Is the universe infinite?

[modest]

I agree with Boerseun. We can only see so far. It rather reminds a person of the ancient world, perhaps pre-Hellenistic Greece. They must have wondered if the land under their feet went on forever or if it had an end. They could only see see so far and they must have used philosophy saying something similar to Michael's earlier comment:

Space must be infinite. Why? Because the alternative, an "end of space" is a no-brainer absurdity.

They would say:

"The land must be infinite because the alternative, an "end of the land" is an absurdity"

And, it is kind of absurd. If the land ended then all the water of the oceans would drain off the edge. Certainly ancient philosophers could have convinced themselves that the amount of land is infinite if it has no boundary, and the very idea of an actual physical boundary seems quite philosophically displeasing.

 

By the time of Pythagoras they figured out a 3rd possibility: that there is only a finite amount of land, yet there is no boundary. In 330 BC Aristotle provided evidence that, indeed, there is only so much land under a person's feet, yet that person could walk with those feet for an eternity without falling off the philosophically displeasing edge.

 

So, it is, I guess, a little surprising that many years later Kant gives his Antinomy of space where unbound is assumed to be infinite. As is explained in The Ontology and Cosmology of Non-Euclidean Geometry, Einstein's general relativity provides an answer to Kant's Antinomy in the same way that Pythagoras did with the earth. Both infinite without boundary, and finite without boundary are possible.

 

Given the assumption that the matter in the universe is homogeneous and isotropic (The Cosmological Principle) it can be shown that the corresponding distortion of space-time (due to the gravitational effects of this matter) can only have one of three forms,

 

 

as shown schematically in the picture at left. It can be "positively" curved like the surface of a ball and finite in extent; it can be "negatively" curved like a saddle and infinite in extent; or it can be "flat" and infinite in extent - our "ordinary" conception of space. A key limitation of the picture shown here is that we can only portray the curvature of a 2-dimensional plane of an actual 3-dimensional space! Note that in a closed universe you could start a journey off in one direction and, if allowed enough time, ultimately return to your starting point; in an infinite universe, you would never return.

 

Before we discuss which of these three pictures describe our universe (if any) we must make a few disclaimers:

• Because the universe has a finite age (~13.7 billion years) we can only see a finite distance out into space: ~13.7 billion light years. This is our so-called horizon. The Big Bang Model does not attempt to describe that region of space significantly beyond our horizon - space-time could well be quite different out there.
  
  

WMAP Big Bang Concepts

 

~modest

[Michael Mooney]

I, as always, challenge the ubiquitous assumption (since Einstein/Minkowski invented "spacetime" as something with shape) that space has shape.

Obviously "things existing in space" have shape. But no matter how many times the various "shapes of space" are asserted and illustrated graphically, as above...

If space is emptiness, the lack of "things" in which things exist, then there is no boundary, shape, or any properties whatsoever attributable to that no-thing-ness, emptiness, simple volume... and it must be infinite, as logically presented in my last post.

 

You may argue the premise (the "if"), but if it turns out to be true, the conclusion ("then") must follow.

And again, please consider the ontology of "time" from the perspective of "presentism" (the formal philosophy which best expresses my perspective) before you assume the ontological existence of time as a mandated given or fact.

 

Consider also why it (time, space and spacetime) would cease to exist if matter disappeared, as Einstein said. "It's" ontological status is obviously dubious if it does not exist independently of matter.

 

Michael

[lemit]

I, as always, challenge the ubiquitous assumption (since Einstein/Minkowski invented "spacetime" as something with shape) that space has shape.

Obviously "things existing in space" have shape. But no matter how many times the various "shapes of space" are asserted and illustrated graphically, as above...

If space is emptiness, the lack of "things" in which things exist, then there is no boundary, shape, or any properties whatsoever attributable to that no-thing-ness, emptiness, simple volume... and it must be infinite, as logically presented in my last post.

 

You may argue the premise

 

Thanks. I think I will.

 

What if space is a state of nature we don't fully understand because we have so much trouble measuring it? I hope somebody can pick that up and run with it, although picking up something like space might be a little difficult.

