How Many Stars Are *Really* In The Universe?

How Many Stars Are *Really* In The Universe?

Over the weekend, I heard a song playing in the background at the Pacific Science Center that was ostensibly a piece of pleasant science-themed audio scenery. Its chorus repeatedly posed a pretty simple question: "how many stars do you think are in the universe?" (PS - I can't find this song online for the life of me, but if you know it, let me know!)

It's had me thinking ever since. Of course, there are some answers to that question that are commonly accepted in science. Answers (1, 2, 3, 4) seem to range between 10^21 and 10^24. But those answers are only estimates based largely on the assumptions being made about the universe, and we've been wrong about these assumptions before. I've been wondering what the true answer to that question might be.

We'll Never Know The Answer

It's actually physically impossible to count the number of stars in the universe. It's not a figurative "physically impossible," as in the number is so big we can't count that high in practical terms. It's genuinely physically impossible, as in the laws of physics say we cannot know the answer to that question.

Under general relatively, we know two things: nothing can travel faster than the speed of light, and the universe is expanding. Together, these facts limit our ability to gather information to the observable universe (side note: I'm still not fully convinced we don't live in our own separate observable universes). It turns out because the rate of expansion of the universe is increasing (1, 2, 3), there are things we can see in the universe today that, eventually (like, millions or billions of years from now), our descendants will not be able to see anymore because they will have moved too far away, with our last possible glimpses of them redshifted below the visible spectrum. We also know that because the laws of physics are time invariant, there are things that used to be a part of the observable universe which are no longer part of the observable universe for us today.

Additionally, because light has a finite speed, the deeper we look into space, the farther back into time we look. This means the light we see from stars billions of years away may very well be from stars which have long since gone supernova or otherwise advanced into another phase of the stellar lifecycle. In fact, this concept is a key outcome of special relativity: that there is no such thing as simultaneity. A question like "how many stars in the universe are there right now?" has no specific meaning, because there is no such thing as an absolute "right now."

Taken together, these factors mean there is actually no way to observe all the stars that might exist in the universe. The laws of physics prevent us from doing so. This is also not something outside the common understanding of science, but it is the background behind the main thing I've been wondering.

Is There Actually An Answer To This Question?

If the laws of physics mean we can never know the answer to this question, are we sure there is an answer to the question at all?

A problem people sometimes relate to counting the stars in the universe is counting the number of grains of sand on a beach. While that would be extremely cumbersome, there is nothing in the laws of physics which forbids us from designing a fancy machine or just grabbing a few thousand of our closest friends and eventually counting up all the grains of sand in any volume we have on Earth. So we are sure that, even if it's hard to get, there is an answer to the question "how many grains of sand are there on Beach X" or even "how many grains of sand are there on Earth."

We do not have the same assurances about the number of stars in the universe. Neither us nor any entity we could conceive of, all of us being bound by the same laws of physics, can ever see all the stars in the universe, whether relative to our frame of reference or in some sort of absolute manner. 

This is what I've been hung up on: if the laws of physics say we cannot answer a question, does that question actually have an answer?

A Finite Or Infinite Universe, And What We Can Know About It

Relatedly, there is some debate (well, maybe a lot) about whether the universe is finite or infinite. If the universe is infinite, it's possible it could contain infinite stars, which means there really is no answer to this question (besides "infinity"), and all the estimates of the number of stars are bunk. On the other hand, if the universe is finite, or if it is infinite but contains a finite number of stars, then there must be some integer number of stars that are in the universe, even if we can't see them all.

The lack of an answer to this question if the universe is infinite and contains infinite stars is easier to digest than the other one, where the universe contains a finite number of stars. If the universe contains infinite stars, the question lacks an answer directly because there are infinite stars. There isn't some number that enumerates the stars in the universe. This conclusion is straightforward. In practice, we are used to the idea that something can be "infinite," and thus it's not something we can really count to completion. But if the universe is finite, or otherwise contains finite stars, it's harder to say what a good answer to the question "how many stars are in the universe " might be. In fact, it might be that such a question has no answer at all.

A similar question on the opposite end of the size spectrum is Heisenberg's famous uncertainty principle. While original (and often still mistakenly) described in terms of the observer effect, what we have come to learn is that it is actually a fundamental property of subatomic particles that, for example, the precision with which one can know related quantities, like the position and momentum of a particle, are inversely related. I emphasize "can know" because it really means "how much the laws of physics allow to be known," not simply something related to our ability to measure or observe the particles.

