'A Universe From Nothing' by Lawrence Krauss, AAI 2009

Skolon

Thank you again, but I already knew that.

My question was about that: to measure the flatness of Universe the mean density of Universe if measured and it is compared with critical density. If I understood correct, this is how we can tell today that the Universe is "very close to flat".
But, every popular article about this subject stop here. I look for article that discuss about the effective shape of Universe for the flat case.

Chalnoth

Quote by Skolon

Thank you again, but I already knew that.

My question was about that: to measure the flatness of Universe the mean density of Universe if measured and it is compared with critical density. If I understood correct, this is how we can tell today that the Universe is "very close to flat".

Well, sort of. The way that this measurement is actually done, though, is by drawing triangles. Two measurements for this are the cosmic microwave background and baryon acoustic oscillation measurements.

The "triangle" drawn from the CMB is composed of the typical distance between the "acoustic peaks" which is set by the age of the universe at the time the CMB was emitted. Comparing this distance to the angle that we see and the distance to the CMB gives us our triangle.

The "triangle" drawn from BAO measurements comes from the fact that these measurements are measuring a typical distance between galaxies in the more nearby universe, a distance that is correlated to the same distance seen in the CMB. We can thus draw a different triangle as the typical separation between galaxies compared to the distance to those galaxies and their angular separation.

By contrast, other measurements of the contents of the universe that don't end up effectively drawing triangles, such as supernovae to measure the expansion rate as a function of time, don't measure the curvature at all.

Schlofster

Quote by Chalnoth

Er, well, no. A torus is not closed in that sense. It's flat.

Closed is a statement about curvature. Whether or not the universe wraps back on itself is a statement about topology. It is perfectly possible to have a flat universe with a topology that wraps back on itself. Just as it is, in principle, possible to have a closed universe that doesn't extend far enough to wrap back on itself.

Hi Chalnoth,
Please can I ask you to elaborate on this, as I am struggling to conceptualize it?
To me the property of being closed (angles of a triangle add up to more than 180) implies that the topology will wrap back on itself.
Can you give some examples of shapes where this is not the case - closed, but does not wrap back on itself?
Also, I seem to remember Krauss talking about flatness implying that it is infinite in spatial extent (or am I just misunderstanding him again?) - doesn't "infinite in spatial extent" rule out a topology that wraps back on itself?

Yes, I still don't quite have a handle on all this ;-)

Thanks :-)

Chalnoth

Quote by Schlofster

Hi Chalnoth,
Please can I ask you to elaborate on this, as I am struggling to conceptualize it?
To me the property of being closed (angles of a triangle add up to more than 180) implies that the topology will wrap back on itself.

Well, there are a few different possibilities here:

1. What if the curvature changes before it wraps back on itself?
2. What if it spirals in or some such instead of neatly meeting itself?
3. What if it just ends before meeting itself?

I mean, sure, in the simplest case with absolutely constant curvature in all dimensions, we'd be talking about a sphere, which obviously wraps back on itself. But what if it isn't quite so simple?

Quote by Schlofster

Also, I seem to remember Krauss talking about flatness implying that it is infinite in spatial extent (or am I just misunderstanding him again?) - doesn't "infinite in spatial extent" rule out a topology that wraps back on itself?

I don't think he actually said that. If he did, he's wrong. But yes, if it so happened that our universe was infinite in spatial extent, then it clearly couldn't wrap back on itself.

GoldPheonix

I should state that I've met Krauss on several occasions and listened to several of his lectures and colloquiums; I do research under one of his previous colleagues (This isn't to say at all, however, that he remembers me). Krauss is an interesting fellow, to say the least.

Quote by Schlofster

I think that I might be starting to see a pattern emerge - it seems to me that the intellectual abilities that scientists like Krauss are so far beyond what ordinary humans are capable of, he cant even articulate them at all in a way is intelligible by the majority of humans on this planet.

Ordinary humans would understandably respond with incredulity, and since they pay his salary, I suggest that people like him should only make statements that are logically intelligible ordinary people.
I think that public lectures like this just serve to polarize the voting public, against science.

I am rather interested though in what the evolutionary consequences of this cavernous gap between the intelligentsia and the rest of the human population would be.
Is it possible that we eventually see a divergence in the species - this may also be accelerated if people are selected for establishing a human colony on another planet like Mars.
Presumably the criteria for selecting the people for this mission would be heavily biased in favour of intellect.