 

--lemit

[Michael Mooney]

Thanks. I think I will.

 

What if space is a state of nature we don't fully understand because we have so much trouble measuring it? I hope somebody can pick that up and run with it, although picking up something like space might be a little difficult.

 

--lemit

Yup. If it ain't nutin' but empty volume (without end) what's to "pick up?"

So, anyway lemit, with what do you disagree in my presentation of "space as emptiness, the lack of 'things' in which things exist?"... no-thing-ness... simple volume...?"

 

How exactly do you disagree (if you do) with my statement that

"...all things that exist" is a different set than the "space" in which all things exist?"

 

Maybe there is another big misunderstanding here between the concept of "stuff" distributed through space in a manner described by the often repeated various graphics shared again above by Modest... and "space itself" (as if it were an entity of some kind) having those shapes.

What say you?

Michael

[lemit]

Some friends of mine are working on a theory that, oversimplified, says "We can't understand space because we can't understand space."

 

Slightly less oversimplified, the nascent theory, as I understand it, is that space might just be a form of matter we haven't figured out yet, and that the premises all of us use might be wrong, since they don't seem to be giving us very good results. They become defenses of themselves in circular logic that can start arguments but can't end them.

 

We certainly haven't done very well in figuring out dark matter. But at least there we seem to know there's something wrong with our thinking, something we're missing.

 

I probably shouldn't suggest that here, since if people start agreeing with it, they might stop saying they know what space is, and Hypography would go out of business. But I kind of doubt that's going to happen.

 

I personally like the as yet unnamed theory because it is humble. It doesn't make claims it can't support, because it avoids making many claims at all. Maybe it could be called the No-Name Theory, or the No-Theory Theory, since it suggests we need to look for a new premise.

 

I have a feeling I've misrepresented their theory. I hope I haven't embarrassed them so thoroughly that they will now avoid associating themselves with the theory or with me. We'll see.

 

--lemit

[plumber]

Some friends of mine are working on a theory that, oversimplified, says "We can't understand space because we can't understand space."

 

Slightly less oversimplified, the nascent theory, as I understand it, is that space might just be a form of matter we haven't figured out yet, and that the premises all of us use might be wrong, since they don't seem to be giving us very good results. They become defenses of themselves in circular logic that can start arguments but can't end them.

 

We certainly haven't done very well in figuring out dark matter. But at least there we seem to know there's something wrong with our thinking, something we're missing.

 

I probably shouldn't suggest that here, since if people start agreeing with it, they might stop saying they know what space is, and Hypography would go out of business. But I kind of doubt that's going to happen.

 

I personally like the as yet unnamed theory because it is humble. It doesn't make claims it can't support, because it avoids making many claims at all. Maybe it could be called the No-Name Theory, or the No-Theory Theory, since it suggests we need to look for a new premise.

 

I have a feeling I've misrepresented their theory. I hope I haven't embarrassed them so thoroughly that they will now avoid associating themselves with the theory or with me. We'll see.

 

--lemit

 

Right on dude, stir that pot! We are smart...but not that smart. A glance a little closer to home bears this out. Thank you, Plumber

[Michael Mooney]

Hey lemit,

Please answer my questions to you in post 38 above.

Thanks.

Michael

[johngetup]

Ok this is a very difficult question to answer. The fact of the matter is until we understand more about spatial dimensions (without even including space time) this question will continue to cause a conflict between scientists. Lets take a look why.

 

The Universe we exist in (as to our own perception) is the 3 dimensional Universe, and coupled with the theory of the Big Bang is finite. It started at a single point in space, and expands form this position...or does it?

From measurements of the speed in which the Galaxies are moving away from one another, we find that each is accelerating and thus we live in and accelerating Universe. Now, imagine our own Galaxy has formed at the point in which the Big Bang took place, then this measurement causes great confusion when thinking in the 3rd dimensional world. If you imagine for the time being that the Milk Way is stationary, and looking through a telescope we see two more Galaxies in line with each other which we will call A and B; A being the closest and B the furthest away; then this model of the Universe would suggest that B was moving faster away from us than A. As Galaxy A travels, let’s say, at the speed of 10mph away from us, Galaxy B is travelling 10mph away from A. Then to our perception B would be moving 20 mph from us. If we added 1000 more Galaxies in this scenario, imagine how fast the one at the end of the line must be travelling...basically 10 to the power of 1000. This is impossible, so where have we gone wrong. How can Galaxies be moving at equal speeds away from one another?