In part, the uncertainty principle is a reflection of the imperfection of modeling subatomic particles as particles. It's well-known that at the quantum scale, particles sometimes are better described as particles, and sometimes they are better described as waves. It turns out that the position and momentum of a particle are better described as waves. Even so, modeling them both as particles or waves are abstractions we make in order to try and describe our observations. All abstractions have limitations or eventually break down when certain fundamental assumption they require are violated.

So, the uncertainty principle tells us something we know we can't know: we know there is no possible way we can know both the position and momentum of a subatomic particle to an arbitrary precision, because those concepts don't map to the quantum domain in the same way they do for larger objects. The inability to know these things is not a failing of humans or our technology; it is a property of the universe that these quanties cannot be known to arbitrary position simultaneously. In the same way asking "what color is something that is white and black at the same time" is nonsensical, asking "what's the exact position and momentum of this electron" is also nonsensical. Those words don't mean what we think they mean.

Can We Reasonably Ask How Many Stars Are In The Universe?

If the universe contains infinite stars,  then of course there is no numerical answer to the question of how many stars there are. But if the universe is finite or otherwise contains a finite number of stars, then is asking the question "how many stars are in the universe?" nonsensical?

We can never know the answer to that question because the laws of physics do not allow it. But if the universe is finite, it must contain finite stars, so there must be some number that is correct, right?

I have come to think that in fact there is no such number. In the same way that we can't know the position and momentum of an electron (in part because such concepts are abstractions for electrons, which are more nuanced than macroscopic objects), we can't know the number of stars in the universe.

In such cases where the laws of physics prevent an answer from being known, I would argue that the answer does not exist at all. Not because we are too stupid or inept to answer the question, but rather because the laws of physics mandate that there is no possible answer to that question. The answer doesn't exist because of practical purposes or limitations on us imposed by the laws of physics, not merely our technical shortcomings finding an answer. The answer doesn't exist because it's a nonsensical question, a question which arises because of the flaws in our abstractions about the universe lead to contradictory or undefinable answers.

For the uncertainty principle, it's a faulty premise to suppose that subatomic particles are tiny little bits of matter that have position, momentum, and otherwise behave like really tiny billiard balls. If you map the principles in your abstraction of billiard balls down to subatomic particles, you can start asking a bunch of irrelevant, nonsensical questions, or drawing a bunch of incorrect conclusions. The story of twentieth century physics, in fact, was the realization of this fact and the development of new models which better fit observations, even when those models contradicted our observations at everyday scale.

If it's nonsensical to ask "how many stars are in the universe," then, what are the pieces of our everyday abstraction we are mapping to the universe at large that lead to the bad question? Well, assuming we suppose the universe really exists, one is certainly the concept of simultaneity. Part of the reason this question is nonsensical is there is no definition of "right now," so defining a specific time in which to count all the stars is impossible.

However, even if we restrict ourselves to how many stars there are in the universe from our current frame of reference, thus eliminating the problem of simultaneity, we still have a problem. There are stars outside the observable universe we cannot and will not ever know about. In our every day lives, we are used to expecting that anything we can count a little bit, we can count all the way. Some people with deeper mathematical knowledge are used to the idea that there are "countable infinities," like the set of even numbers or the set of combinations of letters in the alphabet. But our flaw related to asking how many stars are in the universe is different than these. It's a finite number we can't count -- an "uncountable finity" -- at least in the physics sense if not the mathematical sense (set theory only allows for finite, countably infinite, and uncountably infinite sets).

Conclusion: There Is No Answer To The Question Because It Is Nonsensical

I haven't gotten much farther with this issue than that, probably because I lack the mathematical tools to try and be more formal about it. I also don't mean to suggest a problem in set theory, because I don't know set theory well enough to find a problem in it. But, in terms of the question of how many stars are in the universe, that language expresses the closest thing I have come up with to describe why it is flawed to map our everyday understanding of counting and finiteness to the universe at large.

By way of trying to summarize: on one hand, if the universe is infinite and contains infinite stars, the question is nonsensical on its face. On the other hand, if the universe is finite, or infinite with finite stars, the question is nonsensical because it maps everyday abstractions into an inappropriate physical context. Counting and finiteness work as concepts when applied solely to objects wholly contained within the observable universe, but stop functioning for anything larger than the observable universe because the laws of physics do not allow information from outside the observable universe in. Counting is fundamentally a process of accumulating information, so it only applies when a counter can access 100% of the information about that which they would count. Whenever they have less than 100% of the information required to count the objects, the objects being counted are an "uncountable finity."

Thus, there is no answer to the question "how many stars are in the universe," because such a question is nonsensical. Of course, if you modify the question slightly and make a song about "how many stars do you think are in the universe," we can answer that question, because we are entitled to think whatever we want even if we are wrong.