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I can expound on the specifics, but simply put my species is the only sentient one on their planet, receive their energy from photosynthesis, and are otherwise completely closed systems, recycling waste products back into nutrients internally. They have no appendages and are motile by shifting their center of mass to move around. They communicate with vision and bioluminescence at significantly faster than human rates, have human level intelligence, and virtually perfect memory, which persists generation to generation due to how they reproduce. They as such have no need for writing or records, which is convenient as they cannot hold a pencil. Or make one. Or understand the concept of a tool.

Despite their overall difficulty in affecting their environment, they have formed a complex, planet-wide collectivist society focused on art, science, and philosophy. They meticulously observe and memorize their environment, including having tracked their stars for countless millennia. And with an equally long time to develop mathematics from first principles, they have a pretty solid grasp of Newtonian mechanics. Can they go beyond?

They do not have a moon which perfectly eclipses their star, and even if they did, without telescopes could they notice its gravitational lensing? What about the anomalous precession of the innermost planet to their star? Distant galaxies? I presume even the best organic eyes fall short of even Galileo’s simple scope, but could individuals on opposite sides of their planet effectively coordinate to even approach a crude telescope? And could a biological eye be a good enough spectrometer to notice redshift?

And even still, the mathematics of relativity was motivated much by available technology at the time. Without a notion of electricity or magnetism, would they have a concept of light as a wave with a fixed speed? And surely, they would not be able to measure that speed given their biological reaction times. Could they have come about the concept of a Stress-Energy or Ricci Tensor from purely first principles, and have any motivation to suspect their physicality?

I don’t need an answer to all these subquestions, if you can provide a plausible pathway whereby these creatures could have discovered and/or motivated the idea of General Relativity given their limitations, or show that they reasonably cannot, I will accept that answer. I have a similar question for Quantum Mechanics, but I will keep this question focused on just relativity for now.

(P.S. Humans arriving on their world causing a massive culture shock and scientific awakening is a plot point of my story, so I do not want an extraterrestrial origin of this information. As the humans are surprised at the extent of their knowledge without outside assistance, I would like to explore what the limits of that knowledge are)

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    $\begingroup$ Comments have been moved to chat; please do not continue the discussion here. Before posting a comment below this one, please review the purposes of comments. Comments that do not request clarification or suggest improvements usually belong as an answer, on Worldbuilding Meta, or in Worldbuilding Chat. Comments continuing discussion may be removed. $\endgroup$
    – L.Dutch
    Mar 6 at 20:16
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    $\begingroup$ How are their senses? $\endgroup$
    – DKNguyen
    Mar 6 at 20:40
  • $\begingroup$ Is the important factor for you that 1) They have no technology or 2) They are nearly inanimate and plant-like? Because I know how they could be (2) and still have technology, but I don't want to post that answer if that's not what you're looking for. $\endgroup$ Mar 7 at 11:48
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    $\begingroup$ There are all sorts of non-intuitive truths about the universe it makes no sense for slow, planet bound creatures to grasp. But they can intuitively grasp how to throw a sharpened stick through a running deer at 20 feet despite the complexity of the equations governing this sort of thing. A vast, slow, long lived creature that navigates solar system spanning distances and intuits incredibly accurate predictions of where planets will be years into the future, will naturally grasp GR even if they can't express it mathematically. Would that be good enough? $\endgroup$ Mar 7 at 16:01
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    $\begingroup$ If they can't understand the concept of a tool then they are too dumb to discover relativity or much of science. doing one thing to affect a diffrent thing is fairly basic concept. science and technology are a feedback loop new tech grants new information and experimentation which yields new tech. your species is doomed to stagnation, its the roman philosopher problem. All theorem no experimentation. $\endgroup$
    – John
    Mar 7 at 21:38

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Einsteinian General Relativity is an extension of Special Relativity, motivated by the principle of equivalence which requires that a gravitational field be locally indistinguishable from plain acceleration. Einsteinian Special Relativity is an extension of the classical Galilean Relativity, motivated by the requirement that not only the laws of Mechanics but also the laws of Electromagnetism are the same in all inertial frames of reference.

