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Some artistic and civic-minded aliens want to put a bust of their glorious leader, Rigel Rigelius R, in every solar system in the galaxy. Interstellar spaceships are very expensive, and slow besides, so they'd rather not use them. Instead their plan is:

  • Locate a suitable airless moon in the target system
  • Send an extremely precise, concentrated beam of highly structured light, varying slightly over time, at where the moon will be when the light gets there
  • The light arrives, still very concentrated. It acts as a laser cutting tool, carving out the shape of glorious R.R.R. from moon rock.

Ignoring the engineering difficulties, is there any inherent physical reason why they could not do this? That is, is there a fundamental, physical requirement for any beam of light, no matter how engineered, to spread by a certain amount over vast distances? Of course, all our human-built lasers spread somewhat, but is that an inherent limitation or just an engineering limitation?

If the structured light physically cannot work for some reason, would it be physically possible to send, say, a beam of neutrons at 0.9c to do the same thing? Or would a neutron beam also have some unavoidable spread?

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    $\begingroup$ Any beam of anything, no matter how it is produced, will spread such as that its intensity is inversely proportional to the square of the distance. Better engineering can only change the constant of proportionality. (And calculating the distance to the random moon in a random star system, and its orbit, with the required precision is most definitely not a trivial task. As far as I know, at present we don't have even the foggiest idea how to do it.) $\endgroup$
    – AlexP
    Aug 26, 2021 at 21:29
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    $\begingroup$ (1) No we cannot assume that the aliens can calculate the distance and orbital elements of the moon perfectly unless we have at least a believable hypothesis of how they could possibly do it. As I said, it is far from trivial. For example, we cannot even calculate the position of our very own very local Moon with any precision over long timespans. (2) If we assume that the beam is produced and aimed by some sort of material device much larger effects come into play long before going down to the scale of the uncertainty principle. How flat can the most perfectly flat material mirror be made? $\endgroup$
    – AlexP
    Aug 26, 2021 at 22:05
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    $\begingroup$ Ah and about those top-notch telescopes... There is a direct relationship between the best theoretical angular separation power of an ideal lens and the physical diameter of the lens... $\endgroup$
    – AlexP
    Aug 26, 2021 at 22:07
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    $\begingroup$ Also, even if we had perfect information about where the target moon is now (or rather when the light we're studying now was reflected) that doesn't mean we can project where it will be when the light hits it. Orbital models are only projected to a certain degree of precision, and can't be solved analytically as far as we know. $\endgroup$
    – Cadence
    Aug 26, 2021 at 22:53
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    $\begingroup$ For a tidally locked Moon, you would want the image on Nearside, so you will have to aim that very high energy beam just past the planet (and possibly its atmosfere), hopefully without annoying the inhabitants (and assume that that moon will not be inhabited when the beam arrives) $\endgroup$ Aug 27, 2021 at 10:32

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O Glorious Leader, Rigel Rigelius R!
Allow us of Bespoke Worlds to introduce you to our astounding line of CNC Planetary Modification Devices! As you are undoubtedly aware, Bespoke Worlds has aeons worth of experience in the planetary system design, fabrication, repair, upgrade and removal industries. Our innovative engineers and designers have been meeting and exceeding the expectations of our clients for more than seven billion years, and we are certain that our Mark VII Planetary Modification Device will suit your wonderful plan of civic beautification for ages to come!

You might ask: how is it a design and build company can make such a boast!? Why, it is easy to say! The answer is to be found in our very motto: Ignoring the Engineering Difficulties Since the Dawn of Time! We never let the naysayers and can't-be-doners get in the way of either our solid worldbuilding record or good ad copy!

But enough about us -- let's look at the Mark VII-PMD!

We've read through your technical enquiry letter, and believe this device will solve your problem. Clearly, a single point origin laser carving array is economical and sufficient for small or regional projects, such as milling out large moons or even planets within a solar system. But as you have discovered, even the best designed & implemented energy beams will diverge and become useless light shows over the vast distances of interstellar space.

Hence the Mark VII-PMD: Bespoke Worlds has perfected a multi-phasic energy beam carving array that, when interfaced with your central datanet and coded with the art files and necessary lunar locations to be civically improved, will deploy a wide field Daisunn Array of solarship mounted energy beam carvers. Able to quickly and easily interface with one another and your central network, the array can expand or contract automatically from near solar swarm orbit out to 100,000 standard astronomical units.

