Universe has to have finite size - doesn't it?

[Sxlcartron]

Hi, one thing always bothered me about the argument on the size of the Universe.
If it started about 13.7 bn years ago then how could it possibly be infinite in extent?
Once the time was finite its not possible to attain infinite extent - no matter how fast
it expands. Also if there was sufficient mass to halt the expansion and start the 'Big Crunch'
and if the Universe was infinite it could never collapse to a point in finite time.
So,finite age limits size.
(Assuming that 'Universe'=whats evolved since the Big Bang)

 

[marcus]

A singularity is not necessarily a point.

There is no reason to suppose that the U was finite in spatial extent at the moment that expansion started.

The word "singularity" confuses people because it makes them imagine a single point.

 

[newjerseyrunner]

All we know is that what we can see started in a much much much smaller amount of space, we can make no assumptions about what's beyond the cosmic horizon. Think about it backwards from now, not from the big bang. If you imagine the universe as infinite with an infinite amount of stuff in it, compress it down, further and further and further. At some point, you compress the entire observable universe down to essentially nothing, but you've done the same thing with what's beyond, so what are you doing with the universe? You are dividing it. Divide infinity by anything, and you still get infinity. You can have an infinitely dense point, with an infinite amount of space, these concepts do not contradict each other.

 

[Hornbein]

Hi, one thing always bothered me about the argument on the size of the Universe.
If it started about 13.7 bn years ago then how could it possibly be infinite in extent?
Once the time was finite its not possible to attain infinite extent - no matter how fast
it expands. Also if there was sufficient mass to halt the expansion and start the 'Big Crunch'
and if the Universe was infinite it could never collapse to a point in finite time.
So,finite age limits size.
(Assuming that 'Universe'=whats evolved since the Big Bang)

If it started out finite, then it must be finite still.

But it might have started out infinite.

It is very helpful to keep in mind that singularity means WTF do we know.

 

[rootone]

'The Universe' being referred to here beginning with the 'big bang' is the OBSERVABLE universe.
That IS finite in size and is getting bigger over time, but it cannot become infinite.
We don't know if there is more stuff beyond the observable universe, but if there is it may or may not be infinite.

 

[marcus]

Ordinarily when people say "universe" they mean all, the universe. If you want to refer to the portion we are now able to observe then I'd suggest you say so clearly, say something like currently observable portion of the universe.

The currently observable portion is constantly increasing as light (and other signals) comes in from farther and farther away.

 

[newjerseyrunner]

The currently observable portion is constantly increasing as light (and other signals) comes in from farther and farther away.

I was under the impression that the observable portion was decreasing as objects beyond it are being expanded away from us faster than light?

 

[marcus]

...

It is very helpful to keep in mind that singularity means WTF do we know.

A mathematical singularity occurs where a function blows up or fails to be defined.
Like f(x,y) = 1/x has a singularity on the entire y-axis, where x=0. The singularity is the whole line, not a "single point".

A singularity in a physical theory occurs where the theory breaks down, where the functions blow up or fail to give meaningful answers.
It marks the limits to the applicability of the theory.
A theory can fail over an entire 3d region, of the space on which it is defined. The failure, or singularity, does not have to be confined to a "single point".
And it can fail on a set of infinite extent.

In Cosmology, only certain (generally older) cosmic models have a singularity (breakdown) at the start of expansion. Non-singular cosmic models are regularly discussed at the main international conferences. Research on non-singular cosmic models is ongoing. My impression is that the most commonly researched types of non-singular cosmic model are those involving a bounce (quantum effects making gravity repellent at high density) at the start of expansion.

 

[marcus]

I was under the impression that the observable portion was decreasing as objects beyond it are being expanded away from us faster than light?

No, in terms of the amount of matter, the observable portion is steadily increasing. In terms of comoving distance the radius of the observable portion (called the "particle horizon") is constantly increasing.
According to the standard LCDM model it is expected to max out around 62 or 63 billion LY.

The current value of the particle horizon is about 46 billion LY. So it still has plenty of room to grow!
Most of the galaxies within that range are receding faster than light.
What you say does not make sense. Merely because the distance to a galaxy is increasing faster than c does not mean that it is outside the observable region!

Most of the galaxies we can see with a telescope have redshift z > 1.5
But a galaxy with z > 1.5 is currently receding > c.

