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I’m making a fictional galaxy, and I want the inhabitants of this galaxy to be unable to calculate the age of the universe, I want them to be unaware of how much has already happened.

I’ve already decided that most other galaxies once visible from mine, has already passed beyond the cosmological horizon, and redshifted beyond detection; leaving only a few thousand local galaxies, close enough to be gravitationally bound, to be observed.

From what I can recall from school, the age of the universe is calculated by measuring the rate at which galaxies accelerate away from each other.

So would it still be possible to calculate the age of the universe using only these local galaxies?

If it is possible, when is the point (preferably before the heat death of the universe) where determining the age of the universe becomes impossible, or at least highly inaccurate?

Or does someone have a different idea of how I can achieve this without throwing too many laws of physics out the window?

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    $\begingroup$ Edits should not invalidate existing answers. The edit I rolled back invalidated Renan's answer, thus is not legit. $\endgroup$ – L.Dutch - Reinstate Monica Jun 5 '19 at 13:51
  • $\begingroup$ Well, if they are advanced enough for space travel they are advanced enough to have a good idea of the age of their solar system. Now if they are alive, their sun must be something like ours, at least a second generation star. So they have a lower bound for the age of the universe, they know that it is at least some 10 billion years old. I cannot imagine how it could possibly be important to the plot that they cannot guess that instead of 10 billion years old it is really 100 billion years old. It's not as if the galaxies which are not part of the Local Group have any influence on us. $\endgroup$ – AlexP Jun 5 '19 at 14:36
  • $\begingroup$ If we assume your species evolved very late in the history of the universe - difficult, but probably not impossible - then we're left with the fact that while you can redshift light beyond biological visibility, you can't redshift it beyond detection. What's the tech level of your species? $\endgroup$ – JBH Jun 5 '19 at 14:42
  • $\begingroup$ @JBH: You cannot redshift light beyond detection, but you can expand the universe so that galaxies outside the local cluster move away faster than the speed of light so that their light will never reach us. See cosmological horizon and Hubble volume. $\endgroup$ – AlexP Jun 5 '19 at 14:54
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    $\begingroup$ @JBH: The galaxies do not themselves move faster than light; what happens is that the space between them expands so that the distance increases faster than light can traverse it. The largest object which is gravitationally bound so that it does not participate in universal expansion is the local cluster, which, in our case, is the Virgo Cluster -- 1300 galaxies, 54 million light years across; the members of the local cluster will always be with us, while eventually the rest of the universe will recede beyond the cosmological horizon. $\endgroup$ – AlexP Jun 5 '19 at 15:15
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How do we calculate the age of the universe?

A very simple estimate of the age of the universe can be found via the Hubble constant: $$t\sim\frac{1}{H_0}$$ This is only an approximation, though, because the Hubble constant changes over time. A more sophisticated (and exact) technique that corrects for this involves determining the standard cosmological parameters. By this, I mean the various relative densities of dark energy, matter, and radiation ($\Omega_{\Lambda}$, $\Omega_{m}$, and $\Omega_{r}$). We can then calculate the age of the universe by integrating using the scale factor $a$: $$t=\frac{1}{H_0}\int_{0}^{1} \Big(\Omega_{m,0}a^{-1} + \Omega_{r,0}a^{-2} + \Omega_{\Lambda,0}a^2 + \Omega_{k,0}\Big)^{-1/2} da$$ There are a number of ways to determine the Hubble constant and the density parameters:

. . . and many others. We've recently seen discrepancies between some of the values derived by different methods, which implies that our standard cosmological model may be incomplete, but they're nonetheless all valid.

What your setup rules out

We can throw out all methods that require measurements of objects at high redshifts. Regrettably, this includes basically all the techniques I've described here. If you're looking for a time period at which it becomes difficult to determine the age of the universe - well, you picked a good one. All high-redshift sources aren't visible.

One possibility that might remain is looking for anisotropies in the cosmic microwave background (which I alluded to before), from which we can determine $H_0$. Unfortunately, it happens that $H_0$ is degenerate with the radiation density $\Omega_{\Lambda}$ and the equation of state parameter $w$; that is, you need two of those to determine the other one. This means you can only constrain the relationships between these three. Of course, if there was an independent way to determine $w$ and $\Omega_{\Lambda}$, you might be able to get somewhere.

Now, this assumes that the CMB will still be detectable far in the future. The energy density of the CMB scales with redshift $z$ as $\varepsilon\propto(1+z)^{4}$, and redshift scales with time as $t\propto(1+z)^{-3/2}$. Therefore, the energy density of the CMB scales as $\varepsilon\propto t^{-8/3}$, which is significant enough that this far in the future, it will likely be of undetectable intensity (never mind that it will be redshifted significantly, too).

Are stars a possible loophole?

