The Universe has boundary?

[AlexG]

The universe is expanding.

It has been expanding for 13.7 billion years.

If you watch the universe's expansion in reverse, the universe contracts to a small volume.

A small volume is not infinite.

Therefore, the universe is not infinite.

I can't make it any simpler.

 

[AlphaNumeric]

I don't think my ideas of recursion are new.

Can you explain why recursion must include Godel numbers of formulas?

Try to take another look at the recursion theorem.

You are very well uninformed.

Let me try to teach you.

The recursion theorem proves given a function f R->R as in LT, exists a function G such that G(n+1) = f(G(n)).

So, we can start wtih some state and G(n+1) must arrive at only one state.

Can you prove this is true?

Chinglu, you didn't read what I said. This is not the thread to be talking about recursion. And I didn't say it must include Godel numbers, I was listing unrelated, irrelevant pure mathematics things you bring up in threads about physics. It is off topic.

If you want to talk about uncomputability, Godel numbers, the recursion theorem or anything else of that ilke then start a new thread and be clear about what it is you want to discuss. If you mention them again in a clearly physics thread (like you did in Cpt's electrodynamics thread) without making it crystal clear what precise relevance they have to the discussion at hand then you'll find your posts start disappearing.

In case your English isn't too great and I'm being too subtle, if you go off topic with your first order logic stuff again, I'll delete your posts.

 

[Fudge Muffin]

The rate that the universe is expanding in phenomal. Not only is this rate accelerating, but that acceleration is accelerating.

I think our universe is an atom in another universe. Likewise an atom in our universe is another universe.

 

[AlphaNumeric]

Yes, it is. but if the volume is finite, the universe is finite. An expanding universe demands that the universe was smaller in the past. You can't say that an infinite universe was smaller in the past. Nor can you say that an infinite universe contracted. expansion and contraction have no meaning if the universe is infinite.

But if it is infinite now, it must have always been infinite, which doesn't agree with cosmological observation.

It's possible to talk about metric distances and the like changing, even within an infinite universe. For example, consider the 2d Euclidean plane. It's infinite and since I've said it's Euclidean it has the metric $$g(x,y) = x_{1}y_{1}+x_{2}y_{2}$$. Now I attach time to the setup. In purely Newtonian space-time time doesn't have influence on distances but stuff that, I define a new metric $$h(x(t),y(t)) = e^{t}g(x,y)$$. Clearly at any particular t=T you have a Euclidean space, all the overall factor does is dilate things, exponentially moving apart. The configuration of objects and the structure of the plane are unchanged by that dilation too.

In fact, you could swap your point of view and say that it isn't that things are perhaps moving away from one another by the expansion of space but rather your ruler is shrinking and everything else is normal.

This is basically what the a(t) factor in the FRW metric in cosmology does, so it doesn't actually have to address if the universe is finite or not.

Yes. If something is infinite, it is infinite in both time directions. If it's not infinite in one direction, then it isn't infinite.

I'd not agree with that myself. The upper half plane or the positive reals are both infinite sets, ie $$\mathbb{R}^{+} = \{ x \,|\, x>0 \, x \in\mathbb{R} \}$$ is infinite both in terms of cardinality and in terms of the absolute value of it's members.

 

[Rav]

If you watch the universe's expansion in reverse, the universe contracts to a small volume.

Only if it's finite. If you run metric expansion in reverse in an infinite universe, you get an infinite volume. Edward L. Wright put together a decent little illustration here.

The bottom line is that the result of these little extrapolations is dependent on the initial assumption. Is the universe infinite, or not? It's an open question in cosmology.

 

[billvon]

see that is interesting . Something to think about . I am assuming you know what you are saying Alpha. The universe has a visible horizon . That sounds like a fish bowl . What do you mean by horizon ?

It is the place where the very first photons from the big bang have reached after all this time. Since those photons are still moving outwards at the speed of light it's getting bigger all the time.

A bubble comes to mind ? Is the bubble moving I got to ask my self . Besides expanding is the bubble moving ?

It might be moving relative to something else; we have nothing to compare it against.

 

[KilljoyKlown]

Yes. If something is infinite, it is infinite in both time directions. If it's not infinite in one direction, then it isn't infinite.

Not sure I can follow that reasoning. If you have some starting point (A) and there is no ending point, then clearly you have an infinity with a starting point. If not please tell me what you would call that?