You might enjoy getting acquainted with Jorrie's calculator.
http://www.einsteins-theory-of-relativity-4engineers.com/LightCone7/LightCone.html
It implements the LCDM, the standard model that cosmologists typically use. Open the column selection menu and at v_now and v_then the recession speeds corresponding to an object at S = 1+z. Here is a sample:
{\scriptsize\begin{array}{|c|c|c|c|c|c|}\hline T_{Ho} (Gy) & T_{H\infty} (Gy) & S_{eq} & H_{0} & \Omega_\Lambda & \Omega_m\\ \hline 14.4&17.3&3400&67.9&0.693&0.307\\ \hline \end{array}} {\scriptsize\begin{array}{|r|r|r|r|r|r|r|r|r|r|r|r|r|r|r|r|} \hline S&z&T (Gy)&R (Gly)&D_{now} (Gly)&D_{then}(Gly)&V_{now}/c&V_{then}/c \\ \hline 3.000&2.000&3.285125&4.802402&17.294117&5.764706&1.201&1.200\\ \hline 2.940&1.940&3.383846&4.938802&17.000951&5.783044&1.181&1.171\\ \hline 2.881&1.881&3.485415&5.078390&16.705384&5.798883&1.160&1.142\\ \hline 2.823&1.823&3.589796&5.221141&16.407731&5.812205&1.139&1.113\\ \hline 2.766&1.766&3.697102&5.367083&16.107875&5.822845&1.119&1.085\\ \hline 2.711&1.711&3.807453&5.516234&15.805699&5.830627&1.098&1.057\\ \hline 2.656&1.656&3.920805&5.668552&15.501535&5.835537&1.076&1.029\\ \hline 2.603&1.603&4.037277&5.824041&15.195271&5.837396&1.055&1.002\\ \hline 2.551&1.551&4.156992&5.982702&14.886798&5.836017&1.034&0.975\\ \hline 2.500&1.500&4.279895&6.144467&14.576464&5.831389&1.012&0.949\\ \hline 2.449&1.449&4.406109&6.309318&14.264167&5.823322&0.991&0.923\\ \hline 2.400&1.400&4.535759&6.477228&13.949805&5.811618&0.969&0.897\\ \hline 2.352&1.352&4.668779&6.648103&13.633746&5.796271&0.947&0.872\\ \hline 2.305&1.305&4.805292&6.821897&13.315895&5.777081&0.925&0.847\\ \hline 2.259&1.259&4.945426&6.998550&12.996162&5.753840&0.903&0.822\\ \hline 2.213&1.213&5.089100&7.177941&12.674932&5.726547&0.880&0.798\\ \hline 2.169&1.169&5.236437&7.359988&12.352122&5.694995&0.858&0.774\\ \hline 2.125&1.125&5.387565&7.544599&12.027651&5.658967&0.835&0.750\\ \hline 2.083&1.083&5.542385&7.731619&11.701925&5.618472&0.813&0.727\\ \hline 2.041&1.041&5.701020&7.920932&11.374871&5.573294&0.790&0.704\\ \hline 2.000&1.000&5.863594&8.112407&11.046422&5.523211&0.767&0.681\\ \hline \end{array}}

You can see that a galaxy in our observable region with redshift z = 1.5 is NOW receding faster than light.
But back then when the light was emitted and started on its way to us the galaxy with receding < c.
However a galaxy with redshift z = 1.6 is now receding > c and already THEN when it emitted the light we are receiving today was already receding > c.

It's good to understand this and to understand how the light managed to get to us. There is probably something in cosmo FAQ about this, some tutorial.

 

[Sxlcartron]

Thanks for the interesting replies. But for me the problem remains. IF there is anything beyond the observable U , my point is that I cannot
see how it could be infinite. When the age of the U is spoken about , it surely means the time taken to extend to its present size from an infinitesimal size - including
visible + whatever is beyond that. - dosen't it? . As for the initial size being infinite - this brings us back to the Steady State idea which has lost favor.
The infinite extent of the singularity - described above as possibly along the Y axis- would seem to contradict the initial symmetries
believed to be inherent in the early U ( ie no preferential direction).
Again , once finite time was established , the notion of infinite extent cannot follow.

 

[Ken G]

]When the age of the U is spoken about , it surely means the time taken to extend to its present size from an infinitesimal size - including
visible + whatever is beyond that. - dosen't it?

Not necessarily, you tacked on the "from an infinitesmal size", that's not part of the model. The model uses the "cosmological principle", which means there is no difference from place to place, which also means there is no physical boundary. So it's only finite if it is positively curved. We don't know if the universe obeys the cosmological principle, it's just our best model, and we don't know what curvature to put into the model, but we do know that zero curvature seems to work fine-- and that's an infinite model at all ages of the universe. At age zero, we have a singularity, and the size is indeterminate, like 0/0, rather than infinitesmal, like 0. It's probably best not to extrapolate that model too far, but it's the best we've got-- we cannot constrain it any better with observations.

. As for the initial size being infinite - this brings us back to the Steady State idea which has lost favor.

It's not just the steady state model that has that feature, using the cosmological principle with zero curvature is also an infinite model.

The infinite extent of the singularity - described above as possibly along the Y axis- would seem to contradict the initial symmetries
believed to be inherent in the early U ( ie no preferential direction).

The model I described retains all the symmetries. I think what you really mean is simply that you don't think that model could correctly describe reality, but until we have observations to give us a better handle on the situation, we really cannot claim that with any authority. The universe has a way of surprising us.

 

[marcus]

.. . As for the initial size being infinite - this brings us back to the Steady State idea which has lost favor...

No it does not bring us back to Steady State

The most common version of the standard cosmic model the flat LCDM starts expansion infinite in extent.

If it is unfamiliar to you, you might want to practice imagining an infinite extending 3d space expanding. It has no outside or boundary so the expansion is represented by internal distances growing.

The function f(x,y) = 1/x was not to be thought of as a model of the universe. Just as a function with a singularity (the y axis).
The word singularity is a general term that comes up in many contexts, wherever math functions are involved that can blow up or fail to be defined.

Here's another abstract example: f(t,x,y,z) = 1/t
this blows up on the 3d space spanned by the x, y, z axes. If you like think of it as "same in all directions".

So there is a nice fat singularity for you

 

[marcus]

... When the age of the U is spoken about , it surely means the time taken to extend to its present size from an infinitesimal size - ... - dosen't it? .
...

No it does not mean that!
The 3d space spanned by the x, y, and z axes is not "infinitesimal"!

In the most common cosmic model, the flat version of LambdaCDM, which most people use most of the time, the U expands from infinite extent singularity to infinite extent what-we-see-now.

In some current non-singular improvements there is a bounce at extreme density, and then the usual flat version has infinite extent collapsing to extreme density infinite extent and then expanding out to infinite extent what-we-see-now. The bounce does not occur just at a point.