B Does the Expansion of the Universe Affect Gravity?

[PeterDonis]

I've always suffered from the assumption that the universe was analogous to the surface of the Earth in that if you traveled in a "straight" line you'd eventually arrive back where you started

This is the case of positive spatial curvature--in that case, yes, the universe is spatially finite. However, as @jbriggs444 noted, the case of negative spatial curvature results in a spatially infinite universe. That curvature is harder to visualize.

 

[Chris Miller]

That curvature is harder to visualize.

I'll say! Was also thinking that since the the ratio of the finite volume of the universe which contains matter/energy to the infinite rest (v/∞) approaches zero, and the infinite void portion, because it contains nothing, could be argued to not exist except as a mathematical construct. In other words, the universe does not physically exist until permeated by something.

 

[Chris Miller]

Curved does not mean "curved into itself, making a closed, bounded shape". In the case of two dimensions, a saddle shape is both curved and unbounded.

This shape does not look unbounded to me? https://en.wikipedia.org/wiki/Saddle_point#/media/File:Saddle_point.svg

 

[PeterDonis]

This shape does not look unbounded to me?

That's because it's not an image of all of the negatively curved space, only a portion of it. If you saw an image of a "Euclidean plane" on Wikipedia that didn't look unbounded, would you therefore conclude that the Euclidean plane itself was not unbounded?

You need to look at the actual math of the negatively curved space. The actual math makes it clear that it is unbounded.

 

[PeterDonis]

the finite volume of the universe which contains matter/energy

Huh? Where are you getting that from?

In our best current cosmological model, all of the infinite spatial volume of the universe contains matter/energy, and the average density is the same everywhere (at a given instant of time in standard cosmological coordinates).

It might be helpful at this point for you to say what your sources are for your understanding of cosmology; you appear to have a number of fundamental misconceptions.

 

[Chris Miller]

In our best current cosmological model, all of the infinite spatial volume of the universe contains matter/energy, and the average density is the same everywhere (at a given instant of time in standard cosmological coordinates).

Infinity is an algorithm, or function. So to me this (infinite mass/energy) makes no sense.

It might be helpful at this point for you to say what your sources are for your understanding of cosmology; you appear to have a number of fundamental misconceptions.

Pretty much any site I peruse. E.g., https://people.cs.umass.edu/~immerman/stanford/universe.html suggests some very large, but finite, numbers. I wonder how well accepted (much disputed) the `best current cosmological model` is.

 

[jbriggs444]

Infinity is an algorithm, or function

No, it is not.

A course in real analysis is useful.

 

[PeterDonis]

Pretty much any site I peruse.

In other words, no textbooks or peer-reviewed papers. Then the solution is simple: go read some textbooks or peer-reviewed papers.

E.g., https://people.cs.umass.edu/~immerman/stanford/universe.html suggests some very large, but finite, numbers.

Those numbers are for the observable universe, not the entire universe. The site says so (it uses the term "visible universe", but that's the same thing.)

I wonder how well accepted (much disputed) the `best current cosmological model` is.

It's very well accepted. You are simply misunderstanding what you are reading, an issue which, as noted above, can be solved by learning from textbooks or peer-reviewed papers.

 

[Chris Miller]

In other words, no textbooks or peer-reviewed papers. Then the solution is simple: go read some textbooks or peer-reviewed papers.
Those numbers are for the observable universe, not the entire universe. The site says so (it uses the term "visible universe", but that's the same thing.)
It's very well accepted. You are simply misunderstanding what you are reading, an issue which, as noted above, can be solved by learning from textbooks or peer-reviewed papers.

I think the web can be a good source of info, though you have to be discriminating, and guidance such as I get here (on the web) can help. This site seems to coroborate and explain what you're saying: http://www.dailygalaxy.com/my_weblog/2013/02/the-real-universe-is-250-times-bigger-than-the-visible-hubble-volume-todays-most-popular-1.html The title's misleading, since they do say "infinite" and explain how this conclusion was arrived at (some of which is over my head). Interesting that, according to his biography, when John Nash proposed a flat, infinite universe to Einstein, he was advised to study physics.

 

[PeterDonis]

I think the web can be a good source of info, though you have to be discriminating

If you don't already understand the science from a better source, textbooks or peer-reviewed papers, on what basis are you going to be "discriminating"?