 

The answer must therefore be that the space between the Galaxies is expanding. But how can this be the case as the laws of a 3 dimensional Universe negate such a conclusion (If two cars are racing each other then the one in front must be travelling faster than the one in second place). Referring back to the expanding balloon mentioned by 'EWright' above, if the ant was stationary then it would perceive other stationary ants on the same balloon expanding away from him at an equal rate. The 2 dimensional space is expanding, while the ants remain still. This seems to be a good explanation, but while the balloon is 2 dimensional the ants remain 3rd dimension, just like the matter (information) of our Universe, therefore such a conclusion cannot apply in the 3 dimensional world.

 

Now this is where it begins to get really tricky. As we exist in 3 dimensional space, we are aware of the 1st and 2ed dimensions, although we cant truly see them we can imagine them. However the Universe is 3 dimensional, therefore for such a theory to be true, we must except the possibility of dimensions beyond are own perception. That is to say, we need to add a 4th spatial dimension (other than time).

 

A being living in the 4th dimension might perceive the 3 dimensional universe as we do the balloon in the 2end. Of course we could never perceive this 4th dimension, just like a person in the 2end dimension could not perceive our 3rd. Are you still following me? (I suggest you read a book called 'Flatland' by Edwin Abbott Abbott for a more comprehensive description of this scenario). Now, as the balloon is a good representation of an expanding Universe, we are still perceiving this expanse in the 3rd dimension...the balloon gets bigger. Therefore this can not be translated directly into our Universe as information has height, width and breath. The space is expanding, but not the way we perceive the balloon to expand.

 

Think about the ant again, if he walked around the balloon (his 2 dimensional space) he will not find an edge, but instead will eventually end up back where he began. His Universe is then infinite to him, but has clear set boundaries to us in the 3rd dimension. As the space in our Universe expands, as is the case with the balloon, there is no set point in which it is expanding from. Therefore if we flew in a straight line faster than this expansion, we will end up back where we started.

To our perception we would have travelled in a straight line, however to a being on the 4th dimensional plane, we walked round in a circle following the bend of space.

 

Hence forth, our Universe become infinite to us, but finite to the 4th dimension.

 

This is a very hard concept to grasp, but believe it or not evidence 'suggests' that this is most certainly possible. So to answer your question, the 3rd dimension is both finite and infinite according to perception (I told you it was not going to be an easy answer).

 

 

In fact it has been suggested with mathematical evidence, that there could be anything between 11 to 32 spatial dimensions....and even more. Again you must understand that this explanation only takes into account Einstein laws of Relativity, and does not include the laws of Quantum Mechanics. The theory of Relativity explains the world of bodies (Spatial Bodies such as stars), but is not applicable at our present understanding with Quantum Mechanics. Like wise Quantum Mechanics explains the subatomic world (Atoms and smaller), but to our understanding is not applicable with Relativity.

 

If you would like me to go deeper into the subject, or any questions you may have I will be happy to answer to the best of my ability. Thanks for reading.

 

John

[modest]

Hello, John. Welcome to Hypography.

 

I would disagree slightly with some of your reasoning and conclusions, but I think you are very much on the right track.

 

The Universe we exist in (as to our own perception) is the 3 dimensional Universe, and coupled with the theory of the Big Bang is finite.

 

Big Bang cosmology has three possible geometries of space: spherical, flat, and hyperbolic. The geometry is determined by density and determines the topology which is open in the case of flat and hyperbolic, and closed in the case of spherical:

 

 

The density of the universe also determines its geometry. If the density of the universe exceeds the critical density, then the geometry of space is closed and positively curved like the surface of a sphere. This implies that initially parallel photon paths converge slowly, eventually cross, and return back to their starting point (if the universe lasts long enough). If the density of the universe is less than the critical density, then the geometry of space is open, negatively curved like the surface of a saddle. If the density of the universe exactly equals the critical density, then the geometry of the universe is flat like a sheet of paper. Thus, there is a direct link between the geometry of the universe and its fate.

