Universe turned inside out at time zero

[marcus]

Martin Bojowald has a bunch of papers 2001-2003 on loop quantum cosmology including ones which dispose of the time zero singularity-----the glitch which was christened the "big bang" but is actually a breakdown of the 1915 einstein equation: GR fails to compute at time zero and by quantizing it Bojowald gets it to compute.

Recently some other people have been following up on some of Bojowald's results so there is a bunch of papers by other people.
Among other things, inflation has been derived from the quantum GR model. I've posted some links in other threads.

Anyway, John Baez often has the most graphic and intuitive way of seeing things and the most simpatico explanation and he describes the bounce at time zero as a turning inside out of the volume------what preceded the "big bang" was a "big crunch" he says.

Here is an exerpt from John Baez "This Week's Finds #167". A complete collection of TWF, including the one containing this passage, is at Baez website.

"...Here's where things get technical, in a way that tickles me pink, but may bore you to tears:

A funny feature of the volume operator in loop quantum gravity is that it's expressed in terms of the square root of the absolute value of a certain quantity. We can think of this quantity as a sort of "volume squared" operator, but with both positive and negative eigenvalues. This always used to puzzle me, and I've put a lot of thought into this issue. Renate Loll has also written a paper about it. I'm delighted to find that in Bojowald's setup, it becomes a real *virtue* of loop quantum gravity, since it allows us to extrapolate our quantum cosmology to negative times - or more precisely, negative "volume squared"!

How can you visualize this? Crudely speaking, negative-volume-squared states of the universe can be thought of as "inside-out versions" of positive-volume-squared ones. So the way I visualize Bojowald's result is like this: the universe shrinks to nothing as you rewind history back to the big bang, and then expands again "inside out" as you go to negative times..."

To read more about this from TWF #167 see
http://obswww.unige.ch/~lbartho/TWF/week167.html

Thanks to selfAdjoint for the reference to Baez This Week Finds

 

[wolram]

i want it to be true but it is hard, its time for a totally
new theory, this one is to "sticky" 1+1 can = something
1 on its own can only =1.

 

[marcus]

Originally posted by wolram
i want it to be true but it is hard, its time for a totally
new theory, this one is too "sticky" 1+1 can = something
1 on its own can only =1.

Wolram I have always thought of you as having the sober
prudence of an intellectual investment banker (or even a racetrack bookie!) and it is
altogether fitting that you should spend ample time
---perhaps years---doubting this with every skeptical fiber of your
heart

so far be it from me to try to persuade you

That said, I must admit that I fail to see anything especially surprising or "sticky"-----what I find naive is the supposiition that the whole show began at some instant: sprang into existence.
A bounce like what Bojowald discovered strikes me as far easier to accept----far less shocking than what we've been living with
for the past 40 or more years. The expansion we are witnessing had to begin sometime--what more natural than that it began at the high-density end of a contraction phase---and that's what he found came out of the equations when he finally got a workable model

the "inside out" business is Baez extra twist to the story----the rough outlines of Bojowalds basic story doesn't emphasize the inversion of spatial volume but simply says there was contraction that reached a kind of quantum limit and gave way to expansion.

I am not saying this or this is CORRECT. we don't know! There is a lot of checking to be done and then...well we never know anything for certain anyway. What I am saying is that this picture is, for me, kind of unsurprising, unstressful, has the look of reasonable meat and potatoes science, comes out of kind of simple equations that someone was bound to uncover at some time.

Also I don't see Bojowald as some wild-eyed visionary, but basically just a Penn State postdoc doing what he is supposed to do.

 

[Mentat]

Forgive me if I misunderstood, but this sounds a lot like the M-Theory explanation of the Big Bang. I know that it's not exactly the same, and I know that it wasn't attempting to be a "string" explanation, but that is what it sounds like anyway.

You see, in String Theory, the Universe's current perceived expansion, is really both an expansion and a contraction (it all depends on whether you are measuring wound or vibrating strings). So, if there were a Big Crunch, then the Universe would appear to "bounce back" and start expanding again, once it reached a Plank's size - when in reality, it isn't really bouncing back, just (to use the words of the the scientist, quoted in the first post) expanding "inside out".

