In Quest of Infinity - 15 - By Prof. G. Venkataraman

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IN QUEST OF INFINITY - 15

By Prof. G. Venkataraman

 

 

 

 

Previous Articles In The Same Series

 

 

Part - 01

Part - 02

Part - 03

 

 

Part - 04

Part - 05

Part - 06

 

 

Part - 07

Part - 08

Part - 09

 

 

Part - 10

Part - 11

Part - 12

 

 

 

 

Part - 13

Part - 14

 

 

 

 

Loving

Sai Ram and greetings from Prashanti Nilayam. Our quest for Infinity is

taking us on a long journey, is it not? Well, after all it is Infinity

we are after, and we should not be surprised if the quest is long!

However, as long as the quest itself is exciting, I guess there is not

need to feel either tired or bored. With that preamble, let me pick up

the threads from where I left off last time.

 

 

 

 

 

 

Artist's conception of a brane universe

 

 

 

If you recall, I had, after recalling first the ancient versions of the so-called Cyclic Model of the Universe [which I did in QFI – 13],

moved on to a brief narration of how the Cyclic Model came to be

revived in the 20 th Century, and how it came to be abandoned after

four fatal blows were delivered to it, almost till very recently.

And

yet, in a sort of never-say-die spirit, the Cyclic Model is refusing to

give up, incarnating in a new “Avatarâ€, taking the help of modern

String Theory. I briefly hinted about this development in some of my

earlier presentations but this time, I shall go into it in as much

detail as we can in these pages. So on now finally to the “New Improved

Version of the Cyclic Model, with a Magic Additive called String

Theory!†– maybe I could try to sell it that way, just like TV ads try

to sell soap and toothpaste!

Before I proceed any further, let me assure that I am not

about to present a soap opera; on the other hand, this is serious

cosmology. Let us go back a bit and start with a sketch that summarises

the essence of what people believed in, after the original Inflation

Model of the Universe received general acceptance. This schematic may

be seen below; along with this schematic, I also offer another that

captures similarly the essence of the original Cyclic Model [pre

Tolman, that is – see QFI – 14].

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

FIGURE

1: The sketch in (a) shows one of the three possibilities for the

evolution of the Universe, originally considered by Freidmann. In this,

the Universe is born, expands, then contracts, and ends up in a point,

even as it started its existence as a single point. The curve in (b)

shows the scenario as it later became when it was realised that

Universe is not closing, on account of dark matter. It is a further

study of this curve that led to the Inflation Model; the curve

corresponding to this is shown in ©. The curve (d) shows the closed

loop being repeated endlessly, and that is the essence of the original

Cyclic Model. All this is essentially a recap of what has been said

before.

 

 

 

The Cyclic Model of the Universe - With Strings Attached

I

also told you in detail last time how, starting with Richard Tolman,

four blows were struck on the Cyclic Model. That being the case, one

would have thought that the Inflationary Model would now be proclaimed

the victor and rule the scene. However, thanks to Paul Steinhardt and

Neil Turok, the Cyclic Model is trying to stage a comeback [in a “new

and improved form†of course], and the rest of this episode would be

mostly about this revival story.

 

 

 

 

 

Open and closed tensed strings store tremendous amounts of energy

 

 

As

I have mentioned several times [though only briefly and somewhat

casually up to this point], the version of the Cyclic Model that Paul

and Neil offer is based on String Theory; and they are venturing to do

this because in their view, the Inflationary Model [Figure 1(a)] is not

all that faultless. So, before I start describing what exactly Paul and

Neil are trying to do, let me remind you of a few elementary facts

concerning strings and String Theory.

The

first thing is that string can acquire tension and store this tension

energy. If, for example, you consider a small piece of string that is

open and loose, then it would have no tension. However, when pulled, it

would develop tension; moreover, the tension grows linearly, that is to

say, if the length is doubled, the energy also is doubled. If the

length increases three-fold, then correspondingly the energy of tension

also is trebled, and so on. [see Figure 2].

 

Suppose we have, instead of a piece of string, a rubber sheet or

membrane; in this case also the energy due to pulling or applying a

tension or strain energy as it is sometimes called, would increase. By

how much? Well, there is where the thing becomes interesting. If say

the sheet is in the form of a square and as a result of the pull, all

sides double in length. The strain energy would then not just double

but increase four times.. It turns out that if we move over from simple

strings to two and higher dimensional membranes, the energy increase is

proportional to (d)n, meaning the nth power of the dimension

of the [generalised] string.. Thus, in the case of the ordinary string,

the energy increases simply in proportion to (d); in the case of the

two-dimensional string or sheet, it increases as (d)2. In the case of the three-dimensional string, the energy increase follows the rule (d)3, and so on; hope that is clear.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Figure 2: The sketches here show tension being applied to strings of

dimension 1, 2 and 3 respectively. In every case, tension produces

strain, and this results in energy being stored in the string. The

sketches in (a) illustrate the application of tension and the size

enhancement that results. [These sketches are based on what Paul and

Neil provide in their book.] Naturally, as the strain increases, so

does the energy stored. The interesting point is that the increase in

energy is proportional to the nth power of the dimension of the string,

i.e., the increase goes as (d)n where n is the string dimensionality. This is depicted in (b).

