IN QUEST OF INFINITY – 11

By Prof. G. Venkataraman

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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

 

Loving Sai Ram and greetings from Prashanti Nilayam. Ready for another heady day out in quest of Infinity? Perhaps you are still overwhelmed by the “hangover” from the last outing we had! Or may be you are dizzy wondering whether we are going into the future or diving into the past or, doing both at the same time! Well, if you are feeling that way, let me assure we are on the right track because as we go along, it would get more and more amazing as well as astonishing. Whichever way you feel, I can assure you of one thing; when it is all over [and you might well wonder whether it ever would!], no one who has done this trip would ever have any ego left! That is the Tour Operator’s promise! Money back if no satisfaction!!

Hope all that small talk has awakened you for the “Space and Time Walk” for today – makes us all feel like astronauts in the Space Station, does it not, being awakened every day to Earth Time by beings on Earth! Becoming serious, let me remind you about where we have reached after months and months of exploration. We have arrived at a critical juncture where the present is helping us to try to conjecture about the past, so that we can forecast the future! No kidding!

The 'Big Crunch' - artist's depiction of the universe reversing itself and shrinking to a point

Some years ago, after wondering for a while whether the presently expanding Universe would ever start reversing its track and begin to contract, eventually shrinking to a point, people shook their heads and said: “No chance! It looks like it would expand forever.” Actually there has been something like a fashion cycle in this business of forecasting the future. At first people said the universe would be born, then dissolved, then born again, and so on it would go, cycle after cycle; all that was in ancient times.

Then in the early part of the 20th century, Einstein said, as did many Cosmologists of that early twentieth century, “What nonsense!” Then came some young turks who argued, “Why not?” Later came the ‘wise men and women’ of the last part of 20th Century who muttered, “You know something? You can wait untill the cows come home if you wish to, but the fact of the matter is that the Universe is not only expanding but doing so faster and faster every day! So where is the question of the Universe ever shrinking?”

While all this betting game was going on, those who worry about “small things” said, “Eureka, its not particles but little strings, so small you can never see it.” After this the “String Doctors” went to work, spinning one fascinating tale after another and luring most of the smart young ones to their camp like the good old piper did, even as the “elders” shook their heads in despair and murmured, “These brats, will they never learn to get serious?” The bellyache of the “elders” was that the String Theorists were hardly bothered about making contact with the real world [read, making forecasts and checking theory against prediction and so forth].

It all sounds so much like real life, does it not with young people setting their own fashions, breaking away from the “straight guys” and doing daring things, not caring two hoots about what the old fuddy-duddies say, and so forth? It just shows that in whatever we humans do, be it art or music or architecture or even science, sometimes new ground is broken only by the young who choose to dare and be different. And yet, at the end to the day, somehow, those who defy and those who disapprove do find meeting ground, at least of some sort. How that happened in our story is what I shall start with in this instalment, and then take it from there.

If you recall, in the last instalment, I made, towards the end an intriguing statement that I repeat now. I said,

The story does not end with what I have described thus far. Remember I said the graviton would escape from the 2 D world into the third dimension? In terms of the Universe we live in, it means that gravitons that rule gravity here can escape from our Universe [of 3+1 dimensions] into “another Universe” [!] that is so near yet so far!

To make things easier, let me recall that bit of my narration in slightly greater detail so that you do not feel disoriented. I first introduced you to the “String Dogma” that Nature’s Story must be told in many dimensions even though we seem to feel we live in a world that has three plus one dimension [three of Space and one of Time]. So the question arises, “Whatever happens to those dimensions that are in excess of four?” The String Magicians said, “No problem! Those ‘extra’ dimensions as you call them are ‘compactified.’” We don’t want to appear stupid and so we nod our heads and tell these magicians, ‘that’s great!’

The String Doctors then say, “Wait a minute; the story ain’t over yet! Things can escape from our ‘world’ into the compact dimensions, and as a result many weird things can happen!!” We feel this is too much but these String Doctors really want to convert us and now they spin yet another story! They say, “You know while the electron and other such particles are prisoners in their own world because they are string with their ends tied down, the graviton being a loop can escape.” I tried to help you out with an analogy and for your benefit I repeat that figure below:

FIGURE 1: This figure is meant to illustrate the difference in behaviour of the forces associated with particles like the electron which are represented by loops with their ends anchored, and the graviton which is a closed loop. While the forces due to the former are confined to the final 3+1 dimensional world, those associated with the graviton can escape into the dimensions that have been compactified.

You may think this is all a kind of hocus pocus. Not if you think about it a bit, and to assure you that there is a real life analogue to this, I present the figure below.

You are far from convinced and say, “Oh come on! Don’t give me that spin,” and the String Doctors reply, “Honestly this is really true,” and then begin the next chapter in their spin! To grasp what they say, first take a look at the figure below.

