The Curvature of Space: Understanding the Flatness of the Universe

[flatcp]

Good day. I've been reading and reviewing the posts and linked references on this forum for about 3 weeks now (enjoying the heck out of the exchanges BTW) and have assimilated much of the information (I think). I am trying to understand how it fits together and several questions remain. This one is keeping me from fully grasping what the area commonly referred to as "The Universe" looks like.

Does the area of space which 13.3 BLYs ago was occupied by the surface of last scattering still exist today? I know we are seeing the remnants of it today and that we have receded some 45BLYs while the photons traveled to where we are now. Does the point or points in space from where the photons were emitted 13.3 BLYs ago still exist as a physical place in the current “Universe”? Set aside, if you can, that in either case we will likely never be able to travel to it.

While I’m at it, evidence supportive of Hubble’s Law includes the observed proportional redshifts of objects throughout space as a result of expansion: how does this happen? Is it coincidence that as space expands photons stretch or is there a deeper connection between them? Are photons tethered to space tagging along for the v > c ride? Are they stretched in the wake of space expansion?

Thanks

 

[Chalnoth]

Does the area of space which 13.3 BLYs ago was occupied by the surface of last scattering still exist today? I know we are seeing the remnants of it today and that we have receded some 45BLYs while the photons traveled to where we are now. Does the point or points in space from where the photons were emitted 13.3 BLYs ago still exist as a physical place in the current “Universe”? Set aside, if you can, that in either case we will likely never be able to travel to it.

Well, first a bit of a pedantic point: one of the primary lessons of relativity is that there is no such thin gas a global "now". "Now" is only well-defined locally. But there are many ways to define "now" far away. One way, for instance, is to just define "now" far away as that which you are seeing now. In that instance, the region of space from which the CMB photons are emitting are, well, emitting CMB photons "now" because we see them now.

Another way of defining "now" far away is to take "now" to mean the time at which this particular point in the universe will be the same distance in time from the "big bang" as we are. In that sense, again, that region of space which emitted the CMB some 13.7 billion years ago is now populated with galaxies, just like our region is.

While I’m at it, evidence supportive of Hubble’s Law includes the observed proportional redshifts of objects throughout space as a result of expansion: how does this happen? Is it coincidence that as space expands photons stretch or is there a deeper connection between them? Are photons tethered to space tagging along for the v > c ride? Are they stretched in the wake of space expansion?

The photons are stretched by the expansion. Basically, these photons are an electromagnetic wave, and the way the wave knows how to wiggle depends upon the space-time, so if the space-time expands, the wave expands in the same way.

This effect can be derived trivially just by taking a photon in an expanding universe in General Relativity and calculating what happens.

One sort of roundabout way of doing this is to consider a photon fluid instead of a photon. In that case, the way the energy density of this fluid changes with expansion is determined by how the energy density of the fluid relates to its pressure. In the case of photons, their pressure is 1/3rd their energy density. Plug this into the equations of a uniform fluid in an expanding space-time in General Relativity, and you quickly get that this fluid scales in energy density as the fourth power of the scale factor: if the universe expands by a factor of two, then the energy density of photons is reduced by a factor of 2<sup>4[], or 16.

Since the total number of photons is not affected by the expansion but the density of photons is reduced by the increase in volume, there is an extra loss of energy of each photon by one power of the scale factor. If you know your photon physics, you know that the energy of a photon is proportional to the inverse of the wavelength, which means that this loss of energy comes from an increase in the wavelength, given precisely by the amount of expansion.</sup>

 

[marcus]

...

Does the area of space which 13.3 BLYs ago was occupied by the surface of last scattering still exist today? I know we are seeing the remnants of it today and that we have receded some 45BLYs while the photons traveled to where we are now. Does the point or points in space from where the photons were emitted 13.3 BLYs ago still exist as a physical place in the current “Universe”? ...

Flatcp, welcome! Glad you have been enjoying the conversation here. If you are talking about the passage of time please say "billion years" not "billion light years". A lightyear is a measure of distance---the distance light in a non-expanding universe would travel in one year.

(since the expansion rate changes over time, a lightyear would not be welldefined if you threw in the effect of expansion)

Let's see how your question would look with that small change. If it is time you are talking about, say BYs (billion years) in stead of BLYs. Some people also say Gy for "giga-year" which means the same thing. But let's stick to your abbreviation and replay the question:

...
Does the area of space which 13.3 BYs ago was occupied by the surface of last scattering still exist today? I know we are seeing the remnants of it today and that we have receded some 45BLYs while the photons traveled to where we are now. Does the point or points in space from where the photons were emitted 13.3 BYs ago still exist as a physical place in the current “Universe”? ...

Yes sir! I believe so anyway . I hear supper dishes on the table so I may have to run. Will get back to this soon. Interesting question.

 

[sylas]

Does the area of space which 13.3 BLYs ago was occupied by the surface of last scattering still exist today?

Yes; and we are occupying that area of space, right now.

