# How small can the universe be while still appearing infinite?

I'm working on a concept of universe creation. The best way to describe it in a sentence is the Judeo-Christian Creation Story but from God's point of view.

My question is, staying as close to hard-physics as possible, what is the minimum amount of universe needed to be created to prevent humans from figuring it out. The mechanism of creation is handwaved at the moment, but the two I'm considering is a Dyson sphere type construction that would be built in the "higher" universe (so a sharing of actual space, but humans would effectively be in a confined area). The other option is a simulation. I'm leaning towards the simulation idea because of quantum mechanics propensity for not being "defined" until observed (like an RNG that doesn't generate data until needed). However, for either option, the following constraints are in place.

• 6,000-10,000-year-old universe
• must give the impression of a 13 billion-year-old universe

I'm less concerned with Earth itself since you can create something that looks old. It's more the celestial side of things that is giving me problems. Like how to make light appear to be coming from outside the limit of the universe. How big does the universe need to be to compensate for actual measurements taken from earth (like how we use the orbit of earth to get the distance of stars). Etc.

Voyager 1 is something like 11 billion miles away, so I guess that's the minimum. Certainly, it would be hard to get smaller than the solar system. But in a hard-science environment (at least inside the universe*) how small can I make it so that humanity would not figure it out with modern technology.

* What I mean is that inside the universe, physics is exactly like ours as we understand it right now (unless necessary for this concept to work). And so any limitations on the universe would have to be undetectable to modern equipment

If God created the universe, and it’s 10,000 years old (in God’s inertial reference frame), then it only needs to be 20,000 light years across, centred on the solar system. The light that appears to come from further away could have been created, already in motion, at the same time as the rest of the universe.

• I think this is the simplest answer. It gives way to an interesting phenomenon that could be exploited for the story: astronomers will at some point see all galaxies and all stars further than 10000 ly away suddenly vanish from the sky without a trace, when the furthest created light rays (and neutrinos, gravitational waves, etc.) finally reach the Earth. – pregunton Aug 24 '18 at 8:12
• @pregunton What would be really interesting is if the light disappears but the gravitational waves continue. – Mike Scott Aug 24 '18 at 9:13
• Interestingly (correct me physicists), if you also make the universe continuously expand (like ours), the light from the furthest parts will never reach them, and they'll never be able to tell whether the universe was in fact infinite or not. – Bilkokuya Aug 24 '18 at 15:59
• The answer holds only for a flat, static universe described by the Minkowski metric. @Bilkokuya is right that in an expanding universe, the radius doesn't necessarily coincide with the distance given by speed of light * age of universe; for example, our universe is estimated to be 13.8 billion years old while the radius of the observable universe is 46.6 billion light years. – George Aug 24 '18 at 17:15
• @George My impression from the question is that the universe must look pretty much like our universe, which is locally flat and static enough for expansion to make no difference within a 10,000 light year sphere. If the universe is expanding fast enough for it to be important, I’m not sure how the inhabitants could think it was 13 billion years old. – Mike Scott Aug 24 '18 at 17:41

If your Godlike masters have the power of holography, there is no lower bound beyond the size of the creatures they are imprisoning.

There is a theory in modern physics called the holographic principle. It is the idea that the behavior of a volume of space can be encoded on its surface. This is easily shown to be true for light, because we can construct holograms. The behavior of the 3d space of the apparent object is captured on a 2d surface of the holographic media. The holographic principle is the idea that this works for all physical behaviors, not just the properties of light. It is used in all sorts of neat ways. For instance, Stephen Hawking was striving to prove that black holes did not destroy information. Instead, he argued that they should encode that information on their surface.

If this is true, then these godlike creatures need only provide a thin film around the creatures which encodes the state of the apparent world beyond.

