# Effects of being hit by an object going at FTL speeds

This will be a question that I am fine with having less realism in. I was thinking of a weapon, like a spear, that can go at FTL (faster than light) speeds. To be clear, the spear is FTL due to propulsion (that is where the realism fades) rather than being a miniature Alcubierre Warp Drive (that creates a space-time bubble that eats matter around it), so when the spear hits someone, they are still being hit by a solid object (that is, if the spear does not get destroyed immediately).

The thing is, I have little idea of the ramifications of being hit by something going FTL. I know that an object that is moving at speeds nearing that of the speed of light can already have enough power to create earthquakes and rival nuclear weapons in terms of devastation. But what about beyond the speed of light? Can kinetic energy even be used anymore for such a weapon?

EDIT: Since you want to know how the FTL was supposed to work, I was thinking of using concentrated Dark Energy as a propellant, expanding space behind the spear to make it look FTL.

I'm not sure on what happens when the spear reaches its FTL speed, but you're going to have issues while the spear is accelerating to FTL speed. Because it is constantly hitting something, namely "the air", and just the force exerted on the air itself is going to be bad news for anything in the vicinity of this weapon speeding up.

I'm not sure if you're familiar with the What if? series on XKCD, but the very first one handles the effects of an object suddenly going relativistic (a baseball, in the example) and they're.... catastrophic to say the least.

Basically the spear turns into a nuclear explosion nanoseconds after it starts accelerating and obliterates the wielder, the target, and anything within a mile or so of the event, before it even manages to reach the speed of light.

So unless your weapon is operated in the vacuum of space (not a good place for spears) or accelerates to FTL speed instantaneously, there's probably no serious difference between stabbing someone with it and detonating a briefcase nuke you're carrying around.

• To be precise, that comic does NOT address acceleration. It just assumes the ball leaves the pitcher's hand at 0.9c, which then results in a massive fusion explosion from the ball colliding with air molecules. – Nelson Dec 14 '20 at 4:07
• That is about a relativistic in atmosphere. – Loren Pechtel Dec 14 '20 at 4:54
• That xkcd is about baseball; had it been cricket, the result would obviously have been different, since the rules are much more complex, and anyway, we British are more civilized. – j4nd3r53n Dec 14 '20 at 12:37
• @j4nd3r53n - indeed. I would imagine the remaining subatomic particles of the umpires would have briefly discussed matters before calling an early lunch (or tea) to discuss matters in the rapidly-expanding cloud of the former pavilion. These things shouldn't be rushed, after all. For what it's worth, my bet would be on "Rain (of relativistic remnants of Lord's) stopped play". – Spratty Dec 14 '20 at 16:38
• I'm not so sure that space is not a good place for FTL spears. One should be well capable of damaging enemy ships. – val is still with Monica Dec 15 '20 at 10:05

Kinetic energy quantifies the momentum imparted to a particle from an interaction. Current physics is restricted to four classes of interactions (forces). Since all interactions in current physics are mediated at or below the speed of light, there is no theory that describes how the FTL object would impart momenta, and thus such an event cannot be described in terms of well defined physical quantities such as kinetic energy.

An object moving at the speed of light would destroy the universe.

Kinetic energy under relativity increases to infinity, so everything in the universe that could be hit by a sphere of energy moving at light speed would be destroyed.

This would likely kill your enemy, your enemy's world, and their galaxy.