A culture which cannot make electric generators and electric motors and electrical transformers has no reason whatsoever to develop a mathematical theory of electromagnetism. A culture which does not have a complete mathemical theory of electromagnetism does not have any reason whatsoever to develop special relativity, and perforce even less reason to develop general relativity.

No tools and no metals means no mathematical theory of electromagnetism. No electromagnetism means no special relativity, because without electromagnetism plain old Galilean relativity is plenty good enough. No special relativity means no general relativity, because there is nothing to generalize.

Moreover, the mathematics required for Einsteinian special relativity is not really so much more advanced than the mathematics required for classical electromagnetism; but the mathematics required for classical electromagnetism is easily sufficiently complex for its development to be very unlikely in the absence of a strong incentive... Remember that in real history even Newton's rudimentary calculus engendered strong opposition from philosophers¹, who argued that infinitesimally small quantities are absurd, unsound, and logically impossible; physicists and mathematicians shrugged and pointed out that calculus works, and that's where physics and philosphy parted ways, and have remained happily divorced ever since.

¹) Philosphers such as the great George Berkeley, Bishop of Cloyne of the Anglican Church of Ireland, who wrote and published the superbly titled The Analyst, or A Discourse Addressed to an Infidel Mathematician: Wherein It Is Examined Whether the Object, Principles, and Inferences of the Modern Analysis Are More Distinctly Conceived, or More Evidently Deduced, Than Religious Mysteries and Points of Faith. Not that I'm of the opinion that Bishop Berkeley had anything worthwhile to say on any practical subject; but, for our sins, he was considered a Very Serious Philosopher and some people still so consider him.

Honestly, I strongly believe that in the absence of fairly advanced technology even the development of plain old classical mechanics is a stretch. Observing stuff in nature is nowhere near enough; to develop classical mechanics a culture needs to be able to measure² lengths and angles and weights and time intervals with sufficient precision and accuracy, and that's just not possible without instruments. Galileo Galilei's discovery that acceleration is proportional to the applied force involved measuring the motion of bodies sliding down carefully constructed inclined planes; Newton's discovery of universal gravitation was based on Kepler's laws of planetary motion, and Kepler's discoveries depended on Tycho Brache's painstaking observations made using the largest and most expensive astronomical observatory ever built... Naked eye astronomy does not mean cheap astronomy; building the Uraniborg observatory consumed a decidedly non-trivial fraction of the GDP of Denmark: in the 16th century, as well as now, one needed rich and powerful sponsors to do serious astronomy.

²) Let alone Tycho Brache's gigantic and supendously expensive instruments, even the old ancient Greek and then Hellenistic astronomers relied on accurate instruments to make their observations, and those observations where a necessary stepping stone in the development of astronomy. And of course to make those instruments the astronomers relied on the services of skilled artisans. We should strive to avoid underestimating the level of technological knowledge required to make a good astrolabe.

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    $\begingroup$ Tycho Brahe posessed 1% of whole Denmark wealth at some piont in time in 1580's $\endgroup$ Mar 6 at 6:07
  • $\begingroup$ Even non metal working cultures possess metal from asteroids or just swept together gold leftovers for the priests and kings. Add to that natural electric phenom a like thunderstorms and highpoints +old g(r) weeks and you can get there given time? $\endgroup$
    – Pica
    Mar 6 at 19:17
  • $\begingroup$ @Pica: This particular culture we are speaking about is made of spherical blobs of green goo. They have no appendages, they cannot manipulate the shiny gold they might find. But this is still irrelevant. What is relevant is that they cannot develop even the most rudimentary form of physics without actually measuring things with measurement instruments. Simply staring at thunderstorms (like a calf staring at a new gate, as we say in Romanian) won't lead to $\nabla \times \mathbf{E} = -\partial \mathbf{B} / \partial t$. $\endgroup$
    – AlexP
    Mar 6 at 19:45
  • $\begingroup$ What about carbon fibres? en.wikipedia.org/wiki/Carbon_fibers Can they bake cotton? $\endgroup$
    – Pica
    Mar 6 at 20:27
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    $\begingroup$ @Pica Interest only: Tutankhamen's dagger is made of iron - from an age when they could not make iron. They could, however, find meteorites. $\endgroup$ Mar 7 at 1:23
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The other intelligent life that preceded them told them about it. The advanced alien botanist who wanted plants that would sing back, or their own mobile, open-system ancestors, or the out of control AI, or the ancient wizards, or God, or the star gods, etc. There is no way this species evolved like this naturally while being plant-like. Their senses confer no survival advantage because they don't search for food or avoid hazards or signal pollinators or any other sort of active resource acquisition. Communication provides no advantage because survival and reproduction related cooperation is impossible. Intelligence does nothing, they have no problems that they are capable of solving with it.

