From Infinitesimal to Infinity and Beyond

[emc]

“Our” universe is finite because we are bound by light, right? But just because we can’t see doesn’t mean the universe is finite nor does it mean it’s infinite. How do you comprehend infinity anyway? I have a lot of trouble with that. I try thinking of it as a growing number without end but that leaves me hanging like trying to run a marathon with no finish line. Or go the other way to infinitesimally small but that feels like there’s an event horizon waiting for me in there somewhere.

[Chris Peterson]

“Our” universe is finite because we are bound by light, right?

The region of the Universe that we can interact with is called the observable universe, and its boundaries are determined by the speed of light. Anything outside the observable universe is moving faster than c with respect to us, and is therefore unable to influence us in any way. The volume of the observable universe is certainly finite. Every point in the Universe has its own unique observable universe around it.

But just because we can’t see doesn’t mean the universe is finite nor does it mean it’s infinite.

Correct. There is a broad consensus that the observable universe is only a tiny part of the Universe as a whole. But there isn't a consensus on whether the Universe is finite or infinite, bounded or unbounded, flat or curved. These remain open questions.

How do you comprehend infinity anyway?

Some people can probably do this better than others. But from a scientific standpoint, visualization is not required. The concept is fully manageable with well understood mathematical tools.

[Ann]

Chris, you talked in another forum about the possibility that the universe is flat and yet finite, because of its topology. How likely is it that the universe has a "complicated" topology?

Let me rephrase that. Astronomers like yourself can say that life on other planets is likely because we understand the basic chemistry behind life, and we can make an educated guess that something comparable to what has happened on the Earth thanks to "the chemistry of life" has probably happened on other planets in other solar systems (or even below or near the surfaces of free-floating planets), too.

But can astronomers say that it is likely that the universe has a complicated topology? Is a complicated topology of the universe equally likely as the existence of life on other planets in the universe? If so, why is it likely? Do certain equations make better mathematical sense if the universe has a non-trivial topology? Are there other reasons that make it likely that the universe has such a topology?

And if the universe has a complicated topology, are there any ways that we could find out about it? Could we observe it?

Or is the topology of the universe "merely" "a mathematical figment" that cosmologists came up with when they asked themselves if there is a way that the universe can be flat and yet bounded and finite?

Finally, if the universe has a topology, how likely is it that this topology will impart "boundedness" to a flat universe, rather than, say, "hasten its path" to infinity?

Ann

[emc]

How do you comprehend infinity anyway?

Some people can probably do this better than others. But from a scientific standpoint, visualization is not required. The concept is fully manageable with well understood mathematical tools.

Thanks Chris!

It is a visualization issue with me because I'm “looking” for an “end” that doesn’t exist.

You are a good guy to have around. I hope you stay ‘till you can’t type!

[Chris Peterson]

But can astronomers say that it is likely that the universe has a complicated topology? Is a complicated topology of the universe equally likely as the existence of life on other planets in the universe? If so, why is it likely? Do certain equations make better mathematical sense if the universe has a non-trivial topology? Are there other reasons that make it likely that the universe has such a topology?

The best supported cosmological theories (like LCDM) lead to simple topologies. That's about all I can say. Other possibilities certainly exist.

And if the universe has a complicated topology, are there any ways that we could find out about it? Could we observe it?

The most likely scenario would not involve direct observation. Rather, a theory would be developed that requires some particular topology, and an experiment would be devised to test for that- probably indirectly (like the example of measuring the inside angles of a triangle, or the ratio of a circle's diameter to circumference).

Or is the topology of the universe "merely" "a mathematical figment" that cosmologists came up with when they asked themselves if there is a way that the universe can be flat and yet bounded and finite?

Finally, if the universe has a topology, how likely is it that this topology will impart "boundedness" to a flat universe, rather than, say, "hasten its path" to infinity?

I think the topology of the Universe is a real, physical thing, as much so as the Universe itself. That is, it isn't just a mathematical tool to explain things (unless we consider every representation of natural law to be just a mathematical tool, not really a physical thing... which some do).

I don't know how to assign any likelihood to the possibilities. The only intellectually honest answer right now is that valid variations of well supported theory lead to different conclusions, and more testing is needed before a high degree of confidence can be placed on any of them.