You should send him an e-mail... He'd probably actually respond to you if you phrased it that way.

Quote by Schlofster

what I said is that most of the mass of protons and neutrons can be attributed to virtual particles.. it is that mass that we can calculate using the theory of the strong interaction and powerful computers..

_______________________________
Lawrence M. Krauss
Foundation Professor
Director, Origins Initiative
Co-Director, Cosmology Initiative
ARIZONA STATE UNIVERSITY
College of Liberal Arts and Sciences
School of Earth and Space Exploration
http://krauss.faculty.asu.edu

On Nov 3, 2009, at 5:04 PM, Jessica Lee wrote:

------ Forwarded Message
Date: Wed, 28 Oct 2009 06:48:23 -0700
Subject: A Question For Prof Krauss.

Hi Jessica,
Please could I ask you to send this question on to Prof. Krauss?

Hi Prof Krauss,
I loved your recent public lecture <http://www.youtube.com/watch?v=7ImvlS8PLIo> at AAI 2009, but I don't understand something,

and I was hoping that you might be able to spare a few moments to clear it up for me.

First of all let me state that I am no physicist, so I am rather certain that my
misunderstanding is due to an incomplete grasp of the mathematical model that you
attempt to describe in natural language. I do understand that it is actually impossible to
do this since the mathematical model cannot be expressed in natural language.

In the lecture you say that you have calculated the mass of the universe, and have calculated that
most of the mass in the universe is as a result of virtual particles "popping in and out of existence" in empty space,
while matter particles constitute a very small fraction of the mass of the universe.
Considering this, and since you are able to calculate the mass of the universe to be a finite quantity,
it seems to me that a conclusion that the universe is infinite in spatial extent would be logically incompatible with a universe of finite mass.
I say this because if empty space itself constitutes most of the mass of the universe, then if the amount of empty space is infinite,
then the mass of the universe must also be infinite.

Thanks very much & kind regards,

------ End of Forwarded Message

Tell me how this goes. I'm interested to see what he replies with.

By-the-by, he's neither wrong nor right. We don't know if the universe's curvature is zero or not. We know that, right now, however, it is very small and close to zero (and possibly negative, if memory serves).

George Jones

Quote by Skolon

Yes, maybe a torus is mathematically flat shape but is a strange kind: a torus shape Universe is closed (going on any direction you will finally arrive at the same point) but for each direction other "diameter" of Universe exist. So, it seems like each direction have its own properties.
In our Universe all directions seem to have the same properties, at least until now. Or I don't know well?

Yes, this model is closed, and is different in different directions (anisotropic).

Quote by Chalnoth

Er, well, no. A torus is not closed in that sense. It's flat.

Closed is a statement about curvature. Whether or not the universe wraps back on itself is a statement about topology.

I don't think so. "Closed" is a statement about topology, not about curvature. A universe is closed iff its spatial sections are topologically compact. I think that this usage is standard. I cant think of how to use (the) curvature (tensor) to distinguish between "closed" and "open."

Quote by Chalnoth

Just as it is, in principle, possible to have a closed universe that doesn't extend far enough to wrap back on itself.

I'm not sure what this means.

Quote by Chalnoth

But in any case, it's still perfectly possible that the circumference in each direction is identical.

But this model is still anisotropic. Along the axes of symmetry, there are geodesics that close, but there also are geodesics "between" these axes that wind around the torus, never closing.

A flat three-dimensional torus is a model for a closed, homogeneous, anisotropic universe. The only flat universe that obeys the Cosmological Principle is one for which space is R³.

Chalnoth

Quote by George Jones

Yes, this model is closed, and is different in different directions (anisotropic).

Well, that doesn't have any meaning in observational cosmology, as when we refer to "closed" we exclusively refer to the curvature, not to the topology (which is unobservable). Well, I mean, a topologically closed universe could, in principle, be observed. But the fact that it hasn't so far seems to indicate that if our universe is topologically closed, then we won't ever be able to tell (because the distance is just too great, by current observational limits).

Quote by George Jones

But this model is still anisotropic. Along the axes of symmetry, there are geodesics that close, but there also are geodesics "between" these axes that wind around the torus, never closing.