• This seems too simplistic. Photons, complex as they are, do appear to have a modicum of rest mass, although the jury's still out. If they do, then we're bombarded with light-speed objects al the time and the Universe is still with us. This feels too much like expressing theory as if it were equal with fact with a bit of hyperbole. If an infinite amount of kinetic energy were applied to our sun, what would happen to the universe? Nothing, unless you can show a relationship between KE and space-time. – JBH Dec 13 '20 at 17:59
• You are reading that page wrong. It says that photons have 0 rest mass, but still have momentum. " If the rest mass of the photon were non-zero, the theory of quantum electrodynamics would be "in trouble" primarily through loss of gauge invariance, which would make it non-renormalisable; also, charge conservation would no longer be absolutely guaranteed, as it is if photons have zero rest mass." Photons do not appear to have a modium of rest mass they seem to have exactly zero mass and no experiment has contradicted this. – James K Dec 13 '20 at 19:09
• You are still reading this wrong. It says "E^2 = p^2c^2 + m^2rest c^4" Is a formula that should work for all particles. Classical theory of light has E=pc so m_rest =0. Quantum electrodynamics has "particles" of light with zero mass. There are experiments that place an upper limit on the mass of a photon. There are no experiments that place a lower limit. It contradicts what you claim: It appears that light does not have a non-zero rest mass. This is not a case of "the juries still out". – James K Dec 13 '20 at 20:10
• If the photon does have mass then we are not bombarded with light speed particles. Because if photons have a rest mass then they travel slower than "the speed of light" (which would then be a misnomer), The "speed of light" is the speed of massless particles. If photons do have mass then they don't travel at the this speed. A massive (10^-27 eV) photon at the speed of light would have infinte energy and destroy the universe (etc) – James K Dec 13 '20 at 20:11
• It only destroys (of subset of) the observable universe (as it can only destroy it at the speed of light). – Peter Mortensen Dec 14 '20 at 13:30

I don’t think it could hit anything at all, in the sense that you mean. When two objects hit each other, they are affected because of the electromagnetic forces between their component atoms. But those forces are mediated by virtual photons travelling at the speed of light, and so can’t affect something travelling faster than light. Your FTL spear is going to effectively be dark matter, not interacting with regular slower than light matter.

• I've gotta +1 this answer because the possibilities for storytelling are endless. The whole idea that, should FTL be possible as a physical speed and not a shortcut like wormholes or warp bubbles, allows them to pass through their comparatively static counterparts is COOL. Suddenly I can explain ghosts: they're humans vibrating FTL. You can "see" them because they're all there in one spot, but they can move through walls! – JBH Dec 13 '20 at 20:54

So far it seems all these answers rest on misunderstandings of relativity

Relativity does not actually preclude objects moving faster than light, only objects travelling at the speed of light. As such, relativity prohibits objects accelerating from sublight speeds to superluminal speeds, but if we wave our hands around when we break the light barrier, and only consider the object once we already have it travelling faster than light we get pretty reasonable physics out again

A few starting points (working in natural units where c = 1):

The energy of a relativistic object (including its rest energy, which is just m) is:

$E=\frac{m}{\sqrt{1-v^2}}=m\gamma$

The momentum of a relativistic object is:

$\bold{p}&space;=&space;m\gamma\bold{v}$

Because both of these equations feature a factor of $m\gamma$ you will sometimes see a concept of "relativistic mass" invoked, which is equal to this factor. Such a concept is generally considered deprecated in physics these days, because as soon as you start doing anything more complex than basic kinematics, it starts making things more complicated rather than less, and leads to some unhelpful intuitions

As an object approaches the speed of light (from either direction), $\gamma&space;\rightarrow&space;\infty$ and so both $E,&space;\bold{p}&space;\rightarrow&space;\infty$. This is known in the business as a Bad Thing, and means something unphysical is happening. This is why relativity predicts no objects can cross the lightspeed barrier. Luckily for us, the spear is made of handwavium and has a way around this

Unfortunately now we have a different problem. Because we now have v > 1, $\gamma$ is imaginary. In order for a bunch of other physics to make sense, we need Energy to be a positive real number, and so any tachyons in the universe (including our spear) must have negative imaginary mass, so the factors of i & -i in $m,&space;\gamma$ cancel out

Again though, our spear is made of handwavium, and so as part of crossing the lightspeed barrier, its mass becomes negative and imaginary

Now we have a spear travelling at faster than light speed. The first thing to note is that it will emit gravitational Cherenkov Radiation. Cherenkov Radiation is normally encountered around nuclear reactors and is why they seem to glow blue, and is roughly the electromagnetic equivalent of a sonic boom. The normal sort is electromagnetic and occurs when a charged object travels through a medium faster than the speed of light in that medium. Gravitational Cherenkov Radiation is the equivalent with gravitational waves instead of electromagnetic waves, and will occur whenever a massive (gravitationally charged) object travels faster than speed of gravity in that medium (as we are in space, this is just the speed of light here)

As such, our spear will be emitting a bunch of weird, high energy gravitational waves, causing it to rapidly lose energy