 

The simplest version of the inflationary theory, an extension of the Big Bang theory, predicts that the density of the universe is very close to the critical density, and that the geometry of the universe is flat, like a sheet of paper. That is the result confirmed by the WMAP science.

WMAP- Shape of the Universe

 

Big bang does not, then, necessitate that space be finite. If the density of matter and energy is low then the typology is open and space is infinite.

 

It started at a single point in space, and expands form this position...or does it?

From measurements of the speed in which the Galaxies are moving away from one another, we find that each is accelerating and thus we live in and accelerating Universe.

 

I agree, though I would word it a bit differently and say that expansion is currently accelerating. There's also no way to look at a galaxy and tell if it is accelerating away from us or if it has a steady velocity. To determine that the rate of expansion is recently (last couple billion years) accelerating requires supernovae standard candles and a model capable of interpreting redshift vs. brightness data.

 

If you imagine for the time being that the Milk Way is stationary, and looking through a telescope we see two more Galaxies in line with each other which we will call A and B; A being the closest and B the furthest away; then this model of the Universe would suggest that B was moving faster away from us than A. As Galaxy A travels, let’s say, at the speed of 10mph away from us, Galaxy B is travelling 10mph away from A. Then to our perception B would be moving 20 mph from us.

 

I agree. This assumes that B is the same distance from A as A is from us. More importantly, it assumes that the distance you're talking about is the comoving distance. In special-relativistic coordinates the same would not be true which is why the comoving velocity of an observable galaxy can be greater than c while the special relativistic velocity cannot be. This explains in some detail:

Many Distances

 

If we added 1000 more Galaxies in this scenario, imagine how fast the one at the end of the line must be travelling...basically 10 to the power of 1000.

 

If all the 1,000 galaxies are each the same distance from the one next to it then the final velocity would not be 10 to the power of 1,000, but rather 10 times 1,000. But, regardless, I don't quite agree with your reasoning in the following:

 

This is impossible, so where have we gone wrong.

 

How can Galaxies be moving at equal speeds away from one another?

 

The answer must therefore be that the space between the Galaxies is expanding...

 

I see what you are saying: that the further away something is the faster it is going away from us. As those distances get arbitrarily large so too must the velocity get arbitrarily large. But, that would be impossible because things can't go faster than the speed of light.

 

It is, however, necessary to note that things cannot go faster than the speed of light *in special relativity*. But, in special relativity velocities are not added such that AB = 10 and BC = 10 therefore AC = 20. Velocities should rather be added according to:

[math]w = \frac{u+v}{1+uv/c^2}[/math]

where

AB = u

BC = v

AC = w

It's explained in detail here: Relativistic Velocities

I, therefore, would not agree with your method of concluding that space must be expanding. It's more appropriate to say that space is expanding in the Robertson Walker metric which big bang cosmology uses to model the evolution of the universe according to the Friedmann equation. In that metric velocities can be greater than c, but as it defines simultaneity differently than special relativity there is no problem with arbitrarily large velocities.

 

Essentially: expanding space versus things moving through space ends up being a coordinate choice. This is supported here:

Are galaxies really moving away from us or is space just expanding?

 

This depends on how you measure things, or your choice of coordinates. In one view, the spatial positions of galaxies are changing, and this causes the redshift. In another view, the galaxies are at fixed coordinates, but the distance between fixed points increases with time, and this causes the redshift. General relativity explains how to transform from one view to the other, and the observable effects like the redshift are the same in both views. Part 3 of the tutorial shows space-time diagrams for the Universe drawn in both ways.

Frequently Asked Questions in Cosmology

and explained in more depth here: What Causes the Hubble Redshift?