 

[KilljoyKlown]

It is the place where the very first photons from the big bang have reached after all this time. Since those photons are still moving outwards at the speed of light it's getting bigger all the time.

It might be moving relative to something else; we have nothing to compare it against.

Can you explain the following examples on the link below? I think I understand what they are trying to show, but am not sure I believe any of it.

The cosmic light horizon, animated

http://www.phys.ksu.edu/personal/gahs/phys191/horizon.html

 

[markl323]

When we say that universe is expanding, we are not making the claim that it is getting bigger. Rather we are saying that the distance between gravitationally bound clumps of matter is increasing locally. That's all we can definitively say.

we believe that at least the local universe is expanding in terms of volume because expansion of space implies an increase in volume. otherwise we would have said that galaxies are simply flying away from each other without mentioning space expanding. an increase in the volume of the local universe automatically adds volume to the global universe. imagine a smaller baloon expanding inside a bigger balloon. the bigger balloon must also expand to accomodate it.

i think the biggest proof of space expansion is the uniform nature of the CMBR. if you only had an explosion in space without space expanding, the CMBR measurements would not have been the same everywhere in the sky. (i'm using the answer you once gave me).

Light takes the same time to travel the distance involved before and after expansion.

there are galaxies that move away from us so fast, faster than the speed of light that their light will never reach us. doesn't this automatically imply that space expansion actually increases the travel time of light?

 

[KilljoyKlown]

there are galaxies that move away from us so fast, faster than the speed of light that their light will never reach us. doesn't this automatically imply that space expansion actually increases the travel time of light?

It might, if there was any actual proof that some galaxies are moving away from us at faster than light speed. Also, I am still not satisfied with mainstream theories on the red shift. There are alternate theories that haven't been disproved. So in my opinion there is a great deal of room for doubt about the real expansion rate of our visible universe.

 

[OnlyMe]

EDIT: There is an error in how the expanding universe model is treated in this post, which I have attempted to correct in post 173. I did not attempt to correct the issue here as this post has been up to long for that to be an effective correction.

there are galaxies that move away from us so fast, faster than the speed of light that their light will never reach us. doesn't this automatically imply that space expansion actually increases the travel time of light?

Understanding how space or the universe expands, resulting in a Doppler effect in the wavelength of light without affecting the velocity of light can become somewhat controversial. However, it is the Doppler shift in light that supports the expanding universe model and the acceleration of that expansion.

Superficially this would seem to suggest that the distance is growing and in some sense that may be true, however where light is concerned only the wavelength is affected by the expansion not the time of travel or velocity, c. This means that if a distance of one light year expands such that the Doppler affect or lengthing of the wavelength of light doubles (i.e. the space expands to twice is initial dimension), the only way the wavelength could be stretched is if the light still took only one light year to travel the expanded distance.

This can lead to a number of paradox discussions...

Still if light took longer to cross the expanded space its wavelength would not become Doppler shifted or stretched out, and our evidence for the expansion would not exist. So if the Doppler effect does prove an expansion of space, light has to travel through the expanded light year of space, in the same time it would have traveled through an unexpanded light year of space, its wavelength being stretched out in the process.

The expansion of the universe or space, is not directly associated with objects moving away from one another.., with increasing distances... Though there are very often analogies and examples, by even some respected scientists that describe it in just that way.

 

[OnlyMe]

It might, if there was any actual proof that some galaxies are moving away from us at faster than light speed. Also, I am still not satisfied with mainstream theories on the red shift. There are alternate theories that haven't been disproved. So in my opinion there is a great deal of room for doubt about the real expansion rate of our visible universe.

The only real challenge to the expanding universe explanation of the Doppler effect, that I am aware of, is a tired light model. And while there is some merit to some of the tired light models I have seen, I cannot think of any credible modle that rigorously duplicates and explains current observations and experience. That said as with a few other fringe areas I have mentioned in the past, tired light is interesting and has has some potential, along with a number of stumbling blocks to overcome.

 

[KilljoyKlown]

Understanding how space or the universe expands, resulting in a Doppler effect in the wavelength of light without affecting the velocity of light can become somewhat controversial. However, it is the Doppler shift in light that supports the expanding universe model and the acceleration of that expansion.