This structure can be as small as one wishes, as long as it can enclose the inhabitants. In theory it could be as small as our brain (or even smaller... our brain could be the illusion while our real "thinking machine" is something else). However, if its gets small, we may notice things:

• If you can't create an actual holographic representation because you lack the technology or the holographic principle turns out to be false, then you can rely on false holograms like Pepper's ghost, and the projection versions of it. These would have to be large enough to make sure we could not detect effects like parallax. Real holograms do not have this limitation.
• If you have a static representation of the space (like our static holograms today), then you can only represent a static space. The individuals will start to notice that these far reaching spaces appear to simply not move. They seem frozen in time.
• If you have a playback representation of space, then you can make the far reaching spaces appear to move. Any physical limitations on this playback might be detected. For example, if you play it like a movie at 24fps, people might notice a 24fps jitter, if they can take fine enough measurements.
• If you have a dynamic representation of space, then there is no limit to how small it can be. The key way to notice the static and playback holograms is to try to interact with it. You can see a holograph of a beautiful woman talking on the phone, but if you try to reach out and touch her, you quickly find your hand touching a piece of plastic. This is because this static hologram cannot respond and adapt to your interactions. If you had a smart enough simulation that could generate new holograms on the fly, it could fake interactions. Once you can fake interactions, you now have Plato's Cave, where you cannot trust your own senses.
• This entire concept seems more like an implementation of Descartes' Demon than Plato's Cave. – Racheet Aug 24 '18 at 16:44
• @Cort Ammon As far as I know a holograph can't look any deeper than its physical size. If a holograph is 1 foot thick nothing in it can look more than 1 foot farther way than another object in it. And some stars have parallaxes indicating they are tens, hundreds, and thousands of light years farther away than others. – M. A. Golding Aug 24 '18 at 17:20
• @M.A.Golding I'm not sure if I follow. If I'm interpreting your statement correctly, if a holograph is a thin film, like a 1/8" surface, it can't show anything deeper than 1/8", but that's clearly not true. The whole point of holography is the ability to encode particular 3d properties onto a 2d surface. – Cort Ammon Aug 24 '18 at 18:11

You don't need to set a fixed-size at the creation

Initially at the creation, the universe could be as small as the Earth itself. Then, at the fourth day, God makes lights in the vault of the sky to give light on the earth. The Sun and Moon serve a practical purpose, but the stars themselves are mostly decorative.

The first design might have just consisted on a sphere around the Earth, as pictured on some early conceptions. The Sun and Moon could be the only bodies moving a that point, although positioning them inside a larger Solar system would be needed for a proper design of the Sun as a burning star (instead of providing the heat in a different way).

The stars could have been static leds there, but we can assume that these decorative lights would vary since quite early, with different star designs each season. Also note that sometimes new stars are lit or faded.

At one point, God decides to improve the design (which already was good) giving it more depth, by moving some stars to places a few light-years away, while keeping the overall picture when viewed from Earth, this way the shades provided are slightly nicer (maybe imperceptible for humans, but God strives for perfection; and what is making the universe thousand times larger for Him?).

When humans sent the Voyager probes, God would have needed to enlarge the Universe on their path out, so they didn't reach/collide with the "end of the Universe" (if it wasn't big enough already, which it probably would). Also note it would be enough that there is Universe up to wherever they reach by approx 2032 AD, at which point they will be unable to transmit.

We need to change the basic assumption of parallax

Stand in front of a telephone pole and look at a building beyond. As you move back and forth, you can see the pole covering different aspects of the building at different distances. Since you know your distance from the pole and the distances you're walking, you can use simple trigonometry to calculate the size and distance of the building beyond. That's parallax.

But it depends on nothing we don't understand distorting the transmission of light.

Scientists once felt the vastness of space was filled with aether. It allowed scifi authors to play with the idea that space ships were little different from naval ships and we could walk around on the decks.

Then we started actually putting things in space.

But, as we developed more complex mathematical models of our universe, some of the math didn't work. This necessitated bringing back the idea of aether. I suspect a number of scientists simply didn't want to be embarrased, so they called it another name: dark matter.

Let's use the concept of "dark matter" as a lens, not unlike looking through a fluid, which distorts the flow of light over long distances

The consequence of this is that what looks to we humans to be a 13 billion+ light-year sized universe could actually be just about anything you want, especially if the distorting effect of light travelling through the "dark matter" was logarithmic, not geometric.