 

 

Now

why am I telling you all this? Just to convey two important facts: The

first is that if we want an efficient energy reservoir, then we should

consider strings of higher dimensions or branes. The second and the

related fact is that developments in String Theory do offer scope for

considering branes, rather than just simple strings themselves.

 

Initially, hardly anyone even thought of connecting String Theory with

Cosmology; there were problems in the theory itself, which, let us

remember, was still in a rudimentary stage. One problem was that there

seemed to be so many versions; the question was: “Which one of these

was to be taken seriously?†Then came Witten, who, waving a magic wand

as it were, assured the community that though there appeared to be

diversity, there was really a basic underlying unity – I described this

in QFI – 10. [Reminds us of Swami’s saying, “Jewels are many but gold is oneâ€, does it not?]

 

 

 

 

 

 

The five known string theories reveal an underlying larger theory, called M theory

 

 

 

Soon

after the Witten magic, many thought, “Maybe, we can use the M theory

and explain inflation. If we do that, then inflationary cosmology would

have a foundation in fundamental physics.†There was great excitement

in the air, even as many worked hard to get there first. But then came

the bad news and the crash – the M theory, if invoked to explain

inflation, did predict inflation but the inflation happened too fast.

By

this I mean the universe after inflation had too many wrinkles and it

was not smooth by any means, which went against experiment. In Physics,

experiment always has the final say; if its vote is negative [meaning

the experiment comes up with a result that does not agree with theory],

then out goes the theory, no matter how distinguished and famous the

author is! Well, that is exactly what happened in this case, though

there were no star competitors.

Physics and Cosmology Attempt to Agree

That

was one down for M theory, no entry into cosmology, at least right

then. We move on now to the late 1990’s when a scientific meeting was

arranged at the Newton Institute in Cambridge, [recall QFI – 12

where I discuss the birth of this Institute]. The main aim of this

particular meeting was to bring leading string theorists and

cosmologists together to the same venue, hoping that proximity and

stimulating talks would induce the two communities to break new ground

by coming up with innovative ideas. That indeed happened.

 

 

 

 

 

 

 

The 10th dimension exists as the space between two parallel branes (one brane being our universe)

 

 

It

all started with a talk by Burt Ovrut, a highly respected string

theorist and a colleague of Paul Steinhardt during the latter’s stay at

the University of Pennsylvania. Ovrut who was not only a good physicist

but also blessed with artistic talent, made his talk come alive with

evocative drawings and sketches, even as he explained complex ideas.

Ovrut started by reminding the audience that space in string theory is

multi-dimensional [see QFI – 13].

He

then drew on the board, two close sheets that were close and parallel.

Although the sheets shown in the sketch were two-dimensional, Ovrut

asked the audience to imagine that these two-dimensional sheets really

represented nine-dimensional space. [by the way, in Physics and

cosmology too, we must consider not only space but also time, which, by

the way, has the status of a dimension, though of a different type.

Here, for simplicity, we keep the time aspect out.]

 

Are we not missing something here? Is not the Witten theory supposed to

have ten space dimensions rather than nine? Sure there are ten space

dimensions in all and we are not forgetting the tenth

dimension. Ovrut said that the gap between the sheets lies along the

tenth dimension. In other words, the gap represents the tenth dimension

of sheet 1, and it also represents the tenth dimension of sheet 2 (at

right).

Ovrut added

something more. He said that the sheets [which, remember are really

branes], are not ordinary ones. Branes normally have space on both

sides [this sentence may sound confusing; if it does, think of it this

way: branes are like “carriers†for space dimensions]. But Ovrut’s

branes were special; they represented the boundaries of the tenth

dimension. Put this way, space [taking all dimensions into

consideration] exists only on one side of the two branes and between

the two branes; the side of the brane that is chosen, faces the gap. I

am aware that all this is a bit difficult to grasp [and also maybe to

swallow!].

To repeat,

 

There are two branes facing each other and close to each other. Each brane is a carrier for space. Each brane has nine plus one space dimensions. The tenth dimension lies between the sheets, while the remaining nine are confined to one side of the sheet only.