In a comment, Mark mentioned that you could use the earliest stars to measure the age of the universe. While this indeed gives you a sanity check of any other measurements you've made - if you see a star that seems to be 40 billion years old while your other methods tell you the universe is 13.7 billion years old, you have a problem - it's not going to give you more than an estimate.

In our universe, for instance, stars didn't form for a hundred million years or so after the Big Bang. Moreover, these stars didn't necessarily form in every galaxy simultaneously; some might have experienced star formation later on. Therefore, measuring and modeling the oldest stars, while seemingly a loophole, has some problems.

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    $\begingroup$ "Well boys, we've been scooped." - if you have radio telescopes capable of picking up the CMB, then the jig is up. $\endgroup$ – Mazura Jun 5 '19 at 22:22
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    $\begingroup$ @Mazura Fair point! I edited to acknowledge that the CMB's intensity at this point should be . . . tiny. $\endgroup$ – HDE 226868 Jun 5 '19 at 23:41
  • $\begingroup$ The question asserts that all galaxies outside the Local Group have been redshifted to the point of undetectability, and the CMB is already far cooler and dimmer than they are. So yes, the CMB will definitely be undetectable. $\endgroup$ – Someone Else 37 Jun 7 '19 at 19:15
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The current 'measurements' of the age of the universe are actually measurements of some astronomical effects, that get mixed into calculations involving many constants. Most of what we know about the universe is (mostly implicitly) followed by '... if those values are indeed constant.'.

Some weird effects are actually easier to explain when we assume the constants to be not that, i.e. slightly changing over time (or space).

If your civilization realized that some important constant was actually variable, and a function of time that was not easily extrapolated (e.g. not a continuous function), their measurements might not be precise enough (maybe it would even be physically impossible to be precise enough) to pin it down, thus making the whole calculation impossible.

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    $\begingroup$ The only issue with changing natural constants is that they all hang together. Change them, and you quickly find out you turned matter unstable, or everything should collapse, or some other consequence that makes the current universe impossible. So it is always possible to constrain constants to some degree what they must have been. $\endgroup$ – Whitecold Jun 5 '19 at 14:07
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    $\begingroup$ @Whitecold Many universal consonants are based on an incomplete understanding. For example, Pythagoras knew that A² + B² = C² where Θ = 90°. And for nearly 2000 years, you could only calculate the sides of a triangle where Θ is a constant of 90°. Then al-Kāshī realized he could expand the formula to A² + B² - 2ABcos(Θ) = C². This change did not invalidate the truth of Pythagoras's work, it just expanded it to new frames of reference. Likewise, a variable "constant" may not change our observations from Earth, but would from the Andromeda Galaxy. $\endgroup$ – Nosajimiki - Reinstate Monica Jun 5 '19 at 16:30
  • $\begingroup$ @HDE226868, the age of the universe is calculated three different ways: from the inverse of the Hubble constant, from the temperature of the cosmic microwave background, and from the age of the oldest stars. All three are indirectly dependent on various constants being constant. $\endgroup$ – Mark Jun 5 '19 at 23:53
  • $\begingroup$ @Mark For now, I'm removing my comments because despite what I said above, I don't think my argument is watertight, so I'll retract them until (unless?) I'm more confident in them. I still think that the relevant calculations cover time evolution of the cosmological parameters implicitly, but I'm not as confident in arguing that they could be measured in the first place on scales where any change in constants wouldn't impact them much. $\endgroup$ – HDE 226868 Jun 6 '19 at 1:10
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Your idea is sound. In the very far future when most galaxies are invisible and the cosmic background radiation has faded to the point of undetectability, evidence about the state of the early universe will be impossible to obtain at our current technology level, and some kind of steady-state theory may well be just as well supported by the available evidence. But remember that the visible universe will be very different from the one that we see around us today -- we're talking very far future, perhaps a trillion years from now. See this article.

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  • $\begingroup$ Came here to say this - eventually it will be impossible to determine a possible age of the universe with at least modern understandings of how physics works. Now maybe there's more data out there that we just don't know yet, but it seems unlikely based on current understanding. $\endgroup$ – Andrew Alexander Jun 6 '19 at 0:34
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You can just have them be primitive.

Roll safe

Alternatively, they did have the knowledge and tech to do it. They just lost or broke all their satellites and telescopes.

Edit: you edited the question to mention they do have technology. Alright, have them be surrounded by nebulae, such as the Eagle:

Eagle nebula

Or the Horsehead:

Horsehead nebula

Those are thick enough that we cannot see past them, at least not in every frequency. If your inhabitants are in a bubble of dust, they won't be able to measure the doppler shift of distant galaxies.