The Daisunn Array configuration, as I'm sure you'll soon appreciate, solves the beam spread problem by reversing the problem itself and solving all the difficulties at the front end. Rather than a cone of uncertainty spreading from your engineering platform out into the vast depths of space, we simply turn the problem on its head and deal with the spread close to home, giving your civic engineers a cone of certainty at the business end of the beam array!

Long story short, o glorious leader! --- at the centre of all the Mark VII convergent cones of uncertainty shines brightly and energetically a finely honed carving tool ready and waiting to blast your effigy upon a squillion binjillion unsuspecting moons!

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    $\begingroup$ +1 just for the wording of the story :D $\endgroup$
    – orithena
    Aug 27, 2021 at 9:43
  • $\begingroup$ So an array of laser beams, all converging on the face of a moon, carefully designed so that the interference pattern among all of the lasers is sufficient to create a holographic image of RRR? Even if there is dispersal, the beams need to disperse wider than the moon? In fact. the interference pattern ASSUMES some dispersal. The face of the man on the moon takes on a whole new meaning? The stock ticker symbol of your company BS-W. $\endgroup$ Aug 27, 2021 at 14:14
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There is a way to achieve close to what you want using Nicoll-Dyson Beam

This collimated laser beam would not disperse like the usual ray of light and stay highly focused for many light years. The downside is that the width of this laser beam is quite wide, so it won't be possible to carve small details. At the distances exceeding 1 light year, the light beam can not be focused narrower than 1000 km, however, this can be somewhat improved if we use X-ray or gamma-ray laser.

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  • $\begingroup$ A pixel that is 1000 m wide? That is some BIG bust. $\endgroup$ Aug 28, 2021 at 20:27
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There are many reasons. I will list them in no particular order:

  1. Lasers (and other similar particle beam weapons) have their power fall off according to the inverse square law. Therefor, the power budget for this thing becomes absolutely absurd from any significant distance. Sure, Kardashev II civilizations might manage things from a few AU away, or even a large fraction of a light year, but past that it's just... impossible.
  2. Lasers aren't knives or chisels. They don't carve anything. They ablate solid materials where they strike by heating them... but the removed material doesn't wink out of existence. It will float around until gravity or atmospheric currents cause it to land somewhere else. Even when you carve wood with a CNC mill, the sculpture is often covered in sawdust. The same would happen here, but with nothing to remove it.
  3. It's impossible to calculate where any astronomical body will be if it's more than a few light years away. Someone seeing imagery of our moon from 1000 years ago has no idea if something else has knocked it around billiard-ball-style such that it'd still be in its orbit... supposing of course they can resolve enough detail to be able to calculate its orbit 1000 years later.

Besides, he'd be the first to tell you that he's not a glorious leader, but only a dominar.

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  • $\begingroup$ 1. The question is about how much the laser must spread by physical principles. Just stating that it does spread is not an essential problem, unless it spreads too much to be used for carving. Power density isn't the issue, the issue is detail resolution; if the beam is precise enough that the details can be resolved, then essentially all the initial energy arrives at the destination. Power density only starts to fall off from 100% if the beam spreads so large that most of it misses the target, and it would cease to be useful for detail carving looong before that. $\endgroup$
    – causative
    Aug 26, 2021 at 23:11
  • $\begingroup$ 2. The laser can heat the material until it becomes a gas. The gas molecules will then bounce away due to their thermal energy. 3. For aliens with arbitrarily good telescope arrays spanning across their whole solar system, and arbitrarily fast computers for orbital dynamics, I think they could cross this engineering hurdle. $\endgroup$
    – causative
    Aug 26, 2021 at 23:11
  • $\begingroup$ @causative What do you think happens to gaseous regolith after it cools down? What do you think it does while it's bouncing around, white-hot? All the energy may arrive in the general proximity of the destination, but the moon's how many thousands of miles in diameter? The detail resolution is far smaller than that, and as for calculating where a moon will be 50,000 years from now... that's just not possible. Doesn't matter how much cpu you throw at it, you're asking for clairvoyancy, not orbital mechanics. $\endgroup$
    – John O
    Aug 28, 2021 at 6:50
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For anyone interested in hard science lasers, my goto refernce is this: http://www.projectrho.com/public_html/rocket/spacegunconvent2.php

(Actually the whole site is amazing, although fair warning: Infinite time sink)

Ignoring the engineering difficulties, is there any inherent physical reason why they could not do this?