And the beautiful thing is, we're talking about such vast distances (even with a universe having a radius of only 10,000 light years) that we could easily be talking about a particle so rare that our own modern-day science has yet to actually detect its physical existence (if it exists, let's assume it does!).

So... dark matter distorts the transmission of light such that the method of measuring distances, parallax, makes the universe appear much, much larger than it actually is.

• Actually parallax works only for stars which are very close by. Distances to stars which are not in the immediate vicinity, and even more so for distant galaxies, are measured using very different methods. See the WIkipedia article on the cosmic distance ladder. (And dark matter, whatever it may be, is not at all similar to the luminiferous aether. If anything is reminiscent of the luminiferous aether it is the Einsteinian curved spacetime.) – AlexP Aug 23 '18 at 20:20
• @AlexP From the article you link to, "The most important fundamental distance measurements come from trigonometric parallax." Nearly all measurement methods depend on reference points that were first found using parallax. And try as anyone might, dark matter really is just the latest incarnation of aether: an unknown mass-bearing substance that rationalizes what we don't understand. I'm using it as nothing more than a useful plot hook with some humor. But, if you have a better answer, it would be to the benefit of the OP. – JBH Aug 23 '18 at 20:29
• Actually, the use of type 1A supernovae being a standard candle, coupled with the red shift and apparent luminosity is the most common reference point for distant objects. – Mathaddict Aug 23 '18 at 20:47
• @Mathaddict, after the fact. Do you really not understand the history of astronomy? The derivation of distance by standard candle was achieved after determining distances of closer objects using parallax. You're trying to tell me calculus can exist without arithmetic. It's amazing how many people believe that science as it is today is all there has ever been and all there will ever be. it's an odd kind of intellectual blindness. – JBH Aug 23 '18 at 21:02
• @Mathaddict, Unecessary. Parallax and the optical distortion of light is the first common denominator with a distance-relevant failure condition (which is why I picked it). The calculation of the astronimical unit is too close to home. The "adjustment" that allows the failure of parallax to work requires enormous distances. – JBH Aug 23 '18 at 23:53

Keep in mind that most of our observations and measurements about the universe assume that the cosmological principle is true. That is, they assume that the laws of physics we observe on and close to Earth are the same as what we would observe anywhere else in the universe. That's a serious assumption that we don't have the capability to prove. If this assumption turns out to be false, then everything we know about the wider universe is wrong (or is at least called into serious question).

If the "higher" universe that you mentioned did not have uniform laws of physics or if the creating entity had the ability to adjust the laws of physics within the scope of the "created universe", then you can get away with a fairly small universe. Imagine if instead of the speed of light being constant, it was a function that changed as you got farther away from the Earth. If the speed of light, the passage of time, the strength of gravitational forces, etc were all non-uniform like this, then an Earth-bound observer who assumed a universal set of physical laws would see the universe in a very incorrect way. A tiny universe could appear massive, or vice versa. If you can assume that your created species would never be able to travel far enough beyond their planet to detect the inconsistencies, then you wouldn't need a very large "universe" at all.

I don't know how small you can make the universe in your story without violating any major scientific laws.

I suggest that the universe has to have a radius at least millions of times (possibly many times that) the farthest distance that humans can travel for humans to not discover any spherical shell with lights on it to represent stars and galaxies.

I would suggest that your universe might have to be thousands or tens of thousands of light years in diameter at the present, and your god or gods might have to be prepared to enlarge the other shell and move it much farther out in the future, and replace images of stars, etc. on that shell with real physical stars, etc. at the proper distances. And quite probably be prepared to do it multiple times, as he, she, or they might have done multiple times in the past.

According to the current scientific understanding of the universe based on observation and the laws of physics, the observable universe has a radius of about 46 billion (46,000,000,000) light years (14 billion parsecs) and thus a diameter of about 96 billion (96,000,000,000) light years (28 billion parsecs).

