesn't work that way.

Edit it is important to note that some of the energy being released is going to actually push the bullet back, or push other molecules out of the way to some degree. That said, the more velocity you put into the bullet, the more of it will be annihilated because the gamma radiation released has to counter a greater initial momentum. What fragments may make it through would do so only because it would be riding a bow wave of gamma radiation and plasma, but it won't be a bullet anymore in either case.

The good (?) news is that with a mass of (say) 10 grams forming the 7mm 'shell' when it hits the armour, the energy release is going to be so massive it's unlikely that the armour will be sufficiently strong or robust so as to withstand the sudden onslaught of gamma radiation, meaning that all the people behind it are likely dead from the radiation generated even if they don't flash burn because of heat release, which they most likely would.

The short answer is that you can't have your AM bullet look like bullet after passing through mass really quickly. Contact is all that is required to set off the reaction and as such, they'll go off with the first contact with ANY regular mass. They are not kinetic weapons, and you can't think of them as such. They're energy release weapons with a contact trigger.

• Let’s not forget that the bullet has to get to the target without encountering ANY matter along the way. That can be tricky depending upon where you are firing. – SRM Dec 23 '19 at 8:42
• "Fission is effectively just breaking large complex molecules up into smaller ones" - that'd be "atoms" rather than "molecules." – JRE Dec 23 '19 at 8:43
• @JRE thanks, good catch. – Tim B II Dec 23 '19 at 8:45
• I find this line a very pleasant description: "They're energy release weapons with a contact trigger" – Martijn Dec 23 '19 at 14:53
• A lot of the other uses of "molecules" would probably be better stated as "atoms" as well. – Loduwijk Dec 23 '19 at 17:01

There's a very relevant xkcd - What if? on this. Granted, the projectile is not made from antimatter, and it's a bit bigger than your bullet. However, it does discuss speeds at which "the atoms are literally passing through each other". That's in the section about 99% the speed of light.

It also mentions that air atoms penetrate roughly three meters into a body at that speed. Obviously, antimatter projectiles would be stopped sooner than that, because they do disintegrate at the first actual collision. But, as I cited, at these speeds the atoms move right through each other. The higher the speed, the further the antimatter particles can penetrate into matter before they manage to annihilate with one of the particles they are passing through.

So, the answer is: You need your antimatter projectile to be significantly faster than 99% of the speed of light. This will allow some of the bullet's particles (not full atoms, only individual positrons, antiprotons and antineutrons) to pass through the target and continue their journey unimpeded.

Note, that at these speeds the particles weight more than ten times their rest mass. Matter-antimatter annihilation would not be the major energy source. Direct kinetic energy would be. So, if you want to play it safe, you can just make do with ordinary matter, and stick to what is described in the link I gave.

• And remember that whatever fired this must deliver the same energy and will experience the same recoil. We are looking at about 43kt of annihilation energy at .99c has a gamma of about 7 so we are looking at around 300kt of kinetic energy. That's some mighty impressive gun. I also wonder if you would have pair production issues trying to accelerate the bullet that fast. – Loren Pechtel Dec 24 '19 at 5:28
• You'll probably find that .99c is higher than necessary. That's about 6GeV per nucleon, and even in something as dense as uranium you might get away with 2.5GeV, and with more conventional targets you can get away with <1GeV. – Starfish Prime Dec 24 '19 at 14:11
• @StarfishPrime The problem with an antimatter projectile is that the first collision of a particle with matter is the last one. So, it's the mean free path length before the first interaction that counts. When you shoot matter at matter, the total penetration depth is much larger than the mean free path length because you get many interactions where your projectile particle only looses a small part of its energy, which gradually slow the particle down. That's why I preferred to err on the high side. – cmaster - reinstate monica Dec 24 '19 at 18:49
• @cmaster-reinstatemonica I understand this. The mean free paths of the energies I listed are enough to allow some portion of the projectile through. They are conservative estimates; lower energes will still penetrate to some degree. – Starfish Prime Dec 24 '19 at 19:42

What would be the minimum speed at which the bullet needs to move in order to pierce through 1 meter of material and exit without entirely blowing up?

It depends on what you mean by "entirely blowing up" or "resembling a bullet" ;-)

TL;DR: you're out of luck, unless you count a few stray antineutrons coming out the far side.

There's basically no speed that a 7mm long bullet made of any kind of normal matter (anti- or otherwise) could penetrate a 1m thick block of normal matter. The mean free path is just too short... every incoming atom will interact with an atom of the target material in pretty short order, either causing deflection and heating (for normal matter) or partial or total annihilation (for antimatter).