In what sense? Given that a torus is finite, any geodesic must necessarily come back to itself eventually. Some will take longer than others, of course, but it must eventually occur.

Quote by George Jones

A flat three-dimensional torus is a model for a closed, homogeneous, anisotropic universe. The only flat universe that obeys the Cosmological Principle is one for which space is R³.

In the sense that the word "flat" is used in observational cosmology, a torus is quite flat. But I thought you said it wasn't anisotropic? Of course, it is anisotropic in the sense that not all geodesics that wrap around a torus come back after the same distance is crossed (like a sphere). But it is very much flat in terms of curvature.

George Jones

Quote by Chalnoth

Well, that doesn't have any meaning in observational cosmology, as when we refer to "closed" we exclusively refer to the curvature, not to the topology (which is unobservable).

If "closed" is defined using curvature, and is not equivalent to topological compactness, I guess I need a precise, mathematical definition of "closed" in terms of curvature, and at least one of:

a space that is closed in terms of the precise, mathematical curvature definition, but that is not compact;

a space that is compact, but that is not closed in terms of the precise, mathematical curvature definition.

Quote by Chalnoth

In what sense? Given that a torus is finite, any geodesic must necessarily come back to itself eventually. Some will take longer than others, of course, but it must eventually occur.

Here's what I had in mind. For simplicity, consider only two spatial dimensions. The flat torus is constructed by putting an equivalence relation on the 2-dimensional plane, with (x, y) ~ (x + n , x + m) for all integers n and m. Now consider the geodesic y = pi*x in the plane, which goes the point (0, 0). The only way that this geodesic can close in the torus is if the line goes through a point in the plane that is equivalent to the point (0, 0), i.e., if the line goes through a point (n, m) for some integers n and m. But a line that goes through (0, 0) and (n, m) has a slope that is a rational number, which can't be equal to the slope pi of the original line.

Consequently, this geodesic in the flat torus induced by the geodesic y = pi*x in the plane doesn't close in the torus.

Quote by Chalnoth

In the sense that the word "flat" is used in observational cosmology, a torus is quite flat.

I agree, and I didn't write anything that contradicted this.

Quote by Chalnoth

But I thought you said it wasn't anisotropic?

I didn't writes this, and I didn't mean to give the impression that I believed this. Quite the opposite; in the first sentence of my previous post, I explicitly stated that the flat torus is anisotropic.

Quote by Chalnoth

Of course, it is anisotropic in the sense that not all geodesics that wrap around a torus come back after the same distance is crossed (like a sphere).

Quote by Chalnoth

But it is very much flat in terms of curvature.

Yes.

Chalnoth

Quote by George Jones

If "closed" is defined using curvature, and is not equivalent to topological compactness, I guess I need a precise, mathematical definition of "closed" in terms of curvature, and at least one of:

From the parameter k in the FLRW metric:

k < 0: open
k = 0: flat
k > 0: closed

This is the terminology usually used in observational cosmology. Clearly these terms were inspired by topology, but bear no direct relationship.

Schlofster

Quote by Schlofster

time index: 19:35
what could contribute a term like this, and we know the answer - nothing - by "nothing", I don't mean nothing, I mean nothing.
If you take empty space, and that means get rid of all the particles, all the radiation, absolutely everything,
so there is nothing there, if that nothing weighs something, then it contributes a term like this.

Quote by Schlofster

time index: 21:20
It turns out, most of the mass of the proton comes not from the quarks within the proton, but from the empty space between the quarks.
these fields produce about 90% of the mass of the proton, and since protons and neutrons are the dominant stuff in your body,
empty space is responsible for 90% of your mass.

I am sorry to bring this up again, but I have just understood why I drew the conclusions I did from what he says here.
The only way that I can see these two statements being logically compatible is if the space between the quarks within a proton is no different from the empty space between protons.
If the virtual particles 'popping' in and out of existence are a property of empty space whether that space is within a proton or not.
Is this incorrect, or is there another way to understand it that is still allows the two statements above to be logically compatible?

Thanks

Chalnoth

Quote by Schlofster

I am sorry to bring this up again, but I have just understood why I drew the conclusions I did from what he says here.
The only way that I can see these two statements being logically compatible is if the space between the quarks within a proton is no different from the empty space between protons.
If the virtual particles 'popping' in and out of existence are a property of empty space whether that space is within a proton or not.
Is this incorrect, or is there another way to understand it that is still allows the two statements above to be logically compatible?