Because of the expansion of space between galaxies, the light from more distant objects can never reach Earth and be seen by Earthlings because space between more distant objects and Earth is expanding faster than the speed of light.

Because we cannot observe space beyond the edge of the observable universe, it is unknown whether the size of the Universe in its totality is finite or infinite.3[52][53] Estimates for the total size of the universe, if finite, reach as high as {\displaystyle 10^{10^{10^{122}}}} 10^{10^{10^{122}}} megaparsecs, implied by one resolution of the No-Boundary Proposal.[54][b]

A megaparsec is one million parsecs, or 3,261,563.777 light years. And there seem to be at least 122 zeros in that number. Thus it is possible for the universe, even if finite, to have gazillions of times the volume of the observable universe.

Thus the problem of making the actually universe in your story much smaller than the universe of scientific research while not breaking any of the know laws of physics becomes very complex.

And it seems to me that the main problem with trying to make the universe the size of, for example, the solar system out to a few times the orbit of Neptune, with a spherical shell around it containing images of allegedly more distant objects, is trigonometry, a branch of geometry, and its implications for parallaxes.

Everyone has experiences with parallax. Hold out your hand at arms' length and hold up a finger so that it lines up with an object in the background looking at it with both eyes. If you close your right eye your finger will appear to jump to the right of the background object, and if you close your left eye the finger will appear to jump to the left of the background object.

And if you line up a tree and a telephone pole, for example, and then take a step to the right, the nearer one will seem to move to the left of the farther one.

As a child riding in cars at night, I often noticed the moon seeming to follow the car, disappearing behind buildings or trees and then reappearing from behind them at the same angle relative to the car as before. And that is because the Moon was usually millions of times as far away as the nearer buildings and trees and so the parallax of the buildings and trees was millions of times greater.

And the same phenomenon can see with clouds and trees, buildings, etc. when riding in a car in the daytime. The clouds are thousands of times closer than the moon, but many times farther away than nearby trees and buildings, which thus have many times greater parallaxes than the clouds.

Modern astronomers have developed techniques to measure incredibly tiny angles, probably down to about a trillionth of a full circle at the present, and will develop improved techniques to measure ever smaller angles in the future, which means they can measure ever smaller parallaxes of ever more distant objects.

I discuss stellar parallaxes in other answers to other questions.

Here, for example:

And here:

So it seems to me that you will probably have to make stars which have measured parallaxes and distances of tens, hundreds, or thousands of light years from Earth really at those distances, and thus put the spherical shell, decorated with shining lights impersonating more distant stars, at an even greater distance from Earth.

And it is quite possible that results from the Gaia satellite mean that your god or gods has already had to move the spherical shell out to a distance of tens of thousands of light years.

As I remember, the distance to the Pleiades Star Cluster is very important for astronomers because it contains the nearest examples of some classifications of stars that are used as "standard candles", their apparent brightness as seen in different star clusters, etc. as compared to their calculated absolute luminosity enabling the distances of clusters containing them to be calculated.

And about 25 years ago the parallaxes of the stars in the Pleiades Star Cluster as measured by the Hipparchos satellite were controversial because they were different from those obtained by less direct means and suggested that using the Pleiades stars as "standard candles' would have to be re calibrated.

At the present time various studies and the preliminary results from Gaia suggest that the Hipparchos distance is an error.

It seems to me that you could use various controversies about the distances of various astronomical bodies to suggest that there has been some sort of foul up in impersonating a vast universe, thus implying that the universe could be much smaller than it looks.

And possibly characters in your story wonder when results from the Gaia satellite (or possibly some future successor of it) will be announced, and some may speculate that the delay is due to the observations proving that the more distant stars are lights on a spherical shell and the astronomical community is covering them up.

Since astronomers can measure parallaxes out to distances many millions of times at least the length of the baseline they use, and since it would be possible to increase the length of the baseline with observations in outer space, you might have your god or gods create an invisible but impenetrable force field around Earth, the entire solar system, or the nearby stars, and then create stars in 3D space out to a distance of millions of times at least the diameter of that force field, with the spherical shell with lights to impersonate stars and galaxies being beyond those stars in 3D space.