Superficially this would seem to suggest that the distance is growing and in some sense that may be true, however where light is concerned only the wavelength is affected by the expansion not the time of travel or velocity, c. This means that if a distance of one light year expands such that the Doppler affect or lengthing of the wavelength of light doubles (i.e. the space expands to twice is initial dimension), the only way the wavelength could be stretched is if the light still took only one light year to travel the expanded distance.

This can lead to a number of paradox discussions...

Still if light took longer to cross the expanded space its wavelength would not become Doppler shifted or stretched out, and our evidence for the expansion would not exist. So if the Doppler effect does prove an expansion of space, light has to travel through the expanded light year of space, in the same time it would have traveled through an unexpanded light year of space, its wavelength being stretched out in the process.

The expansion of the universe or space, is not directly associated with objects moving away from one another.., with increasing distances... Though there are very often analogies and examples, by even some respected scientists that describe it in just that way.

"expanded light year of space" Talk about your paradox discussions?

 

[markl323]

This means that if a distance of one light year expands such that the Doppler affect or lengthing of the wavelength of light doubles (i.e. the space expands to twice is initial dimension), the only way the wavelength could be stretched is if the light still took only one light year to travel the expanded distance.

i have never heard of this contradiction/paradox before. do you have a source for this? correct me if i'm wrong but i think you made it up.

first of all, red shift can be caused without space expanding. (i.e a tail light of a car moving away can also emit red shift). so it is not the expansion of space that produce the red shift, it is the side effect of it, which is objects moving further apart.

second, light doesn't travel from one point to another instantly. so before it reaches its destination, the space of the untraveled distant expands and automatically increases its travel time. this occurs independently from what happened during the the distant light had already traveled, the distant in which it might or might not have "sped up" to accommodate the expansion.

 

[OnlyMe]

EDIT: There is an error in how the expanding universe model is treated in this post, which I have attempted to correct in post 173. I did not attempt to correct the issue here as this post has been up to long for that to be an effective correction.

i have never heard of this contradiction/paradox before. do you have a source for this? correct me if i'm wrong but i think you made it up.

first of all, red shift can be caused without space expanding. (i.e a tail light of a car moving away can also emit red shift). so it is not the expansion of space that produce the red shift, it is the side effect of it, which is objects moving further apart.

second, light doesn't travel from one point to another instantly. so before it reaches its destination, the space of the untraveled distant expands and automatically increases its travel time. this occurs independently from what happened during the the distant light had already traveled, the distant in which it might or might not have "sped up" to accommodate the expansion.

There is a velocity related Doppler effect that can be observed for near by galaxies that shifts both red and blue.

However, the cosmological redshift has for a very long time been explained as being caused by an expanding universe. Once light is emmited the velocity of its source cannot contribute to any additional or additive Doppler effect as it does for nearby galaxies.

How would a photon know that space itself is expanding? And how does the wavelength of light get stretched by the expansion of space? If the speed of light remains constant and the expansion of space essentially increases distances, the wavelength would not change the light would just take longer to travel the increased distance.

Even if space expands near c when comparing distance objects locally to the emission of light it can be considered just as flat as it is locally to earth.

I mentioned that you could talk this into a number of paradox discussions. You can run the math in a number of different ways, depending upon where you begin.

Few question a local curvature of space, length contraction and time dilation, when talking about gravity. There are equally few who see the global ramifications of curvatures in the reverse scales.

Close in to a gravity well time dilation and length contraction, due to GR effects results in light taking longer to move shorter distances.., or what from an external FoR appears shorter due to the curvature of space, time slows to a near stand still as you approach the event horizon of a BH....

How is it so difficult to apply the reverse to the great voids between gravity wells, where as the gravitational forces fade the curvature of space and time dilation run to the opposite extremes? It is hard to see because few ever explore it closely.

And to some extent you are correct! These are to a significant degree my own musings. Still it is generally consistent with GR.

Or as another option you could attribute some real physical character to space itself, which as it expands affects the wavelength of light directly, but that begins to sound like an ether model... Or once again there are any of several tired light models....

The truth is any of these three models could be at play we really have no direct way to tell one from another at this time.