If it can't have evolved these while being plant-like, either they evolved them before they were plant like, or they didn't evolve (and hence were designed). In either case the problem is solved: somebody else - a mobile, tool using somebody - did it for them.

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    $\begingroup$ Maybe I should have explained the biology a bit more. I actually do go quite in-depth into the evolutionary history of this species, since it is an unusual one. This creature originally evolved intelligence to avoid predation and find breeding grounds. Communication alerted to dangers and coordinated breeding season, which is a very vulnerable time for this creature. As the creatures became more intelligent and communication improved, they were able to essentially alert each other so well they drove all predators to starvation. $\endgroup$ Mar 5 at 18:38
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    $\begingroup$ As to your answer, while I do like it and think its an interesting solution, I think it falls under an extraterrestrial origin for the idea. I upvoted but don't think I will accept. $\endgroup$ Mar 5 at 18:43
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    $\begingroup$ Having alerted each other what are they supposed to have done to avoid these predators? As described in your question, they could have done nothing. $\endgroup$ Mar 6 at 9:57
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    $\begingroup$ Terrestrial plants already do communicate for survival advantage via several well-known mechanisms. Extraterrestrial plants doing so for reproductive advantage hardly seems impossible by the standards we work with on this site. ncbi.nlm.nih.gov/pmc/articles/PMC3405699 ncbi.nlm.nih.gov/pmc/articles/PMC10458600 $\endgroup$
    – Jay McEh
    Mar 6 at 15:28
  • $\begingroup$ @JayMcEh Terrestrial plants also move and interact with their environments. I probably should have said "terrarium-like". $\endgroup$
    – g s
    Mar 6 at 16:41
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I would vote no.

The problem is, as you mentioned, observation based. General Relativity is the extension of Special Relativity which itself has almost sweet nothing to do with things you can easily observe. The fact the speed of light is constant for all inertial observers is not intuitive.

For us the discrepancy between predictions and measurements of Mercuries orbit was vital to even considering something like General Relativity. Because we knew definitively our theory (Newton) was wrong. We could only be certain of that because all other sources of error were accounted for. Your Organisms cannot do that. They cannot make equipment precise enough to rule out way simpler answers to apparent discrepancies.

Take for instance Vulcan, the theorized planet within Mercuries orbit thought up to account for Mercuries orbital motion. Without a moon to make eclipses and precise measuring equipment there is a 0% chance your creatures could rule out that another planet causes these issues.

Moreover, since their memory is so perfect they would know how much Planetary orbits wobble and shift just in principle. Since all bodies effect each other. They might just come to the conclusion their models are right, but they just dont have the tools to accurately use them. Similar to how early models of the Solar System acted like each planet was its own isolated two body problem, instead of N-Body.

The last issue i can see is that Newtonian Mechanics just work too well for your guys to become suspicious. To give you an example, the "Event Horizon" radius of a Darkstar (Black Hole equivalent in Newton) is $\frac{2GM}{c^2}$, the Schwarzschild Radius. Outside of the most extreme environments, Newtonian mechanics do a remarkably good job.

So to sum up, why no ?

  1. Special (let alone General) relativity are not Intuitive. You need a very good understanding and ability to make measurements to motivate either. Which your guys dont have.
  2. They cannot rule out easier explanations to apparent discrepancies with observations / measurements like we could.
  3. Newtonian Mechanics work to well.
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To quote Wikipedia:

Incandescence is a 2008 science fiction novel by Australian author 
Greg Egan. The book is based on the idea that the theory of general 
relativity could be discovered by a pre-industrial civilisation.

I was given the book as a gift, and I read it without reading reviews, so I had the great pleasure of realizing part way through "Wow, they are discovering GR without first discovering Galilean and Newtonian mechanics."