[rstevenson]

How do you comprehend infinity anyway?

Back in the dark ages when I was attending high school my math teacher, near the end of a particularly boring digression into what I now know was calculus, said firmly "No one can imagine infinity." I sat there glumly, thinking, "I'm doing it right now."

Rob

[emc]

How do you comprehend infinity anyway?

Back in the dark ages when I was attending high school my math teacher, near the end of a particularly boring digression into what I now know was calculus, said firmly "No one can imagine infinity." I sat there glumly, thinking, "I'm doing it right now."

Rob

Your confession somehow reminded me that I once told my kids (when they were young and impressionable and had asked me why we celebrate New Year) that at midnight everything in the universe mirrored on itself renewing all things. I further explained that since we were part of the mirroring that there was no perceivable change from our vantage point. Being very young they bought it… for a little while anyway until their mother scolded me.

[Ann]

emc wrote:

Thanks Chris!
...

You are a good guy to have around. I hope you stay ‘till you can’t type!

I agree!

Ann

[Moonlady]

Some people can probably do this better than others. But from a scientific standpoint, visualization is not required. The concept is fully manageable with well understood mathematical tools.

Thanks Chris!

It is a visualization issue with me because I'm “looking” for an “end” that doesn’t exist.

You are a good guy to have around. I hope you stay ‘till you can’t type!

Don't worry, when he can't type, his brain will be wired and connected with the internet and Apod forum, he will still be able to communicate
It's in the policy, every member agrees to support APOD!
Like Neufer will be cloned ( though he is a little scared but we can change his DNA to a warior without fear) and me, I will just hanging around till infinity

[emc]

There are many interesting and “good to have around” people in this APOD community! It’s a fun place to hang out… you never know exactly what to expect except that most folks here are respectful and patient. We’re all different (gee where have I heard that?) and here it shows apparent. We have our common bond in love for the stars.

[owlice]

Back in the dark ages when I was attending high school my math teacher, near the end of a particularly boring digression into what I now know was calculus, said firmly "No one can imagine infinity." I sat there glumly, thinking, "I'm doing it right now."

Rob

Made me laugh out loud here, Rob!!

[emc]

Rob is my motorcycle buddy. We both came close to seeing stars on our Triumphs.

[orin stepanek]

when I was a kid I tried to imagine what it was like at the end of the universe; and I thought there must be something beyond that! It's mind boggling; so I quit wondering about it!

[Beyond]

when I was a kid I tried to imagine what it was like at the end of the universe; and I thought there must be something beyond that! It's mind boggling; so I quit wondering about it!

So since then, you've boggled your mind with closer things.

[BMAONE23]

I have wondered what it would be like to live in a system that is at the farthest reaches of an arm in a galaxy. At certain times of the year, your entire home galaxy would be spread out before you in the night sky while at other times the only light in the night sky would be the hazy blobs of other distant galaxies

[Chris Peterson]

I have wondered what it would be like to live in a system that is at the farthest reaches of an arm in a galaxy. At certain times of the year, your entire home galaxy would be spread out before you in the night sky while at other times the only light in the night sky would be the hazy blobs of other distant galaxies

I don't think the view would be much different from what we have here.

[Ann]

Source: http://1000awesomethings.com/2010/05/10 ... ely-empty/

When I was a teen, a friend of mine mused, when we discussed the universe and the concept of infinity:

"Maybe the entire universe is just the front wheel of a bicycle in another universe a gazillion times the size of our own. Maybe someone is just riding down a street, carrying our universe along, because it's just a small part of his front wheel.

Wonder where we are going?"





Ann

[emc]

Interesting Ann! Your muse reminded me of the first Men in Black movie. I think there was a “universe” inside a very small something like a ring or pendant… my memory’s a little foggy.

[emc]

when I was a kid I tried to imagine what it was like at the end of the universe; and I thought there must be something beyond that! It's mind boggling; so I quit wondering about it!

I’ve always thought that it would make an interesting loop animation to start with the “camera” zoomed in on an eye of The Thinker (filling the frame) and pan away and up changing the perspective to looking down at the top of the statue keeping a steady zoom outward (like a spaceship heading out into space) keeping the view to the rear. As the “spaceship” continues its steady and ever increasing speed outward past the Moon, Solar System… past the Milky Way continually zooming outward until a transition point where the imagery smoothly becomes a microscopic view of matter… still zooming "outward" gradually taking shape until the eye of The Thinker takes form as at the start. It’s like the universe makes a complete cycle from atomic to cosmic. Kind of M.C. Escher like. The idea is for the audience to not be aware of the cosmic to atomic transition until the first frame is showing again completing the loop.