FIGURE 3: This figure is meant to highlight the implications of the previous figure. It shows an infinite Universe that is folded over and over; in the schematic above, only two folds are shown. We are supposed to be in the fold at the bottom, and the Strong, the Weak and the Electromagnetic forces we are familiar with act strictly in the plane. Gravity too operates in the same manner but is not exclusively confined to our fold or “our Universe”. The other folds above represent “parallel Universes,” each with its own galaxies and God knows what else! These other folds are separated from us by the so-called extra dimensions. A funny thing; this parallel fold may be just one “mm” away but in another sense it is far away because it is a “parallel Universe”! What it means is that light leaving a galaxy G2 say in a “parallel Universe” would have to travel a very long distance [along the folds] before reaching ours; and when it does, its signal would be too weak to detect. So that galaxy, even if is shines in its own “Universe” would be “dark” for us; as result, if we depend on the light emitted, we would never know that such galaxy exists. However, since gravitons can take the short cuts between the parallel Universes, we here in our Universe, can experience the pull of other galaxies elsewhere. However, the pull would not follow the usual Newton law; as explained in the earlier issue [QFI - 10], it would follow a different law. Thus, the curious gravity law I told you about last time has deep and unbelievable consequences! Yes, truth is indeed stranger than fiction!!

I am sure you are feeling dizzy after studying the above figure, wondering what on earth it means. Let me try and explain it the following manner. The so-called parallel Universe is not really different from our own but a piece of our Universe that is folded in such a way that it produces unusual and even astonishing effects. Let us try and absorb that slowly. First of all let us take light and its propagation. Since only the graviton can actually leave the fold, light must travel along the along the “sheet” to reach elsewhere. Keep this in mind.

Look again at the puzzling figure. There is a galaxy G₁ in the lowest fold, and let us say we belong to that galaxy. Now look at the fold just “above”. In terms of distance as the “crow flies” it is just one mm away. What kind of crow is that can fly in this manner? Not the crow we are familiar with but the graviton. This is where Figure 1 is helpful. OK, the graviton can fly as crows do in the world we know about; only, the crow is the graviton. Thus the graviton can take a short cut from the galaxy G₂ to galaxy G₁ in which say we are.

Alright, what about light? That is a different ball game. Why? Because the quantum of light namely, the photon simply cannot fly like gravitons can. So how does one expect the photon to travel? The hard way; which means? It means that the photon has to chug along the length of the fold. Now consider a photon leaving the galaxy in the upper fold. Let us say that very instant, a graviton also leaves the galaxy G₂ in the upper fold. The photon “carries” the electro magnetic force while the galaxy is “transporting” the gravitational field. OK, but where is the difference? Well, the graviton can fly like the “crow” meaning it has to travel just a small distance as Fig. 3 shows. What about the photon? It has to do it the hard way, travelling along the entire length of the fold and that is a long distance.

In short, when we look at the other galaxy from ours, in terms of the distance travelled by light, it is an enormous distance away; but look at it in terms of the distance travelled by the graviton. Thanks to its ability to jump across compactified dimensions, the graviton can do a short hop and be here in no time at all while poor photon has to do it the hard way. I don’t know how many of you know the story often narrated on the occasion of Vinayaka Chathurthi, describing how Vinayaka and His younger brother Subrahmanya went round the Universe, using different strategies! I am very much reminded of that, when I describe this incredible hypothesis of a Universe that has a peculiar geometry on account of compactification!

I guess I have taxed you enough with this kind of stuff and now let me turn to inflation for a change and bring to your notice how attempts have been made to go beyond the original model crafted by Alan Guth [see QFI – 08]. These attempts have led to another astonishing scenario, which I shall now attempt to explain. As a prelude, I must recall something I said about phase transitions in an earlier issue [see QFI – 09]. For a start, let me invite your attention to Fig. 4 below:

FIGURE 4: This figure has two parts; in (a) are shown curves you have seen before. They basically show how the energy of a “hot system" varies with the state of the system. As I told you before, the state preferred is always that which corresponds to the minimum energy. Above Tc the transition temperature associated with a change of physical state [e.g., water to ice], there is one kind of minimum energy state [the state with “disorder” but “high symmetry” – all this has been explained before]. Below Tc, the state of minimum energy is different. The sketches in (b) take us though the details of how things change over near the critical temperature Tc. Hopefully, this would give you some idea of how the change over takes place. The black dot is to help you visualise, step-by-step the cross over from the high temperature state to the low temperature state. These considerations would become important in what follows.

The figures like the ones presented above are what solid state physicists regularly use while discussing say the change of the magnetic state of iron, for example. [See QFI – 09]. I am calling attention to these type of curves because they are relevant in the context of the early Universe also. Wonder why? Just look at Fig. 5 below, which is a reproduction of what you have seen earlier [in QFI – 09].