Further, and this is a point I did not mention earlier in order not to

confuse you too much, six of the nine are really extra dimensions; they

curl up or are compactified [see QFI – 10]. The branes are something like stages for universes to reside. On one brane resides our Universe. About the other, we do not know; nor are we bothered.

We are stuck like files on flypaper, that is to say, we are confined to

our Universe which is attached to one of the two branes forming a pair

in a strange cosmic pair!

 

 

This is the starting picture of Ovrut. Why does Ovrut want this other

parallel brane? What purpose does it serve? Why is he not satisfied

with just one brane? According to Ovrut, the proximity of two such

brane worlds could lead to spring-like forces between the two branes,

and as a result, the branes could move back and forth. Could they

collide? Maybe! Could the collision produce a Big Bang? Perhaps!

 

 

 

 

 

 

So you get the idea, don’t you? Bringing in branes and all that, even

opens up the possibility of explaining why the Big Bang occurred! Wow!!

However, things are often not that simple in Physics; it is one thing

to get a bright idea but quite another to work out the details

mathematically. And physicists are pretty hard-nosed people who don’t

accept mere handwaving! If you have an idea, you must first spell out

all the details mathematically and give a framework that enables people

to do their own calculations and make predictions. After that, one

waits for experiments; and that is when the jury is out. After that the

final outcome; do the experiments agree with experiments or not? If

they do not, then out goes the theory, no matter how beautiful and

elegant it is mathematically and how famous its author! In this case,

the mathematics of the colliding branes, at least the first cut, proved

too tough. And that is how the curtain came down on scene 1.

Great Minds Struggling with Gigantic Theories

The

curtain rises again, this time on scene 2, which begins in a train

going to London from Cambridge. Time: The evening of the day when Ovrut

gave his talk. Three people are riding the train, all going to London

for the same purpose, to attend a play there, which was supposed to be

a part of the cultural program associated with the heavy scientific

discussions – major conferences and seminars always throw in some event

meant to promote relaxation; often it is a party [and I guess you

understand what that means!] but in this case, Cambridge being a

high-brow place, the organisers just gave the participants tickets to a

high class play then running in London.

 

Huddled in the train speeding to London were Paul, Neil and Ovrut. They

were lost in discussion, hardly aware of the landscape speeding by.

They realised that brane collisions were unavoidable in M theory. Next,

a brane collision would in no ways be unique; if there was a collision,

then there must have been others before, and that concept had of

course, huge implications; it meant – back to the Cyclic Model! What?!

How could that be? That model had been killed four times and buried

four fathoms deep! However, it seemed that in the M theory, the Cyclic

Model could not be dismissed all that easily!

 

 

 

 

 

 

 

Paul Steinhardt

Neil Turok

Burt Ovrut

 

 

 

Meanwhile, the train pulled into London, and the brain-storming session

had to stop. However, the seeds of a new idea had been sown, at least

in the minds of Paul and Neil, and that is how scene 3 begins!

 

Scene 3: Paul and Neil decide to work and do so intensely to see if

they could pull something out of all this. Sure it was not easy, but

then, exciting problems seldom are. However, history has shown many a

time that if one is steadfast, never loses hope and persists in

nibbling away at the difficulties the model posed, then one day, one

might even hit the jackpot. It was that hope that kept the two going.

 

Paul roped in an associate, Justin Khoury, and the two worked closely,

holding daily meetings to discuss progress. Paul and Ovrut also met

once a week, though one was in Princeton and the other in Pennsylvania

– that was the kind of magnetic pull that the new idea provided. What

about Neil? Well, he was on the other side of the Atlantic, sometimes

in Cambridge where he had settled, and sometimes in his native South

Africa, where he was trying to set up the new African Institute for

Mathematical Sciences. Between Neil and the trio in America, there were

countless phone calls, e-mails, and faxes, so that everyone was in

touch with everyone else all the time. Digressing for a moment, these

days, we take all such conveniences for granted; thus, we scarcely

appreciate how different it was say in 1900 or, for that matter, even

in 1950. We must keep that in mind, when we reflect on the way science

developed back then.

 

Scene 4: Something emerges after all this furious tossing of ideas and

scribbling hundreds of equations on pieces of paper all the time. The

four mentioned above have a model, a model based on M theory, a model

that addressed the question of the birth and the evolution of the

Universe, our Universe of course. What was the big deal about this new

idea, apart from the fact that it relied on M theory to kick off the

birth of the Universe? The big deal [schematically illustrated in

Figure 3] is that it tries to explain why our Universe is presently the

way it is, WITHOUT bringing in inflation.

Remember what I said about inflation when I introduced it to you to in QFI – 08?