Looking at the equation above for energy, and ignoring the pesky imaginary factors that we're cancelling with our handwavium, we see that whereas we're normally used to energy increasing as you speed up, energy actually increases as you get nearer the speed of light. As such, superluminal objects lose energy by accelerating, and so, as our spear loses energy by Cherenkov radiation, it accelerates. As this causes it to move at an even greater speed, it starts to lose energy even faster, and its speed rapidly heads towards infinity, and its energy heads back down to its rest energy m

Now this is where it gets interesting. From quantum mechanics, we know that the wavevector (essentially a vector consisting of the wavelengths in each direction, with a slightly different normalisation), and substituting our expression above for the momentum p:

$\mathbf{k}&space;=&space;\frac{\mathbf{p}}{p^2}&space;=&space;\frac{1}{m\gamma&space;v^2}\mathbf{v}$

As v > infinity, this goes to 0 in all directions

The reason this is interesting, is that from studying interactions in particle physics, we know that a particle will only interact with an object if it's wavevector is of a similar scale to that of the object. As the wavevector rapidly goes to 0, and any real object has non-zero size, the probability of the spear interacting also goes to 0

So where does that leave us?

The spear itself is not the danger, as the probability of it interacting will be essentially 0 shortly after it breaking the lightspeed barrier

What is dangerous though is the burst of Gravitational Cherenkov Radiation. This circular blast wave (perpendicular to the velocity of the spear) centred on the point at which the spear crossed the lightspeed barrier will carry almost all of the energy that went into accelerating the spear. Depending on how much of the crossover the handwavium applies to, this could be an astronomical amount

So, the spear allows you to concentrate the energy you build up propelling the spear into a circular blast wave where it breaks the lightspeed barrier. With a long enough run up, that's a lot of energy in a very concentrated burst and, because it's gravitational radiation, won't be able to be effectively blocked in the same way electomagnetic radiation might be able to. As such, it will get around shields, or physical armour. The downside is that gravity is comparatively weak and so you'll need to put more energy in the burst to do the same damage

• This answer is fucking awesome. Would the "increasing" negative mass create an infinite amount of energy? There is no limit how low the negativ mass can go. Will it become a white hole? – stupidstudent Dec 16 '20 at 0:58
• the mass is not negative, but negative and imaginary, which is different. It also doesn't change, except when it first becomes imaginary – Tristan Dec 16 '20 at 10:04
• My mistake, I assumed the energy for the gravitational radiation comes from the mass of the spear. And since the mass is negative, it will become even more negativ. Like from -10 kg to -20 kg. And this lost mass powers the radiation. – stupidstudent Dec 16 '20 at 11:29
• ah no. So what happens is the energy is always positive, and greater than the rest energy (i.e. the mass) of the spear. The energy going into the gravitational wave burst is going to be whatever the kinetic energy is (i.e. the total energy it has when it exits the handwavium bubble at superluminal speed minus the rest energy). This is likely a hell of a lot, but it will all need to have been put in to propelling the spear at the start – Tristan Dec 16 '20 at 13:48
• From recollection, this was the design of the FTL drive in the "Colonial Marines Technical Manual". The "Tachyon Shunts" there had some additional weird effects on the passage of time on board, too, but the key takeaway that 0 kinetic energy in FTL meant vanishing into the end of time was there. Its a neat mechanic for plot and game balancing. +1 for mentioning this mechanism and giving the only sensible explanation of the nature of FTL matter. – Starfish Prime Feb 19 at 12:37

It's impossible to say what the effects might be as we have nothing to go on. We can't use the existing scientific framework which would normally be used in such a circumstance (relativity) because such FTL travel violates relativity. All we can do is to invent some new science and try to explain it with that.

Edit: Following from comments made by Razor I would add that although relativity does not preclude objects from being brought into existence traveling at speeds faster than c, such objects would have imaginary mass and would violate causality and remain beyond the existing scientific framework.

