# Is the mass of the universe finite (collection of objects)?

Whenever I attempt to research this question, my search results yield "Is the Universe Infinite" where the question ALWAYS refers to the volume of the universe. This question is usually answered along the lines of: "If the universe is closed, than it's volume, aka it's 3D surface area in 4-space, is finite, otherwise if the universe is 'flat' or 'open' it's volume is infinite." And yes, I'm aware that's a crude nutshell version of the answer.

The question I've always wondered is: "Is the mass of the universe finite."

I've come across statistics that measure "how many atoms are in the universe," but upon further inspection they always mean "in the observable universe."

Do we in fact know whether or not the mass of the entire universe (including the unobserverable universe) is finite?

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wabbit
Gold Member
No, I am pretty sure this is unknowable even in principle.

Bandersnatch
Why are you not satisfied with the answers regarding volume? They answer the question about mass too. In each unit volume there is some mass. Under the cosmological principle the average amount of mass per unit volume is constant. So, whatever you read about spatial extent (volume) applies to mass as well.

wabbit
Gold Member
The cosmological principle, if meant to imply a universe homogeneous at any scale, is a pretty big assumption though and not something we know as a fact - nor is it even particularly likely imho but that is just an opinion - or rather, a speculation about something we cannot know.

Bandersnatch
I think it's been validated pretty well so far. Sure it's still just an assumption, but looks like a good one. One needs to always keep in mind that our views on the structure of the universe as a whole must by definition be based on the patch that we can observe.

Of course, in principle it is unknowable, and that's no different to the question of whether the universe is spatially open or closed, finite or infinite - after all, these predictions assume that the laws of physics don't change across the universe, under the same cosmological principle.

wabbit
Gold Member
It's been validated for the observable universe, and the assumption that this is part of a (much) larger homogeneous region sounds reasonnable (very much so even, otherwise this would imply an extrordinary coincidence), but as I understand it (admittedly vaguely) even within standard models of inflation, homogeneity of the observable universe is related to the possibility of information exchange within a certain radius, and they do not as far as I know assume homogeneity at all scales if the universe is infinite.

The farther we go beyond the observable, the weaker the evidence supporting any assumption becomes. At 10^100 Hubble radii away? Metaphysics only can answer.

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"If the universe is closed, than it's volume, aka it's 3D surface area in 4-space, is finite...

- the further the object we observe, the faster it is receding
- these receding objects would be subject to length contraction
- where these objects' recession velocity approaches c relative to us, their thickness along the radial direction of line of sight approaches contraction to zero
- approaching the limit, there is "room" for an indefinite number of these "thin" objects
- this looks like a curved space where within a finite radius (where recession approaches c) there is an infinite internal volume
- there is "room" within this space for an indefinite quantity of expanding objects subject to length contraction
- for any observer, most of this "room" in this space is "close to the edge"

If all that is coherent, it seems that a closed expanding universe whose recession limit approaches c at a finite radius from an observer may support an infinite expanding space with an infinite number of objects.

The observable universe actually includes a region slightly beyond this limit, so one might wonder if the mass of the observable universe is already infinite, and if so, so be the universe as a whole.

But maybe here is a flaw in this picture?

wabbit
Gold Member
I think there is a flaw. The relativistic effects are taken onto account when estimating local densities far away. Also, observing something length contracted does not change its proper dimensions, and the assumption of homogeneity is, for distant regions, that they have on average the same density in their proper frame (well, in comoving frames actually) - not that they look the same.

But inhomogeneous models have been proposed (what I've seen in this respect seemed rather ad hoc, but this is indicative of my limits, not theirs), I don't know how well they do with recent observations.

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I think there is a flaw. The relativistic effects are taken onto account when estimating local densities far away. Also, observing something length contracted does not change its proper dimensions, and the assumption of homogeneity is, for distant regions, that they have on average the same density in their proper frame (well, in comoving frames actually) - not that they look the same.
If I'm understanding you, I'm not in disagreement with those three points, but I don't see how they suggest a flaw. Can you explain?

wabbit
Gold Member
I'm not sure I understood you actually : )
But you say
it seems that a closed expanding universe whose recession limit approaches c at a finite radius from an observer may support an infinite expanding space with an infinite number of objects.
I'm not sure what "closed" means here, I think usually it means spatially finite. But to me it sounds like what you are describing is a relativistic Achille's Tortoise - you are dividing space into thinner and thinner slices as you go further out, and these happen to look equally thick because of relativistic perspective. But a given object also occupies more depth in these coordinates, the perspective distortion does not create more space, and the sum of all these slices is still a finite amount of space.