 

But how can this be the case as the laws of a 3 dimensional Universe negate such a conclusion (If two cars are racing each other then the one in front must be travelling faster than the one in second place). Referring back to the expanding balloon mentioned by 'EWright' above, if the ant was stationary then it would perceive other stationary ants on the same balloon expanding away from him at an equal rate. The 2 dimensional space is expanding, while the ants remain still. This seems to be a good explanation, but while the balloon is 2 dimensional the ants remain 3rd dimension, just like the matter (information) of our Universe, therefore such a conclusion cannot apply in the 3 dimensional world.

 

The link I gave on special relativistic velocity addition will explain the race car thing. The balloon example is best understood with 2-dimensional beings while the third dimension is either non-existent or unobservable. A better analogy, I think, since we're talking about infinite space is to imagine an infinitely large rubber sheet with dots on it. The distance between any two dots increases with time.

 

Think about the ant again, if he walked around the balloon (his 2 dimensional space) he will not find an edge, but instead will eventually end up back where he began. His Universe is then infinite to him, but has clear set boundaries to us in the 3rd dimension.

 

The balloon is an example of spherical geometry. If the density in our universe were greater than [math]\Omega = 1[/math] (and the cosmological constant were zero) then the geometry would be spherical and the universe would be closed like the balloon. Assuming expansion were not too great we could shine a laser in any direction and it would eventually hit the back of our head—like you say. I would disagree with your use of the word infinite however. A closed universe is said to be "spatially finite and unbound". That is to say: there's only so much space, but you can move around without ever bumping into a boundary.

 

As the space in our Universe expands, as is the case with the balloon, there is no set point in which it is expanding from. Therefore if we flew in a straight line faster than this expansion, we will end up back where we started.

 

The current standard cosmological model which fits best with astronomical evidence (ΛCDM) says that the universe is flat or nearly flat. In that case space is infinite and unbound. Shine a laser and it will continue forever never coming back around to hit you in the back of the head.

 

Hence forth, our Universe become infinite to us, but finite to the 4th dimension... So to answer your question, the 3rd dimension is both finite and infinite according to perception....

 

I think it would avoid confusion to call a universe with three spatial dimensions, closed topology, and extrinsic curvature into a 4th unseen spatial dimension:

"spatially finite in both 3 and 4 dimensions"

and

"unbound in the third dimension but bound in the fourth"

 

 

You certainly do hit the correct topics, so don't think I'm entirely disagreeing with you :)

 

"Be glad of life, because it gives you the chance to love and to work and to play and to look up at the stars." ~Henry Van Dyke

 

~modest

[johngetup]

Thanks very much for that, i will look into all you suggest and look forward to discussing that matter further with you. Thank you once again :)

 

John

[Little Bang]

Whether or not the Universe is finite is dependent on you view. If there was a BB then the Universe is finite because if there was a beginning to the Universe then it must have a boundary. If it is static then infinite.

[HydrogenBond]

If you travel at the speed of light, infinite distance will appear to contracted to a point according to SR. Or at the speed of light C, the math says an infinite universe could be seen as contained within your point (of view). Although matter does not have this reference, the energy within our finite universe has a reference all the way to infinity.

 

But this creates a paradox. If at C, infinity looks like a point, which is the smallest unit of size, what does the finite universe, look like at C? Since the visible universe is smaller than infinity (subset) this finite universe would look smaller than a point at C, which is a contradiction in terms. What is 10% of a point, if the point is already the smallest by definition? Does that mean energy can only see as far as the outer edge of the finite universe, so the finite universe does not look like a fraction of a point, which can not exist by definition. Does finite wavelength and frequency create an overall C speed composite, that has C speed nearsightedness, to avoid the fractional point paradox?

 

Does this means that infinity is not allowed or else photons moving at C could not see anything smaller than infinity (point), and could never find targets such as atoms, since they would be smaller than the point seen?

[Dyothelite]

I should have searched all the pages of this thread before I posted this but have we discussed Big Bounce Theory yet? An infinite amount of Big Bang cycles?

[snoopdogg]

These questions may never be answered with any absolute precision but the standard model views our local universe as a finite sphere. Nevertheless, our local universe may be contained within a larger megauniverse which may be infinite in nature. Hopefully this defination does not confuse things for you.