[emc]

I have wondered what it would be like to live in a system that is at the farthest reaches of an arm in a galaxy. At certain times of the year, your entire home galaxy would be spread out before you in the night sky while at other times the only light in the night sky would be the hazy blobs of other distant galaxies

I don't think the view would be much different from what we have here.

We have a pretty good view but there's always room for improvement. Maybe a fast ship and a good navigator!

[BMAONE23]

I have wondered what it would be like to live in a system that is at the farthest reaches of an arm in a galaxy. At certain times of the year, your entire home galaxy would be spread out before you in the night sky while at other times the only light in the night sky would be the hazy blobs of other distant galaxies

I don't think the view would be much different from what we have here.

I think there would be a marked difference since at some poing during their year, there would be no stars in the sky in the equatorial regions while the polar regions would have stars in only half their skies and higher latitudes would have a belt of stars similar to the Belt Of Venus during some times of the year

[Chris Peterson]

I have wondered what it would be like to live in a system that is at the farthest reaches of an arm in a galaxy. At certain times of the year, your entire home galaxy would be spread out before you in the night sky while at other times the only light in the night sky would be the hazy blobs of other distant galaxies

I don't think the view would be much different from what we have here.

I think there would be a marked difference since at some poing during their year, there would be no stars in the sky in the equatorial regions while the polar regions would have stars in only half their skies and higher latitudes would have a belt of stars similar to the Belt Of Venus during some times of the year

I guess I don't understand the geometry you are talking about. A system anywhere in the disc (that is, outside the bulge) will see the Milky Way as a band in the sky. The closer you are to the edge, the more asymmetric the band will be, with the bright side towards the center and the dim side towards the outside (just as we see on Earth, although even more asymmetric if the system is closer to the outside). Most of the night sky will be looking outwards at any time of year, meaning you'll mainly only see your local stars except in the Milky Way band... again, just like here.

[BMAONE23]

What I am attempting to describe, but apparently failing to, is a situation where the only local stars that could be viewed are in fact only on one side of the planets orbit, the side which faces the galactic center. This hypothetical planet is proposed to be orbiting a star that is at the farthest point away from the center of its parent galaxy. Just over 180deg of view would have no local stars, except for near the polar regions.

[Ann]

What I am attempting to describe, but apparently failing to, is a situation where the only local stars that could be viewed are in fact only on one side of the planets orbit, the side which faces the galactic center. This hypothetical planet is proposed to be orbiting a star that is at the farthest point away from the center of its parent galaxy. Just over 180deg of view would have no local stars, except for near the polar regions.

A part of M31. Photo: NOAO.

I think that the "stellar density" decreases so gradually in the spiral arms of a large galaxy that you would hardly notice any difference in the population of local stars in any direction around you, no matter where in the spiral arm your planet is located. The luminous disk of a galaxy like the Andromeda galaxy is about 100,000 light-years in diameter, but there is a vast halo of stars, including many bright red giants, outside the luminous disk. It would be very hard to point at a specific location in the outskirts of the Andromeda Galaxy where there would be a lot of stars in one direction of the sky but no stars in the opposite direction.

M13. Source: http://www.learn.usa.canon.com/resource ... ques.htmlp

On the other hand, if you were on the outskirts of a globular cluster, you should most definitely be able to see a difference in stellar density in different directions of the sky. Consider globular cluster M13, which contains about 300,000 stars. The diameter of M13 is less than 200 light-years, small enough that many bright red giants should be clearly visible in the direction of the core of the globular. In the opposite direction, there should be a noticeable dearth of bright stars.

Ann

[emc]

I pictured BMAONE23’s description as placing us at the end of a cul-de-sac with the forest (deep space) behind us and houses (Milky Way) in front of us. But Ann and Chris are explaining that even if we were to be the outermost star in a spiral arm we would still see a lot of local stars in our night sky. But the cul-de-sac view would perhaps work from the outer fringe of a globular cluster.