FIGURE 5: Just to remind you, what is shown here is the time line for the splitting of the original Cosmic Unified Force into the four distinct basic forces as we know them today. Every splitting can be visualised like a symmetry breaking process [see QFI – 09], which means we can lean on ideas borrowed from the realm of conventional phase transitions [ice to water etc]. All this is recalled because we are going to need some of this basic knowledge while asking now the question: “In what way can quantum fluctuations influence inflation of the early universe, if at all they can?”

I have perhaps used the word quantum fluctuations many times before and I need to explain it now because it is crucial in influencing the fate of the Baby Universe. Fluctuations are not all that unusual; they are very much a part of every day life. What we usually mean by that word is that the value of something we have in mind is changing with time, and may be also with place.

Let me make myself a bit clearer with some common garden examples. If we take a stock exchange for example – it could be Tokyo, Hong Kong, Singapore, Mumbai, Frankfurt, London or New York – in every exchange, the share values keep constantly changing. In fact, these changes, hour to hour and sometimes even minute to minute are followed with keen interest by those whose fortunes are tied up shares and things like that. These would be the so-called market fluctuations [when they become steep and sudden, they become big news also!]

Next let us take a big city, like Mumbai for example. If we monitor the temperature at various points, we would find they are slightly different. When the weather man gives the temperature for Mumbai over the radio or TV, he quotes what might be called the average temperature. In fact, even this average temperature keeps on varying throughout the day, which is why the met office always gives the maximum and minimum temperatures for everyday.

And so on it goes; prices can fluctuate, crop yields can fluctuate, job opportunities can fluctuate and so on. In the world of physics, fluctuations are closely connected to the restless motion of atoms [in water, for example], and in fact, in the latter part of the 19th century, great advances were made when the theory of heat could be linked to the microscopic motion of atoms – this is the so-called kinetic theory of heat.

Could quantum fluctuations be the 'stuff' of our universe?

Fine. A totally new element entered into this business of fluctuations with the advent of quantum mechanics. Quantum fluctuations are rather difficult to explain and I shall do my best. Actually, there are two broad stages in our understanding of this quantum fluctuations. In the first stage, people said, “Listen; everything takes place within the framework of space and time. Space-time, as we know, is Prof. Einstein’s territory; out of respect for him [he dislikes quantum theory!] we shall say there is no such thing as quantum fluctuation where space-time is concerned! But in everything else, we had better not ignore this quantum jumpiness, uncertainty, call it what you will!” Everything else thus meant processes involving the strong interactions, the weak interactions and electromagnetic interactions. That meant everything from solid-state physics to elementary particle physics [at not too small distances], cosmology excluded.

With that preamble, let me now try and explain what quantum fluctuations mean. Using rather simplified language, it means the following: Remember the four forces [see QFI – 06, where these were introduced]? I have made a reference to them just a little above [see Fig. 5]. Let us say there is an electron at some point A. All around the electron there would be an electric field - this I am sure you would understand, considering all that has been said before. OK, since the Universe is full of all kinds of particles, we have fields of the three basic types existing all over place.

Let us now focus on one point in space and somehow monitor the strength of the field, say electromagnetic field at that point. It would be no surprise if we find the value of that field to be changing from instant to instant. After all, if we monitor say the air temperature at some point in the atmosphere, we do expect to keep on fluctuating and even changing, don’t we? Well, these changes happen in the normal course of events because things are never steady – I mean the sun is moving, the wind is blowing, factories are emitting heat and so forth, and it is no big deal if the temperature at the observation point keeps fluctuating and even changing.

OK, suppose now everything is made absolutely still; this is just a proposition, and so let us not bogged with the question, “How are you going to do that?” Suppose this situation does obtain. Quantum mechanics now springs a big surprise; it says, “Folks, in the mysterious quantum world ordained by God Almighty, there is a perpetual restlessness that has nothing to do with the kind of fluctuations you have known before. Even if all of these cease totally, this quantum restlessness can never be stopped; no power on earth, and no machine of man can do it. The Universe comes with it and you had better get used to it!”

In the scientific world they use the word quantum fluctuations instead of quantum restlessness, because physicists want to sound respectable! These quantum fluctuations have incredible consequences in the world of the small and how they impact inflation is what we are going to examine now. Let us start with the figure below; please study it carefully and after that I shall continue.

FIGURE 6: In this figure, we explore the implications of quantum fluctuations vis-à-vis inflation in a one-dimensional universe. Suppose there were no quantum fluctuations; then what happens in this universe would be uniform across the whole of space [here 1 D]. The occurrence of inflation in this scenario can be described via a single figure as in (a). Here we see a “ball” in two positions, one before inflation and the other after inflation. Clearly, the state of energy associated with the position of the ball is different in the two cases, and the difference in energies between the two scenarios is what leads to inflation.