 

[PeterDonis]

This site seems to confirm and explain what you;re saying

But it doesn't give a link to an actual paper. That's always a red flag with me. How do I know the actual research says what the article claims it says? Journalists in general often don't have a very good grasp of the subjects they report on, and science journalists are usually even worse than the average journalist, because the subjects they report on require much more background to understand properly.

 

[Chris Miller]

No, it is not.

A course in real analysis is useful.

Until this infinite universe thing, I would've called infinity a conceptual construct. Still kind of do.

 

[Chris Miller]

If you don't already understand the science from a better source, textbooks or peer-reviewed papers, on what basis are you going to be "discriminating"?

Math and science are way too specialized for anyone to understand as a whole now, and so we must accept the findings and research of those who've gained our trust. I trust you guys.

 

[PeterDonis]

Math and science are way too specialized for anyone to understand as a whole now, and so we must accept the findings and research of those who've gained our trust. I trust you guys.

Thanks for the kudos.

 

[Chris Miller]

Thanks for the kudos.

I'm serious, and you're welcome. I feel I've learned a lot here, and wonder sometimes what you all get out of it.

I appreciate the recommendations that I read (i.e., study) textbooks and peer-reviewed papers. And while I do read and enjoy some of the simpler papers linked to and occasionally authored by some of you here, most serious texts would require a lot of study, exercise, and probably mentoring, for me to properly appreciate.

I must admit that while I try to harbor no beliefs, only hypotheses, the answers provided in this thread have inspired a kind of faith crisis. I've always been taught that the universe began as a very small dense particle that has, over billions of years, expanded into its current 4D shape and size, estimated to be about 90 billion ly in diameter. Now I'm told (I think) that the best current model suggests that this naked singularity I've always thought constituted "everything" occurred and exists within the context of infinite space and matter/energy. I know the math doesn't translate well into written language, and I can almost get my head around an infinite void (i.e., infinite nothing). But are you saying that matter and energy are also infinite? That there are theoretically infinite galaxies now? I've always said that existence as we perceive it is impossible by our understandings. But I guess I wasn't quite ready to have this so well exemplified.

 

[jbriggs444]

Now I'm told (I think) that the best current model suggests that this naked singularity I've always thought constituted "everything" occurred and exists within the context of infinite space and matter/energy.

The singularity does not "exist" at all. It is not something that lives within the model. It is something more like a boundary at the end of an open interval.

The model uses manifolds and manifolds use "open" sets. Open sets do not contain their own boundaries. An infinite line is, for instance, an open set. It does not contain either endpoint "at infinity". It has no endpoints.

 

[Grinkle]

@Chris Miller You only need to change one thing in your visualization. The universe was denser in the past than it is now. Where you are picturing a tiny point, instead picture an infintie universe that is as dense as possible, more dense than we have models or theories to describe. Then picture that universe becoming less dense - this is the big bang / expansion etc. Its not very different from your picture, and to me at least, it makes a lot more sense than your picture. I was also carrying the picture you describe in my head for a long time - and replacing the point with a dense infinite-expanse universe was a big light-bulb moment for me - it resolved my confusion / wondering what the small point was expanding into if it was already everything.

It left me with the problem of needing to grapple with a universe that is infinite in extent somehow becoming larger, but for no good reason that I can articulate that doesn't bother me as much as the expanding point visualization did.

I don't think you need to be having any crisis in faith - just tweak your mental model a bit!

 

[plillies]

Because spacetime is curved. If spacetime were flat, your reasoning would be correct. But it isn't flat; it's curved. And in a curved spacetime, the intuitive relationship you are assuming between "speed of light" and "distance" no longer works.
.

Hmmm! The light from 13.8 billion l-ys. Isn't it just the light from the sphere 13.8 billion l-ys in diameter that started out toward us 13.8 billion years ago? As it traveled those 13.8 billion l-ys, it cooled from 3000 K radiation to 2.7 K radiation.

 

[PeterDonis]

The light from 13.8 billion l-ys. Isn't it just the light from the sphere 13.8 billion l-ys in diameter that started out toward us 13.8 billion years ago?

No. The quote you gave from me already explains why.

