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

[Schlofster]

I started this https://www.physicsforums.com/showthread.php?t=313501" a while ago talking about Stephen Hawking's "No Boundary Condition".

I think that I finally got a handle on it, but now Lawrence Krauss has discussed http://www.youtube.com/watch?v=7ImvlS8PLIo" why he thinks that the universe is not closed, but flat, and he says by implication, 'infinite in spatial extent'.
(he also claims to have empirical evidence of the flatness of space-time on the largest scales)

I don't understand how he can reconcile this with the big bang (which he also seems to accept).
If the universe is infinite in spatial extent, at what point did it become infinite, because when the universe was 1 second old, it was not infinitely large (I think that this is the scientifically accepted view).
He is obviously a widely respected physicist, and I am not a physicist, so I expect that I just don't understand what he is saying.

Could anyone explain it to me, or can it not be expressed in natural language?

Thanks,
Schlofster

 

[mikeph]

If the universe is infinite in spatial extent, at what point did it become infinite, because when the universe was 1 second old, it was not infinitely large (I think that this is the scientifically accepted view).

I don't think this is scientifically accepted. When the universe was 1 second old, all we can say is the scale factor was a lot smaller than today, nothing about the size of the universe.

For me the idea of an infinite universe is troubling when you think what happens at time zero, but for all positive times there is no mathematical problem, an infinite space can still expand as much as it likes. And when you think about time zero with whatever perspective of the size of the universe you will be uncomfortable thinking about it, so I don't think an infinite universe has any relative disadvantage from this perspective.

 

[Schlofster]

In the talk, he claims that they have used mathematical calculations to calculate the mass of the universe, and he claims that most of the mass in the universe is as a result of virtual particles "popping in and out of existence" in empty space.
Considering this, and since he is able to calculate the mass of the universe to be a finite quantity, how is it then possible to say that the universe is infinite in spatial extent, because this then implies that the mass of the universe should be infinite since empty space itself constitutes most of the mass of the universe?
Is my logic flawed?
If it is, please show me where, because I would really like to understand this if it is possible to express the answer in natural language.

Many thanks,
Schlofster

 

[mikeph]

Are you sure he says mass and not density? I can't watch it because I'm in a library.

Your logic seems fine here.

 

[qraal]

In the talk, he claims that they have used mathematical calculations to calculate the mass of the universe, and he claims that most of the mass in the universe is as a result of virtual particles "popping in and out of existence" in empty space.
Considering this, and since he is able to calculate the mass of the universe to be a finite quantity, how is it then possible to say that the universe is infinite in spatial extent, because this then implies that the mass of the universe should be infinite since empty space itself constitutes most of the mass of the universe?
Is my logic flawed?
If it is, please show me where, because I would really like to understand this if it is possible to express the answer in natural language.

Many thanks,
Schlofster

An infinite Universe is merely a possibility of the chosen topology - in this case a 'flat' Universe. There's no evidence that it is infinite, merely philosophical presumption.

 

[marcus]

I saw that talk several days ago.
It is delightful. Some very funny remarks, great quotes----sly pokes at this and that.
I would urge everybody to watch the video, just for entertainment!

However it is scientifically so sloppy as to be almost useless to us in Cosmo forum.

Krauss is a worldclass cosmologist, but he is talking at a total layman level and, as he explicitly says, nothing is to be taken seriously---he calls his statements lies because they are purely verbal---no rigorous definitions, just impressionistic approximate language.
He uses the word "lies" in reference to his own statements, explaining that what he is saying is not mathematical, not quantitative, imprecise.

So it is a wonderful talk but don't try to translate anything into hard empirical fact.

