Exploring the Mystery of Space

[tolove]

edit: Messed up the title! Although, I suppose it's related.
edit: What is space?

Context for this question: I am starting my junior year in physics, so not all that bright on the subject.

In short, what is space? Maybe if someone tries to answer this question I'll get a bit of understanding:

Imagine a universe where there exists nothing but two large masses. Each mass is given a massive velocity 180 degrees apart, far exceeding any gravitational pull back toward each other.

As time approaches infinity, what exists at the initial point where the two masses were located?

 

[mfb]

what exists at the initial point where the two masses were located?

Vacuum.

What is space?

A framework in our description of the universe.

 

[BruceW]

In general relativity, space (or, really space-time) is not just the backdrop which stuff happens in. Space-time can have curvature. Mass and energy are a source for this curvature, and Newtonian gravity is the limiting case, when there is only a very slight curvature (i.e. Newtonian gravity is only correct when the gravity is weak enough, so it doesn't work for black holes, e.t.c.)

Also, space-time can have non-trivial curvature even when there is no matter around. So space-time is not just 'a place for matter to exist in'. I keep saying space-time, because in general relativity, time is put on equal footing as space, so there are simply 4 'coordinates'.

What I find pretty hilarious is that we don't even know if the universe is closed, or open or flat. A closed universe corresponds to the 'surface of a balloon analogy', where the entire universe has a finite size, but no boundary. The flat universe corresponds to an infinite universe which has no overall curvature, but has curvature 'fluctuations' (for example, a galaxy causes a fluctuation in curvature). Lastly, the open universe is one where there is negative curvature (as opposed to positive curvature in the closed universe), and the geometry is hyperbolic.

I'm not totally sure what your question means. Is your question "do the masses come back to the same place?"

 

[HomogenousCow]

Gravity is the aspect of nature which breaks certain symmetries, for example we don't just fall in any direction but rather towards the center of the earth. Our model for it will change over time as we refine our understanding of nature, so whether it is a force or space time "curvature" just depends on which model you are using right now.

 

[tolove]

Vacuum.

And to BruceW,

Does space exists without matter? If matter and space are attached to each other somehow (like everything else seems to be), then what happens when two masses are shot apart? Is there ever a section of 'no space' between them?

The whole concept confuses me!

 

[mfb]

Is there ever a section of 'no space' between them?

Not in current physics.
Matter bends space(time) - without matter, you just have unbent space(time).

 

[tolove]

Not in current physics.
Matter bends space(time) - without matter, you just have unbent space(time).

Is this what is meant by an open model of the universe? Space and time exist in all directions toward infinity? Your use of the word 'framework' makes sense in this context.

If so, then under a closed model, would space be different at that initial point?

What's the terminology for these subjects? I don't want to bother you with too many questions when I'm sure there a wiki page I could read through.

 

[soothsayer]

What I find pretty hilarious is that we don't even know if the universe is closed, or open or flat.

We know it's pretty darn flat.

We can't know if it is exactly flat or just absurdly close to it one way or another, even with our excellent measurements up to this point, But our "local" universe: everything we'll ever be able to see, is definitely flat for all intents and purposes.

 

[soothsayer]

Is this what is meant by an open model of the universe? Space and time exist in all directions toward infinity? Your use of the word 'framework' makes sense in this context.

If so, then under a closed model, would space be different at that initial point?

An open universe means that space and time exist in all directions infinitely and are expanding ever faster forever.

A closed universe is not finite in a four-dimensional sense: You can start at one point, and never reach the "edge" of the universe, but you will loop back around the same point over and over if you travel far enough; imagine traveling on the surface of the Earth...This universe will eventually stop expanding and collapse back on itself, without dark energy, that is. Nothing would be different at the "initial point", since the degree to which a universe is "open" or "closed" is a global quality, and not a local property--nothing distinguishable can really be said about anyone localized point in space.

You can also have a flat universe: one that is perfectly balanced between open and closed, so that it expands forever, but at an ever slower rate, such that at infinity, the universe will be in a completely steady state, although it would never actually reach it. Interestingly enough, our own universe would appear to be completely flat, but there is the presence of dark matter, which acts as an anti gravity force on long, long distance scales, which pulls the universe apart. There are differences between an open universe and a flat universe with dark matter that I could explain, if you were interested.

What's the terminology for these subjects? I don't want to bother you with too many questions when I'm sure there a wiki page I could read through.

This is all really under the subject of Cosmology. You can wikipedia that and find a wealth of related information.

Have fun!

Soothsayer

 

[BruceW]

We know it's pretty darn flat.