• I have some problems with the 'we don't know' answers because we perform relativistic collisions quite frequently, at energies approaching 2c. Admittedly that is with single pairs of particles at a time but we know they do in fact have time to react under those conditions. – SoronelHaetir Dec 13 '20 at 16:42
• In any relativistic collision no objects are observed to travel faster than light in any inertial reference frame. Relativity tells us that this must be true. If we are told that objects can travel faster than light as in this example then relativity must be wrong. If relativity is wrong then what else have we to go on? – Slarty Dec 13 '20 at 17:16
• @SoronelHaetir We may set up an experiment in which one particle is coming from the left at nearly c and the other is coming from the right at nearly c, but in either particle's frame of reference the closing speed is still less than c, and relativity says that either of those frames is appropriate for predicting the interaction of the particles. – David K Dec 13 '20 at 18:00
• @SoronelHaetir actually not true. Because you need increasing amounts of energy to push something closer to lightspeed you can get infinitely close to the speed of light without ever really reaching it. Two particles going .98C and crashing into eachother would represent a collision of something like .9999999C instead of 1.96C. – Demigan Dec 15 '20 at 12:58
• @Demigan Actually, 2 particles, each at 0.98C collide at 0.9998C formula (u+v)/(1+u*v/c^2). Lengths and times distort to make this work out. – Donald Hobson Dec 15 '20 at 21:20

FTL is essentially magic (Clarketech). It could vary from destroying the universe, to doing absolutely nothing, to turning the target into a confused sperm whale or a pot of petunias.

You want to do it without magic though. That's just not possible. The question of what it would do is meaningless. Pushing something to make it go faster than light is like slowing something down to slower than not moving at all.

The problem with this is that relativistic mass is given by the following formula:

$$M = m \times \sqrt{1 - \frac{v^2}{c^2}}$$

Where $$M$$ is the relativistic mass and $$m$$ is the rest mass.

At speeds higher than c, your relativistic mass is your rest mass multiplied by the square root of a negative number, which is imaginary. That is kinda impossible to imagine though.

Yes, I know. This is , not . So the first thing that comes to mind is that an FTL projectile would become a beam of high-energy tachyons. They would have to be focused on a point in time and space in order to be effective. You will shoot at some time and it will hit a target in the past and another in the future. Then it will keep causing some damage going in both directions in time. Could make for a nice sci-fi story.

• relativistic mass is generally considered to be a misleading concept and not generally used in physics these days – Tristan Dec 14 '20 at 10:54
• @tristan source for that? – The Square-Cube Law Dec 14 '20 at 13:31
• not to hand, but none of the relativity courses during my degrees (BA & MSc in physics) at Cambridge, across four years and many different lecturers and supervisors ever used the concept and multiple explicitly rejected it – Tristan Dec 14 '20 at 14:59
• it's common in pop science explanations, because it makes basic kinematics look more Newtonian, but if you start trying to do anything more complicated, and particularly when you move to General Relativity you find yourself forced to use "m0" most of the time anyway, so overall there's no gain in terms of simplifying equations – Tristan Dec 14 '20 at 15:01

Two things to consider:

1: at orbital speeds (not even relativistic speeds!) Metals impacting each other will act like liquids rather than solids. Going faster will just mean more materials will act this way as by the time the surrounding matter can react, the impacted molecules are already pushed much farther away. So there is no "solid impact" possible.

2: mass and energy are connected. Light is massless, but if you concentrate enough light energy on one point they can create a black hole we call a Kugelblitz and these suddenly have gravitational attraction! That gives us a problem: when you approach the speed of light you have to put in increasing amounts of energy to speed up, but you'll never reach the actual speed of light unless you find a way to put in infinite energy. Going FTL means adding infinite energy+1. Even without impacting anything your projectile would turn into a black hole that expands at the speed of light to swallow the whole universe forever, only the parts beyond the visible universe (due to universe expansion) are safe. And that is assuming the black hole wont remain traveling at FTL speeds in its original direction which it probably would.

Frankly, as with all kinetic weapons, it depends as much on the size of the slug as it does the speed of the slug... maybe...

I'm all for ignoring relativity — which is a requirement if we're going to examine an FTL object from a purely classical-physics point of view and ask "what if?"

So, what does would might happen?