There is no evidence that the U. is spatially flat. Only that it is NEARLY so. The current 95% confidence interval on the curvature allows for finite volume spacetime with circumference lower bound of 600 billion lightyears.
Krauss does not indicate he has anything different from the most recent WMAP report, that you or I can get from NASA or from arxiv.org.
When talking to a complete nonscientist, nonmathy audience we can understand saying that that the U is spatially flat and spatially infinite. But you cannot as a scientist talking to other scientists maintain this. It is possible. It is one consistent interpretation. But another equally good interpretation of the data is that space is finite volume and if you could freeze expansion so that you could make the round trip, it would take 600 billion years traveling at the speed of light.

His scholarly papers on arxiv.org are different from his stand-up entertainer pop-talk to general audience. I'm a fan of Krauss. He is first class in either category---pop-sci or real-sci. More power to him.

 

[Chalnoth]

I saw that talk several days ago.
It is delightful. Some very funny remarks, great quotes----sly pokes at this and that.
I would urge everybody to watch the video, just for entertainment!

However it is scientifically so sloppy as to be almost useless to us in Cosmo forum.

Krauss is a worldclass cosmologist, but he is talking at a total layman level and, as he explicitly says, nothing is to be taken seriously---he calls his statements lies because they are purely verbal---no rigorous definitions, just impressionistic approximate language.
He uses the word "lies" in reference to his own statements, explaining that what he is saying is not mathematical, not quantitative, imprecise.

So it is a wonderful talk but don't try to translate anything into hard empirical fact.

There is no evidence that the U. is spatially flat. Only that it is NEARLY so. The current 95% confidence interval on the curvature allows for finite volume spacetime with circumference lower bound of 600 billion lightyears.
Krauss does not indicate he has anything different from the most recent WMAP report, that you or I can get from NASA or from arxiv.org.
When talking to a complete nonscientist, nonmathy audience we can understand saying that that the U is spatially flat and spatially infinite. But you cannot as a scientist talking to other scientists maintain this. It is possible. It is one consistent interpretation. But another equally good interpretation of the data is that space is finite volume and if you could freeze expansion so that you could make the round trip, it would take 600 billion years traveling at the speed of light.

His scholarly papers on arxiv.org are different from his stand-up entertainer pop-talk to general audience. I'm a fan of Krauss. He is first class in either category---pop-sci or real-sci. More power to him.

Yes, definitely. It's also worth mentioning that he also listed out the current experimental limits at about 1% (which is correct).

 

[robertm]

I was going to ask about this as well.

It seemed to me that he is particular to the (relative) theoretical simplicities that a zero-sum universe would provide.

I generally enjoy Kruass, and I did quite enjoy this talk, but I just can not imagine that he thought a general audience would not be able to comprehend the idea that he is biased toward the flat case, which does fit the current data, but that more data is needed in order to make any definite statement either way (flat or closed). Especially since, as far as I understand the data, the closed universe seems to be slightly favoured.

He specifically and deliberately stated multiple times that the universe IS flat; it just seems to me to be a sloppy and unnecessary short cut that is guaranteed to cause confusion in his target audience.

But I guess this sort of thing is just what you get, even from world class popularizing.

 

[Chalnoth]

For all practical purposes, as long as the dark energy continues to act much like a cosmological constant, our universe might as well be perfectly flat.

 

[Schlofster]

I am sorry to ask, (maybe this is because I have only done some undergrad physics and therefore don't understand your answer) but I still don't see how Prof. Krauss can claim to conclude that the U is infinite in spatial extent when he also claims that the U has a finite mass, and he also claims that completely empty space accounts for 70% of the mass of the U.
This still seems to me to be a non sequitur, because the empirical measurements of the finite mass of the U must then imply that the U must be finite in spatial extent (using my admittedly simple logic).
Since Krauss says that a flat U would be infinite in spatial extent, this must then imply that the universe must be closed (again using my admittedly simple logic).

Do I make any sense at all, or should I just give up trying to use my folk logic to understand how the conclusions cosmology are internally consistent?

Were I to show this video to my theist friends (I am not a theist), I think that it would seriously damage the reputation of science in their eyes - a first class cosmologist making logically (folk logic of course) inconsistent statements.