We can't know if it is exactly flat or just absurdly close to it one way or another, even with our excellent measurements up to this point, But our "local" universe: everything we'll ever be able to see, is definitely flat for all intents and purposes.

I think this is a misconception that is propagated by proponents of the inflationary theories. For inflationary theories to give a good description of our universe, they require that the universe is pretty darn flat. The current 'standard cosmological model' is that the universe is pretty darn flat, and inflation happened. I guess that's because this is judged to be the simplest working model. (But there are other models).

But this doesn't mean that the universe is pretty darn flat. In fact, according to Jerzy Plebanski and Andrzej Krasinski, in their book "An introduction to general relativity and cosmology", they say "Current real knowledge gives no grounds to assume that $\rho_0$ is greater than $0.3 \rho_{crit}$" (where rho_0 is observed density and rho_crit is the density at which the universe is flat).

But then the supernovae observations imply that dark energy can account for over 1/2 of the total density of the universe (which will bring up the total density to something greater than $0.3 \rho_{crit}$). Of course, this doesn't mean that the observed density is even close to $\rho_{crit}$. As far as I know, a flat universe has not been ruled out. But also, as far as I know, they have not measured the total density of the universe to be even close to the critical density.

Maybe they have measured the density of the universe with greater accuracy than I thought. I have not read any recent journals. Only textbooks which are half a decade old. Do you know much about this? I might do a google search...

 

[BruceW]

Not in current physics.
Matter bends space(time) - without matter, you just have unbent space(time).

I thought that in a universe without matter, there is still 'non-trivial' solutions. And that the maximally symmetric solution is a 'de Sitter universe'

 

[mfb]

There are more solutions, but I don't see any reasons why this space should have any significant deviation from the trivial solution.

 

[WannabeNewton]

I think there's a wording misunderstanding here. Bruce you are correct that a region of space time can have curvature even if there is no local mass energy distribution (vacuum) given there is mass energy somewhere else. This curvature is codified by the Weyl curvature tensor. The most familiar example is of course the Schwarzschild solution. I think mfb was talking about no mass energy anywhere in space time.

 

[soothsayer]

But this doesn't mean that the universe is pretty darn flat. In fact, according to Jerzy Plebanski and Andrzej Krasinski, in their book "An introduction to general relativity and cosmology", they say "Current real knowledge gives no grounds to assume that $\rho_0$ is greater than $0.3 \rho_{crit}$" (where rho_0 is observed density and rho_crit is the density at which the universe is flat).

Really? I've had several Cosmologists tell me that verified observational evidence has put Ω at 1 to within a surprisingly small experimental error.

 

[BruceW]

Really? I've had several Cosmologists tell me that verified observational evidence has put Ω at 1 to within a surprisingly small experimental error.

I think that is only true if we assume inflation. I might be wrong.

 

[BruceW]

I think there's a wording misunderstanding here. Bruce you are correct that a region of space time can have curvature even if there is no local mass energy distribution (vacuum) given there is mass energy somewhere else. This curvature is codified by the Weyl curvature tensor. The most familiar example is of course the Schwarzschild solution. I think mfb was talking about no mass energy anywhere in space time.

Yeah, I mean the same as mfb. That there is no matter anywhere. So then there is only dark energy. And the maximally symmetric solution (of a universe with no matter anywhere) is a 'de Sitter universe'. Is this right? I don't know much about GR and cosmology. Always learning though :)

 

[WannabeNewton]

Yeah, I mean the same as mfb. That there is no matter anywhere. So then there is only dark energy. And the maximally symmetric solution (of a universe with no matter anywhere) is a 'de Sitter universe'. Is this right?

yeah, see paragraph 2: http://en.wikipedia.org/wiki/De_Sitter_space

Or see problem 3 of chapter 5 in Wald (in particular part b), if you have access. It would be more exciting than reading a wiki article haha.

 

[petm1]

What is space, like the question what is time, can no longer be answered one without the other. Myself I have been wondering what part of time is space, other than the present we all share.

 

[soothsayer]

I think that is only true if we assume inflation. I might be wrong.

I'm pretty sure you're wrong about that. I don't see anything having to do with Inflationary assumptions factoring into the observational methods that astronomers are using to determine Ω. WMAP uses CMB anisotropies to determine the geometry of the universe based on the FLRW model alone, and the results are within 0.4% of flat.

http://arxiv.org/pdf/astroph/0302209.pdf

 

[soothsayer]

Also, Bruce, remember that the main reason Inflation was theorized in the first place was to explain why it was that the universe seemed to be so flat. It wasn't a "I believe Inflation is correct, so the universe MUST be flat" sort of thing, it was a "The universe is so flat that we need some sort of theory that can explain why", and that's how Inflation was born.

http://en.wikipedia.org/wiki/Flatness_problem

 

[Dale]

Does space exists without matter? If matter and space are attached to each other somehow (like everything else seems to be), then what happens when two masses are shot apart? Is there ever a section of 'no space' between them?