Yes

Quoting the above site:

Laser beams are not subject to the inverse-square law, but they are subject to diffraction. The radius of the beam will spread as the distance from the laser cannon increases.

This is governed by the following equation:

RT = 0.305 * D * L / RL

where:

  • Rt = beam radius at target (m)
  • D = distance from laser emitter to target (m)
  • L = wavelength of laser beam (m, see table below)
  • Rl = radius of laser lens or reflector (m)

One light year (ly) is very roughly 9.46*10^15 meters. The galaxy is around 200,000ly across. Even if R.R.R. lives close to the centre, that is still 100,000ly to the furthest solar systems.

Sadly, therefore, to focus the laser precisely enough across the galaxy would require a mirror so large it would collapse under its own gravity.

Particle Beams suffer even worse dispersion than lasers.

May I recommend Von Neumann machines to his Imperial Majesty? It may take a couple of million years, but they will get the job done eventually, and at relatively low cost...

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  • $\begingroup$ How about a 'laser beam' one photon wide? $\endgroup$ Aug 27, 2021 at 13:55
  • $\begingroup$ @JustinThymetheSecond, if it's one photon wide, then dispersion shows up as a high chance that the one photon will miss the target entirely. You can see this effect with the single-photon variant of the two-slit diffraction experiment: despite photons going through the mechanism one at a time, and hitting discrete points on the target, they still form a diffraction pattern. $\endgroup$
    – Mark
    Aug 27, 2021 at 20:25
  • $\begingroup$ @Mark I am not sure that demonstrates what you think it demonstrates. What I am referring to is one beam, one photon wide. no slit, no interference, no diffraction. Remove the splitter, remove the slit, and just shoot the photon directly at the target. $\endgroup$ Aug 28, 2021 at 3:58
  • $\begingroup$ Lets assume that we can generate a beam of single photons. (I'm not sure we can, but for the sake of argument). The problem we have now is there is not enough energy in the beam to do more than warm the target up slightly. The energy is conducted away as heat faster than we can impart it. $\endgroup$
    – ShellGhost
    Aug 28, 2021 at 12:46
  • $\begingroup$ @JustinThymetheSecond, any directed photon source is going to diffract. It's inherent to the nature of optics. It doesn't matter if it's a light bulb, a laser, or a stream of photons shot out one at a time: the photons are going to spread out, forming a well-defined pattern. $\endgroup$
    – Mark
    Aug 28, 2021 at 20:54
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Face on the full moon

I would attempt to do this with moons in tidal lock, always showing the same face to the planet.

Maybe some very precise interference pattern could be devised that works on light years distance, but the easiest - and safest - way to yield sharp facial features is sending a robotized high energy laser to orbit the moon. Rather than evaporating parts of the moon, use the laser to sculpt large dark and light regions on the surface, to give the portrait clearly recognizable features, when seen from the planet. When the face is not round, create near-black, non-reflecting regions next to the cheeks, they will not be visible from the planet. A perfect portrait of the leader will be visible on every full moon.

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Are we talking about quantum physics, or Einsteinian physics, or real physics?

Given a sufficiently long enough time, a sufficiently advanced civilization could do it. However, it would not be a LARGE bust.

The idea of light 'fanning out' assumes either a wave theory of light, or that the photons are sent in a 'beam' of many photons' width.

Projecting one single photon at a time in one stream of individual photons, would not disperse any more than a 'charged particle' would expand as it travels through the universe, whether by the 'square cubed law' or 'inverse square proportion law' or any other law. So by beaming one photon at a time, at exactly the same target, every photon would expect to hit that target. There is no dispersal. However, one photon at a time would take a VERY long time, and would be feasible only for a VERY small sculpture.

The problem, of course, is that photons do not travel in a perfectly straight line. They are influenced by such things as, well, gravity. Physics at the quantum level, however, does not seem to experience such a problem.