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  • $\begingroup$ Clearly I should have been more specific, I'm not even mad. $\endgroup$ – Nobbe Jun 5 '19 at 13:16
  • $\begingroup$ Infrared light (among other wavelengths) will still be able to penetrate the cloud at a few microns; cosmological measurements of the Hubble constant have been made at around those wavelengths, give or take a micron or two. They'll be able to measure high-redshift Doppler shifts; it'll just take a little ingenuity. :-) $\endgroup$ – HDE 226868 Jun 5 '19 at 23:53
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First why not, and then how maybe ...

I'm not convinced this is possible for an advanced technological society capable of space travel.

One of the things they have to figure out on the way to getting that developed is the General Theory of Relativity. Although Einstein gets all the credit for this publicly, that's a gross simplification of a lot of investigation and discussion and ideas and theories that helped, so a society is going to get to it.

Almost as soon as you can do anything with this theory, people will inevitably start trying to develop a model of the universe. What we got (and this model is also pretty likely to be found by someone) is the FLRW metric. Expansion is what we found going on, but even in your scenario, they'll see effects in their "Local" galaxies (which won't be all that local any more !).

They'll also become aware of dark matter and dark energy, because this affects the motion of galaxies and even the motion of stars in galaxies.

Note even in the late universe when it's "dark" and they're all alone, even the fact that you are alone with nothing obvious to see will be useful data in terms of fitting it to a model of the FLRW type.

Quantum theory is also going to be found. Again inevitably people will seek explanations for the origin of the universe and look to it to provide explanations.

Like us they'll look for ways to combine quantum theories and general relativity (which we haven't quite managed yet :-) ). These will result in concepts that tell them to look at e.g. the relative distribution of different isotopes as evidence for their origin (this is one piece of evidence we use).

So they'll inevitably find clues and look for explanations, and go looking for more clues to test theories and find more data. They'll keep looking until they get an answer, because if there is one trait I suspect all intelligent life shares it's going to be "unrestrained nosiness". :-)

How to avoid this ...

One word : Desperation.

Give them a world that is in turmoil, always at war with itself, with an ecological nightmare that makes staying alive hard as blazes.

That pushes resources and all the inquisitive people into more practical work (if necessary in chains).

Also keep in mind that the main motivation for all that "going into space" stuff was not (in our case) pure scientific interest. We were building rockets to throw nukes at each other and science gave an excuse that didn't sound so insane. But in doing that we came extremely close to wiping ourselves out.

So we (and they) could just as easily have gotten to space travel and promptly almost wiped out most of the planet's life, including ourselves. (And the option is still there, kiddies - vote for sane people, please :-) ).

I don;t know about you but if e.g. the Cuban missile crisis had gone full scale nuclear exchange, none of us would care one iota about the age of the universe or studies to find out about it.

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    $\begingroup$ But we know that general relativity and quantum theory can’t both be right — they are incompatible. So they're probably both very good approximations to some other theory that we know nothing about (except that it approximates to quantum theory at small scales and to general relativity at large scales). And that theory may have different implications for cosmology. $\endgroup$ – Mike Scott Jun 5 '19 at 19:13
  • $\begingroup$ @MikeScott I would not say they both can't be right. They're both spectacularly accurate theories in their intended domain. Any theory replacing them has to be practically the same as GR and QM in their respective domains. So a replacement theory would be expected to reproduce the results from GR we already have, including the cosmological results. QM and GR aren't incompatible - we have theories that mix them fine, but the problem is that these theories don't quite fit the data - we're looking for the "Goldilocks" theory. But theories mixing GR and QM - no problem - we've loads. :-) $\endgroup$ – StephenG Jun 5 '19 at 20:38
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There are 3 factors that work together to tell us the age of the universe.

  1. Redshift: Which we can use to map out the speed of the universe's expansion.
  2. Age of Stars: By looking at the ages stars and ratios of stars, we can tell a lot about the universe's age from what we can infer from star life cycles.
  3. The CMB: A uniform background radiation in the universe that is consistent with exploding superheated.

While redshift is helpful for getting predictions of the universe's age accurately, no explanation that discredits it would actually make the age of the universe completely uncertain due to other factors.

Ages of stars can also be tricky. The universe would have to be at least 100 billion years old for us to be able to observe the whole life cycle of every kind of known star. This means any universe younger than that (such as our own) would be easy to make assumptions about. While making a universe more that 100 billion yrs old seems to be the answer, by that point, you may still be able to calculate from what ratios of star types are left to make a good approximation all the way up until the cold death of the universe and final evaporation of all black holes.

The best place to undermine our understanding of the universe's age is to mess with the CMB. We live in a part of the universe where we can only detect 1 CMB, where all matter is apparently expanding, and seems to have originated at the same time. This tells us there was a single big-bang at the "beginning of time", but as our instruments get better, we may one day discover other older or younger CMBs. The existence of multiple bangs could knock out the very concept of the beginning of time. If we find out that our universe intersects another bang, then it could be inferred that what we know to exist today is just part of a greater pattern of big bangs that have been going back for unknown quadrillions of years well beyond out powers of observation.