I found the discovery process using simple measurement tools quite plausible given the exotic environment.

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  • $\begingroup$ Thanks for the resource! This is just the thing I was hoping to find! $\endgroup$ Mar 6 at 18:37
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If they don't have technology, they won't have any chance to develop any model of their universe, not even at the level of the turtle on the turtle on the turtle...

To make you understand why, think that if you want to find someone in the homo lineage who doesn't have technology, you will have go back to the time were we didn't diverged yet from apes, or even before that.

Stone tools? That's technology.

Sticks to harvest honey or termites? That's technology

Fire making? That's technology.

And mind that those people who had just those rudiments of technology to make their life easier didn't go past an animist like vision of the world, where anything is a spirit. Talking about physics for them is even further away than talking about a smartphone to Galileo.

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    $\begingroup$ They are not thermodynamically impossible, they receive their energy from photosynthesis. It is entirely possible to make a close-loop biological system with only an energy supply, just look at "Ecosystems in a bottle". I saved the details from my question, but these creatures have a microbiome, like we do, which completes their nitrogen cycle and respirates excess O2 back into CO2. $\endgroup$ Mar 5 at 17:59
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    $\begingroup$ Lol, you beat me to it, Anthony. I was going to make the same point. Your species basically sounds like sealed-bottle terrariums that somehow build more of themselves. $\endgroup$
    – Qami
    Mar 5 at 18:01
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    $\begingroup$ Yes exactly, to your point, I also saved details about their reproduction since it wasn't the focus of the question, but they enter an extremeley vulnerable period when reproducing where they basically find a nutrient-rich pond, become permeable, and grow to double their size and then binary fission to produce offspring. $\endgroup$ Mar 5 at 18:11
  • $\begingroup$ @AnthonyKhodanian, removed that part since it's not pertinent to the question $\endgroup$
    – L.Dutch
    Mar 5 at 18:32
  • $\begingroup$ The rest of your answer is a fair criticism, but humans at those technology levels did not have modern human levels of intelligence. While those tools did certainly assist humans in evolutionarily growing to modern intelligence, given that intelligence I do not think the tools would be required to then utilize it. I do not believe that if you took humans from 200,000 years ago, when we think they possessed modern intelligence, and took away their tools, you could not then succesfully teach and discuss with them Galilean levels of math and physics. Whether they can derive it is another issue. $\endgroup$ Mar 5 at 18:56
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They live in the vicinity of a black hole

Near enough so that they see the gravitational lensing effect, but with enough distance that they don't get fried by the accretion disk's radiation. Alternatively, assume the black hole hasn't eaten a star in the last few billion years; some interstellar gas will still produce a weak accretion disk.

They won't see redshift. Not because their eyes couldn't detect infrared, but because the radiation is too weak. So... their cosmology will be limited to a few dozen or maybe hundreds of parsecs around them; they may be able to observe that stars do indeed move, but they won't observe how galaxies move, and they will probably know that galaxies do rotate because their orientation will slowly change.

They might see gamma ray bursts, if they can see how they create particles in the upper atmosphere. They will collect pretty little data, but since they keep a perfect record, they should have enough; they might even be able to detect their origin, particularly if they can detect polarized light.

They will have a really hard time grasping chemistry, or even detect Brownian motion (which is a strong hint that atoms exist but requires some experiments to validate that the moving particles aren't moving because they live but because they are hit.

Quantum theory is probably out of reach, subatomic theories are as well. They probably have been debating what's keeping the stars burning since the beginning of science, with no significant progress. In general, they will be pretty much in the same situation as human cosmologists around the 80s: No way to make experiments, so a lot of questions are open until we are lucky to see something. On the plus side, they can accumulate observations with much more ease than humans.

I'm a bit worried about the biological concepts. An immobile organism has little use for intelligence: If you can't run away, there's no use in detecting dangers, or in communication with your peers to organize better survival. Even logistic interaction (like: I have a surplus of mineral A on my spot and you have B, let's exchange materials) requires almost no intelligence, bacteria communities and slime molds do this without a single brain cell. Another source of intelligence could be conflict - or, rather, competition. It means negotiations, and if your neighbour is better able to understand your position than your ability to understand him, he has an advantage, so the race as a whole will have a strong drive towards better prediction and what-if abilities. (Given that the human brain consumes a whopping 20% of human basal metabolic rate, the most plausible theory I see about the evolutionary drive behind it is social interaction: If I can figure out what motivates you, I get more mating options and reproduce more. Thing is: With immobile creatures, there's little incentive to be smarter than your neighbour, because it will mate with you anyway, sooner or later...)