 

[Eh]

If the universe were expanding and contracting at the same time, why the redshift of galaxies?

 

[Mentat]

Originally posted by Eh
If the universe were expanding and contracting at the same time, why the redshift of galaxies?

Because electromagnetic radiation propogates on vibrating strings. These are (currently) expanding apart, and thus the redshifting.

 

[Eh]

When the universe shrinks down to zero volume, is length keep at a finite value?

 

[Mentat]

Originally posted by Eh
When the universe shrinks down to zero volume, is length keep at a finite value?

Yes. According to M-Theory, nothing ever get's smaller than a Plank's size.

 

[Eh]

Originally posted by Mentat
Because electromagnetic radiation propogates on vibrating strings. These are (currently) expanding apart, and thus the redshifting.

If it's expanding and contracting, the net change should be zero. No blueshift, no redshift.

 

[Eh]

Originally posted by Mentat
Yes. According to M-Theory, nothing ever get's smaller than a Plank's size.

Well the question was more aimed at what happens in LQG when the universe shrinks down to having no volume or area at all.

 

[wolram]

please excuse the ignorance, but it has been said that this
theory "seems" like M theory, can anyone give an opinion
relative to LQC.

 

[marcus]

Originally posted by wolram
please excuse the ignorance, but it has been said that this
theory "seems" like M theory, can anyone give an opinion
relative to LQC.

I think I may understand your request, wolram, or perhaps understand it in several possible ways. Speaking
purely for myself my thought is "let a hundred flowers grow"
or whatever that chinese leader is supposed to have said----though I believe that particular episode ended badly for the flowers.

the two determining characteristics of LQG are its
focus on quantizing General Relativity and its economy of means.

There is an additional wrinkle that in 1986 the classical unquantized theory of GR changed character by developing a new set of variables (e.g. "connection"-based description of the geometry instead of "metric") but that is just analogous to changing variables in calculus or algebra to make something easier. In 1986 it was still the old classical theory but it had some
new tools to work with.

LQG tries to quantize GR using Ashtekar's new variables for GR, without throwing in additional structure. So it is a post-1986 continuation of something that had gone on since before 1960.

Nobody particularly wanted there to be loops or graphs or networks or "polymeric" quantum states or discrete values of area and volume. these things came out of quantizing the possible geometries of the manifold as described by the new variables. And then trying to catalog the quantum states of the geometry in an efficient way. Spin networks came in when Rovelli and Smolin found they allowed for an efficient cataloging of the quantum states

Then someone found that the network was behaving like a real thing that conferred area and volume to patches of surface and regions and actually gave the right answers----allowing area and volume "operators" to be defined.

In a quantized theory an "operator" is like a big matrix that keeps track of all the possible results of a certain measurement, in the various possible states the system can be in when its made. It is part of a maths rigamarole for organizing information and uncertainty which has been canonized by years of practice.
I can imagine on another planet they might not have Hilbert spaces and Operators on them. But these things work and one must have some formal tools. They are in a way, generalized multifaceted "numbers" so if you can accept numbers for modeling the world you are already in a fair way to accept "operators".

Anyway the fiendish strange business of LQG is that when they got the Area "operator" they found that it had a smallest possible positive value. There is a list of possible results of a measurement which are the "eigenvalues" or the "spectrum" of the operator which basically is talking about the diagonal terms in the matrix. There turned out to be a smallest one. Area could only get so small. And volume likewise.

Nobody put this in by hand, they were just trying to do their job and finally get Einstein 1915 equation quantized, without adding
new junk like extra dimensions or whatever. And they ran up against this. And one of the effects was that when you ran the model back to the big bang it didnt stop at time zero but kept on going,

After it was quantized the model didnt break down at time zero any more but just kept on running.

Of course this is just a sketch. But what I am stressing here is
the "conservatism" which several commentators like Baez, Rovelli, Thiemann have stressed. What makes the results particularly interesting is the "no new structures" idea of taking the 1915
theory (which is background independent, invariant from the word go under smooth deformations) seriously and trying to quantize it without any brilliant contraptions and just seeing what you get.