 

[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 can't 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.

 

[Chalnoth]

I am sorry to ask, (maybe this is because I have only done some undergrad physics and therefore don't understand your answer) but I still don't see how Prof. Krauss can claim to conclude that the U is infinite in spatial extent when he also claims that the U has a finite mass, and he also claims that completely empty space accounts for 70% of the mass of the U.

I don't see how he's claimed any of these things. Except that last one, which is basically what we understand the cosmological constant to be.

This still seems to me to be a non sequitur, because the empirical measurements of the finite mass of the U must then imply that the U must be finite in spatial extent (using my admittedly simple logic).

Er, what? There is no such measurement that has been performed, because the limits of our ability to measure do not extend to the entire universe.

 

[Chalnoth]

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 can't even articulate them at all in a way is intelligible by the majority of humans on this planet.

It has nothing to do with that. It's a matter of language. What we understand the universe to be, as well as the experimental results that place limits on our universe's behavior, are placed in the extremely precise language of mathematics. It is unfortunate but simply true that most people don't understand this language, due to a lack of training, and also due to a lack of use. And so people, when attempting to engage the public, attempt to explain things in the language that people outside their own field understand: colloquial language.

But colloquial language isn't nearly as precise as mathematics. Many of the mathematical statements about what we currently know just don't have any meaning at all in colloquial language, and can't be translated. Various popularizers of science make use of different attempts at performing this imperfect translation. Many disagree on precisely how to do it, even in cases where there is no disagreement in the underlying science that is in the language of mathematics.

In the end, what this means is twofold:
1. You can't hope to have an actual understanding of the science unless you take the time (and it is quite a lot of time, unfortunately) to understand the mathematical language of the science in question. You can definitely get a vague impression, or some superficial understanding. But you can't hope for that understanding to be entirely accurate.
2. If you want to try to find fault with a theory, you really need to go to the only language in which it is accurately described: mathematics. Due to the inaccuracies of plain language, and due to the fact that plain language doesn't exactly describe the mathematics, you're more likely to find fault with the way in which the person translated from mathematics to plain language than with the underlying theory. The only way to be sure is to go to the underlying mathematics.

In sum, it's not about intelligence, it's about taking the time to understand the language of the science. Which few people have the time or take the time to do (as it generally takes years of study).

 

[Schlofster]

In sum, it's not about intelligence, it's about taking the time to understand the language of the science. Which few people have the time or take the time to do (as it generally takes years of study).

Well, you seem to be implying here that most humans are born with the potential to understand the most advanced math that humanity has produced.
As far as I know, that is not accepted to be the case, but I do take your point - most humans pay very little attention to developing their mathematical skills resulting in the expected inability to understand the science.

In a way, this is congruent with my point above - If you know that the average person won't understand what you are saying and will think that it is illogical, then don't say it if they are paying your salary (even though they are the ones who are deficient)!
Unfair, I know :-(

 

[Chalnoth]

Well, you seem to be implying here that most humans are born with the potential to understand the most advanced math that humanity has produced.

For the most part, yes, I think this is likely to be the case. However, let me stress that in terms of these theories, it is most definitely not necessary to understand the most advanced mathematics that humanity has produced. The mathematics behind what is being talked about in this thread, though more complex than most people are exposed to, are generally quite simple. They're nowhere near as complicated even as the mathematics you see in quantum field theory, let alone what the mathematicians generally work on. I would find it exceedingly strange that a student who could do well at basic algebra could fail to do well, given time and effort, at the mathematics required here.

In a way, this is congruent with my point above - If you know that the average person won't understand what you are saying and will think that it is illogical, then don't say it if they are paying your salary (even though they are the ones who are deficient)!
Unfair, I know :-(

Well, they won't necessarily think it's illogical. And I am perfectly happy to help people who want to understand to do so. I think it's great when people are curious about the science, and honestly want to know what's going on. Just bear in mind that scientists are not dummies, and I can virtually guarantee you that any objection you have ever thought of, if it is a valid objection, has already been thought of a thousand times over by scientists all over the world.