Thanks

Yes, that's basically right. The only difference with the empty space within a proton is that you've got these strong nuclear forces between the quarks that cause additional excitations of the vacuum.

Schlofster

Thanks, does that then mean that if we were ever able to verify that the universe has a finite mass, it would imply that the universe must be finite in spatial extent, and therefore not perfectly flat?
Conversely if we were able to verify that the universe is flat on the largest scales, would it imply that the universe's mass is infinite?
Does Prof. Krauss' claim that the universe is flat refute Hawking's 4d closed manifold hypothesis?

Unto

This is about the Ex Nihilo right? I too believe in this and will post why when I come back from lectures.

Schlofster

1)

Quote by Chalnoth

Yes, that's basically right. The only difference with the empty space within a proton is that you've got these strong nuclear forces between the quarks that cause additional excitations of the vacuum.

2)
time index: 21:20
"It turns out, most of the mass of the proton comes not from the quarks within the proton, but from the empty space between the quarks.
these fields produce about 90% of the mass of the proton, and since protons and neutrons are the dominant stuff in your body,
empty space is responsible for 90% of your mass."

3)
time index: 25:00
"The universe can be one of three different geometries: open, closed or flat"

4)
time index: 25:30
"And an open universe would be infinite in spatial extent as would a flat universe"

5)
time index: 29:25
"we know how many protons and neutrons there are in the universe, we can actually measure that"

Please show me where I am going wrong:

a) (1) AND (2) AND (4) implies that a flat or an open universe would have an infinite mass.

b) (a) AND (3) AND (5) implies that our universe can't be open or flat - it must be closed.

but (b) cant be true because evryone here including Prof Krauss says that we have observationally shown that the universe is so close to perfectly flat, that it may as well be.

this is the exact reason why I cant reconcile the logic, please can someone show me where I am going wrong?

Chalnoth

Well, I think in point (5) he's actually not talking about everything, just the observable universe. So the problem here is that we're talking about two different uses of the word 'universe'.

Freeman Dyson

He also says in this lecture:

"What’s so beautiful about a universe with total energy: zero? Well, only such a universe can begin from nothing. And that is remarkable because the laws of physics allow a universe to begin from nothing. You don’t need a deity. You have nothing, zero total energy, and quantum fluctuations can produce a universe."

Wouldn't that universe have to disapear in under a second?

shoejunk

Here's my amateur's take on the implications of a flat universe, having just watched Krauss' lecture and read these comments and done some of my own thinking. Please, let me know whether I'm making sense. In a flat universe, it's possible for there to be infinite mass and infinite space if the universe is expanding, because due to relativity, all the mass that is far enough away would be moving away from us faster than the speed of light and all of that mass would not be observable or have any affect on us in any way. It would be as if that mass doesn't exist for us. That leaves only a finite amount of mass that is not moving away from us faster than the speed of light, which is our observable universe, which is finite in both mass and spatial extent. So it's possible that the 'actual' universe is infinite in space and mass while our observable universe is finite in both ways.

Another thing I was thinking about is Krauss' picture of the future of the universe, when galaxies get so far apart that all galaxies are moving away from each other faster than the speed of light, and so as far as any observer could then tell, only the galaxy that is around the observer exists. Now consider the empty space between the galaxies. In that space, if all galaxies are moving away from the empty space faster than the speed of light, it would be as if there was absolutely nothing in the universe at all from the 'point of view' of that empty space. Now, isn't that the same situation that we were at at the beginning of the universe? So if the conditions are the same, shouldn't the outcome be the same? Shouldn't we expect quantum fluctuations to create universes from nothing? So what we end up with as a picture of our universe is an ever expanding universe in which matter keeps spreading out more and more, but in which more galaxies keep popping up within the empty spaces, albeit perhaps only when they are so far away that we can't notice them.

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Unto	This is about the Ex Nihilo right? I too believe in this and will post why when I come back from lectures.

Chalnoth Recognitions: Science Advisor	Well, I think in point (5) he's actually not talking about everything, just the observable universe. So the problem here is that we're talking about two different uses of the word 'universe'.