Hmmm... I have a vague impression I'm missing your point entirely.

phinds
Gold Member
2019 Award

- the further the object we observe, the faster it is receding
- these receding objects would be subject to length contraction
- where these objects' recession velocity approaches c relative to us, their thickness along the radial direction of line of sight approaches contraction to zero
- approaching the limit, there is "room" for an indefinite number of these "thin" objects
- this looks like a curved space where within a finite radius (where recession approaches c) there is an infinite internal volume
- there is "room" within this space for an indefinite quantity of expanding objects subject to length contraction
- for any observer, most of this "room" in this space is "close to the edge"

If all that is coherent, it seems that a closed expanding universe whose recession limit approaches c at a finite radius from an observer may support an infinite expanding space with an infinite number of objects.

The observable universe actually includes a region slightly beyond this limit, so one might wonder if the mass of the observable universe is already infinite, and if so, so be the universe as a whole.

But maybe here is a flaw in this picture?
All of this is predicated on the utterly incorrect belief that recession speed can be treated the way local speed is treated. Recession speeds are just "things getting farther apart". Things at the edge of our observable universe are ALREADY receding from us at 3c.

William Henley
Well, it depends on whether you think the Universe will continue expanding forever or not. If it does continue expanding forever then the mass of the universe is infinite because it can keep gaining mass but if it doesn't continue expanding then the mass is finite.

phinds
Gold Member
2019 Award
Well, it depends on whether you think the Universe will continue expanding forever or not. If it does continue expanding forever then the mass of the universe is infinite because it can keep gaining mass but if it doesn't continue expanding then the mass is finite.
And where does it gain this mass from? I think what you have here is an unsupportable personal theory.

wabbit
Gold Member
Well, it depends on whether you think the Universe will continue expanding forever or not. If it does continue expanding forever then the mass of the universe is infinite because it can keep gaining mass but if it doesn't continue expanding then the mass is finite.
I don't think that's true. If you're talking about the mass of the whole universe then it's either always infinite or always finite (if defined) - for the observable universe what you say may be true in some cases but not in general, and not in the presence of a cosmological constant which if I am not mistaken limits the ultimately observable universe to a finite comoving region.

PeterDonis
Mentor
2019 Award
If it does continue expanding forever then the mass of the universe is infinite because it can keep gaining mass but if it doesn't continue expanding then the mass is finite.
Why do you think the universe is gaining mass if it is expanding? Can you give a reference for where you got this?

PeterDonis
Mentor
2019 Award
- the further the object we observe, the faster it is receding
- these receding objects would be subject to length contraction
This is not correct; SR does not apply over cosmological distances. It only applies within a local inertial frame.

- this looks like a curved space where within a finite radius (where recession approaches c) there is an infinite internal volume
This is not correct. What you are talking about is our observable universe, and our observable universe has a finite spatial volume.

This is not correct; SR does not apply over cosmological distances. It only applies within a local inertial frame.
So length contraction applies to objects receding "near by" but not when they are far enough away (in an expanding space)? If I monitor the contraction of a nearby spaceship eventually catching up with a distant comoving object, what would that plot of the magnitude of contraction look like? It sounds like you are saying that the comoving object will not appear contracted, and so the spaceship catching up to the comoving object would also not appear contracted, but then what of the spaceship between here and there? Initially contracted, but then what happens? Does the spaceship "decontract" as its relative velocity to me approaches the distant point at which this velocity is the comoving velocity? It it this portion of the relative velocity between me and the spaceship that becomes comprised of the comoving component that indicates the extent of the local inertial frame beyond which SR does not apply?

PeterDonis
Mentor
2019 Award
So length contraction applies to objects receding "near by" but not when they are far enough away (in an expanding space)?
It's not a matter of which objects it "applies" to; it's a matter of in what coordinates you can apply it. You can only apply the standard length contraction formula in standard inertial coordinates in an inertial frame. There is no inertial frame that covers the entire region from Earth to the Hubble radius.