In order to identify if a question is scientifically meaningful, the best thing to do is to consider how one could devise an experiment to answer it. For example, how could you test for the amount of 'no space' between two masses separated by 1 m of space? And how could you test for the existence of space without matter?

 

[narf0708]

Seems like this topic is very similar to what was discussed in the 2013 Isaac Asimov debate.

Long, but well worth the watch.

 

[BruceW]

I'm pretty sure you're wrong about that. I don't see anything having to do with Inflationary assumptions factoring into the observational methods that astronomers are using to determine Ω. WMAP uses CMB anisotropies to determine the geometry of the universe based on the FLRW model alone, and the results are within 0.4% of flat.

http://arxiv.org/pdf/astroph/0302209.pdf

The CMB anisotropies are assumed to be a remnant from the "quantum fluctuations in the inflaton field that caused the inflation event" (I am shamefully quoting wikipedia http://en.wikipedia.org/wiki/Cosmic_microwave_background_radiation) So we must make assumptions about inflation, so that measurements of the CMB tell us more things about the universe. Take the extreme example, suppose inflation did not happen, then we don't even have an explanation for the CMB. (And then the CMB would just be some mysterious radiation that we observe coming from the sky).

On the other hand, other measurements are in agreement with the predictions of inflationary theory. For example the paper you linked to mentioned how their value for the Hubble parameter was in agreement with the value measured by the Hubble key project. So I can understand why the concept of inflation has become part of the 'standard model' of cosmology.

Also, Bruce, remember that the main reason Inflation was theorized in the first place was to explain why it was that the universe seemed to be so flat. It wasn't a "I believe Inflation is correct, so the universe MUST be flat" sort of thing, it was a "The universe is so flat that we need some sort of theory that can explain why", and that's how Inflation was born.

The Robertson-Walker equations have the Gaussian curvature as a parameter (often called k). This is what people referred to as the 'flatness problem'. Not because the universe is flat, but because we have this parameter k, and we don't know what it is, and of course, we would prefer to have less free parameters in a physical theory, if possible. Now, inflationary theory requires k=0 (or very close to zero, I am not sure, I don't know enough about it). So they see this as a 'solution' of the problem of what to choose for k. But of course, they are also introducing free parameters, in the details of how inflation happened. So they have not really got rid of the problem, they have just moved it somewhere else.

P.S. I don't mean to sound hostile. I am pretty new to this cosmology stuff, so I am just trying to understand it all, by having a lively debate :)

 

[mfb]

Take the extreme example, suppose inflation did not happen, then we don't even have an explanation for the CMB. (And then the CMB would just be some mysterious radiation that we observe coming from the sky).

The CMB would still be there, but it would come from areas without causal connection, so you would expect different fluctuations (no two-point correlation without causation, in particular).

 

[soothsayer]

Thanks for handling that first point, mfb. the CMB comes from the Big Bang, not Inflation. As mfb pointed out, all that would be different is that we wouldn't expect thermal equilibrium within the CMB from a pure Big Bang model, which is a moot point, because the CMB is clearly in equilibrium whether or not inflation took place.

Also, let's take a look at another method used to measure Ω: standard candles. Astronomers have collected data on type 1a supernovas at many different z values, corresponding to varying points in the universe's history. Since we know that all type 1a supernovas have an essentially identical brightness. We can use the apparent magnitude and redshift to determine the expansion of space between us and the supernova throughout history, and these results are in perfect agreement with measurements from WMAP and Sloan Sky Survey results on the CMB, that the universe has been at critical density from the very beginning. I think you'll agree that this standard candle method cannot be influenced by Inflantion, since the inflationary period happened LONG before any type 1a supernovas could possibly have taken place. So what we can say with absolute certainty is that the curvature of space has not changed since recombination, when the CMB formed, nor since the epoch at which type 1a supernovas began. These happened after inflation, and thus, regardless of whether Inflation truly did happen, the universe was very closely flat from very early on.