The Newtonian approximation for impact penetration is $$d \approx l_p \frac{\rho_p}{\rho_t}$$ where $$d$$ is the penetration depth, $$l_p$$ is the length of the penetrator, and $$\rho_p$$ and $$\rho_t$$ are the densities of the penetrator and the target respectively. This should give you a very rough idea of how deep an antimatter projectile could possibly penetrate... in reality other effects would destroy it long before it reached that depth, but it'll do as a starting point. As you can see, even if your bullet was made of anti-tungsten and the target was made of water you cannot possibly penetrate any further than about 14cm.

This is why real world armour penetrating rounds are long and thin, like this APFSDS antitank round:

If you fired your bullet at relativistic speeds (say, 90% of the speed of light or more) you might find that some of the incoming round makes it out of the other side, perhaps in the form of a few stray antineutrons, but I'm guessing that isn't really what you wanted. Also, if you've got a relativistic gun, you may as well fire regular matter out of it, because all the oomph is in the kinetic energy, and the contribution of the mass-energy in an antimatter bullet would quickly become negligible and certainly not worth the hassle.

Now, you should also note that your depleted-antiuranium kinetic penetrator will also not be able to punch through huge chunks of matter and come out intact. The problem you'll have is that upon contact with the target, annihilation will begin. This will almost certainly not simply blow the bullet back out of the target.

What you will get is a spray of electron-positron annihilation gamma rays (511keV), high energy prompt gamma rays from nucleon annihilation (MeV-energy), some very short ranged neutral pions which will almost immediately decay into more gamma rays (two each, totalling >135MeV) and a bunch of charged pions which will travel short distances before interacting with regular matter and being stopped, and then either decaying producing further gamma rays or causing ionisation and heating. The gamma rays are highly penetrating. This means they'll travel some way through both the target and the penetrator before interacting with it, generally causing ionisation and heating. A big chunk of the target and most of the penetrator will therefore heat up quite a lot and explode. This will produce a cloud of hot, dense ambiplasma which will then finish annihilating itself in relatively short order.

Most of the impactor will therefore be annihilated, with most of the energy being released in a fairly broad volume of matter around the impact point. A small amount of the back of the impactor will be fly away, un-annihilated.

The take home message should be "don't use antimatter if you want armour-piercing rounds".

• If you fire your bullet at relativistic speeds, you'll have another completely different problem, which strangely, has very similar effects to the original problem. – vsz Dec 23 '19 at 13:17
• @vsz please read the very first sentence of the question. Seriously :-/ – Starfish Prime Dec 23 '19 at 13:29
• I know. But the same problems will kick in during the travel through that 1 meter of material (armor, ship hull, whatever) as with the travel through air in the xkcd example. At such speeds it doesn't matter if air or iron molecules are blocking your path. – vsz Dec 23 '19 at 13:33
• @vsz now please reread the paragraph I wrote talking about a relativistic projectile. – Starfish Prime Dec 23 '19 at 13:34

The closest that we can get to a numerical answer to this question would be:

How fast would the AM bullet need to go, so that if it struck a wall with more mass than itself, then every positron and antiproton is annihilated rather than shot back out from the force of energy released from annihilations happening in front of it?

We can probably assume that the energy released will expand in a relatively spherical burst of gamma and x-ray radiation. (Relativity pun intended, since we're working on high energy EM radiation.) Fortunately, since things are happening at relativistic speeds AND much of the energy is traveling at the speed of light by definition, this means that we don't need to worry about reference frames very much. The energy expands as a sphere, whether your frame of reference is the bullet or the ship... And if you're either, then you won't need to worry about reference frames after the impact, either.

So, in the moment of annihilation for each particle, roughly half of the energy is working to move the ship out of your way, and the other half of the energy is working to slow the bullet down.

In order to figure out how much kinetic energy we need, we take the 86 kilotons ("borrowed" from Salda's excellent answer) of explosive energy, cut it in half, and convert it to joules. In less than than it takes for a human to think, there is going to be 179,912,000,000,000 joules delivered into the bullet that we'll need to overcome.

At 2 grams, if relativity didn't exist our bullet would need to be traveling at ~360,000,000,000,000,000 m/s, or about a billion times the speed of light.

Fortunately with relativity, we don't need to go that fast (but we DO need to pump in that much energy into our 2g bullet). We merely need to accelerate our bullet to 99.999999999% the speed of light, or thereabouts.