This was definitely my experience when I was training to be a scientist. When I was new at this, working as a young student, I had all sorts of ideas of how certain things might be wrong, or of potential alternative ideas that might be right. As it turned out, when I learned more, I found that every single one of my ideas was either blatantly and obviously wrong, or had already been developed, and in vastly more depth, by somebody else.

The only time amateurs really have much of any chance at all of contributing something novel is when a field is brand-new and still only has a very small number of people working on it, where the amateur is on relatively equal footing with everybody else because everybody in the field is an amateur. But this just isn't the case in modern cosmology.

 

[Schlofster]

nice reply - thanks - I put this question to Prof Krauss, and he responded to me, pointing out where I was going wrong.
I have asked him if I can post his reply here, I will do so if he gives me permission.

 

[Schlofster]

I am sorry to ask, (maybe this is because I have only done some undergrad physics and therefore don't understand your answer) but I still don't see how Prof. Krauss can claim to conclude that the U is infinite in spatial extent when he also claims that the U has a finite mass, and he also claims that completely empty space accounts for 70% of the mass of the U.

I don't see how he's claimed any of these things. Except that last one, which is basically what we understand the cosmological constant to be.

This still seems to me to be a non sequitur, because the empirical measurements of the finite mass of the U must then imply that the U must be finite in spatial extent (using my admittedly simple logic).

Er, what? There is no such measurement that has been performed, because the limits of our ability to measure do not extend to the entire universe.

Well, I have transcribed some relevant sections of the talk, and it seems to me that my bewilderment by his contradictions is not irrational.

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.


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.

time index: 23:48
we should test what the energy of empty space is, how do we do that? well we 'weigh' the universe,
how do we do that? well we stand on the shoulders of giants.

time index: 24:53
and the point is, we can use gravity to 'weigh' the universe including the weight of empty space

time index: 25:30
and an open universe would be infinite in spatial extent, as would a flat universe

time index: 40:20
but just like Goldilocks, in a flat universe, it is just right, in fact it is right now we know to an accuracy of better than 1 percent.
The universe is flat, it has zero total energy, and it could have begun from nothing, and I have written a piece,
although of course, I got a lot of hate mail, saying that in my mind, this answers this crazy question that religious people keep throwing out
which is: "Why is there something rather than nothing", the answer is: there had to be, if you have nothing in quantum mechanics, you will
always get something, it is that simple, it doesn't convince any of those people, but it is true.

time index: 41:01
Now, great, we know the universe is flat, but if you have been awake, 10 minutes ago I proved that the universe is open,
there is only 30% of the stuff in the universe needed to make it flat, where's that other 70%?
Well, if you put energy in empty space, so that empty space weighed something, you wouldn't see it, it is the empty space between the galaxies,
you're far away from those galaxies, you wouldn't see it.
But what would that empty space do if you put energy in it, well, produce a cosmological constant, that would cause the expansion of the universe
not to slow down over time, as any sensible universe would do, but to speed up over time.
In 1998, people measuring these supernovae at large distances to measure the Hubble diagram tried to measure what was happening at large distances
to see if the universe was slowing, well they all knew that the universe was slowing down, they wanted to measure how much.
This doesn't look like much, but it was a revolution in cosmology.
I can draw a straight line through that dataset there and bring the whole thing down and make it horizontal, and if the universe was slowing down,
these distant supernovae should have followed this curve.
Much to the surprise of the observers, the supernovae lay above the straight line, and the only way to explain this, well there is two ways,
either the data is wrong , which it usually is, or the universe is accelerating, speeding up.
And if just for fun, one believed it was speeding up, and one asked just how much energy would you have to put in empty space to make it speed up
by the amount we measure it, it is exactly the amount we are missing.
Everything holds together, our new picture of cosmology is that we live in a universe dominated by nothing.
The largest energy in the universe, 70% of the energy in the universe, resides in empty space, and we don't have the slightest idea why it is there.