I still think, Bruce, that you have the flatness problem wrong. By the 1970's, scientists had realized that at the Big Bang, had Ω been minutely greater than or less than 1, that small amount of curvature would have blown up extremely quickly, much faster than 13.5 billion years. In the case of very slightly above 1, the universe would have quickly recollapsed due to closed curvature. Remember that open and close curvatures change throughout time. Ω>1 grows very rapidly to infinite, and Ω < 1 goes very quickly to zero. Even in the 70's, when we hadn't figured out the cosmological constant, the density of matter as a fraction of critical density was directly observed to be 0.3. Had that really been the whole universe, and had the rest been negative curvature, it would STILL be incompatible with a universe that was even slightly open at the big bang, because 13.5 billion years later, matter density would have essentially become negligible. With the discovery of dark matter, the problem was exacerbated. This is the flatness problem.

And don't worry about sounding hostile, I love good, lively debate about cosmology!

 

[BruceW]

my point about the CMB is that it only gives us a measurement of the current density of the universe if we assume an inflationary model. Without an inflationary model, it does not give us a value for the current density of the universe, right? The other (non-CMB) measurements, like the 'standard candles', don't require an inflationary model. I have started reading a bit of Alan Guth's 'pioneering' paper "Inflationary universe: A possible solution to the horizon and flatness problems". Where he has some good references to some books that I'm going to try to get from library. I get the impression from what he was saying, was that the 'standard candles', e.t.c. give the current density of the universe to be somewhere between 0.01 and 10, while the CMB observations give the density to be within 0.01 of 1. (i.e. 0.99 to 1.01). I suppose that some of the discussion depends on whether you would say these are 'pretty flat' values or not. I definitely will be looking for more information on the (non-CMB) measurements of the density.

Also, yeah, I understand what you mean about the value of the density (omega), and how (after inflation), it is going to diverge from 1. So even if it is now between 0.1 and 10, then a long time ago, it must have been a lot closer to 1. But is this definitely true in a universe with dark energy? The equation is:
$$( \Omega^{-1} - 1) ( \rho + \frac{\Lambda c^2}{8 \pi G} ) a^2 = \frac{-3kc^2}{8 \pi G}$$
I understand that if Lambda was not in there, then since 'rho' decreases faster than 'a^2' increases, this means that Omega diverges from 1. I suppose that the universe was mostly radiation and matter dominated, so it is a good approximation to forget about the affect of Lambda in the past. It is only in the present era and beyond that Lambda will become important.

So Omega was very close to 1. This doesn't really mean that the universe was very flat. Curvature and density are two different things. Curvature is constant at all times. But density does change with time. Maybe this is where I have misinterpreted the 'flatness problem'. Am I now right in thinking the flatness problem is that a long time ago, the density of the universe must have been close to the critical density? And so the inflationary model explains this because it caused the density to be very close to critical density? Hopefully I have got it right now, thanks to your help soothsayer (and some wikipedia searching). I personally still feel it is not a very good explanation - we have removed one kind of 'fine-tuning', and replaced it with another 'fine-tuning', which we must do to make the inflaton field have the exact properties required such that it causes the density of the universe to become very close to the critical density. Although, I suppose since inflationary theory helps to explain other things, maybe we are reducing the total number of 'fine-tuned' parameters :)

 

[soothsayer]

my point about the CMB is that it only gives us a measurement of the current density of the universe if we assume an inflationary model. Without an inflationary model, it does not give us a value for the current density of the universe, right? The other (non-CMB) measurements, like the 'standard candles', don't require an inflationary model.

I still think that the CMB measurements hold even if you don't assume an inflationary model. I haven't been able to find anything that explicitly states that, but what I know about CMB anisotropy measurements, I don't see where inflation is involved a priori.

http://www.ams.org/notices/199811/cornish.pdf

This is an interesting article which explains the process of determining the geometry of the universe, especially when it comes to measuring the CMB. The numbers and theories are a bit outdated (this paper still thinks the universe is matter dominated, and calls the Cosmological constant domination implication of standard candle experiments "inconsistent", which I found hilarious). However, the observational techniques remain the same.

I have started reading a bit of Alan Guth's 'pioneering' paper "Inflationary universe: A possible solution to the horizon and flatness problems". Where he has some good references to some books that I'm going to try to get from library. I get the impression from what he was saying, was that the 'standard candles', e.t.c. give the current density of the universe to be somewhere between 0.01 and 10, while the CMB observations give the density to be within 0.01 of 1. (i.e. 0.99 to 1.01). I suppose that some of the discussion depends on whether you would say these are 'pretty flat' values or not. I definitely will be looking for more information on the (non-CMB) measurements of the density.

Remember that standard candle measurements have improved significantly since that paper was written. Unfortunately, I'm having trouble finding actual recent data from those observations up to this point, but I know they are pointing increasing toward zero curvature.