To illustrate using the particular example you give, consider a light ray just arriving on Earth now that was emitted 13.8 billion years ago. The point from which that light was emitted is not now 13.8 billion light years away from us. It's much further away than that (about 47 billion light-years). And when the light ray was emitted, 13.8 billion years ago, the point it was emitted from, then, was much closer than 13.8 billion light years to the point where the Earth would have been if it had existed then (and had maintained the same motion from then to now, which of course would not have happened, but we can consider it as an idealized thought experiment).

 

[Chris Miller]

The singularity does not "exist" at all. It is not something that lives within the model. It is something more like a boundary at the end of an open interval.

The model uses manifolds and manifolds use "open" sets. Open sets do not contain their own boundaries. An infinite line is, for instance, an open set. It does not contain either endpoint "at infinity". It has no endpoints.

"The singularity does not "exist"... It is something... a boundary... Open sets do not contain their own boundaries."

You see my confusion?

 

[Chris Miller]

@Chris Miller You only need to change one thing in your visualization. The universe was denser in the past than it is now. Where you are picturing a tiny point, instead picture an infintie universe that is as dense as possible, more dense than we have models or theories to describe. Then picture that universe becoming less dense - this is the big bang / expansion etc. Its not very different from your picture, and to me at least, it makes a lot more sense than your picture. I was also carrying the picture you describe in my head for a long time - and replacing the point with a dense infinite-expanse universe was a big light-bulb moment for me - it resolved my confusion / wondering what the small point was expanding into if it was already everything.

It left me with the problem of needing to grapple with a universe that is infinite in extent somehow becoming larger, but for no good reason that I can articulate that doesn't bother me as much as the expanding point visualization did.

I don't think you need to be having any crisis in faith - just tweak your mental model a bit!

Thanks, Grinkle. Maybe "crisis" was too strong a word. More frustration, or maybe confusion, mixed with interest. For me, your tussling with the theory is of greater consolation (thanks again) than your resolution's model. While I understand (mathematically) how infinite sets may be contained by "larger" ones, I cannot at all picture an infinite physical universe of nigh infinite density, which would describe infinite mass/energy. It's much easier to picture the infinitesimally small, nigh infinitely dense expanding universe (of unknown context/origin) that's been taken away from me here in this thread. Q: Does this new, improved universe contain infinite mass? Infinite galaxies? Or are these finite within infinite space? Or, somehow, neither?

Also, could it just now be so large that our tiny observable segment only appears flat (i.e., is immeasurably curved)?

 

[jbriggs444]

"The singularity does not "exist"... It is something... a boundary... Open sets do not contain their own boundaries."

You see my confusion?

It does not exist as an entity within the model. It is a feature that we refer to when we talk about the model. Like the graph of $f(x) = \frac{1}{x^2}$ . There is a pole at x=0. There is no point on the graph where x=0. That point does not exist on the graph. Yet we can talk about a "pole at x=0" when talking about the graph.

 

[Chris Miller]

It does not exist as an entity within the model. It is a feature that we refer to when we talk about the model. Like the graph of $f(x) = \frac{1}{x^2}$ . There is a pole at x=0. There is no point on the graph where x=0. That point does not exist on the graph. Yet we can talk about a "pole at x=0" when talking about the graph.

Thanks, yes, I see. Where $y = \frac{1}{x^2}$ both the x-axis and positive y-axis are poles, in that two y-symmetric curves approach but never touch either. Translating this into a model/description/explanation of the physical, material universe though still evades me.

 

[jbriggs444]

Thanks, yes, I see. Where $y = \frac{1}{x^2}$ both the x-axis and positive y-axis are poles, in that two y-symmetric curves approach but never touch either. Translating this into a model/description/explanation of the physical, material universe though still evades me.

It is an example of something which does not "exist" within a model but which nonetheless has a name. We can say "look, a pole" even though there is no point on the graph that is a "pole".

We can take the FLRW model and say "look, a singularity" even though there is no point in the model that is a "singularity".

 

[plillies]

No. The quote you gave from me already explains why.

And when the light ray was emitted, 13.8 billion years ago, the point it was emitted from, then, was much closer than 13.8 billion light years to the point where the Earth would have been if it had existed then

Now why would the point it has been emitted from be much closer than 13.8 billion light years. Remember we are talking about the image of the surface of last scattering here. The light was emitted; that surface disappeared. The light traveled travelled for 13.8 billion years. So the point where it was emitted was 13.8 billion light years away.