Well, they won't necessarily think it's illogical.

A comment by Marcus seems appropriate to me:

However it is scientifically so sloppy as to be almost useless to us in Cosmo forum.

As far as I can see, it is not only scientifically sloppy, it is more broadly logically sloppy (the little matter of whether the universe is infinite in spatial extent is muddled here).
I understand that it is impossible to express the mathematical model in natural language while still maintaining logical consistency, but I feel that in this case, no attempt should be made, because it damages his reputation and the reputation of science in general in the eyes of non scientists.

 

[Ich]

And where's the contradiction? Where does he claim that the universe has a finite mass?
"we 'weigh' the universe" - is that the phrase which bothers you?

 

[Bob_for_short]

I voted "Yes" meaning the Minkowski space-time with the gravitational filed to be physical one similar to other physical fields rather than variable curvature of the Riemann space-time where not additive conservation laws are possible.

 

[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

 

[Schlofster]

And where's the contradiction? Where does he claim that the universe has a finite mass?
"we 'weigh' the universe" - is that the phrase which bothers you?

Yes, it does bother me, are you saying that he measured that the 70% of the mass of the universe is caused by dark energy, but also that the mass of the universe is infinite because it is infinite in spatial extent, and therefore the mass of the dark energy is also infinite?

What also bothers me is I can't show this lecture to any theists or deists because he says:
"Why is there something rather than nothing", the answer is: there had to be, if you have nothing in quantum mechanics, you will always get something, it is that simple, it doesn't convince any of those people, but it is true.
They will just respond: where did the quantum mechanics come from?
When in reality, he has shown that there are 2 different definitions of "nothing", I think that he means the physics definition where empty space can be called "nothing", and this may be empty space in some wider reality before the universe was created in the big bang.
This would confuse the layman, because they would tend to use their own definition of nothing - which really is nothing - no empty space, no quantum field or fluctuations - literally nothing.
I think that his mixing of language here will really confuse the general public.

I know that he qualifies all of this by saying that you must not take him literally all the time because he can't express the mathematical model in natural language, but I am asking whether this kind of confusing talk in natural language is a good idea in a world where people often dismiss scientists as being biased against any deistic solutions.
(I am neither a deist nor a theist)

 

[Ich]

are you saying that he measured that the 70% of the mass of the universe is caused by dark energy, but also that the mass of the universe is infinite because it is infinite in spatial extent, and therefore the mass of the dark energy is also infinite?

Basically, yes.
Read that text again with this in mind. I think you'll find that at no place he says something that can convincingly be interpreted as the mass of the universe being finite. You will also find that the wording "...of the mass of the universe..." - which could be such a hint - is yours, not his.
For the theist debate: Don't believe that physics can prove that there must be something rather than nothing. At least not yet, and maybe such a proof is impossibe. It's not the fault of the theists if they don't buy into it.

 

[Schlofster]

Basically, yes.
Read that text again with this in mind. I think you'll find that at no place he says something that can convincingly be interpreted as the mass of the universe being finite. You will also find that the wording "...of the mass of the universe..." - which could be such a hint - is yours, not his.
For the theist debate: Don't believe that physics can prove that there must be something rather than nothing. At least not yet, and maybe such a proof is impossibe. It's not the fault of the theists if they don't buy into it.

Thanks for clarifying that :-)

 

[Schlofster]

I know that he qualifies all of this by saying that you must not take him literally all the time because he can't express the mathematical model in natural language, but I am asking whether this kind of confusing talk in natural language is a good idea in a world where people often dismiss scientists as being biased against any deistic solutions.
(I am neither a deist nor a theist)

I was wrong - I have just given this to an intelligent, but very non mathy person, and she is glued to the screen - laughing hysterically and obviously fascinated by what science can tell you.