If I monitor the contraction of a nearby spaceship eventually catching up with a distant comoving object, what would that plot of the magnitude of contraction look like?
If you use "comoving" coordinates, the spaceship will never be contracted at all, because those coordinates are not inertial coordinates in an inertial frame. If you use standard inertial coordinates centered on the Earth, they won't be valid all the way; the spaceship will very soon leave the region in which those coordinates are valid, so you won't even be able to make the plot in the first place.

what of the spaceship between here and there? Initially contracted, but then what happens? Does the spaceship "decontract"
Initially contracted in inertial coordinates centered on the Earth. In comoving coordinates, the spaceship is not initially contracted; it's never contracted at all. Length contraction is a coordinate phenomenon. The spaceship itself never notices anything, so there's nothing to "decontract".

as its relative velocity to me approaches the distant point at which this velocity is the comoving velocity?
Its velocity is never the comoving velocity, because by hypothesis it is moving from Earth to some distant comoving object, hence it is moving relative to both Earth and the distant comoving object. An object with the comoving velocity never moves relative to any comoving object.

I think it would be very helpful to you to reframe your question in terms of some invariant measurement that you think shows "length contraction". Then we could discuss how that measurement would change during the spaceship's trip (or whether it would even be valid for the entirety of the spaceship's trip).

Why are you not satisfied with the answers regarding volume? They answer the question about mass too. In each unit volume there is some mass. Under the cosmological principle the average amount of mass per unit volume is constant. So, whatever you read about spatial extent (volume) applies to mass as well.

This is stated in the OP.

I think it's been validated pretty well so far. Sure it's still just an assumption, but looks like a good one. One needs to always keep in mind that our views on the structure of the universe as a whole must by definition be based on the patch that we can observe.

Of course, in principle it is unknowable, and that's no different to the question of whether the universe is spatially open or closed, finite or infinite - after all, these predictions assume that the laws of physics don't change across the universe, under the same cosmological principle.
Basically this is they type of answer I'm looking for. Thanks. So the CC implies that the density of the universe if generally homogeneous, and density is a function of both mass and volume.

Though that does beg the question:
If the universe is expanding, is its density decreasing?

If the density is not changing, then mass is being added to the universe?

- the further the object we observe, the faster it is receding
- these receding objects would be subject to length contraction
- where these objects' recession velocity approaches c relative to us, their thickness along the radial direction of line of sight approaches contraction to zero
- approaching the limit, there is "room" for an indefinite number of these "thin" objects
- this looks like a curved space where within a finite radius (where recession approaches c) there is an infinite internal volume
- there is "room" within this space for an indefinite quantity of expanding objects subject to length contraction
- for any observer, most of this "room" in this space is "close to the edge"

If all that is coherent, it seems that a closed expanding universe whose recession limit approaches c at a finite radius from an observer may support an infinite expanding space with an infinite number of objects.

The observable universe actually includes a region slightly beyond this limit, so one might wonder if the mass of the observable universe is already infinite, and if so, so be the universe as a whole.

But maybe here is a flaw in this picture?
Sounds like a Poincere disc. It's not that farfetched.
http://theiff.org/oexhibits/oe1c.html

I used to scribble on the board in junior high about "bounded infinity" and one day a substitute math teacher (Mr Hammel, who became a mentor) showed me that I was describing a rudimentary form of a Poincere disc and that I was describing a projective Reimann Sphere went I went into 3 dimensions.

http://theiff.org/oexhibits/oe1c.html

phinds
Gold Member
2019 Award
If the universe is expanding, is its density decreasing?
yes

If the density is not changing, then mass is being added to the universe?
meaningless, since the density IS changing.

yes

meaningless, since the density IS changing.
A false statement is never meaningless, since it implies the truth of its negation.

In fact the majority of certain knowledge is proved through contradiction (proving the negative false).

phinds
Gold Member
2019 Award
A false statement is never meaningless, since it implies the truth of its negation.

In fact the majority of certain knowledge is proved through contradiction (proving the negative false).
I don't follow you. The fact that the universe IS expanding does not in and of itself prove that the density is not changing, so I don't see what you think is a "proven negative".

I don't follow you. The fact that the universe IS expanding does not in and of itself prove that the density is not changing, so I don't see what you think is a "proven negative".
If the volume of the universe is increasing, then the density must be decreasing, unless mass is being added to the universe.

D = M/V