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  • $\begingroup$ Great answer, living near or even in orbit to a black hole is actually a really smart idea I might just use! And by the way, I put in my question that they are in fact mobile. By barely such I was merely implying that they were not fast by human standards, but they do indeed move and yes, originally evolved intelligence to signal each other to "run" away from predators. A genuinly useful answer, thanks. $\endgroup$ Mar 6 at 18:42
  • $\begingroup$ If they have some level of hive mind, they could use the fact that they are spread all around the planet to effectively become a huge telescope, the same way on earth we use a lot of small telescopes in a grid array to be able to get a better resolution $\endgroup$
    – Tofandel
    Mar 7 at 16:06
  • $\begingroup$ @Tofandel To combine multiple telescopes in this way, you need a "phased" array, i.e. the signals need to be combined in a way that preserves the phase information. Human technology can do this for radar using high-speed electronics, but not for light, and I do not think it can be done with organic eyes, otherwise herd animals would be doing this to spot predators from afar and at better resolution. $\endgroup$
    – toolforger
    Mar 28 at 8:02
  • $\begingroup$ Herd animals are not hive minds, which is why I think it would be possible to some extent, because a hive mind is akin to a planet sized computer and they definitly fit the definition of a phased array, they just need some kind of fiber optic appendage that they can point in a specific direction. From the description it seems they are already communicating using light pulses much like optic fiber, meaning they have higher and different capabilities than human eyes. Light is electromagnetic waves just like the rest. There is exactly what is needed to have this capability in theory $\endgroup$
    – Tofandel
    Mar 28 at 9:26
  • $\begingroup$ @Tofandel Intermediate individuals would have to amplify the signal, and they'd need mechanisms that can switch within the time that half a wavelength passes through them, and there's simply nothing in biology with that switching speed. Also, the individual that does the phased-array processing would have to be able to process the entire visual input from multiple individuals, and without any pre-filtering; that's hopeless, even an individual cannot process better than locally (correlating the input from neurons near to each other), phased-array needs global analysis. $\endgroup$
    – toolforger
    Mar 29 at 11:39
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Curiosity.

I don't think you need an observable motivation. You just need someone to wonder, "what if..."

You already have a species with language and arts. Sure, maybe they aren't holding paint brushes, but language alone is enough for art. Poetry, storytelling — these are probably some of the oldest forms of art. With art comes imagination. With imagination comes, "what if..." That's all you need. Someone being curious.

Without the use of tools, it is difficult to imagine how you could experimentally verify many parts of, well, any scientific theory. That doesn't mean your species can't have grand ideas about the universe, it just means they can't test some of the finer points.

They can still think things like "what if light were instantaneous? What if light has a finite speed?" They can still think of the math equations used to make predictions based on observations. They just might be stymied by the "observation" part due to a lack of tools.

A lack of tools to make observations supporting the expansion of the universe didn't stop Einstein from coming up with the math to make predictions of what we should see if the universe was expanding. He also had math making predictions of what static and contracting universes would look like. At the time he invented the math, he had no idea which one was correct. Oddly enough, it often requires imagination and math to give us the yardstick by which we measure our world to see if our grand ideas have any truth.

The important bit about general relativity is the "relative" part: everything is relative to the observer. Perhaps your species might not understand black holes, but they might be capable of observing the night sky to notice that nothing really moves around a central point. They can imagine the speed of light being finite or instantaneous. They can imagine the repercussions of each scenario and even come up with math equations that would allow them to predict what they should see.

Without the use of sophisticated tools, they just can't find the experimental evidence. But when has that stopped anyone from asking, "what if..."