Keep in mind that these are all back-of-the-envelope, spherical cow on an infinite, frictionless plane types of calculations. If there is less than 2g of matter in an AM bullet's path, this is how fast it will need to go in order to guarantee that some parts of it makes it through. It won't resemble a bullet, but it will be bits of antimatter that is still going in the right direction.

If the target ship has less shielding, you don't have to slow down quite as much, of course... I.e., if there will only be 1g of matter in front of your antimatter bullet, you'll only need to be going half as fast, about 99.999999995% of c (that is, you'll only have to put half as much kinetic energy behind the bullet, which due to the nature of relativity, only seems like a very minor change in the fraction of the speed of light that our bullet is traveling, despite being quite significant.)

Regardless of whether your bullet is antimatter or not, it won’t penetrate to 1m.

Your bullet is 7mm long. It will be a similar density to the target’s armour. So Newton’s law of impact depth tells us it’ll penetrate to about 14mm.

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

The other answers were long and wordy, and so if this is already covered, my apologies.

The reason that bullets made by ordinary matter can penetrate armor (or any obstacle that's not too resilient) is because the first contact between the bullet and the target will be the electrostatic forces of the electrons of the atoms comprising both bullet and target. The electrons repel each other (so much so that the atoms really never do touch each other), and the momentum of the bullet pushes the material of the target out of the way.

With an anti-matter bullet, it's not going to work that way. The positrons of the anti-atoms of the bullet, and the electrons of the atoms of the target, will be drawn to each other and annihilate each other, and then the anti-protons of the bullet will be drawn to the protons of the target and the will annihilate each other in a similar fashion (dragging the anti-neutrons and neutrons into the festivities).

There will be no penetration unless the armor is much thinner than the diameter of the bullet, and then only if the momentum of the surviving anti-atoms has not been impeded by the violence of the matter-antimatter annihilation.

What you seem to be looking for is the ultimate armor piercing high explosive bullet, correct?

If that's the case, instead of antimatter bullets, you want to shoot micro black holes at relativistic velocity.

See, all black holes evaporate and radiate energy away in the form of Hawking radiation. The bigger the black hole is, the slower it radiates. Tiny black holes are essentially ridiculously powerful bombs, because that radiation ramps up like crazy in the last few microseconds of the black hole's existence. The faster it radiates the faster it shrinks, and the smaller it gets the faster it radiates.

Now combine this with the time dilation caused by traveling at a relativistic velocity. If you carefully control how fast you launch the black hole, you can very precisely time when it evaporates completely. The faster it's going, the longer it lasts from your, and your target's point of view.

No amount of armor can stop a black hole. Every atom of armor the black hole hits just falls into the singularity.

So put it all together, and what you have is a black hole weighing as much as a train punching a hole a few molecules across through the target's armor, and detonating inside with energy similar to the impact that killed the dinosaurs.

• I'm not looking for a "super piercing bullet". I just want to know if there's a speed at which an AM bullet can be shot at a target and still exit as something resembling a bullet. – John Zhau Dec 23 '19 at 6:27
• "No amount of armor can stop a black hole. Every atom of armor the black hole hits just falls into the singularity." No. Subatomic black holes don't have enough gravity to pull regular atoms into them, and will not interact with matter that does not pass through their event horizon. – The Square-Cube Law Dec 23 '19 at 22:41
• @Renan then it goes between the atoms and still penetrates. – Ryan_L Dec 23 '19 at 22:43
• No damage done though. – The Square-Cube Law Dec 23 '19 at 22:53
• @Renan until it finishes evaporating. The point isn't to put holes in the armor, it's to set off a giant explosion inside the target. – Ryan_L Dec 23 '19 at 23:22

Try using strange matter. Let us know the experimental outcome.

Degenerate neutron matter (a.k.a. neutronium) was my first choice, but their is no reason to expect this to be stable outside of the intense gravity field of a neutron star.

If the strangelet hypothesis is true, it might be possible. Since the strangelet would be electrically neutral, in will pass through matter, only interacting if if manages to hit the very small target particles in the atoms themselves.

Being electrically neutral, this interpenetrates matter to a much greater extent than normal anti-matter (Maybe, s.b.)

However, as a 1 meter thick target would require missing roughly 50-100 million atomic nuclei to exit with contact (actual numbers depend on target material), so statistically very unlikely.

Re: the Maybe above - certainly the properties of a strangelet of unknown, and it may be quite likely that you can not simply treat this as a stable collection of loosely interacting quarks, where each quark has to impact a particle to. In fact, for strangelets to exist, they are probably quite tightly bound together, preventing this from working.

So, although I don't expect strange anti-matter to get the job done, we don't really know. So run the experiment, and write-up your results for publication.