The word "surface" might be misleading. It is a surface in a 4 dimensional spacetime picture of the universe. Alternatively, the "surface" of last scattering is all of space at the TIME of last scattering.

Set aside for the moment the notion that the universe might be radically different somewhere off far beyond anything we can measure or detect. Everything we see tends to look pretty much the same as far as a "universe" goes. It has galaxies, and stars, and light, and laws of physics just like we measure at home. Models of the universe generally tend to have the universe looking much like where we live, everywhere. Or at least several times beyond what can can measure.

This applies for the background radiation as well. The space from which those photons come is not any different from the space we are in; it just comes from long ago. The matter from which you and I are made was once a hot mix of hydrogen and some other light elements that emitted thermal radiation at a temperature of about 3000K, some 13 to 14 billion years ago. The photons we emitted back then are still going, somewhere, and are "now" passing by distant galaxies that themselves condensed out of a hot mix of hydrogen and helium; just like our Milky Way galaxy.

It might even be that there are alien scientists "now" in galaxies some 45 billion light years away who are studying the background radiation as well, and wondering what has happened to the gas which emitted it. They are formed from the gas which emitted those background photons that are now passing through the Milky Way, just as we are formed from the gas which emitted those background photons that they now study, and wonder about.

----

Or think of it this way. 13 something billion years ago, ALL the universe was filled with a hot dense mix of hydrogen and helium, with traces of lithium. It was all expanding and reducing in temperature and density as it expanded. Once it cooled to about 3000K, the universe became transparent to light, and so the photons emitted everywhere in the universe were no longer being absorbed back into a hot plasma, but were free to stream through all space, in all directions, from every point. They are streaming still.

The ones that have just now reached us came from far far away; and the ones we emitted ourselves are now far away in the distance. The stuff they came from is receding from us at enormous velocity, and this means we see the photons as being enormously redshifted. Alternatively, the photons we see have been stretched out as the universe expands. Two ways of describing the same effect. We now see them with a temperature of about 2.7K; cooled down by a factor of about 1100.

The "surface of last scattering" is all space at the time when the universe first became transparent to light, about 380,000 years after the "Big Bang".

Cheers -- sylas

 

[Chalnoth]

I'd like to point out that there was a significant error in my post (besides the obvious typos):

In that instance, the region of space from which the CMB photons are emitting are, well, emitting CMB photons "now" because we see them now.

I should have added that these are the photons that we see today. The CMB was emitted everywhere. We just see a particular slice of it today, the slice that took about 13.7 billion years for the light to reach us.

 

[Austin0]

. Alternatively, the photons we see have been stretched out as the universe expands. Two ways of describing the same effect. We now see them with a temperature of about 2.7K; cooled down by a factor of about 1100.
The "surface of last scattering" is all space at the time when the universe first became transparent to light, about 380,000 years after the "Big Bang".

Cheers -- sylas

What is the calculated expansion of volume that produced the 1100 to 1 ratio of wavelength expansion ?

 

[sylas]

What is the calculated expansion of volume that produced the 1100 to 1 ratio of wavelength expansion ?

Scale factor increases by 1100. The co-moving volume increases by about 1.33*10⁹ times.

Cheers -- sylas

 

[flatcp]

Thanks for your replies and clarifications. BY = Time. BLY = distance. Got it! I think I also misunderstood the nature of the where the CMB is as a result of looking at images.
Based upon the responses it seems I failed to frame my question properly though some of the responses were provoking on there own.

Yes sir! I believe so anyway .

Thanks for the welcome Marcus. Is this belief mainstream or part of a model you hope to become mainstream? Do string theory and LQG arrive at different conclusions on this question?

Yes; and we are occupying that area of space, right now.
It is a surface in a 4 dimensional spacetime picture of the universe.

So we are occupying that area of space, right now and we are seeing right now what that area of space emitted 13Bys ago? That’s a bit mind bending and almost observational time travel. Wouldn’t a 4d universe with a surface = 5d composed of Left\right, back\forth, up\down and time plus the surface dimension? Or am I incorrect in imaging you are referencing an additional boundary surface?

Thanks again

 

[sylas]

So we are occupying that area of space, right now and we are seeing right now what that area of space emitted 13Bys ago?

Yes; if you take "that area" to mean a humongous volume including everything we can see of the universe.

We are occupying a volume of space which now extends for hundreds of billions of light years, in every direction, in all probability. But we can't see all of space.

All of that volume is filled with galaxies, though not uniformly. (Galaxies gather together in clusters and sheets with great voids between them.) The galaxies are all dispersing further and further from each other (expanding, or spreading out). We see galaxies nearby, and galaxies far away, and we see them in all directions. The light from all those galaxies is also streaming through all the universe, at every point and in every direction. The galaxies that are furthest away we also see from long ago, because light with which we see them takes time to get to here from there.