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  • $\begingroup$ I guess part of my question is actually the can they come up with the math to make predictions? The math of relativity Einstein came up with is quite advanced, to the point where it may not be possible to come about without some motivation for it. Something they can observe in the natural world besides relativity that could lead to the formulation of tensor calculus perhaps? $\endgroup$ Mar 5 at 18:26
  • $\begingroup$ I see, the main question is one of motivation. Updated my answer, @AnthonyKhodanian. $\endgroup$ Mar 5 at 18:44
  • $\begingroup$ That the speed of light was finite had been known since the 17th century, when the Danish astronomer Ole Roemer first measured it. That all motion is relative had been known since Galileo Galilei in the late 16th century. The question is about an atechnological culture discovering Einsteinian General Relativity, which is a generalization of Einsteinian Special Relativity, which is a modification of old Galilean Relativity, motivated by the requirement to reconcile mechanics and electromagnetism. That the speed of light is constant is a consequence. $\endgroup$
    – AlexP
    Mar 5 at 19:48
  • $\begingroup$ "That the speed of light is constant is a consequence." Wrong. It's the axiom. IIRC there are only two solutions to "the max speed" (which happens to be the one of light, or so it is assumed, experiments continue): It's either infinite or it's the same for everyone. $\endgroup$ Mar 6 at 20:22
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Supreme mathematical knowledge

Their knowledge of pure mathematics is so expansive, they've simply enumerated it as but one of countless possible sets of physical laws that could govern a physical world. Based on eyesight alone, they've observed gravity, and they've observed celestial bodies and considered what occupies space, how visible light emanates and interacts with other bodies, the lifecycle of stars, and comets traveling through space dust, etc. Of course, many of their theories are wrong but they don't know it, but they trust that with the right technology, they could update their understanding of the physical world accordingly. It may help that their world has other visible phenomenon such as supernovae, merging black holes, etc. that is at least partly visible in their oral or literal history.

In true sci fi form, it reveals that what we apparently "know" is simply a function of what we've observed, our beliefs, and the apparent consistency between them. But at any point we could observe things that could/would radically shake what we "know" to a point we would be unable to explain it because we lacked the pure mathematics to expand our beliefs, and it could drive us to a state of hysteria.

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Thier psychic like nature could allow them to become all the tools they need to match all the same functions of terrestrial observatories

Multiple Mirror Telescopes (MMTs) function by combining the light collected from many different smaller sources that are each too small to see a distant object clearly, and combining them into a single, brighter, more clear image than any one mirror could collect. No single organic eye has enough surface to observe gravitational lensing, but millions of eyes focused on the same area of the night sky and feeding into a hive like consciousness could have the resolution of a powerful observatory telescope allowing them to see all the evidence they need with thier naked eyes.

Then the secondary part that makes astronomy difficult is measurements. As it turns out, the first thing you really need to make precise measurements of the night sky is some kind of tool that stays in the same place so that you have a reference point. The good thing about being a plant is that maintaining a stationary point of view comes very naturally to you. You don't need to make a stonehenge because all over the world, plants stay lined up with various geographic features to be able to see how things have traveled.

But you also need to measure time. Again, thier psychic connection means that each plant, all over the world knows precisely when the sun is rising and setting at any given point; so, when one plantling sees the sunlight hit a certain crack in a rock at certain latitude and longitude at the same time that another plantling sees his own time marker hit, the collective can from those two pieces of data determine the exact date and time across the whole globe.

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I'm going to disagree with many of the answers here and say that special relativity can be derived from fairly basic principles, namely the principle of (Galilean) relativity and the invariance of physical laws throughout space and time. From these you can deduce that there are only two logical possibilities: no maximum speed, or a specific invariant maximum speed (which in our universe happens to be the speed of light). See for example https://arxiv.org/abs/physics/0302045v1 or https://en.wikipedia.org/wiki/Derivations_of_the_Lorentz_transformations#From_group_postulates for how this is done.

So a species that is familiar with Newtonian mechanics could at least, in principle, conceive of special relativity as an alternative possibility from first principles. Finding a theory of gravity which reproduced Newton's gravity in the limit and which was Lorentz invariant could certainly lead them to general relativity. This might all be considered as fanciful thinking by most members of the species, but very careful observations of e.g. precessions of planets could at least in principle distinguish between Newtonian and relativistic gravity and cause them to put more stock in relativity.

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