 

If the universe were to be infinite, than every aspect of it would also be infinite. We would have had this discoussion an infinite amount of times. We know from simple observation that this is not the case. An object must be defined by X,Y, or Z, with absolute physical boundaries. We can also look inside ourselves for the answer. For we know that our own experiance in this existance is unique and singular.

[johngetup]

If the universe were to be infinite, than every aspect of it would also be infinite. We would have had this discoussion an infinite amount of times. We know from simple observation that this is not the case. An object must be defined by X,Y, or Z, with absolute physical boundaries. We can also look inside ourselves for the answer. For we know that our own experiance in this existance is unique and singular.

 

Are you so sure about this? If we think of the Universe in Relative terms, then you may be correct in saying such a statement. But then we know that the Relative Universe and our observations of it do not correspond with the Quantum Universe and are observations of that. In other words, what we can see with the eye, our personal self experience is not all there is. In the atomic world particles have boundaries but can dismiss them, disappear and reaper somewhere else, move and change direction without any foreseeable force. Tests have even shown that a single particle can exist in two or more places at the same time, maybe even and infinite amount of places at the same time, corresponding to the 'probability wave'. For this reason we never know where a particle will exist at any given time, and so we have to guess. We have to guess the probability that a single particle will be at a certain point at a certain time...but never a fixed point in space time.

For this reason, it is completely possible that there are an infinite amount of everything, every atom and every choice. In this 'Parallel' model of the Universe we have had this conversation an infinite amount of times, and ones infinitely different. We don't perceive it though because we are made up of clumps of atoms, and so therefore observer the laws of physics that governs this... Relativity.

This is far from a proven theory, but all evidence gathered so far suggests it may well be true. Either way we cant pass over it as nonsense until it is proven one way or the other.

But the facts are, particles do not obey the laws of the observable universe (that being what we experience and see with the naked eye)

[modest]

If the universe were to be infinite, than every aspect of it would also be infinite.

 

If the universe were infinite in every aspect then every aspect of the universe would be infinite. But, if the universe is spatially infinite (i.e. it has infinite volume) that would not necessitate that other aspects of the universe be infinite. For example, a Friedmann universe with a density parameter [math]\Omega \leq 1[/math] is spatially infinite, but the large-scale average density anywhere you look in that infinite space is the same. Like density, not every aspect of an open (and thus infinitely-sized) Friedmann universe need be infinite.

 

We would have had this discoussion an infinite amount of times. We know from simple observation that this is not the case. An object must be defined by X,Y, or Z, with absolute physical boundaries. We can also look inside ourselves for the answer. For we know that our own experiance in this existance is unique and singular.

 

This thread is about the universe being infinite or finite in size. The universe being infinite in size has no correlation to a person recollecting an infinite number of the same conversations. Even if the universe were infinitely old it would not necessitate that a person recollect an infinite number of past events.

 

~modest

[snoopdogg]

Yes the two slit experiment and thus quantum theory is born. We were not talking about position or momentum. We are talking about boundaries and time. I'm sure that you have heard of the P-Brain theories and multi-universes. Let’s think about this. Time and space are the same thing called Space-Time. This is a consequence of our universe. Now if there are other universes that would imply that one came before or after another, this in tern would imply that time is separate from our space and that time is absolutely constant regardless of what existence we are dealing with. Yet we know from the theories of relativity and quantum that time is actually Space-Time. The whole problem with understanding infinite and finite properties is understanding time, and it is time itself that no scientist or theory can explain. For we can only perceive time on a macro level. Let’s think about the electron existing in multiple places at once (its wave properties). Does this really happen or can we think of it in terms of Space-Time moving while the particle stays in just one place. If this is the case yes everything is finite with indeterminate properties. If Space-Time does not move than everything is infinite with determinate properties. Backtracking, the latter would imply that Time is separate and is an attribute to existence itself. Are there infinite you's and me's? NO. This does not pass the feel good test. Simplicity is the key to finding these answers. It is our complex minds that try to hard to complicate science and theories. Existence can only be one way, this way, otherwise nothingness would have prevailed.