Now bring in quantum fluctuations. Let us examine the BEFORE inflation situation at a given point and see how the “energy meter” reading might vary with time; it might be as in (b). At a given time, the variation across the 1 D universe might be as in (c). Different points have different values of energy because of fluctuations; these happen simply because of the dictates of quantum mechanics. If now we consider three representative points A, B, C in this 1 D universe, the energy scenarios corresponding to these three could be as in (d). The net result of such factors is that (i) inflation might occur at some favourable points and not at all in others, and (ii) the extent of the inflation itself might vary at the different points where it occurs. The outcome of such a scenario is sketched in (e). This is a spectacularly different result from what we had before. Basically, in this case, one “mother gives birth to three babies”! In other words, “baby Universes” are born where conditions are favourable.

I hope you have taken a good look at the figure above and reflected on it for a while. The following points emerge:

Figure 7 shows the “mother and child” scenario when the “mother’ is a 2 D space to start with while Figure 8 repeats this exercise for a “3 D mom”!

FIGURE 7: This shows a “mother” Universe that is 2 D from which are born several Baby Universes that inflate to different extents.

 

FIGURE 8: This figure extends the concept of the previous figure to the 3 D case. The complex bubble decoration pattern depicts a “mother Universe” having “daughters, grand daughters” and so on.

In brief, what the above illustrations show is the following:

Lots of puzzles there, wouldn’t you say? One thing we can say perhaps: If we are in one particular bubble, then our bubble was born from one that pre-existed ours; in that sense, our Universe had a “mother”! Maybe, it was the “mother” that gave the energy deposit that was needed to kick off the creation of our Universe. In fact, there are whole families with not only mothers but also grand mothers, great grand mothers and so on.

Another thing that comes out in this scenario is that it seems as if Universes are being born and expanding; no talk of contraction and collapse of the Universe, unless there is some “infant mortality” [about which I am not at all sure].

By the way, for the record, I should mention that this above picture which is sometimes referred to as the Chaotic inflation model is the outcome of some pioneering ideas due to Linde. I should also mention that in the above discussion on quantum fluctuations I did not mention an extra-ordinary possibility, which is that when we are considering the state of the Universe immediately after birth, by which I mean something like 10^-50 seconds or so, then even quantum fluctuations in space-time would become important! No one knows anything about such fluctuations at present but everyone is agreed that such fluctuations must exist and must be playing their own important role. Possibly they might not affect inflation which occurs later perhaps. On the whole, while quantum fluctuations might not affect our daily lives, in Nature, they make an impact in many situations, often subtle but quite important. Yes, subtle is the Lord, as Einstein once famously said.

Prof. Andrei Linde, Soviet theoretical physicist		One Chaotic Inflation Model describes extended branching of inflationary 'bubbles' or universes

I am sure your head must be spinning; the amazing thing is that fifty years ago, no one knew that were so many complications and amazing possibilities. Maybe I should do a bit of recap and offer a summary.

 

As I write this, I am simply wonderstruck and often feel at a loss for words. I am sure many of you must be aware of the great buzz that went around when Swami was supposed to give the Cosmic Darshan. Later, there was a huge industry churning out pictures of Swami appearing on the Moon, pictures that any kid with some computer training and Photoshop can create in a few minutes. Many of these were in fact sent to us and we had an amusing time identifying these pictures with those in our huge library.

As far as I am concerned, it would not come as a surprise if Swami chose to appear on the Moon; is it a big deal for Him? What is a big deal for all of us is that He is choosing to spend time here, giving Darshan everyday, sitting through Bhajans and thereby inducing us to purify ourselves a little bit.

What we should all realise – and it is time we did – He is not just what He appears to be. Arjuna made that huge mistake but that was corrected by Krishna on the battle field. I hope Sai devotees would not clamour for a repeat of that demo. There is no need to. Just look at the sky above and recall what we have been trying to draw attention to. Recall also the Bhajan that starts with the words “Brahmanda Nayaka…” in adoration of the Cosmic Swami.

We should not also forget what Swami often tells us: “I am in you, …” What that means is that it is the Divine Power within man that has enabled man to unravel so many mysteries of the Cosmos as I have been trying to describe. It should be a humbling experience for all of us to be given the role of being custodians of Divine Love and Power. I do hope that while admiring the amazing manifestations of God as revealed all across the Physical Universe, we also spare a moment to reflect on the fact that we have HUGE responsibility to use the Infinite Power deposited in us for useful purposes, instead of frittering them away in ways that are not only meaningless but sometimes even dangerous.

Think it all over please! See you again one month from now.

God bless, Jai Sai Ram.

 

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