I have to now concede that what he is doing is very important - taking science to the masses and by making it accessible by sacrificing accuracy and coherency for in favour of creating an immersive, entertaining experience, inducing the awe and wonder in the audience that our universe is worthy of.

 

[Chronos]

Flat looks very attractive given current observational evidence. What flat means is subject to interpretation. There are a number of ways to induce this impression that are model dependent.

 

[Ich]

Flat looks very attractive

OTOH, curved looks very attractive, too. :!)
Sorry, OT.

 

[yogi]

My take - while enjoyable and informative - Krauss pontificates at several places which are, as pointed out in the above posts, not yet established - in particular, the notion of an evolving infinite universe. Perhaps Asympotical Flatness leads to a spatal distension that approaches infinity at some infinite time - its hard to imagine an infinite universe that instantly sprang into being like Athena emerging full grown from the head of Zeus. Seems like Krauss has an agenda - that of selling Flat Universes.

 

[Chronos]

LOL, Ich. Curved is very comely. A lot if it has to do with philosophy and aesthetics. In a finite universe of finite age, you are inevitably faced with a choice between a universe from nothing, or a cyclical universe. It is a difficult choice. Something from nothing seems illogical, but, so does a universe that can reincarnate itself in perpetuity - both forward and backward in time - without gaining or losing a single quark in the process.. An infinitely old and large universe, a third option, just doesn't work for me without a compelling solution to Olber's Paradox. There is also a fourth option - parallel universes. This, imo, is fairy dust until someone figures out how to detect them.

 

[Skolon]

I voted No. Why? Shortly because:
1. The BB Theory say that the Universe is not expanding in space, instead the space of Universe is expanding. At the beginning the Universe has a finite and little "amount" of space. An "outside" space doesn't exist.
2. The expansion of Universe is without center and without bounders.
3. I can't imagine a flat shape without bounders (name me a 2D flat geometrical shape without bounders and than extend it to 3D).

So, my believe is that the Universe it is flat only at our observational scale. It is like a humane eye observation of Earth shape: it just look like to be flat.

 

[Chalnoth]

3. I can't imagine a flat shape without bounders (name me a 2D flat geometrical shape without bounders and than extend it to 3D).

A torus.

But really, I don't think anybody genuinely believes that our universe is perfectly flat. Just that it is very, very close to flat. And the generally-accepted explanation is inflation, which drives the universe to near perfect flatness in a tiny fraction of a second.

 

[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?

 

[Chalnoth]

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.

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.

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?

We'd be hard pressed to determine if the different directions wrapped back on one another after different distances, as long as all distances were beyond our horizon. But in any case, it's still perfectly possible that the circumference in each direction is identical.

 

[Skolon]

Thank you for yours answers.

Please tell me, what is the meaning of "flat" for cosmology?

 

[Chalnoth]

Thank you for yours answers.

Please tell me, what is the meaning of "flat" for cosmology?

If you draw a triangle on a flat surface, its angles add up to 180 degrees.

If you draw a triangle on a "closed" surface, its angles add up to greater than 180 degrees. For example, if you draw a triangle on a sphere by starting from the north pole, drawing down to th equator, then across the equator a quarter of the way around, then back to the north pole, you've just made a triangle where each angle is a right angle: you've made a triangle whose angles sum to 270 degrees.

If you draw a triangle on an "open" surface, the reverse is true: the angles sum to less than 180 degrees. A saddle is an example of a surface that has this property.

When we're talking about the curvature of the universe, this is what we mean: we draw triangles by looking at the passage of light from place to place in the universe. The angles that they make tell us what the overall curvature is. And it's very very close to flat.

 

[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]

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]

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]

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?

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.

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 can't 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.

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]

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).

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 can't think of how to use (the) curvature (tensor) to distinguish between "closed" and "open."

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.

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]

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).

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.

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]

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.

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.

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.

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.

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.

Yes.

 

[Chalnoth]

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]

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.

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]

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)

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) can't 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 can't 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?