 

[Bandersnatch]

Now why would the point it has been emitted from be much closer than 13.8 billion light years. Remember we are talking about the image of the surface of last scattering here. The light was emitted; that surface disappeared. The light traveled travelled for 13.8 billion years. So the point where it was emitted was 13.8 billion light years away.

Visualise expanding space as a band of rubber that is being stretched. On this rubber band, an ant is walking from point A to point B. The ant represents a light signal sent from the emitter at point A to the observer at point B.
Let's say the initial distance is 100 cm, the ant walks at the constant speed of 1 cm/s, and the rubber band stretches by 1% every 1 second (we're assuming the rate is constant, for simplicity).
So, after 1 second, the ant will have traveled 1 cm of the 100 cm, but the expansion of space will have stretched the remaining 99 cm by 1% to 99.99 cm. During the same 1 second, the original distance from A to B will also have increased by 1% to 101 cm.
After another second, the ant goes another 1 cm onwards, but the expansion pushes it back by 1% of the distance to 99.9799 cm. Point A will have receded to 102.01 cm.

Can you see how:
1 - by the time the ant arrives at B, more than 100 seconds will have elapsed?
2 - by the time the ant arrives at B, point A will be much farther than 100 cm?
3 - the time the ant has traveled times its speed is neither the original distance between A and B, nor the final one?

 

[plillies]

Visualise expanding space as a band of rubber that is being stretched. On this rubber band, an ant is walking from point A to point B. The ant represents a light signal sent from the emitter at point A to the observer at point B.
Let's say the initial distance is 100 cm, the ant walks at the constant speed of 1 cm/s, and the rubber band stretches by 1% every 1 second (we're assuming the rate is constant, for simplicity).
So, after 1 second, the ant will have traveled 1 cm of the 100 cm, but the expansion of space will have stretched the remaining 99 cm by 1% to 99.99 cm. During the same 1 second, the original distance from A to B will also have increased by 1% to 101 cm.
After another second, the ant goes another 1 cm onwards, but the expansion pushes it back by 1% of the distance to 99.9799 cm. Point A will have receded to 102.01 cm.

Can you see how:
1 - by the time the ant arrives at B, more than 100 seconds will have elapsed?
2 - by the time the ant arrives at B, point A will be much farther than 100 cm?
3 - the time the ant has traveled times its speed is neither the original distance between A and B, nor the final one?

You seem to be suggesting that a photon (the ant) would be affected by the movement of space? My understanding is that objectifying space is a very Newtonian way of thinking. According to relativity, light always travel at the same speed except in the presence of a strong gravitational field, no? And then the speed only changes for an outside observer. To my way of thinking the CMB was at a temperature of 2.7 K 13.8 billion years ago, and that is why we perceive it at that temperature when the light reaches us today. Why not?

 

[Drakkith]

You seem to be suggesting that a photon (the ant) would be affected by the movement of space? My understanding is that objectifying space is a very Newtonian way of thinking. According to relativity, light always travel at the same speed except in the presence of a strong gravitational field, no? And then the speed only changes for an outside observer.

This has nothing to do with the speed of light changing, it has to do with the fact that the two observers (the sender and receiver) are moving apart. Even in SR a light signal would take far longer to reach an observer who is traveling at high velocity away from the sender than one who is not (time and velocity measured relative to the sender). Expansion adds another complication. Not only are the two observers moving apart, but the rate at which they move apart, the recession velocity, is increasing over time.

To my way of thinking the CMB was at a temperature of 2.7 K 13.8 billion years ago, and that is why we perceive it at that temperature when the light reaches us today. Why not?

Because the CMB only makes sense in the context of the big bang theory, which incorporates expanding space. There are simply no plausible mechanisms by which the CMB could have been emitted at 2.7K.

 

[stoomart]

You seem to be suggesting that a photon (the ant) would be affected by the movement of space?

The light wave (ant or CMB) doesn't change speed during its trip, but it's path is affected by the changing geometry of spacetime, both from expansion and gravitational lensing.

 

[plillies]

Because the CMB only makes sense in the context of the big bang theory, which incorporates expanding space. There are simply no plausible mechanisms by which the CMB could have been emitted at 2.7K.