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Make your universe highly anisotropic.

First, I should start with the disclaimer that general relativity is a very complicated subject, and while I have a cursory familiarity with it I am in no way an expert, so take this with a grain of salt. With that being said, the idea behind this is that in general relativity, the coordinates that someone measures depend on the path they take through space and time.

This is because in general relativity, spacetime is described by a manifold, which is a fancy way of saying that it seems normal and flat close up, but globally it can have some funky structure. The classic analogy is how the Earth looks flat when you're standing in west Texas, but if you walk long enough in one direction you'll end up where you started which is a decidedly not flat thing for geometry to do*. The difference here is that while the Earth is embedded in 3 spatial dimensions, spacetime isn't embedded in any higher dimensional, flat space. This may not seem like a problem at first, but it actually causes issues if you want to define coordinates that everyone can use.

To see why, say you were a two dimensional creature who lived on a spherical manifold like the Earth, only it wasn't embedded in a flat 3D space you could interact with. Like any good, scientifically minded 2D creature, one day you have the thought that life for everyone would go so much smoother if everyone on your world could have some common way of giving directions. So, you grab a stick, point it in a direction, and secure it firmly to the ground. You then declare this to be the standard direction everyone should use for giving directions from now on (let's call it 'weast').

Of course, a standardized direction like this is pretty useless if it's only in one spot, so you need a way for others to 'sync' their directional sticks with yours and then take them to new places across the world. The syncing part is pretty easy-- they just need to bring their stick next to yours and point it in the same direction. They need to be careful transporting it though. Clearly, if they travel back to their hometowns doing doughnuts in their 2D mustangs, the stick is gonna be completely disoriented by the time they arrive. Being the smart scientist you are, you come up with a solution: any time they're walking in a straight line, they should keep the stick so that it has a constant angle with respect to the direction they're walking, and any time they make a turn, they should rotate the stick in the opposite direction they turn by the same amount. The math for this is straightforward, it's just some 2D Euclidean geometry after all! Content, you lean back and wait for the thank you letters to start rolling in.

Much to your dismay, several days later agitated letters start pouring in from around the world. They complain that the different messengers they sent with sticks came back with them pointing in completely different directions. But how can this be?! Well, since we have the luxury of living in a 3D world, let's look at this from the viewpoint of a sphere imbedded in 3D space. Say both the messengers start on the equator and are headed to the north pole. If one of the messengers travels directly to the north pole along a meridian while the other goes a quarter of the way around the equator before heading up a meridian, when they get to their destination, their sticks will be pointing perpendicular to one another! Here's a picture to help illustrate in a less confusing way:

enter image description here

It seems our flat friend has made a fatal error-- he was doing math for a flat world, when he lived in a curved one. In fact, once space is curved it is impossible to come up with a way of translating a coordinate system in a way that doesn't depend on path-- this is the subject of parallel transport and connections in differential geometry. It may be tempting to say that there is a consistent way of transporting coordinates by considering the flat 3D space the sphere is sitting in, but remember that manifolds aren't required to be imbedded in higher dimensional space. Even if it were, the 2D aliens have no way to access this space to make measurements, so it's a moot point.

Finally, getting to the point: general relativity works in a very similar way, only it complicates things by getting time into the mix as well. In relativity, time is not an absolute coordinate. It can get mixed up with the spatial coordinates and the end result is that much like the 2D messengers, two astronauts carrying clocks can start with them synced and end up out of sync when they arrive at the same place. So how is it that cosmologists are always talking about the age of the universe? Well, they use something called the FLRW metric which describes how coordinates evolve in an homogenous, isotropic, expanding universe (basically all those words mean that the universe is modeled to be the same everywhere). If you look at the sphere picture, you might be able to work out that the amount the arrows are out of sync is positively correlated to the percentage of the sphere's surface area the two paths contain. What this means functionally is that if the curvature of spacetime is not that great, or our two astronauts don't diverge far in their paths, then the proper times they measure will not be significantly different.

Since the FLRW metric describes a homogenous universe, it is "easy" (at least by GR standards) to tease out a time coordinate that is useful for everyone as long as a few conditions like low comoving velocity are met. It just so happens that the assumptions of the FLRW metric are a good model of our universe, but this doesn't necessarily have to be the case. One could imagine a highly anisotropic universe with no CMB, many very dense collections of matter in some parts and huge voids in others, all moving at relativistic speeds to one another. In such a universe, giving a single useful age of the universe would be difficult because there would be so much path dependence and the conventions taken would be so abstract and unintuitive. Of course, this kind of universe might not be very conducive to life, but I'll let someone else sort that out as I've written enough already.

* Ok, technically this isn't true because tori exhibit the same behavior and have no curvature but you know what I mean

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