There may indeed be plenty of ways of getting theories that
do all kinds of wonderful stuff (avoid breakdown at time zero, reproduce Beckenstein's BH entropy formula, have quantized area and volume and whatever) and they will probably be less
conservative and more creative in a certain sense.

You may have been asking about M-theory. I don't know if you were. I have not heard anything about a background independent M-theory that would qualify as an attempt to quantize GR, or, if there is such an offshoot of the background dependent theory, whether it gets any of those other result goodies which one wants a QGR theory to get. Someone else will have to cover that topic.

 

[jeff]

Originally posted by Mentat
in String Theory, the Universe's current perceived expansion, is really both an expansion and a contraction (it all depends on whether you are measuring wound or vibrating strings). So, if there were a Big Crunch, then the Universe would appear to "bounce back" and start expanding again, once it reached a Plank's size - when in reality, it isn't really bouncing back, just (to use the words of the the scientist, quoted in the first post) expanding "inside out".

T-duality is irrelevant to this thread. It's a symmetry that relates string theories compactified on large and small tori - which do not include the usual non-compact spacetime dimensions - by interchanging winding and (compact) momentum of closed strings. The result is that the space of inequivalent theories is given by values R of the radius of compactification satisfying R≥α′^1/2 with α′ being the string scale, not Planck's constant.

 

[Mentat]

Originally posted by Eh
If it's expanding and contracting, the net change should be zero. No blueshift, no redshift.

Not if it's expanding in 3 dimensions and contracting in the other 7. "Wound" strings move along the other 7 dimensions, and (because of the way that these other dimensions are "curled up") the expansion/contraction of space in these dimensions is inversely proportional to the expansion/contraction of space in the 3 that we are used to.

 

[Mentat]

Originally posted by jeff
T-duality is irrelevant to this thread. It's a symmetry that relates string theories compactified on large and small tori - which do not include the usual non-compact spacetime dimensions - by interchanging winding and (compact) momentum of closed strings. The result is that the space of inequivalent theories is given by values R of the radius of compactification satisfying R≥α′^1/2 with α′ being the string scale, not Planck's constant.

I stand corrected, except for the part about it's not applying to the usual "non-compact" dimensions. Are you sure about this (it's not the way it was explained to me, though I have difficulty with a lot of the math in string theory, and have gotten most of my information from more "watered-down" texts)?

 

[jeff]

Originally posted by Mentat
...it's not applying to the usual "non-compact" dimensions. Are you sure about this

Though T-duality operates on non-compact dimensions as well, the aspect you referred to relates the exchange of compact dimensions of large and small radii to the switching of closed string winding number and compact momentum, and strings can't wind round non-compact dimensions like the real line, but can around compact ones like a circle.

 

[Mentat]

Originally posted by jeff
Though T-duality operates on non-compact dimensions as well, the aspect you referred to relates the exchange of compact dimensions of large and small radii to the switching of closed string winding number and compact momentum, and strings can't wind round non-compact dimensions like the real line, but can around compact ones like a circle.

But aren't the 3 dimensions, that we are used to, the ones that are supposed to "curl" in the other dimensions/directions?

In the analogy of a two-dimensional world, being curled in the third dimension, it is the third dimension that is considered "wound", but the two other dimensions are the ones that actually "curl" in that direction.

 

[jeff]

Originally posted by Mentat
But aren't the 3 dimensions, that we are used to, the ones that are supposed to "curl" in the other dimensions/directions?

In the analogy of a two-dimensional world, being curled in the third dimension, it is the third dimension that is considered "wound", but the two other dimensions are the ones that actually "curl" in that direction.

The cylinder ℜxS¹ is a 2-dimensional manifold which is non-compact in the first direction - no "curling" - and compact in the second. If the radius of S¹ is very small, the cylinder will look like the non-compact 1-dimensional manifold ℜ.

The conventional string theory picture of our universe is of a product MxK with M the usual (3+1)-dimensional spacetime and K a very tightly wound 6-dimensional compact space (which is not necessarily a manifold). In the case of T-duality, K=T⁶, a 6-torus. In M-theory there is an additional compact dimension.