Then humans may discover the invisible force field when space probes or star ships crash into it and explode, and learn the truth about the universe.

13.7 billion light years. Anything happening outside this radius will never reach an observer that far away. This could be modified by adjusting the Hubble constant (roughly the rate of universal expansion) in your universe. Note that current theory indicates that the Hubble constant is not constant and changes over time.

This is very convenient for your story as they would still be able to see the cosmic microwave background radiation at a 13 billion year old universe.

Unless...

You only plan on having your humans exist for a certain amount of time, then you only have to make sure it's c*time humans exist (c being the speed of light). The universe could just stop expanding and the light from this phenomenon wouldn't reach the place where the humans are until after they are all gone.

Play with time ratio. There's no better way to fake something than no faking it at all so... don't create an universe and then tweak it in different places in order to make it look different.

Either with a simulation or with a magic-handwaved stuff, just create the universe as big as you want and set the time speed 1.3M times faster (like pressing fast-forward on your radio tape but more extreme) wait for some thousands of years and then set the time ratio at 1 again.

Then you can select (or create) a proper place for your tiny puny humans to be.

Doing things this way you're less prone to errors that your humans may notice if they get smart enough like: "We learned how to measure the age of photons and this light should be 13By old but appears to be only 15Ky old, isn't that odd?".

With the idea of an all-powerful god, you don't even need a universe. You just need the perception of everything going on around an individual in the universe.

This god could be creating everything as the individual perceives the world around them. This is why a pen that you put on your desk a minute ago is not able to be found when looking at your desk, until you find it again right where you left it sometime later, still on your desk.

Depending on how busy you want this god to be, everything gets destroyed when it goes unobserved, so everything outside of the individual's level of perception is destroyed. So, turning the corner in a building causes the creation of the building around the corner and destruction of the building behind the corner.

If you want to go even smaller, your god could simply be inputting sensations directly into a brain so it only believes it has a body and is perceiving a world an universe.

Maybe god decides to change it up on occasion and make a large universe for a while, and eventually decides that's too boring. Then goes really small, and gets wore out constantly creating all the personalities and matter the individual interacts with. Decides on a medium size of the Earth + atmosphere, and simply imitated the rest.

Neal Armstrong didn't actually go to the moon. He, his crew, and craft disintegrated beyond the atmosphere, was impersonated by the deity for the duration, then was re-materialized on re-entry. All the memories, materials gathered, equipment left behind, etc. was all faked by god, since there really isn't a moon anyway.

All the star radiation is continually created for is humans to "observe" the cosmos, which doesn't exist. Voyager 1 no longer exists, except as an imitated data stream that the deity impersonates.

Your story could encompass a history/snippets of the various points in "history" where god made these different size decisions. He could also have a brief antagonist that finds a technology to detect these changes, only to wipe them out as if they never existed.

You can even go to the extreme end of the story and have god decide that his creation has run the limit of his interest and wipe it out to start over. Even during the middle of the story, you can have god take a nap, eat supper, try separate mini-experiments, all with the ease of putting us on "pause" the same we do with a video game.

Maybe she even takes a few year hiatus (her time frame), and starts things up again. This could account for the middle ages. She was getting tired and annoyed, so she had everyone warring and dying of plague. Then she decides to "take a break", and when she comes back with renewed vigor and ideas, we get the industrial revolution. Everything was paused, so there's no gap in control, just a different desired direction for everything to follow.

Since this is god, it can control "time", so it can closely watch a dozen different people in the same time frame. It decides to study Thomas Edison and how he competed with Nicola Tesla, but at sometime later decides to watch Tesla and see how it felt to be harassed by Edison.

You know what, I think I've described a different novel than what you wanted. Sorry. Feel free to use these ideas or even write another book based on this post. This can still fit the Judeo-Christian idea of god, since we really don't know what god does, now that he's done "creating" the "universe".