The very furthest parts of the universe that we can see now, are seen as it was way back even before galaxies were formed; although by now that part of the universe is (we presume!) filled with galaxies much like our own neighbourhood. Those galaxies we presume have since formed from the gas we can see, are now about 45 billion light years away.

This oldest light is the background radiation. It's light from when the universe was simply a hot cloud of gas. We were like that also in the past... though of course we can't actually see ourselves in the past. Rather, we are part of a vast volume of space, all of which is filled with galaxies, all of which was once a hot gas, and all of which is filled with a background of radiation.

In two dimensions, it is like looking out at the ocean from a ship. All the ocean is the same, as far as we can see. There's a horizon; but there's nothing special about it. The horizon is ocean just like everything else. Things might be radically different far beyond the horizon (there may be land that-a-way) but what we see is just water, everywhere.

What we see in the horizon is not ourselves directly; but another similar part of the whole ocean, which is pretty much the same as the water passing directly beneath our bows.

The difference with the universe is that the universe is 3 dimensions, not 2. And it's much much bigger, so that it takes a long time for light to get here from the horizon. The reason for a horizon is a bit different. And also the universe changes over time... and so what we see at the horizon is what the universe used to be like, everywhere.

The background radiation is light from our horizon of visibility, looking out into the universe. There's a horizon because past that the light doesn't go: the universe was originally opaque. We can't see further, but everything from here out to the horizon, and much further in all probability, is pretty much the same, though seen at different times. The stuff we can see in the distant horizon is now formed into galaxies as well, and presumably looking at the hot gas that made up our own immediate neighbourhood, long ago.

We don't see ourselves, but we do see the past.

That’s a bit mind bending and almost observational time travel. Wouldn’t a 4d universe with a surface = 5d composed of Left\right, back\forth, up\down and time plus the surface dimension? Or am I incorrect in imaging you are referencing an additional boundary surface?

You may be over-thinking this a bit... but you're right about the observational time travel. We look into the past when we look long distances.

The universe is what you are used to. Three dimensions of space and one of time. When you look at light from 100 million light years distant, you are looking at material from a spherical "slice" with radius of 100 million light years, as it was 100 million years ago... a sort of time slice through the continuous material of the universe.

There's a little bit of weirdness going on because the matter in the universe is expanding, but it's not all that odd. The universe is expanding in much the same way as gas on the inside of a balloon expands as you blow it up; everything just moves apart from everything else. (Usually we use the continuous 2D skin of a balloon as an analogy for the universe, but you could also think of the 3D inside, as long as you have an "infinite" balloon with no boundary; just imagine the gas expanding everywhere and getting less dense everywhere.)

The weirdness creeps in because space and matter affect each other, as described by general relativity, which means distances can be defined in different ways (different co-ordinates), but as a start, an infinite cloud of expanding gas is a good analogy.

Cheers -- sylas

 

[flatcp]

Yes; if you take "that area" to mean a humongous volume including everything we can see of the universe.
We are occupying a volume of space which now extends for hundreds of billions of light years, in every direction, in all probability. But we can't see all of space.

That wasnt what I meant but I do get that. I was referencing a specific though hypothetical point in the CMBR 13 BYs ago verses now. For some reason I chose not to infdorm you of that :).

You may be over-thinking this a bit... but you're right about the observational time travel. We look into the past when we look long distances.
When you look at light from 100 million light years distant, you are looking at material from a spherical "slice" with radius of 100 million light years, as it was 100 million years ago... a sort of time slice through the continuous material of the universe.

If I think about this it leads me towards thinking the appearance of the universe,specifically it's depth, as I look up is an illusion caused by the the distance of galaxies to us and time. I've read that the latest data suggests the universe is flat (I almost chuckle when I read that remembering the great debate centuries ago regarding the flatness of the earth) and if that's true could all the matter in space be lined up across a flat surface where, because of time delays for distant light to reach us (time slices?), the sources of the light only appear to be positioned around us? I hope that is readable and makes half sense!

There's a little bit of weirdness going on because

I appreciate the effort Sylas but for me the weirdness results from not bad analogies but from to many seemingly contradictory ones. I'll let it stew for a while and see where it leads.

 

[sylas]

I've read that the latest data suggests the universe is flat (I almost chuckle when I read that remembering the great debate centuries ago regarding the flatness of the earth) and if that's true could all the matter in space be lined up across a flat surface where, because of time delays for distant light to reach us (time slices?), the sources of the light only appear to be positioned around us? I hope that is readable and makes half sense!

The curvature is a curvature of 3D space. It doesn't mean matter is lined up in any way on a surface; matter is still distributed in the same way throughout space, whether space is curved or flat.

Basically, curvature of space would mean that for a large sphere, the surface area would be more (negative curvate) or less (positive curvature) than 4πR².

So briefly, the answer to your question would be "no". It's got nothing to do with lining things up on surfaces, or presenting an "appearance" of things being positioned around us. Since the universe is flat, or as near as darn it, you don't need to worry about curvature for getting the basic ideas.

Cheers -- sylas