1. I'm standing on my world, minding my own business, when Skeletor unleashes his FTL spear at me...

Between Skeletor and I exists an atmosphere that, at this moment, can only be described as inconvenient. Referencing what is perhaps the most referenced XKCD in history, we discover that mere moments after the spear is unleashed, the friction/compaction between the front of the spear and the atmosphere causes fusion. The resulting explosion would certainly defeat me, Skeletor's nemisis, but it would also defeat Skeletor, which is no bueno, and a good chunk of the kingdom, too. So, in this condition, long before we even got to FTL speeds, everybody dies. And I didn't even get hit by the spear. In fact, I can't be hit by the spear, which means the only practical answer to your question for this condition is "nothing." I love this site.

2. I'm floating in intergalactic space, lowest particle-count-per-square-mile possible, minding my own business,1 when Skeletor unleashes his FTL spear at me...

Now we're cooking with gas! The spear actually has a chance of hitting me at full speed! What happens? Well, per that previously linked XKCD, as the spear pierces my space suit and the atmosphere between the space suit and me2 that inconvenient fusion problem happens again and without my ever having even noticed that Skeletor threw the spear3 I convert into a mass of energy that on a galactic scale wouldn't even be worthy of describing with the word "burp." So, once again, I was never hit by the spear. And despite the certain presence of a lot of drama, once again the answer is, "nothing." Oh, yeah. I love this site!

3. Skeletor spent a depressed weekend binge-watching Mythbusters where he learned that a bullet will go through a hat rather than knock it off!. Convinced that he finally figured out how to kill me, he found me sitting in a public restroom,4 minding my own business, reading about the latest conspiracy theories concerning infectious disease and U.S. politics via the world's best investigative journalism, when Skeletor unleashes his FTL needle bullet at me!

OK, technically the FTL object actually touched me this time. But the proverbial millimeter inside my skin... fusion... bang... burp. You get the picture. BUT! At least this time the answer is, "bad honking things happen, Cyclopscore! BAD HONKING THINGS!"5

The unfortunate truth is that most objects with mass traveling at high speeds welcomed by classical physics don't generate substantial heat due to friction as they pass through the victim something. In most cases, unless a really big, flat surface is involved, the object just passes through the target, leaving a big hole.6 The bigger the object, the more it will simply push the target aside with enough NCIS-quality blunt force trauma to make a good Halloween horror movie.

But when you bring speeds even approaching light speed (much less beyond light speed) into it, friction becomes a serious problem. I'm not going to bother with the math, but I doubt a 1mm pellet could get through the human body without the fusion-burp result.

But if you throw \$600,000,000 of Hollywood's best special effects at it, it'd look cool, wouldn't it?

1Actually, I'm on the verge of peeing my space suit because I'm down to 1% oxygen supply in the middle of intergalactic space. But your question doesn't consider the circumstances of the victim... thanks for asking.

2If there is any atmosphere. I can imagine a space suit that only requires oxygen near mouth and nose, the fabric over all other parts of the body being skin-tight, providing heat and capable of wicking away oil and sweat, and otherwise maintaining pressure through elasticity. but let's assume something more traditional. Big honking space suit full of combustible atmosphere!

3This is an interesting question. What would I see? Skeletor rears back, and then maybe my mind imagines a naunce of forward motion. I begin to say something clever like "You Ba...." ... and that's it. I'm not convinced Skeletor would do this. He's all about making sure I know he brought about my doom! But hey, we're suspending certain rules of reality. So maybe Skeletor's happy with proverbially shanking me in the back. It's not like he could ever win in a fair fight. Right?

4In the vacuum of space, of course, I didn't really need that space suit in the last example. I'm He-Man, after all.... You should have known I was just making this up the moment I led you to think anything would cause me to pee the suit. Sheesh.

5I love this site.

6A quick word about kinetic energy. Most of the other respondents are answering as if all that energy would somehow be absorbed by the victim... or in one case all of space-time. That's not really how kinetic energy works. Otherwise shooting a bullet through a piece of rice paper would cause it to burst into flames from the raw infusion of energy. The ability of the target to absorb that energy vs. simply being pushed aside (whether it be a hole in the body or really being pushed aside) has as much, if not more, to do with it. Civil War soldiers were found with holes in their sides 8 inches or more in diameter where cannon balls simply went through them — and they had plenty of kinetic energy left over after passing through the victim. It takes a really large really flat surface (or a really hard really difficult-to-pierce surface) to not simply punch a hole through something. Or that something must be incredibly brittle. I'm not sure the universe is that brittle. Or that wall nailed down.