 

[KilljoyKlown]

i have never heard of this contradiction/paradox before. do you have a source for this? correct me if i'm wrong but i think you made it up.

first of all, red shift can be caused without space expanding. (i.e a tail light of a car moving away can also emit red shift). so it is not the expansion of space that produce the red shift, it is the side effect of it, which is objects moving further apart.

second, light doesn't travel from one point to another instantly. so before it reaches its destination, the space of the untraveled distant expands and automatically increases its travel time. this occurs independently from what happened during the the distant light had already traveled, the distant in which it might or might not have "sped up" to accommodate the expansion.

The question that nags at me about the red shift, is that in order for the photon to change it's frequency towards the red end of the spectrum it has to lose energy. I can see it losing energy gravitationally, but once it's free of whatever gravity well it started from, no amount of space that it has to travel through to reach us should cause it to lose anymore energy.

 

[OnlyMe]

The question that nags at me about the red shift, is that in order for the photon to change it's frequency towards the red end of the spectrum it has to lose energy. I can see it losing energy gravitationally, but once it's free of whatever gravity well it started from, no amount of space that it has to travel through to reach us should cause it to lose anymore energy.

Gravity is different than the other forces in that it never ends... It can be very strong near a large mass and though it drops off proportionally in an inverse square relationship between total mass and distance, it never fades completely away. It just diminishes to the point that it becomes part of a background of the combined gravity wells of all mass. Light essentially is never completely free of some influence of gravity.

On the other hand, empty space can never really be considered empty. Here I don't mean to be referring to the the ever present particle's of cosmic origin that could never be completely excluded. I refer more to the implications of the dynamic relationship between mass and space that results in the curvature of space. For space to be curved both in the usual sense thought of as gravitationally and by the frame dragging effect, or linear motion of matter through space, it has to be dynamically interacting with mass or matter. It must have some intrinsic substance other than a particle nature, through which that dynamic relationship occurs.

There is strong evidence in the success of GR that suggests that space is indeed curved and that the motion of matter within space drags space along, even if only weakly. Both of these can be modeled as curvatures of space. And yet that very same "frame dragging" effect can be interpreted to be very much like a weak inertial interaction between space and matter. Both would seem to be almost indistinguishable from one another in effect.., and yet how we understand them to affect the propagation of light through space is somewhat different.

From the inertial perspective you could wind up easily with a tired light model, in which light loses energy through some weak inertial interaction with space, which we observe as a red shift.

Where the more common curvature model invokes time dilations and length contractions to explain most of what we have observed. From where we are "looking" toward a deep or strong gravity well, time dilation slows time and length contraction compresses or shortens lengths... Looking away from the gravity well and into the depths between galaxies those same relationships lead to time speeding up and lengths getting longer. In either case, the time of travel for light does is not affected by the stretched or length contracted space. What happens is that when space is curved such that lengths are contracted the wavelengths of light are blue shifted and when they are stretched they are redshifted.

I know I am not doing the best job of explaining this..... The more I think on this the more I like the idea that space itself is involved in what we have come to describe as inertia. It works better in most ways, but if also requires a great deal of rethinking some of the mathematical models. And it suggests that there really is no material object that moves without any inertial resistance. An object in motion only appears to remain in motion locally.

This is sliding far into a philosophical approach to physics, though I am sure some mathematical model could be developed.

 

[Rav]

because expansion of space implies an increase in volume.

You've responded to a comment that I clarified later. I do not, of course, deny that what we call expansion is taking place.

 

[Gravage]

Only if it's finite. If you run metric expansion in reverse in an infinite universe, you get an infinite volume. Edward L. Wright put together a decent little illustration here.

The bottom line is that the result of these little extrapolations is dependent on the initial assumption. Is the universe infinite, or not? It's an open question in cosmology.

The universe can be infinite (especially the space between the galaxies), but only if it wasn't created. You can't create something from singularity to have infinite distance.

 

[arfa brane]

You can't create something from singularity to have infinite distance.

Maybe we can't do that. But if the singularity was a point of infinite energy, why shouldn't the diameter be infinite now?
How do we know there was one singularity? How do we know other universes weren't created next to ours, or that they aren't intersecting our universe?

There's the thing about universal history, we only have one of them. Intuitively, we create the past by observing it (or maybe that isn't so intuitive).
That is to say, we don't know how to formulate the boundary of the past; we only assume--because we observe--that the past is somehow "fixed", that history and observation of it are irreversible.