However, there does not seem to be a theoretical limit to how BIG the quantum world can be.

Multiple beans sent in superposition, all 'converging' to form an interference pattern that looks like RRR? A sort of 3D superposition interference pattern holographic image?

What is an 'image' of RRR? Would a 'digital' image (or whatever an image made of qbits would be called) suffice?

Here we have a really interesting prospect. A quantum superposition crystal of the image of RRR, projected intact (or as 'intact' as a superposition particle crystal can be called) across the void, going at the zero velocity speed of c. Do you want to call that a 'beam of light'? Of course, the devil is in the details. STOPPING this would certainly lead to decoherence. Exactly how long do you want this 'bust' to last before it is, well, 'busted'?

But then again, exactly what is 'time'? If time does not exist, and everything exists in the same 'instant', this bust would be timeless.

So what physics do you want to govern?

Us silly humans of so very little knowledge and intellect tend to profess to claim all kinds of things are 'impossible' under our understanding of physics, until of course we find a bust of RRR on the moon, and then promptly explain exactly how it got there, using our newfound knowledge of some quaint hitherto unknown physics or scientific principle we never previously thought possible.

A million qbits in a single crystal?

ADDENDUM

The OP mentioned the 'uncertainty principle' in the comments, opening this up to all models pf physics, known and unknown.

The quantum world has no relativistic framework, because the quantum world is in isolation from everything else. Once the quantum world becomes relativistic, it decoheres. Thus, a quantum particle has no velocity, speed, or position because all of these measurements are relative to something else. In order to measure them, one must place the particle relative to something else.

Thus, the uncertainty principle.

There is no way to ever tell WHERE a quantum particle is in the universe, relative to you, until you measure it WRT where you are. Then, it is no longer a quantum particle, it is a relativistic particle in a relativistic framework. Thus, a quantum photon has zero velocity (and zero position) at any one instant but can travel at c through time.

That is, a quantum particle is EXACTLY Einstein's 'mind experiment' solitary person in an infinite universe with nothing else that exists 'relative to' it. No position, speed, or velocity. And no acceleration, not even the possibility of accelerating, because there is nothing to react against in order to accelerate - nothing to apply a reactionary force against. No 'equal and opposite directions', no Newtons' Law. Every force is applied in EVERY direction equally, thus no unbalanced forces to create any acceleration.

But we know there is no theoretical limit to how big any individual quantum world can be, so there is no limit to how 'big' a world can be that is not in any relativistic framework. That is, there is no limit to how big a 'superpositioned' 'uncertainty' 'non-relativistic' 'non-object object' can be. Wow, that is some string of unqualifiable 'in quotation marks' definitions, but such is the quantum world. An undefinably perfectly defined world.

There is, and can be, of course, no concept of the 'passing of time' in a quantum world, if there is nothing relative to measure it against.

In such an arbitrarily large quantum non-relativistic world, there is no limitation on information transfer, it is instantaneous, because there is no way to 'isolate' where any particular piece of information is. And it can 'decohere' anywhere in any arbitrary frame of reference.

CONTROLING where it decoheres, of course, is another chapter.

The 'conservation' laws - conservation of energy, momentum, etc. are in a CLOSED quantum system, but NOT in any sub-region of that closed system. Energy can be ANYWHERE in a closed 'quantum' system, at ANY particular point in time. The universe is theoretically the limit to the 'closed system' in the quantum world, and there are NO 'sub-regions' because there is nothing to define these regions 'relative to'.