Well, we wouldn't want to deny the big bang theory. I am just having trouble understanding how radiation from the CMB could be at 2.7 K when it reaches us unless it was at that temperature to begin with, allowing, of course, for any relativistic doppler effect that would have added to the apparent cooling. As to how the CMB could have cooled down to 2.7 K before the radiation was emitted, I guess it would have taken some time, enough time for the baryons in the CMB to displace themselves. If temperature is proportional to area, then they would have had to displace themselves quite a bit. If recombination is at 3000 k, then we can calculate a linear displacement of SQRT(3000/2.7) = 33.3.

The light wave (ant or CMB) doesn't change speed during its trip, but it's path is affected by the changing geometry of spacetime, both from expansion and gravitational lensing.

Not sure about the changing geometry of spacetime. I thought that only gravity could change spacetime geometry and in intergalactic space, gravity is pretty weak.

 

[rootone]

... relativistic doppler effect ...

That's how I understand it

 

[stoomart]

Not sure about the changing geometry of spacetime. I thought that only gravity could change spacetime geometry and in intergalactic space, gravity is pretty weak.

Expansion is continually altering the geometry of spacetime, whereas gravity is more of a rearrangement.

Edit: Think of expansion like urban sprawl, only instead of adding more lots, the existing lots get bigger while the homes stay the same size.

 

[plillies]

That's how I understand it

Trouble is if we assume that the apparent cooling (from 3000 K to 2.7 K) is due to relativistic doppler effect alone, then we need to attribute a recession velocity close to the speed of light to the surface last scattering that is presenting itself to us.So if that surface is both now 13.8 billion lt-yrs away and was traveling near the speed of light when the radiation was emitted, then we have a universe that is about twice as old as the generally accepted age, or alternatively, that the radiation from the CMB is arriving at us from half as far (6.9 billion lt-yrs instead of 13.8).

 

[stoomart]

Trouble is if we assume that the apparent cooling (from 3000 K to 2.7 K) is due to relativistic doppler effect alone, then we need to attribute a recession velocity close to the speed of light to the surface last scattering that is presenting itself to us.So if that surface is both now 13.8 billion lt-yrs away and was traveling near the speed of light when the radiation was emitted, then we have a universe that is about twice as old as the generally accepted age, or alternatively, that the radiation from the CMB is arriving at us from half as far (6.9 billion lt-yrs instead of 13.8).

There's a ton of science that goes into analyzing the CMB and determining the age of the observable universe, I suggest starting with the insights written by @bapowell.

https://www.physicsforums.com/insights/poor-mans-cmb-primer-part-0-orientation/

 

[PeterDonis]

Expansion is continually altering the geometry of spacetime, whereas gravity is more of a rearrangement.

This is not correct. First, the geometry of spacetime isn't being "altered" by expansion; "expansion" just means the 4-dimensional geometry of spacetime, which doesn't "change", it just is, has a certain shape.

Second, gravity doesn't "rearrange" the geometry of spacetime; as above, that geometry just is, it doesn't change. "Gravity" is just one way of describing certain effects of the geometry of spacetime.

 

[PeterDonis]

I am just having trouble understanding how radiation from the CMB could be at 2.7 K when it reaches us unless it was at that temperature to begin with

Because of the geometry of spacetime.

allowing, of course, for any relativistic doppler effect that would have added to the apparent cooling

Relativistic doppler is not a good way of thinking about the effect of curved spacetime geometry on light rays. Relativistic doppler is really only a workable model for the case of flat spacetime and a light source and receiver that are in relative motion.

As to how the CMB could have cooled down to 2.7 K before the radiation was emitted

It didn't.

Also, please review the PF rules on personal speculation, which is what the rest of your post after the above quote is.

 

[PeterDonis]

Trouble is if we assume that the apparent cooling (from 3000 K to 2.7 K) is due to relativistic doppler effect alone, then we need to attribute a recession velocity close to the speed of light to the surface last scattering that is presenting itself to us.So if that surface is both now 13.8 billion lt-yrs away and was traveling near the speed of light when the radiation was emitted, then we have a universe that is about twice as old as the generally accepted age, or alternatively, that the radiation from the CMB is arriving at us from half as far (6.9 billion lt-yrs instead of 13.8).

None of this is correct. You need to take the time to learn the correct model from a textbook; a detailed explanation of the model is well beyond the scope of a "B" level thread.

 

[PeterDonis]

This thread is degenerating into speculation and is now closed.