Also, yeah, I understand what you mean about the value of the density (omega), and how (after inflation), it is going to diverge from 1. So even if it is now between 0.1 and 10, then a long time ago, it must have been a lot closer to 1. But is this definitely true in a universe with dark energy? The equation is:
$$( \Omega^{-1} - 1) ( \rho + \frac{\Lambda c^2}{8 \pi G} ) a^2 = \frac{-3kc^2}{8 \pi G}$$
I understand that if Lambda was not in there, then since 'rho' decreases faster than 'a^2' increases, this means that Omega diverges from 1. I suppose that the universe was mostly radiation and matter dominated, so it is a good approximation to forget about the affect of Lambda in the past. It is only in the present era and beyond that Lambda will become important.

Very true, dark energy will actually push a universe flat. It is the same process by which inflation is supposed to have caused the initial flatness. However, the universe has only been dark energy dominated for a very short amount of time, so we can safely assume it has done little to affect the curvature of the universe up to this point. I remember a homework problem I once did that asked me to determine the necessary value of $\Lambda$ in order to prevent a closed universe from collapsing, and an open universe from exploding, and it was...a lot.

So Omega was very close to 1. This doesn't really mean that the universe was very flat. Curvature and density are two different things. Curvature is constant at all times. But density does change with time. Maybe this is where I have misinterpreted the 'flatness problem'. Am I now right in thinking the flatness problem is that a long time ago, the density of the universe must have been close to the critical density? And so the inflationary model explains this because it caused the density to be very close to critical density? Hopefully I have got it right now, thanks to your help soothsayer (and some wikipedia searching). I personally still feel it is not a very good explanation - we have removed one kind of 'fine-tuning', and replaced it with another 'fine-tuning', which we must do to make the inflaton field have the exact properties required such that it causes the density of the universe to become very close to the critical density. Although, I suppose since inflationary theory helps to explain other things, maybe we are reducing the total number of 'fine-tuned' parameters :)

Yes, that's essentially the flatness problem! And of course, Inflation is not a universally accepted theory, and I'm not saying you should believe it (though I personally like it, for the most part). I think you bring up a good point about the fine tuning condition. There are also those who use the Anthropological principle to solve the flatness problem, i.e: we must be in either one of many universes that just happens to be flat in order for us to exist, or we must be living in one local of an infinite universe that has flat curvature, in order to exist. I like these theories as well.

If you ever come across any more interesting information on the topic, or something to support of refute some of the claims I've made, please bring them to my attention!

 

[soothsayer]

Also, do realize that the "fine-tuning" condition required by inflation is not really that "fine", especially compared to the fine tuning condition required by the density of the universe. The inflation field doesn't need to be a super precise thing, it only needs to be just strong enough, and have a negative energy density.

There is so much fine tuning in our universe already, that the only way I see to explain it all from an anthropological perspective in the first place is that we are living in just one of countless many universes with different physical parameters, or there is a God. Since science can probe neither of those theories yet, I see no reason to fuss about it.

 

[BruceW]

yeah, there is a lot of fine-tuning going on in physics anyway. I am definitely of the opinion "we just don't have an answer for it yet", and I only agree with the weak form of the anthropological principle, which is to say that the universe must be capable of supporting intelligent life, because we are intelligent and alive in this universe (so this 'weak form' is pretty much a tautology). Anyway, thanks for your help, soothsayer. I am going to do some more reading on cosmology. I am still uneasy with the statement that the universe is 'flat, for all intents and purposes'. But I guess it is true in a lot of applications of cosmology.

 

[Light Bearer]

"Space has no objective existence whatsoever in the same way that ponderable matter does. By itself it is just a measurement of the distance or the separation between two physical objects, similar to the separation between two points in time. It is also a framework in which ponderable matter can "hang". It is also a void through which force carriers can propagate, but it is the characteristics of the force carriers which determine the way in which they behave and interact with ponderable matter. I believe that this is the most modern view and it replaces the older concepts of space being an aether with properties of its own."

 

[soothsayer]

"Space has no objective existence whatsoever in the same way that ponderable matter does.

In GR, it does.

It is also a void through which force carriers can propagate, but it is the characteristics of the force carriers which determine the way in which they behave and interact with ponderable matter. I believe that this is the most modern view and it replaces the older concepts of space being an aether with properties of its own."

You're talking about the idea of graviton fields replacing spacetime? Certainly a modern treatment of space and gravity, though we haven't found any gravitons, nor come up with one widely accepted theory yet.