### How much kinetic energy exists in 1kg of matter in FTL?

Sci fi doesnt seem to conserve momentum in FTL. For example: every time a ship leaves FTL and is immediately in a high orbit around a planet with the planet visible from the bridge. (Wow - how lucky they were that the velocity was precisely correct). There is a plot-driven creation or destruction of energy in this process. Putting a value on this arbitrary energy interaction helps work out how your FTL spear works.

With no true 0 speed and varying frames of reference (the systems are orbiting the galaxy centre at dozens of km per second relative velocities) maintaining your relative speed is pretty unhelpful. You pop out in one system with the kinetic energy of the previous system and you'll be flying extremely fast. If you're able to adjust your speed after exiting FTL then your ships will be overpowered in maneuverability. This isnt ideal.

If ships exit FTL at c, there'll be huge g forces and a long deceleration run. In atmosphere till be like a nuclear bomb going off. This would make a great FTL spear.

However for the spear to work every other FTL exit needs to decelerate to shed the energy that would otherwise go into the bomb. This isn't great for plot purposes - after an FTL jump every ship needs to spend 3 weeks slowing down in order to enter orbit.

If you do commit to this FTL dynamic - then yeah, an FTL spear is basically a death star blast.

If you don't commit to this dynamic - equivariant mass as a meteor I guess.

FTL is not possible with our current model of how the world works. That leaves you with two possibilities:

• You need to either abandon the theory of relativity and, for example, simply stick with Newtonian physics: There is no relativistic effect of speed, no absolute speed limit, kinetic energy continues to grow quadratic with speed etc. This leads to a host of fundamental logical problems, but those may not be apparent or visible in your story, so ignore them. This is, implicitly, what a lot of space opera does.

• Or you enhance/modify the theory of relativity so that FTL (or something which has the effect of FTL) becomes possible. If you don't want to bend space and time (you said "no Alcubierre drive") then you'll need wormholes or the like. The spear would essentially travel close to c in order to be dangerous and not waste too much time on the first and last light seconds (a bit like walking to and from the subway used to make up a lot of our commute before Corona) but take a shortcut to the target so that your story can continue, which is the whole point, I assume.

AT light speed, an object would have an infinite mass. The formula for kinetic energy is 1/2 Mass x Velocity^2. So it would pretty much destroy everything.

When it comes to FTL impacts, I think the Holdo Maneuver is an interesting metric. (Video link)

The funny thing is that they actually down played the effects of the Holdo Maneuver. Apparently a ship that big aimed at a planet becomes the ultimate budget planet killer.

• Ah, the Holdo Maneuver, AKA "breaking the Star Wars universe". – jdunlop Dec 13 '20 at 23:21
• Hi Jacob. (a) The image no workey. (b) This doesn't actually explain anything, it just points to a 3rd party world and says no more. My star wars-fanatic sister notwithstanding, there are people who have no idea what you're talking about. As-is, this is more of a comment than an answer. Could you edit the post and expand on the example to explain how it answers the question? Thanks! – JBH Dec 14 '20 at 0:48
• The Holdo maneuver is problematic any way you look at it. For example Finn survives it despite the maneuver literally tearing that deck apart and setting everything on fire, how is so much metal deck on fire (and the entire regiment of stormtroopers vaporized) when Finn is OK? If this were a near-lightspeed impact the entire ship would do its best impression of a small supernova and nothing would survive as more than plasma. If it was true FTL (while the ship is running on fumes!) Then it would create an infinitely expanding black hole. Also it breaks conventions in the established universe. – Demigan Dec 15 '20 at 13:07
• @Demigan sure it allows them to do anything they want in their universe! the problem is that they forgot that it can't save them from extrauniversal problems, such as being goddamn hacks. Different authors, you see. – Starfish Prime Feb 19 at 16:29
• @StarfishPrime you are right. Let me correct my statement: plot armor lets the writers do anything they want, but good story telling requires a plausible in-universe explanation. James Bond doesnt pull random gadgets out of his pants! – Demigan Feb 19 at 18:42