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    $\begingroup$ In classic quantum theory, a single photon would disperse just as much as a beam of photons, so shooting one photon at a time won't increase accuracy at all $\endgroup$ Aug 27, 2021 at 11:42
  • $\begingroup$ @Rotem Shalev So you are saying a photon gets larger and larger the further it gets away from its 'source' until it gets infinitely large? The photons that are hitting us from an object one billion light years away must be HUGE. Bigger than our solar system? How do we ever detect them? $\endgroup$ Aug 27, 2021 at 13:54
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    $\begingroup$ @JustinThymetheSecond If I'm understanding quantum mechanics right, then the photon doesn't actually have a single position while it's in transit. It has a cloud of possible positions that steadily disperse. Only when there is an observation does it actually behave like a particle and decide where it is. So the photon itself doesn't get bigger, just the area where it could be. $\endgroup$
    – jb6330
    Aug 27, 2021 at 15:15
  • $\begingroup$ @jb6330 This 'sphere of indeterminism' or uncertainty principle is always the same, a probabilistic number that does not change with distance. In quantum theory, the photon has no way of 'knowing' how far away from the source it is. It is not in any relativistic framework. $\endgroup$ Aug 27, 2021 at 15:56
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    $\begingroup$ @Justin Thyme the Second oh no, that sphere is definitely getting bigger (if that is the right term). Possible location of a particle is described by its Wave function. For a photon which just left the light source this function is very steep, which means it is very likely to find it within certain range. As we move away from the source, the function becomes more flat, which means it is more likely to find this photon farther from the straight line. $\endgroup$
    – Alexander
    Aug 27, 2021 at 16:49
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You ask for beam spread specifically, but let me point out some other "inherent physical reason[s] why they could not do this".

Your (laser or otherwise) beam has to get there. It may get scattered or absorbed by interstellar dust, deflected by gravity (say, a black hole passing by), absorbed by impact against another body (in transit), or stolen by some other civilisation.

Once "there"... where is "there"? You need to know the position of the moon with accuracy. For moons far away, you need long-time predictions. The longer-time the predictions, the more mass you need to account for, including relativistic effects (cf. Mercury), meaning, you might need to know about every mass in (and coming into) the solar system. Also, lest something gets in the way of your beam when you fire (well, when it gets there).

Also, to sculpt a moon, you also need to track the surface of the moon with accuracy. Moons wobble? There is axis precession and whatnot. Perhaps an airless moon cannot have liquid, but if there are bodies of liquid they need to be accounted for (I think?). If there is tectonic activity, it has to be accounted for: you don't want R.R.R.'s face to end up winking or frowning, do you?

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Truly a complex way to do something simple.

Your method :

Build insanely complex devices to try and control something precisely at least half a galaxy width away.

The simple way :

Send an order to the locals to build it.

Why it's impractical in any way ...

Ignoring the engineering difficulties, is there any inherent physical reason why they could not do this?

It's worth noting that if your empire is limited by the speed of light yet spans a galaxy, the great and noble leader is never going to find out if the vast majority of the sculptures will ever be started, let alone finished unless they are able to live for a hundred of thousand years, no matter how they try and have the sculptures built.

Even if the dude lives forever that doesn't mean that empire will. Just normal politics and the limits of light speed will mean that no stable single government is possible for the entire galaxy.

No matter what beam you design and no matter how magically non-divergent you try and make it, you are trying to aim it across half a galaxy width of curved spacetime. No matter what it's a beam of, it will be curved and diverge and over such vast distances you would in no way be able to predict that curve.

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    $\begingroup$ Sorry, I didn't make it clear - the empire doesn't span a galaxy, it's limited to one solar system. They don't have the resources for a galactic expansion campaign, at least not yet. They're just trying to do the equivalent of spray painting their name on someone else's bridges. $\endgroup$
    – causative
    Aug 27, 2021 at 1:25
  • $\begingroup$ in every solar system in the galaxy That's pretty clear to me. In any case the same issue remains - they'll never live to see the result in solar systems. If they can't expand farther than their own solar system, what's the point in trying to "spray paint" something on the other side of the galaxy ? The leader would be dead, as such waste of a single solar system's resources just for an ego trip would just get you killed by those rich people whose resources you are wasting. $\endgroup$ Aug 27, 2021 at 1:48
  • $\begingroup$ @causative hang on, so you're saying that the empire is opening fire on bodies in other, potentially inhabited star systems to create a sculpture that no one in that system wants (and the creation of which may annihilate significant populations)? $\endgroup$ Aug 27, 2021 at 1:51
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    $\begingroup$ You are correct that it is a silly ego trip that probably led to the downfall of their civilization. They live on only in the reserved, yet stern visage of their leader, immortalized on moons across the galaxy. How to tell that this particular arrangement of stone spikes and tentacles is "reserved, yet stern" is a mystery lost to time. $\endgroup$
    – causative
    Aug 27, 2021 at 1:55

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