Alan Guth invented the idea of inflation in order to explain why the

Universe is pretty smooth and rather flat today, which it would not

have been if we had only regular and steady growth/expansion from the

moment of the Big Bang.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Figure

3: This figure compares the history of growth of the Universe in the

Inflation Model and in the Paul-Neil Cyclic Universe Model. In other

words we see here a comparison of how the size of the Universe is

supposed to increase without and with Inflation. Initially, when ideas

were still rudimentary, no one bothered about the early history of the

Universe. But there came a time when one did have to give detailed

consideration to what could have happened in the Baby Universe. That

was when Alan Guth took a bold step and said: “Let us start with the

way the Universe is today, smooth, wrinkle free and isotropic, and

along with it also the current observed rate of expansion of the

Universe. In addition, let us accept that the Universe was born in a

Big Bang around 14 billion years ago, as most people believe. If we

combine all this, then an inflation or a dramatic increase in size, an

increase of the type impossible to imagine, is unavoidable; and that

staggering increase is Inflation!â€

 

That picture slowly got accepted over the years. And now, Paul and Neil

are saying something radically different. In proposing their version of

the Cyclic Model based on M theory, they say, “The Big Bang did not

occur 14 billion years ago but about a TRILLION or so years ago; and

that Bang was due to brane collision. Over the birth, the Universe

evolved slowly, to reach the state it now is in; and in this way, the

Universe escaped Inflation!†[How nice it would be if we could escape

financial inflation in some such manner!]

The picture above captures the spirit of the above two points of view.

 

 

 

 

Now you might wonder: In one of the earlier issues, I told you that

recent high precision satellite experiments had suggested that the

Inflation Model was right; and now I am telling you that maybe

inflation did not occur at all! So what’s going on? Are the physicists

spending huge amounts of public money and using it for engaging in a

huge con game? Not really.

 

You see, when the satellites obtained some data and the authors of the

experiment wanted to know what that data was telling us, they did the

obvious and the most reasonable thing. Now typically, when there are

new experimental findings, the researchers usually say: “Let us see who

has said what about such matters prior to our experiments.†They then

study carefully all the earlier predictions made by model builders or

“forecasters†if I might call them that, and then say, “Well, it looks

like our data are consistent with the predictions made by so and so;

however, there are some differences, ……..†and so on. That is the way

opinions are generally expressed and conclusions drawn. If there is

only one candidate theory available, then that alone is considered

while examining the data. That DOES NOT mean that another theory later

could not explain all these facts in an entirely different way. Such

things do often happen and I shall tell you more about such matters

later, when we consider fundamentals of physics needed to consider

matter, space and time in their entirety.

What

I am driving at is that when the satellite results became available,

the only model generally accepted was the Inflationary Universe Model;

and that was the model the results were compared with, as was to be

expected of course. While the satellite experiments certainly were in

agreement with many aspects of the Inflationary Model [in so far as

they relate to the Universe as it existed after radiation started

dominating – see Fig 06 in QFI –09],

the satellite data could be equally in agreement with an alternate

model [such as we are discussing now] where after about say anywhere

between100,000 to 300,000 years after the Universe was born [an event

we describe via the word Big Bang], the Universe had the same

appearance as it had in the Inflationary Model. As Figure 3 above

shows, in one case, this state when the radiation era begins is

attained, in the Inflation Model by one burst of super rapid expansion.

In the Brane Collision Model now under discussion, this same state is

reached via a slower growth stretched over a longer period. The end

result [i.e., the state of affairs when the radiation era beings] is

the same; what differs is the way the Universe evolves to this era. Is there any way of picking between these two alternatives? There sure is but that would come later.

 

 

 

 

 

 

 

 

The Inflationary Model vs. the Brane Collision Model: which one will win?

 

 

 

Let me continue with what I was telling you earlier. While discussing

what I called “Scene 4â€, I told you Paul and Neil, along with two

others, came up with a model for the Big Bang and the subsequent

evolution of our Universe, that sought to avoid inflation, and yet be

able to describe the Universe the way it is found to be by recently

launched satellite experiments. The model was far from perfect but

seemed very promising.

A Universe of Fire

At

this point, there arose an interesting issue: what name to give the

“new baby� All kinds of suggestions were made from Big Splat to Brane

Smash. However, Paul Steinhardt, who felt that this was too important a

matter to be dismissed with some humorous and funny title, sought the

help of Greek scholars; as a result, the name Ekpyrotic Model was given to this new idea in which our Universe is born out of brane collision. The Greek work ekpyrosis means that the Universes was born out of fire. And this name Ekpyrotic Model has since stuck.

 

 

 

 

 

 

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